Essay Eight Part Three -- Dialectical 'Logic' and Dialectical 'Contradictions'

 

Preface

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As is the case with all my Essays, nothing here should be read as an attack either on Historical Materialism [HM] -- a theory I fully accept --, or, indeed, on revolutionary socialism. I remain as committed to the self-emancipation of the working class and the dictatorship of the proletariat as I was when I first became a revolutionary nearly thirty years ago.

 

The difference between Dialectical Materialism [DM] and HM, as I see it, is explained here.

 

(1) Most of the material presented below began life as a rather lengthy footnote to Essay Eight Part Two (Why Opposing Forces Aren't Contradictions); hence, it assumes the results of that Essay, as well as those of Essay Eight Part One (Change Through 'Internal Contradiction').

 

(2) The first section of this Essay largely concerns the arguments and analysis presented in the best Marxist article I have ever read on the nature of 'dialectical contradictions' (i.e., Lawler (1982)). Anyone who doesn't have access to that article needn't worry; at least 90% of it has been reproduced below (and in Essay Three Part One). The few sections that have been omitted largely concern side-issues or tangential remarks the author directed at the work of other fellow Marxists (who had commented on certain aspects of this topic). Hence, they aren't integral to Lawler's main argument.

 

(3) The theories and ideas of other Marxist Dialecticians who have written on this subject are covered in several other Essays published at this site, but, what they have to say is in general nowhere near as comprehensive as Lawler's account. However, at some future date I will be adding several remarks concerning the work of the authors mentioned in (5) and (6), below.

 

(4) Hegel's actual arguments will be considered in Essay Twelve Parts Five and Six (when they are published -- however, a summary of the some of the points I am going to make can be found here). Having said that, I quote Hegel extensively in this Essay and I also engage with what he had to say, so readers will find my criticisms of Lawler also apply to Hegel.

 

(5) In a later version of this Essay I will consider the exposition found in one of the best Hegelian accounts of 'dialectical contradictions' I have so far read -- i.e., Hahn (2007).

 

(6) This Essay was first written before Redding (2007) was published, and before I had been made aware of the following three sources: McGill and Parry (1948), and Burger et al (1980) -- but, more specifically, Cohen (1980). I will add some thoughts on these four works in a later re-write, too.

 

(7) Update June 2012: I have now written and published a detailed examination of Michael Kosok's ill-advised and egregiously unsuccessful attempt to 'formalise' Hegel's 'logic'. As far as can be determined, this represents the very first detailed study and take-down of this 'formalisation' published anywhere.

 

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It is worth adding that phrases like "ruling-class theory", "ruling-class view of reality", "ruling-class ideology" (etc.) used at this site (in connection with Traditional Philosophy and DM), aren't meant to suggest that all or even most members of various ruling-classes actually invented these ways of thinking or of seeing the world (although some of them did -- for example, Heraclitus, Plato, Cicero, and Marcus Aurelius). They are intended to highlight theories (or "ruling ideas") that are conducive to, or which rationalise the interests of the various ruling-classes history has inflicted on humanity, whoever invents them. Up until recently this dogmatic approach to knowledge had almost invariably been promoted by thinkers who either relied on ruling-class patronage, or who, in one capacity or another, helped run the system for the elite.**

 

However, that will become the central concern of Parts Two and Three of Essay Twelve (when they are published); until then, the reader is directed here, here, and here for further details.

 

[**Exactly how this applies to DM will, of course, be explained in other Essays published at this site (especially here, here, and here). In addition to the three links in the previous paragraph, I have summarised the argument (but this time for absolute beginners!) here.]

 

Some readers have complained about the number of links I have added to these Essays because they say it makes them very difficult to read. Of course, DM-supporters can hardly lodge that complaint since they believe everything is interconnected, and that must surely apply even to Essays that attempt to debunk that very idea. However, to those who find these links do make these Essays difficult to read I say this: ignore them -- unless you want to access further supporting evidence and argument for a particular point, or a certain topic fires your interest.

 

Others wonder why I have included links to subjects or issues that are part of everyday knowledge (such as recent Presidents of the USA, UK Prime Ministers, the names of certain rivers and mountains, or specific words that are in common usage). I have done so for the following reason: my Essays are read all over the world and by people from all 'walks of life', so I can't assume that topics which are part of common knowledge in 'the west' are equally well-known across the planet -- or, indeed, by those who haven't had the benefit of education that is generally available in the 'advanced economies', or any at all. Many of my readers also struggle with English, so any help I can give them I will continue to provide.

 

Several of the aforementioned links connect to web-pages that regularly change their URLs or which vanish from the Internet altogether. While I try to update these links when it becomes apparent that they have changed or have disappeared, I cannot possibly keep on top of this all the time. I would greatly appreciate it, therefore, if readers informed me of any dead links they happen to find.

 

In general, links to 'Haloscan' no longer seem to work, so readers needn't tell me about them! Links to RevForum, RevLeft, Socialist Unity and The North Star also appear to have died.

 

Some have complained that my linking to Wikipedia completely undermines the credibility of these Essays. When I launched this project on the Internet in 2005, there was very little material easily available on-line to which I could link other than Wikipedia for the vast majority of topics. In the intervening years alternative sites have become available (for example, the excellent Stanford Encyclopedia of Philosophy and the Internet Encyclopedia of Philosophy), so I have been progressively replacing the vast majority of Wikipedia links with links to these other sources. Having said that, I haven't done so for some of those Wikipedia links -- for instance, any connected with geographical, historical, scientific, biographical (etc.) topics, where the areas covered aren't controversial, at least among fellow Marxists. In every instance, I have endeavoured to avoid linking to Wikipedia in relation to key areas of any of my arguments against DM so that at no point will my case against that theory/method depend exclusively on such links.

 

In addition to the above (as readers will soon see if they consult the Bibliography) I have provided copious references to other published academic and non-academic books and articles (posted on-line or printed in hard copy) in the End Notes to this Essay, which further develop or substantiate anything I argue, claim, allege or propose.

 

Finally, anyone puzzled by the unremittingly hostile tone I have adopted toward DM/'Materialist Dialectics' [MD] might find it informative to read this first.

 

As of June 2022, this Essay is just over 118,000 words long; a summary of some of its main ideas will be published at a later date.

 

The material below does not represent my final view of any of the topics covered; it is merely 'work in progress'.

 

[Latest Update: 25/06/22.]

 

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(1) Well, What Are 'Dialectical Contradictions'?

 

(a) The Best Marxist Article I Have Ever Read On This Topic

 

(b) 'Science Of Thought'?

 

(c) Syntactic And Semantic Confusion

 

(d) Rosa's 'Pedantry'?

 

(2) Hegel Screws Up Big Time

 

(a) Identifying The Problem

 

(b) Not A Tautology

 

(c) 'Law Of Identity' Mis-Identified

 

(d) More Dark Declamations From Hegel's Dialectical Dungeon

 

(e) 'Difference' -- Unrecognisable

 

(f) The Fog Thickens

 

(g) Zeno -- No Help At All

 

(h) Every Magic Trick Requires A Diversion Of Some Sort

 

(3) The Real Main Feature

 

(a) Hey Presto! A Non-Hat Out Of A Non-Rabbit

 

(b) A 'Unity Of Opposites'?

 

(c) The Magical Use Of 'Negation'

 

(d) Hegel's Hermetic House Of Horrors

 

(e) The Dialectical Denouement Looms Large

 

(f) Acid Corrodes Hegel's 'Logic'

 

(g) Infinitely Confused

 

(h) Two Meanings Of "Independent" Conflated

 

(i) Threadbare

 

(j) What A Dialectical Dog's Dinner!

 

(4) Neo-Hegelian Attempts To Dispel The Fog (not yet published)

 

(5) Kosok's Kooky 'Logic'

 

(a) Preliminary Points

 

(b) An Elaborate Hegelian Hoax?

 

(c) One Logician's Formalisation Is Another's Rat's Nest

 

(d) Slippery 'Syntax' And Shifty 'Semantics'

 

(e) Time -- Not On Kosok's Side

 

(f)  Psycho 'Semantics'

 

(g) Sesame Street 'Logic'

 

(h) Sinking Deeper Into Semantic Quicksand

 

(i)  Old MacDonald's Farm

 

(j)  Matrix Re-Loaded

 

(k) Ordinary Versus 'Dialectical' Logic

 

(l)  Kosok Elevated To A Higher Plane?

 

(m) Welcome To The Twilight Zone

 

(n) Matrix Revolutions

 

(p) Outro

 

(6) Appendix A

 

(7) Notes

 

(8) References

 

 

Why I Oppose Dialectical Materialism

 

Abbreviations Used At This Site

 

Return To The Main Index Page

 

Contact Me

 

Well, What Are 'Dialectical Contradictions'?

 

The Best Marxist Article I have Ever Read On This Topic

 

Lawler (1982) is easily the best (Marxist) account of 'dialectical contradictions' I have encountered in my long, tedious trek across the wastelands of 'Dialectical Logic' [DL]. Having said that, I should immediately add that it is the best of the worst, for his analysis of this terminally obscure example of Hegelian gobbledygook is no better than his analysis of Bertrand Russell's criticism of Hegel for confusing the "is" of identity with the "is" of predication discussed in detail in Essay Three Part One.

 

In fact, there are so many logical and philosophical errors in Lawler's article that any conclusions he draws aren't worth the paper on which several notorious Iraq WMD dossiers were printed.

 

Readers who do not, shall we say, appreciate the sort of 'nit-picking' -- i.e., careful -- attention to detail one finds in Analytic Philosophy are advised to skip the first four sub-sections of this Essay, and begin again here. However, having done that they will find that many of the points made later on will be considerably less clear than they might otherwise have been.

 

That point is worth emphasising since I still encounter critics who think that the above sub-sections contain the core of my criticisms of Lawler and Hegel. They don't. They merely set the stage for the rest of the Essay. Indeed, I cover all the issues mentioned in these opening sub-sections in extensive detail again, several times, throughout the rest of this Essay as well as in Essay Twelve Parts Five and Six (yet to be published).

 

[In general in what follows, except where I am directly quoting someone else, I have highlighted in bold most of the logical symbols I have used in order to help distinguish them from ordinary, non-logical letters.]

 

'Science Of Thought'?

 

First of all, running through Lawler's entire article is the (traditional) confusion of logic with the 'science of thought', which the author nowhere tries to defend, let alone justify. Indeed, Lawler simply quotes Engels in support, who in turn also failed to justify this rather odd idea:

 

"Modern materialism is essentially dialectical.... What independently survives of all former philosophy is the science of thought and its laws -- formal logic and dialectics." [Engels (1976), p.31, quoted in Lawler (1982), p.14; Lawler's added italic emphasis here. Throughout this Essay, many of Lawler's quotation marks have been altered to conform with the conventions adopted at this site. That comment will save me having to repeat this caveat!]

 

Lawler then adds:

 

"In view of this passage, in which the distinction between formal logic and dialectics could hardly have been made more clearly, it is difficult to see how Marx and Engels could have confused elsewhere undoubtedly, formal logic with dialectics or, more seriously, rejected formal logic altogether." [Lawler (1982), p.14.]

 

However (as noted in Essay Two), 'Marxist dialecticians' are in general as traditional in their approach to Philosophy as they are confused over the nature and status of any of its results. In that respect they seem both willing and happy to reproduce (if not compound) the errors they inherited from Ancient Greek and early modern Mystics (like Hegel), spinning their own complex webs of a priori gobbledygook, and employing obscure jargon they struggle to explain even to their bemused readers --, or, indeed, to one another.

 

[Exactly how DM-theorists managed to slide into such a deep well of confusion was detailed in Essays Three Parts One and Two, and Twelve Part One. Why they do this is explained in Essay Nine Part Two.]

 

Sure, we have no evidence that Marx himself was this confused about Philosophy and Logic, but there is enough in Engels's writing to reveal he wasn't much clearer than Hegel. In fact, Hegel was far less clear than Aristotle, who tended to confuse logical with psychological and ontological issues much less than that modern-day Hermetic 'genius', which, unfortunately, makes the philosophical and logical views of Hegel and Engels completely worthless in this respect (at least).

 

Moreover, as we have already seen (in Essay Four), it is a serious mistake to describe Logic as 'the science of thought'. If it were, logicians would conduct surveys, perform brain scans and organise psychometric tests; they certainly wouldn't waste their time on all those useless definitions, axioms, and proofs.

 

[On this topic in general, check out my comments over at Wikipedia.]

 

Nevertheless, it would be unwise to allow these relatively minor dialectical defects to distract us from the more serious misconceptions that Lawler's article and Hegel's Logic help promote.

 

Syntactic And Semantic Confusion

 

Lawler next begins a consideration of Hegel's criticism of the LOI, which he regards as central to understanding the nature of 'dialectical contradictions'. But, as we have seen (and will see again below), Hegel's criticism of the LOI is itself worthless since he confused the "is" of predication with the "is" of identity, which then 'allowed' him to conjure an Ideal universe out of this mishandling of the diminutive verb "to be", a stunning trick even David Blaine would struggle to match.

 

[LOI = Law of Identity, which Lawler calls "The Principle of Identity"; DM = Dialectical Materialism/Materialist, depending on the context.]

 

[Lawler's misguided attempt to have the charges of logical ineptitude against Hegel dropped were thrown out of court in Essay Three Part One.]

 

We have also seen that Trotsky's attack on the LOI was even more inept, and while Hegel can't be implicated in Trotsky's misconceptions, these two shared enough confusion in this area to make it difficult for us to tell which one of these two jokers was the Stan Laurel and which the Oliver Hardy of Logic.

 

[However, since Hegel got us into this mess, I reckon he is Stan. What I have said about Trotsky here should in no way detract from his stature as a revolutionary socialist of the highest calibre. Nor should readers conclude that I don't hold him in the highest regard because of that, third only to Marx and Lenin. My only point is that he should have kept well clear of philosophy and logic, as should Engels and Lenin.]

 

Be this as it may, if we now turn to more substantive issues, we find Lawler is just as slap-dash and careless over his use of 'logical' terms and symbols as we have seen is the case with other dialecticians. Indeed, this is the only way he (and they) could make Hegel's 'theory' even seem to work (upside down or the 'right way up').

 

First of all, Lawler is decidedly unclear about the denotation of the many letter "A"s he employs -- or, perhaps better, it is unclear what that letter means since Lawler constantly changes his mind about its mode of signification -- as we will soon discover.

 

[This isn't a minor, 'pedantic', or 'semantic' point, which will become clear as this Essay unfolds. Anyway, Lawler's article is full of 'semantics' and fine distinctions -- as, indeed, was Hegel's 'Logic'. So, anyone who complains about such attention to detail should pick a fight with them, too. On my alleged 'pedantry', see here.]

 

For example, on pp.18-19, in reference to Hegel's discussion of Identity, Lawler had this to say:

 

"Hegel's critique of formal-logical principles begins with consideration of the principle of identity, A = A, or a thing or a concept is itself." [Lawler (1982), pp.18-19. Italic emphasis in the original.]

 

We have already seen that this is a completely inadequate way of characterising identity (either in logic or in ordinary language), but the point at issue here is the fact that Lawler views these "A"s as the Proper Names of objects and/or concepts -- or perhaps even as those entities themselves (hence his reference to  "things"). This is already three different referents for this easily manipulated letter.

 

But, in the very same paragraph he goes on to say:

 

"The other principles follow from this basic one. The principle of noncontradiction, Hegel argues, is the principle [of Identity -- RL] stated negatively. 'A is A' implies 'A cannot at the same time be A and not be A,' or one cannot assert something to be true and at the same time, and in the same respect, assert it to be false. The principle of excluded middle is that something must either be A or not be A: there is no third possibility. By extension, the law of noncontradiction implies that 'A cannot be non-A', where 'non-A' is something that is not A, or some part or property of A." [Ibid., p.19. Italic emphasis in the original; quotation marks in all the passages taken from Lawler have been altered to conform with the conventions adopted at this site. The quotation marks (around the LEM) are missing in the original.]

 

[LEM = Law of Excluded Middle.]

 

As we will soon see, the 'principle of identity' doesn't imply what Hegel -- or even what Lawler himself  -- says it does (Lawler nowhere corrects Hegel), but that criticism isn't of immediate concern. [It will be later.] However, when Lawler qualifies what he takes Hegel to mean it is clear that these "A"s now stand for propositions (or clauses):

 

"'A cannot at the same time be A and not be A,' or one cannot assert something to be true and at the same time, and in the same respect, assert it to be false." [Ibid.]

 

Propositions, indicative sentences, and clauses are capable of being asserted, but that isn't the case with Proper Names: "I assert Socrates" is unvarnished nonsense. So, these "A"s are no longer the Proper Names of objects or concepts, they are the names of, or stand for, propositions, indicative sentences or clauses. That is now five different 'kinds' of things for the 'meaning' of this mercurial letter.

 

Of course, it could be argued that Lawler is merely saying that such things can't be asserted (etc.) of A, making A an object, or perhaps the Proper Name of an object, but that is hardly likely. Lawler and/or Hegel were surely not trying to rattle off a few truths about such names. But, even if they were, A itself would both be an object and what can be asserted of an object (i.e., it might be a predicable, for example).

 

[The word "predicable" is explained here.]

 

Despite the above, Lawler's wording doesn't support that contention, since he pointedly says:

 

"…one cannot assert something to be true and at the same time, and in the same respect, assert it to be false." [Ibid.]

 

As opposed to:

 

"…one cannot assert something to be true of A and at the same time, and in the same respect, assert it to be false of A." [Altered Lawler quote.]

 

If Lawler had meant A to be a Proper Name (or, indeed, that object itself), then he would have used the latter wording.

 

[Anyway, as we will see below, this universally accommodating letter is (unambiguously) used as a propositional variable.]

 

In addition, as pointed out above, it is worth noting that these "A"s (or, at least, those "not-A"s) appear to be properties or property tokens/types (perhaps?). So, that is now seven different 'kinds' of things:

 

"The principle of excluded middle is that something must either be A or not be A: there is no third possibility. By extension, the law of noncontradiction implies that 'A cannot be non-A', where 'non-A' is something that is not A, or some part or property of A." [Ibid.]

 

[A property token is a word or variable that stands for, or which expresses, a given property no matter how many times it is instantiated. A property type is one that stands for an entire class or set of properties (such as blueness). So, in the sentence, "Your blue dress nicely matches your blue eyes" there are two property tokens of "blue", but only one property type, "blue". While we use words to express properties -- typically, but not exclusively, employing simple or complex predicables -- the type/token distinction is generally viewed as an ontological aspect of objects and events. However, as we have seen several times, Traditional Philosophers (and that includes Hegel and Marxist dialecticians) regularly confuse the two, running together talk about talk and talk about things -- i.e., they confuse talk about language with talk about the world. Indeed, it is the only way that Idealism itself can get off the ground. (On the distinction itself, see Wetzel (2006).)]

 

Of course, it is always possible that Lawler is merely echoing a tradition that dominated ancient and early modern logic, which handled logical expressions equally sloppily (and which, as it turns out, is the tradition that helped motivate the bowdlerised version of AFL that Hegel imbibed at University (as, indeed, was true of anyone who studied Philosophy in the 17th, 18th and much of the 19th century -- the sort of sloppy 'formalism' and logical confusion one finds, for example, in Kant's Logic [this links to a downloadable PDF]). This seems to be the most likely explanation for Lawler's own confusions here -- given the other things we are about to discover -- that is, he was relying on logic that was already becoming obsolete a good century before he read anything Hegel wrote.

 

[However, having said that, please note the caveats I have added here.]

 

[AFL = Aristotelian Formal Logic.]

 

Nevertheless, it is this careless and slap-dash approach to logic and logical symbolism that 'allowed' Hegel (and now Lawler) to concoct some rather 'innovative' metaphysics. Indeed, as Bertrand Russell pointed out:

 

"This illustrates an important truth, namely, that the worse your logic, the more interesting the consequences to which it gives rise." [Russell (1961), p.715.]

 

This is in fact reminiscent of the idiosyncratic word-juggling which 'allowed' Anselm, for instance, to concoct his famous 'proof' of the existence of 'God'.

 

[For more on Hegel's confused 'logic', the reader should consult Rosenthal (1998), pp.111-36, and Rosenthal (2001), as well as this.]

 

But, after another flip Lawler now says:

 

"Putting the concept of identity into practical application, as it is interpreted by abstract understanding. We are compelled to say that a cow is a cow, a man is a man, white is white, spirit is spirit, etc. In attempting to express the principle of identity according to the spirit of abstract understanding, we end up paradoxically speaking of an endless number of different things." [Ibid., p.21. Italic emphasis in the original.]

 

Although Lawler doesn't mention "A" directly here, given the context of his overall argument, it has now clearly becomes a "thing" and a predicable, once again -- or, of course, what the latter supposedly stands for. However, on page 22, "A" now transmogrifies into an "entity" (or at least its alleged negation, "not-A"):

 

"'A is A' implies that A is not some other entity which is not-A." [Ibid., p.22. Italic emphases in the original.]

 

And, in the very same paragraph, these "A"s morph into "beings" (or into what is true of such "beings"):

 

"…in the abstract, undialectical understanding of identity, the relation of A to not-A (beings that are not A as well as A's own nonbeing) seems to 'vanish.'" [Ibid., p.22. Italic emphasis in the original.]

 

Here, not only has one of these "A"s been confused with a "being", "not-A" becomes its "non-being". In fact, and to be more precise, it seems that these "A"s might also be predicables once again, or even subjects to which "being" might be predicated. Who can say?

 

At any rate, this so far makes "A" stand for nine different kinds of 'things'.

 

[The reader should now convince herself that if someone says "Bush (Senior) is not Bush (Junior)" or even "Blair is not Bush", that doesn't imply Bush no longer exists (or even that his 'non-being' has somehow been alluded to). Anti-imperialists would surely have consigned one or both of these inveterate war-mongers to 'non-being' had their sticky end been quite so easy to arrange. In the quirky world of Hermetic Hegelianism negation might be the same as 'non-being', but in the material world one has to do much more to one's enemies than merely wish them away -- or merely glue a "non-", or even a "not-", to their names. (I return to consider this topic, and so-called 'ontological contradictions', below.)]

 

Two pages later, these chameleonic "A"s now morph into "terms", or perhaps even propositions again:

 

"The point we have argued is that Hegel is attempting to establish identity, not destroy it. A term 'to be itself,' requires a negative relation to another term…. Does Colletti deny Hegel's point that asserting 'A' is equivalent to saying 'not-not-A'." [Ibid., p.24. Italic emphases in the original.]

 

As noted above, only indicative sentences (and clauses) are capable of being be asserted. [Predicates can be asserted of named individuals (etc.) -- or, perhaps better: true or false sentences can be formed when predicate expressions map Proper Names, or other singular terms, onto such sentences.] As should seem obvious to any language-user, it isn't possible just to assert a bald "term", predicate or concept expression of nothing whatsoever. Uttering "ξ is a warmonger" (or "...is a warmonger", or even "is a warmonger") is to assert nothing (i.e., it is to make no assertion), and the same is the case with simply uttering the word "warmonger".

 

[The use of Greek letters like "ξ" was explained here, and in Note 1. A predicable is a predicate expression that can be predicated of an individual (or which can sensibly be attached to a subject term), whether or not it has been so predicated. Compare it with our use of "sinkable" -- or, indeed, with "edible". If a ship is sinkable that doesn't imply it has actually sunk. So, for example, "ξ is a warmonger" is a predicable; it becomes a predicate when it is used to form sentences like this: "Tony Blair is a warmonger". In that way, "ξ is a warmonger" can be mapped onto a sentence that is capable of being asserted by attaching it to the Proper Name, "Tony Blair", which then expresses the presumed fact that Blair is warmonger.]

 

Of course, in certain contexts the utterance of single word sentences is perfectly legitimate. So, if someone sees Tony Blair and shouts "Warmonger!" we all know what is being said -- i.e., it is elliptical for "You (Blair) are a warmonger!"

 

Naturally, someone could for example point at an animal and utter the word "cat", but that would be the equivalent of saying "That is a cat". Without the pointing gesture, nothing would have been asserted. To be sure, someone could utter the phrase "A cat" in answer to a question, such as, say, "What animal seems to know more logic than Hegel?" In such a reply, the utterance of "A cat" would also be elliptical for the proposition "A cat seems to know more logic than Hegel". The phrase "A cat" on its own wouldn't count as an assertion without that linguistic background providing the relevant context.

 

Admittedly, Hegel appears to think that objects and/or 'concepts' can be true (or, rather he thinks the 'coincidence' between an object and its 'notion' is the sort of relation that can sensibly called "true"):

 

"In common life the terms truth and correctness are often treated as synonymous: we speak of the truth of a content, when we are only thinking of its correctness. Correctness, generally speaking, concerns only the formal coincidence between our conception and its content, whatever the constitution of this content may be. Truth, on the contrary, lies in the coincidence of the object with itself, that is, with its notion. That a person is sick, or that some one has committed a theft, may certainly be correct. But the content is untrue. A sick body is not in harmony with the notion of body, and there is a want of congruity between theft and the notion of human conduct. These instances may show that an immediate judgment in which an abstract quality is predicated of an immediately individual thing, however correct it may be, cannot contain truth. The subject and predicate of it do not stand to each other in the relation of reality and notion." [Hegel (1975), p.237, §172. Bold emphasis added.]

 

Unfortunately, detailed consideration of the above passage will take us too far away from issues raised in this Essay, and into areas that will be covered in Essay Twelve Parts Five and Six (when they are published). Suffice it to say here that Hegel's difficulties (in this case) clearly arose out of his conflation of predicate expressions with singular terms, compounded by the adoption of the Medieval Identity Theory of Predication. [More on that, here.]

 

It is also worth noting in passing that if a doctor is told that an individual is unwell, she will certainly regard it as true that that individual is indeed sick if she then finds that individual has a raging fever, hacking cough and is covered in spots. Even so, no relative of theirs will regard it as an adequate excuse that the doctor failed to treat their now dead relative because "the content" of that claim was "untrue", since the deceased wasn't really ill on the grounds that:

 

"The subject and predicate...do not stand to each other in the relation of reality and notion." [Ibid.]

 

Might this be the reason why Hegel died of Cholera when he did? Maybe whomever was supposed to summon medical assistance -- believing too much of what this 'genius' had told them about 'truth' -- concluded that it wasn't the case that Hegel was at death's door because "Hegel" didn't stand to "is dying of Cholera" in the relation of 'reality to notion', and failed to fetch the local quack.

 

Be this as it may, the conflation of "terms" with "things", and then with linguistic expressions that can be asserted or denied of named individuals (or, once again perhaps better: true or false sentences can be formed if predicables are completed with Proper Names, or other singular terms (etc.)), 'allows' Lawler (just as it 'allowed' Hegel) to derive the sort of "interesting" results we have come to know and loathe.

 

So, that is eleven sorts of things these malleable "A"s are supposed to be.

 

On page 26, these impressively Heraclitean (if not worryingly Cratylean) letter "A"s now morph into relations (that is, so far as can be ascertained!), or perhaps they are even the 'Proper Names' of relational expressions(!):

 

"In view of the criticisms made of Hegel, it is quite significant that Hegel recognises the force of logical contradiction as a weapon of criticism of his philosophical opponents. First they say, Hegel maintains, that identity has nothing to do with difference. Then they say that identity is different. They assert 'A' and then 'not A'." [Lawler, (1982), p.26.]

 

"Hegel's main objective is to show an integral connection between A and not-A, or, in categorical terms, between 'identity' and what is supposed to be the contradictory of identity, 'difference'." [Ibid., p.20.]

 

The only way to understand these two passages is to read the "A" above as standing for "identity" and the "not-A" for "difference" (i.e., "not-identity", one presumes). Of course, this could be to misread Lawler's intentions, but then he simply invites it.

 

That is now twelve, or possibly even thirteen, different meanings given to this denotationally-dithering letter.

 

And, it won't do to argue that in the above passages Lawler is merely reporting what Hegel's opponents might say, since he nowhere even attempts to pull those 'miscreants' up for their syntactic and semantic sins.

 

These morphoholic letter "A"s now stand for propositions, once more, since Lawler says they can be "asserted". That interpretation is confirmed in the next-but-one paragraph:

 

"The contradiction is not any kind of contradiction. For example, first they [the said critics -- RL] affirm that all swans are white and then they deny that all swans are white." [Ibid., p.26.]

 

Well, if Hegel was indeed faced with such simple-minded opponents, it is little wonder he got away with so much logical blather. But, what is so contradictory about someone changing their mind (if that is what one of these 'simpletons' did)?

 

In fact, this is the only way to read this (concocted) example of Lawler's (i.e., that this represents a change of mind by one or more of these fictional individuals -- those "they"s) that doesn't represent Hegel's opponents as sub-literate morons with short-term memory problems.

 

Nevertheless, in the above passages, it seems clear that Lawler's "A"s have transmuted into propositions (and/or predicables), or perhaps even into properties and/or property tokens/types (that is, they are now stand for instances of a property).

 

On the very next page (but in the same paragraph), it looks like these endlessly malleable "A"s have become relations, nominalised relational expressions, or maybe even nominalised relational phrases(?). In fact it is quite plain that that is exactly what they are:

 

"The law of noncontradiction holds, for if 'identity held aloof from difference' (A) is false, then the contradictory 'not identity held aloof from difference' (not-A) is true." [Ibid., p.27. Italic emphases in the original.]

 

Since phrases aren't capable of being true or false, Lawler's reasoning here is, shall we say, 'innovative'; indeed, it is 'innovative' along lines intimated by Bertrand Russell. Nevertheless, these busy "A"s have plainly undergone yet another denotational make-over, and now stand for "identity held aloof from difference"!

 

[The phrase "identity held aloof from difference" might appear to make sense to some, but that would only be because they have become inured to this odd way of talking -- perhaps as a result of reading far more Hegel and Traditional Philosophy than is good for any human being to have to endure in one lifetime. Even so, such individuals might have failed to notice that relational expressions that have been nominalised in the above manner can no longer serve as relational expressions. "A identity A" says nothing, nor does "A difference B". (These having presumably been derived from sentences like the following: "A is identical with A" and "A is different from B", where the verb phrases in each case -- "is identical with" and "is different from" -- have been turned into the Noun Phrases, "Identity" and "Difference", respectively. This Ancient Greek, grammatico-logical tactic -- i.e., nominalise everything in sight, a tactic appropriated by Hegel -- was shown (in Essay Three Part One) to turn propositions into lists of names, which renders them incapable of saying anything at all, true or false.)]

 

The mercurial career of these 'edgy' letter "A"s continues apace, for on page 28 they now metamorphose into indexicals:

 

"Hegel's statement is made in response to Zeno's famous paradox. Zeno's paradox, according to Hegel, is that since motion involves both A and not-A, and since this violates the principle of noncontradiction, it follows that motion is impossible. What should probably be called 'Hegel's paradox' is the assertion that since motion occurs, there must be in some sense both the A and not-A of Zeno's position. It is clear that this assertion cannot be taken in the sense of a strict logical contradiction. Not-A in a purely formal sense means only the denial of A, and is compatible with saying that the object is both 'here' and 'anywhere else,' perhaps also on the moon. Not-A can also mean the simple denial of 'here' -– an assertion that clearly leaves us nowhere….

 

"…Hegel's line of thought here is similar to his approach to the problem of 'abstract identity' or 'identity held aloof from difference.' The paradox arises if we begin with an abstract notion of place, a 'here' which is totally discrete and unrelated to any other place. The common-sense definition of motion as 'change of place' or as a passage of an object through a succession of places runs into insuperable intellectual difficulties if 'place' is understood in this manner. For one thing 'place' is defined as 'fixed place,' i.e., as motionless place. Can motion be explained in terms of a concept which excludes motion? On the other hand, it does not seem possible to eliminate some notion of definite place from our concept of motion, but such a notion must be that of a 'relative place,' a place which is both 'here' and 'there' or, paradoxically, 'here' and 'not-here'." [Ibid., pp.28-29. Italic emphases in the original.]

 

In the above passage, "A" and "not-A" plainly now stand for "here" and "not-here", respectively. That is now at least fourteen different denotations for this impressively accommodating letter!

 

However, as we discovered in Essay Five, the above 'analysis' of motion has more holes in it than a lorry load of Polo Mints. There is no 'commonsense' definition of the things Lawler mentions. Ordinary language -- never mind 'commonsense' -- allows for complex and highly varied expressions for location and movement, which Idealists like Hegel and Zeno simply ignored.

 

On page 32, these change-oholic "A"s slip now into what can only be described as morphological hyper-drive as they become parts (or, perhaps, 'reflected' parts) of one another:

 

"One might readily grant that the definition of A includes A's relating to something that is not A (some non-A which is not-A). This does not mean that non-A or what is not-A is a part of A or part of A's identity…. It is necessary to ask, first of all, whether and in what sense the fact that A necessarily relates to what is not-A permits us to insert not-A in A…. [I]t seems reasonable to look for some 'imprint' of this 'other' in A, so that in some sense not-A is internally constitutive of A." [Ibid., p.32. Italic emphases in the original. Paragraphs merged.]

 

It seems these denotationally-fickle letter "A"s can take on any form whatsoever in order to make this Hermetic Hodgepodge even seem to work. Plainly, Lawler could 'symbol'-juggle for his country.

 

In the Summary of Essay Two, the following was baldly asserted:

 

For over two thousand years Traditional Philosophers have been playing on themselves and their readers what can only be described as a series of verbal tricks. Since Ancient Greek times, metaphysicians have occupied themselves with deriving a priori theories solely from the meaning of a narrow range of specially-chosen (and suitably doctored) words. The 'philosophical gems' that resulted from this were painstakingly polished and then peddled to the rest of humanity dressed-up as 'profound truths' about fundamental aspects of reality, which were then imposed on nature, invariably without the benefit of a single supporting experiment....

 

Even before the first Marxist dialecticians put pen to misuse, they found themselves surrounded on all sides by ideas drawn from this ancient ruling-class tradition.

 

Clearly, the DM-classicists were confronted by a serious problem: if they imposed their ideas on nature in like manner, they could easily be accused of propagating yet another form of Idealism. On the other hand, if they didn't do this, they wouldn't have a 'philosophical theory' of their own to lend weight to their claim to lead the revolution. Confronted thus by traditional thought-forms (which they had no hand in creating, but which they were only too happy to appropriate), DM-theorists found there was no easy way out of this minefield -- or, at least, none that prevented their theory from sliding into Idealism.

 

Their 'solution' was simple and effective: ignore the problem....

 

This isn't to argue that dialecticians weren't aware of the Idealism implicit in Traditional Thought.... On the contrary, their excuse for disregarding the pernicious influence of Traditional Philosophy on their own ideas is that the materialist flip they say they had inflicted on Hegel's system was deemed capable of transforming theoretical dirt into philosophical gold.

 

However, flip or no flip, their own ideas in this direction are thoroughly traditional: they are dogmatic, a priori, and are expressed in a specialised form of jargon lifted straight from the Philosophers' Phrase Book. While few DM-theorists will deny that Traditional Philosophy itself is predominantly Idealist, not one of them has failed to emulate the approach to a priori knowledge it promotes.

 

So, despite the fact that dialecticians constantly claim that DM has hasn't been imposed on nature -- for that would surely brand their theory "Idealist" -- they invariably end up doing just that, imposing their theory on reality. In so doing, they simply confirm the allegation that Traditional Thought has found a new batch of converts among erstwhile radicals.

 

We are now in a position to see why that was asserted quite so forcefully back then. Lawler's defence of Hegel depends solely on his sloppy and careless use of ordinary language and logical symbols -- whereby predicate expressions are turned into Proper Names, objects, 'terms', indexicals and relations/relational expressions, which are then all jumbled together. When they become 'object-like', these 'items' can be put in some sort of spurious relation to one another. In fact, this is the only way the spooky Hegelian "internal relations" can be conjured into existence (as Bertrand Russell correctly observed) -- which mysterious "relations", to this day, still defy scientific detection. Not that anyone in the dialectical fraternity (or beyond) has searched for them all that enthusiastically.

 

Because of his 'innovative' use of language Lawler's attempt to explain what a 'dialectical contradiction' is fails miserably -- as we are about to find out.

 

Of course, it could be objected -- indeed, it has been objected -- that these minor 'semantic' niggles aren't really all that important, After all, it is quite clear what Hegel and Lawler meant. Hence, it might be possible to repair both accounts so that they can successfully negotiate these annoying hurdles, should anyone find it important enough to do so.

 

That, naturally, remains to be seen. But, since:

 

(i) Lawler's article is by far and away the best Marxist defence of this terminally obscure Hegelian notion (i.e., 'dialectical contradiction') I have so far encountered in over thirty-five years of research, the omens aren't too promising. That alone should suggest to neutral readers just how bad things are in this back-water of traditional philosophical myth-making.

 

In that case:

 

(ii) A 'dialectical rescue' is highly unlikely to originate from within this wing of Idealism. Even academic (non-Marxist) dialecticians struggle with this notion and regularly commit serious errors like those highlighted above (and again below). Moreover, they all fail to notice these blunders, let alone acknowledge their existence, even after they have been pointed out to them! Nor do they appear to realise how these blunders vitiate this entire 'theory'/'method'. That shows just how logically purblind the Idealist wing of ruling-class theory has rendered their thought.

 

[The latest examples of this dialectical malaise can be found here (unfortunately, that link now appears to be dead), here, here, here, here, here, here, but especially here.]

 

[Indeed, John Rosenthal's arguments (in Rosenthal (1998, 2001) similarly fell upon dialectically deaf ears. Those allegations will be substantiated in Essay Twelve, where this aspect of Hegel's work (along with that of his 'Marxist' groupies) will be further taken apart.)]

 

Naturally, I exclude Graham Priest's work from the above rather peremptory allegations, not least because (a) It is far from clear whether the 'contradictions' he touts are 'dialectical' to begin with -- that is, if it were possible to decide either way (in relation to such a thoroughly opaque 'concept'!) --, or are even contradictions simpliciter; and (b) He is generally very careful with both his syntax and semantics. Nevertheless, as far as I am aware, he hasn't as yet noticed Hegel's rather obvious logical blunders, exposed in these Essays.

 

Rosa's Pedantry?

 

However, concerning any who think that this sort "pedantry" (aka "semantics") -- which is in reality careful attention to detail -- can be ignored, it is worth pointing out that this is the only way they can even begin to excuse their own sloppy and careless approach to philosophy and logic, and, for that matter, it is the only way they can make their ideas even seem to work, indeed, as Bertrand Russell pointed out.

 

"Surely, such pedantic details are merely academic/semantic", some might be tempted to respond.

 

That attitude wouldn't be tolerated for one second in any of the sciences, or, indeed, in any other branch of genuine knowledge. Can you imagine the fuss if someone were to argue that it doesn't really matter what the Magna Carta actually said, or even what it established, or when, where and why the Battle of the Nile was fought, or what the Declaration of Independence or The First Amendment of the US Constitution actually contained, or what the exact wording of Newton's Second Law is, or whether "G", the Gravitational Constant, is 6.6742 x 10-11 or 6.7642 x 10-11 Mm2kg-2, or something else? Would we accept as a valid response from an employer that the precise wording of one of her worker's employment contract was irrelevant, or what was actually contained in a written agreement between union negotiators and management (after a strike had been settled)? Would we allow anyone to argue that it was of no significance what Marx really meant by "variable capital", or who then complained that Marx had "pedantically" distinguished between use-value and exchange-value -- or, more pointedly, between the "relative form" and the "equivalent form" of value --, and that such petty-fogging details are merely "semantic", or even "academic"? And, how would we react if a lawyer said, "So what if there happen to be serious discrepancies and inconsistencies in the evidence given by a cop against a group of pickets"? Or, if someone retorted "Big deal if there are a few minor errors in this or that e-mail address, or in this mathematical proof! And who cares whether there's a difference between rest mass and inertial mass in Physics! What are you, some sort of pedant!?"

 

As we will see, this is quite apart from the fact that Hegel himself attempted to substantiate his core ideas using a series of 'semantic'/'pedantic' arguments and fine distinctions, as did Lenin and Engels, and as have subsequent DM-theorists. In which case, if this 'pedantic' approach to philosophy and logic is OK for the dialectical goose, it is surely OK for the anti-dialectical gander. Indeed, it was Hegel's (and latterly Lawler's) 'sloppy pedantry' and 'innovative semantics' that created the problem in the first place!

 

[We saw that this was the case in the opening sections of this Essay, just as we will have occasion to highlight it again, below.]

 

Hence, fans-of-the-dialectic can hardly complain when a similar line is adopted in order to try to sort this mess out.

 

Even so, you can be sure dialectical 'anti-pedants' will be examining these Essays with powerful magnifying glasses, nit-picking at the detail, having aimed their selectively focussed and inconsistently pedantic eyes on all I have written in order to highlight the smallest of assumed errors, all the while refusing to examine anything in the DM-Grimoire with even a tiny fraction of this belated and partisan attention to detail.

 

[In fact, they already have! (See also here, and here.)]

 

Even the soft left, reformist UK paper, The Daily Mirror, knows the importance of using the right words (in this case in an article about the political difference between using the terms "migrant" and "refugee"):

 

"Using the right words for the right things is very important. It's how we manage to communicate across languages and borders, via keyboards and tweets and picture captions. Using the wrong words means you stop communicating -- it means that at best you begin to mislead, and at worst you lie. For example, Newton's law of gravity states that the force of attraction between two bodies is directly proportional to the products of their mass. In other words, apples fall downwards because the earth is bigger than an apple. Imagine if just one of those words meant the opposite of what we think it does. We couldn't send a lander to Mars because we wouldn't know where it was, jet engines would make no sense so there'd be no package holidays, and we'd all think dancing on the ceiling like Lionel Richie was an option. If you don't get the words right, you get everything else wrong." [The Daily Mirror, 02/09/2015. Paragraphs merged. Bold emphases and link added.]

 

But, do any of the above 'pedantry-sniffers' and 'semantics-spotters' take Lenin to task for writing passages like the following?

 

"'Sense-perception is the reality existing outside us'!! This is just the fundamental absurdity, the fundamental muddle and falsity of Machism, from which flows all the rest of the balderdash of this philosophy and for which Mach and Avenarius have been embraced by those arrant reactionaries and preachers of priestlore, the immanentists. However much V.Bazarov wriggled, however cunning and diplomatic he was in evading ticklish points, in the end he gave himself away and betrayed his true Machian character! To say that 'sense-perception is the reality existing outside us' is to return to Humism, or even Berkeleianism, concealing itself in the fog of 'co-ordination.' This is either an idealist lie or the subterfuge of the agnostic, Comrade Bazarov, for sense-perception is not the reality existing outside us, it is only the image of that reality. Are you trying to make capital of the ambiguous Russian word sovpadat? Are you trying to lead the unsophisticated reader to believe that sovpadat here means 'to be identical,' and not 'to correspond'? That means basing one's falsification of Engels à la Mach on a perversion of the meaning of a quotation, and nothing more.

 

"Take the German original and you will find there the words stimmen mit, which means to correspond with, 'to voice with' -- the latter translation is literal, for Stimme means voice. The words 'stimmen mit' cannot mean 'to coincide' in the sense of 'to be identical.' And even for the reader who does not know German but who reads Engels with the least bit of attention, it is perfectly clear, it cannot be otherwise than clear, that Engels throughout his whole argument treats the expression 'sense-perception' as the image (Abbild) of the reality existing outside us, and that therefore the word 'coincide' can be used in Russian exclusively in the sense of 'correspondence,' 'concurrence,' etc. To attribute to Engels the thought that 'sense-perception is the reality existing outside us' is such a pearl of Machian distortion, such a flagrant attempt to palm off agnosticism and idealism as materialism, that one must admit that Bazarov has broken all records!

 

"One asks, how can sane people in sound mind and judgment assert that 'sense-perception [within what limits is not important] is the reality existing outside us'? The earth is a reality existing outside us. It cannot 'coincide' (in the sense of being identical) with our sense-perception, or be in indissoluble co-ordination with it, or be a 'complex of elements' in another connection identical with sensation; for the earth existed at a time when there were no men, no sense-organs, no matter organised in that superior form in which its property of sensation is in any way clearly perceptible. That is just the point, that the tortuous theories of 'co-ordination,' 'introjection,' and the newly-discovered world elements which we analysed in Chapter I serve to cover up this idealist absurdity. Bazarov's formulation, so inadvertently and incautiously thrown off by him, is excellent in that it patently reveals that crying absurdity, which otherwise it would have been necessary to excavate from the piles of erudite, pseudo-scientific, professorial rigmarole." [Lenin (1972), pp.124-26. Quotation marks altered to conform with the conventions adopted at this site. Italic emphases in the original; bold emphases and links added. Some paragraphs merged.]

 

"Try for once to think over the words you use to compile your phrases, comrades!" [Lenin, 'Intellectualist Warriors Against Domination by the Intelligentsia', Nashe Ekho, No.5, March 30, 1907. Quoted from here. Bold emphasis added.]

 

If they have ever taken Lenin to task for the above 'semantics' (or his 'pedantry'), they kept it pretty quiet!

 

Clearly, using the right language was important to Lenin.

 

Unsurprisingly, Trotsky concurred:

 

"It is necessary to call things by their right names." [Trotsky (1971), p.56.]

 

With such sloppy disregard for logic, disdain for 'commonsense' and ordinary language, compounded by an unwise appeal to what is in effect Mickey Mouse Science, is it any wonder that genuine ruling-class theorists dismiss the work of Dialectical Marxists as unworthy even of comment -- or, indeed, view it with no little contempt --, and, far more importantly, is it really all that surprising that workers in their hundreds of millions ignore all they have to say?

 

Hegel Screws Up Big Time

 

Identifying The Problem

 

Remember: if you are viewing this with Mozilla Firefox, you might not be able to read all the symbols I have used. I have no idea whether other browsers are similarly affected.

 

Nevertheless, in order to consider every option available to Dialectical Mystics as they try to explain what they mean by "dialectical contradiction" (howsoever weak that attempt has always been), Lawler's, and by implication Hegel's, argument will now be considered on its own merits.

 

However, this is where we will see how and why Hegel and Lawler's syntactic and semantic sins (detailed above) led them both astray.

 

Early on in his article, Lawler endeavoured to revamp Hegel's criticism of the LOI, arguing as follows:

 

"Hegel's critique of formal-logical principles begins with consideration of the principle of identity, A = A, or a thing or a concept is itself." [Lawler (1982), pp.18-19. Italic emphasis in the original.]

 

"A thing or concept is itself"? Is that meant to be serious!? Not only is it a caricature of the LOI, it ropes in "concepts", which aren't objects and so can't be related to themselves. We saw the difficulties traditional theorists got themselves into over precisely this issue in Essays Three Part One and Four Part One.

 

[LOI = Law of Identity.]

 

To be sure, Hegel was writing at a time when little work had been done on this 'law', but Lawler wasn't. And yet he failed to refer his readers to any modern work in this area. Had he done so, Hegel's 'definition' would have been seen for the logical joke it is. [On that, see here, and here.]

 

Putting that serious problem to one side for now, Lawler continues:

 

"The other principles follow from this basic one. The principle of noncontradiction, Hegel argues, is the principle [of Identity -- RL] stated negatively. 'A is A' implies 'A cannot at the same time be A and not be A,' or one cannot assert something to be true and at the same time, and in the same respect, assert it to be false. The principle of excluded middle is that something must either be A or not be A: there is no third possibility. By extension, the law of noncontradiction implies that 'A cannot be non-A', where 'non-A' is something that is not A, or some part or property of A." [Ibid., p.19. Italic emphasis in the original; middle set of quotation marks (around the LEM) are missing in the original.]

 

This is so full of errors it is difficult to know where to begin. Lawler (following Hegel) tells us that two of the supposed principles of FL follow from the LOI, or rather from the latter stated "negatively". These are the LOC and the LEM. But notice, once again, the error that all dialecticians have bought into (which was exposed in Essay Four): that is, thinking that FL has just three fundamental principles from which all else allegedly fiollws.01

 

Notice, too, how every single DM-fan fails to substantiate this constantly repeated assertion about these 'three laws'. And no wonder, it is completely false. Not even AFL was based on them! It seems in this regard, therefore, that academic Marxists (HCDs) are just as benighted as their more lowly LCD brethren were shown to be with respect to these 'laws'. Naturally, this sorry state of affairs isn't unconnected with the additional fact that both wings of Dialectical Darkness think that, to a greater or lesser extent, there is something worthwhile to be learned by studying Hegel's badly mis-titled book (on 'logic').

 

[LOC = Law of Noncontradiction; LEM = Law of Excluded Middle; HCD = High Church Dialectician; LCD = Low Church Dialectician (the latter two terms are explained at the above links); AFL = Aristotelian FL; MFL = Modern FL; FL = Formal Logic.]

 

Neither Hegel nor Lawler offered any proof of this supposed 'inference' -- that the LOI "stated negatively" implies the LOC (or even the LEM), nor could they. The LOI concerns the relation that is supposed to hold between an object and itself (or perhaps between its names, depending on how one reads this 'law'); it doesn't concern the truth-functional link between propositions, which is the proper domain or those other two 'laws'.

 

Lawler follows up with this remark:

 

"The principle of noncontradiction, Hegel argues, is the principle [of Identity -- RL] stated negatively. 'A is A' implies 'A cannot at the same time be A and not be A,' or one cannot assert something to be true and at the same time, and in the same respect, assert it to be false." [Ibid.]

 

But, this 'derivation' only works because of the aforementioned confusion over the denotation of those letter "A"s  -- which explains why I went into all that 'pedantic' detail concerning this very point in the opening sections of this Essay! Lawler first of all tells us that these "A"s relate to "a thing or concept", but then they are immediately transformed into what can or can't be "asserted".

 

[Readers might now like to try and assert "Paris" or "DNA", or even "cat" in the presence of a few relatives, work colleagues or acquaintances in a bar. That is, try to utter and mean sentences like this "I assert cat", or "I assert DNA", as opposed to asserting something about them. E-mail me with the results!]

 

It could be objected that what Lawler says doesn't imply he thinks that A stands for a proposition or something that can be asserted. He says: "'A is A' implies 'A cannot at the same time be A and not be A...'," by which he means that A goes proxy for a Proper Name or a common noun.

 

Maybe so, but he then goes on to say: "[O]r one cannot assert something to be true and at the same time, and in the same respect, assert it to be false." This parallels the last few words of "'A cannot at the same time be A and not be A...',". Here, A becomes something that is capable of being asserted -- i.e., something "cannot at the same time be A not be A", which corresponds with "One cannot assert something to be true and...assert it to be false", as claimed above. So, A now stands for the something that can be asserted, true or false, which suggests it goes proxy for a proposition or a clause.

 

Now, in relation to the LOC, if these letters do in the end designate propositions (i.e., if they are propositional variables), no problem. In which case: "One cannot assert something to be true and at the same time, and in the same respect, assert it to be false" would at least be a passable first stab at a definition of the LOC (and one in urgent need of improvement -- on that, see here and here). But, by no stretch of the imagination can these letters designate propositions when they appear in the LOI. That 'law' doesn't concern the alleged identity of a proposition with itself (which means that, contrary to what Hegel says, the LOI isn't even a tautology -- on that specific point, see below).

 

However, even if this were the case with the LOI (i.e., if it also concerned the alleged identity of a proposition with itself), that would still have no implications for the LOC. The LOC neither rules in, nor rules out, relations of identity between propositions (again, see below), since it isn't concerned with the identity of propositions to begin with. Indeed, if a proposition, per impossible, lacked identity it wouldn't be a proposition. On the other hand, if, per impossible, it possessed identity, it would be an object, not a proposition.

 

[Perhaps better: because a proposition isn't an object it isn't the sort of thing that could either possess or lack identity. On why propositions aren't objects, nor the Proper Names thereof, see Note Two. Concerning the fatal objection that totally undermines Hegel's criticism of the LOI (mentioned three paragraphs below this one, see also the same Note, as well as here.]

 

To be sure, we can speak about two propositions saying the same thing, but that wouldn't be to relate them, but to predicate something of one or both. Any attempt to go further than this stands in danger of confusing a propositional sign (i.e., the physical marks on the page -- i.e., an inscription --, or the sounds propagated through the air giving voice to it), with what that string of words expresses -- the proposition itself. [On this, see below, too.]

 

We have already seen (for example, here, here and here) that the LOI can't express the alleged identity between concepts, or even between predicates -- since, if, per impossible, it could, they would be objects, too (or the Proper Names thereof), and would thereby cease to be concepts/predicates. The LOI can only apply to objects and/or their names (again, depending on how one reads this 'law'), if it applies anywhere. This means that identity statements are at best 'necessary truths' (although I should want to call them "grammatical 'propositions'"), not tautologies, in any straight-forward sense.

 

Even more problematic for Hegel and Lawler is the following fatal objection: Let us assume that A stands for a Proper Name or for an object (again, depending on how we interpret this 'law'). However, if, according to Hegel and Lawler, A isn't identical with A, then one of those As will now have a different denotation. In that case, it might just as well be designated by the letter "B". So, it now transpires that Hegel wasn't actually criticising the LOI by his use of "A isn't identical with A", as he imagined, he was in fact criticising "A isn't identical with B" -- or, of course, "B isn't identical with A." Plainly, neither have anything to do with the LOI!

 

That fatal objection can only be neutralised by those who reject this use of the ridiculous sentence, "A isn't identical with A".

 

What is more, no fan-of-the-dialectic [FOD] can consistently object to the above, arguing that "A isn't identical with B" misrepresents their criticism of the LOI since it substitutes a letter "B" for a letter "A". It would seem that they could only take exception to that substitution by claiming that "A is identical with A", and so can only be represented by A, not B! Clearly, in order to adopt that defence, FODs will have to accept the validity of the LOI, vitiating the whole exercise!

 

It could be objected that Hegel nowhere says "A isn't identical with A". In fact, this is what he wrote:

 

"This identity is, in the first instance, essence itself, not yet a determination of it, reflection in its entirety, not a distinct moment of it. As absolute negation it is the negation that immediately negates itself, a non-being and difference that vanishes in its arising, or a distinguishing by which nothing is distinguished, but which immediately collapses within itself. The distinguishing is the positing of non-being as non-being of the other. But the non-being of the other is sublation of the other and therewith of the distinguishing itself. Here, then, distinguishing is present as self-related negativity, as a non-being which is the non-being of itself, a non-being which has its non-being not in another but in its own self. What is present, therefore, is self-related, reflected difference, or pure, absolute difference....

 

"The other expression of the law of identity: A cannot at the same time be A and not-Ahas a negative form; it is called the law of contradiction. Usually no justification is given of how the form of negation by which this law is distinguished from its predecessor, comes to identity. But this form is implied in the fact that identity, as the pure movement of reflection, is simple negativity which contains in more developed form the second expression of the law just quoted. A is enunciated, and a not-A, the pure other of A; but it only shows itself in order to vanish. In this proposition, therefore, identity is expressed-as negation of the negation. A and not-A are distinguished, and these distinct terms are related to one and the same A. Identity, therefore, is here represented as this distinguishedness in one relation or as simple difference in the terms themselves." [Hegel (1999), pp.412-416, §872 and §882. Bold emphasis alone added.]

 

This is neatly summed up for us by Henri Lefebvre:

 

"Formal Logic asserts: 'A is A'. Dialectical Logic is not saying 'A is not-A'…. It says: A is indeed A, but A is also not-A precisely so far as the proposition 'A is A' is not a tautology but has real content. A tree is a tree only by being such and such a tree, by bearing leaves, blossom and fruit, by passing through and preserving within itself those moments of its becoming...." [Lefebvre (1968), p.41. Bold emphasis added.]

 

Indeed, Hegel himself clarified his position in like manner:

 

"Everything is grounded in this unity of identity and non-identity, of one and another, of sameness and distinction, of affirmation and negation. The absolute is essentially dialectical. Dialectic is the essence of Being or Being as essence. Essence is the sufficient ground of all that seems to be non-absolute or finite. A is non-A: The Absolute maintains itself in that which seems to escape it." [Hegel (1959), p.120. Bold emphases alone added.]

 

Lawler also says as much:

 

"Looking one step further into this matter, Hegel suggests that the relation of A to not-A is doubly negative. Identity is established (not immediately given) through a negative relation to not-A. A is itself in not being not-A. But this negative relation to not-A is itself negated. That is, the identity of A does not consist solely in its being not-A, there is a 'return' to A again -- which Hegel calls 'reflection.' Thus 'A is A' is not a tautologous (sic) repetition of A (as 'abstract understanding' would have it) but an affirmation that has been made possible only through a doubly negative movement, a 'negation of the negation.'" [Lawler (1982), p.22. Italic emphases in the original, bold added.]

 

"It is necessary to ask, first of all, whether and in what sense the fact that A necessarily relates to what is not-A permits us to insert not-A in A. Hegel is quite explicit that this relation is not to be understood in such a way that the results would be the blurring of all identities in a single monistic being -- as he accuses Spinoza of doing: 'Substance, as the universal negative power, is as it were a dark shapeless abyss which engulfs all definite content as radically null, and produces from itself nothing that has a positive substance of its own.'" [Ibid., p.32, quoting Hegel (1975), §151, p.215, in the edition I have used, which seems to be different from Lawler's. Italic emphases in the original, bold added. Quotation marks altered to conform with the conventions adopted at this site.]

 

"If we grant that A's identity involves its necessary relation to what is not-A, and that this not-A is 'its own other' -- a definite other being and not any being whatsoever -- and that this relation to some definite other is necessary for the existence of A or is essential to the constitution of A (A's identity), it seems reasonable to look for some 'imprint' of this 'other' in A, so that in some sense not-A is internally constitutive of A.... In other words, to understand the internal nature of A it is necessary to study the determinate not-A not only as a necessary external condition but as 'reflected' in A. This is not to say that one should expect to find in A some direct and immediate duplication of not-A. The direct identity of A and not-A would constitute the annihilation of the beings involved." [Ibid., pp.32-33. Italic emphases in the original. Quotation marks altered to conform with the conventions adopted at this site.]

 

This is all rather muddled. It seems dialecticians want to have it both ways: that A is A and A is not-A/non-A, but then A also A again! But one thing seems reasonably clear, they aren't asserting that A is identical with A. On the contrary, they are telling us that A is identical with not-A, which is, after all, the 'dialectical principle' underlying the doctrine of 'The Unity and Interpenetration of Opposites' -- as well as the "Identity of Opposites' -- regarded by no less a dialectician than Lenin as "the essence of dialectics".

 

Indeed, that is certainly how Hegel has been interpreted by Marxist dialecticians ever since:

 

"Abstract identity (a = a; and negatively, a cannot be simultaneously equal and unequal to a) is likewise inapplicable in organic nature. The plant, the animal, every cell is at every moment of its life identical with itself and yet becoming distinct from itself, by absorption and excretion of substances, by respiration, by cell formation and death of cells, by the process of circulation taking place, in short, by a sum of incessant molecular changes which make up life and the sum-total of whose results is evident to our eyes in the phases of life -- embryonic life, youth, sexual maturity, process of reproduction, old age, death. The further physiology develops, the more important for it become these incessant, infinitely small changes, and hence the more important for it also the consideration of difference within identity, and the old abstract standpoint of formal identity, that an organic being is to be treated as something simply identical with itself, as something constant, becomes out of date. [In the margin of the manuscript occurs the remark: 'Apart, moreover, from the evolution of species.'] Nevertheless, the mode of thought based thereon, together with its categories, persists. But even in inorganic nature identity as such is in reality non-existent. Every body is continually exposed to mechanical, physical, and chemical influences, which are always changing it and modifying its identity. Abstract identity, with its opposition to difference, is in place only in mathematics -- an abstract science which is concerned with creations of thought, even though they are reflections of reality -- and even there it is continually being sublated. Hegel, Enzyklopädie, I, p.235. [This is a reference to Hegel (1975), pp.169-70, §117; see below -- RL.] The fact that identity contains difference within itself is expressed in every sentence, where the predicate is necessarily different from the subject; the lily is a plant, the rose, is red, where, either in the subject or in the predicate, there is something that is not covered by the predicate or the subject. Hegel, p.231. [This is a reference to Hegel (1975), pp.166-68, §115.] That from the outset identity with itself requires difference from everything else as its complement, is self-evident.

 

"Continual change, i.e., sublation of abstract identity with itself, is also found in so-called inorganic nature. Geology is its history. On the surface, mechanical changes (denudation, frost), chemical changes (weathering); internally, mechanical changes (pressure), heat (volcanic), chemical (water, acids, binding substances); on a large scale – upheavals, earthquakes, etc. The slate of today is fundamentally different from the ooze from which it is formed, the chalk from the loose microscopic shells that compose it, even more so limestone, which indeed according to some is of purely organic origin, and sandstone from the loose sea sand, which again is derived from disintegrated granite, etc., not to speak of coal.

 

"The law of identity in the old metaphysical sense is the fundamental law of the old outlook: a = a. Each thing is equal to itself. Everything was permanent, the solar system, stars, organisms. This law has been refuted by natural science bit by bit in each separate case, but theoretically it still prevails and is still put forward by the supporters of the old in opposition to the new: a thing cannot simultaneously be itself and something else. And yet the fact that true, concrete identity includes difference, change, has recently been shown in detail by natural science (see above).

 

"Abstract identity, like all metaphysical categories, suffices for everyday use, where small dimensions or brief periods of time are in question; the limits within which it is usable differ in almost every case and are determined by the nature of the object; for a planetary system, where in ordinary astronomical calculation the ellipse can be taken as the basic form for practical purposes without error, they are much wider than for an insect that completes its metamorphosis in a few weeks. (Give other examples, e.g., alteration of species, which is reckoned in periods of thousands of years.) For natural science in its comprehensive role, however, even in each single branch, abstract identity is totally inadequate, and although on the whole it has now been abolished in practice, theoretically it still dominates people’s minds, and most natural scientists imagine that identity and difference are irreconcilable opposites, instead of one-sided poles which represent the truth only in their reciprocal action, in the inclusion of difference within identity." [Engels (1954), pp.214-16. Italic emphases in the original; bold emphases added. Quotation marks altered to conform with the conventions adopted at this site.]

 

"To the metaphysician, things and their mental reflexes, ideas, are isolated, are to be considered one after the other and apart from each other, are objects of investigation fixed, rigid, given once for all. He thinks in absolutely irreconcilable antitheses. "His communication is 'yea, yea; nay, nay'; for whatsoever is more than these cometh of evil." [Matthew 5:37 -- Ed.] For him a thing either exists or does not exist; a thing cannot at the same time be itself and something else. Positive and negative absolutely exclude one another, cause and effect stand in a rigid antithesis one to the other. At first sight this mode of thinking seems to us very luminous, because it is that of so-called sound common sense. Only sound common sense, respectable fellow that he is, in the homely realm of his own four walls, has very wonderful adventures directly he ventures out into the wide world of research. And the metaphysical mode of thought, justifiable and even necessary as it is in a number of domains whose extent varies according to the nature of the particular object of investigation, sooner or later reaches a limit, beyond which it becomes one-sided, restricted, abstract, lost in insoluble contradictions. In the contemplation of individual things it forgets the connection between them; in the contemplation of their existence, it forgets the beginning and end of that existence; of their repose, it forgets their motion. It cannot see the wood for the trees.

 

"For everyday purposes we know and can say, e.g., whether an animal is alive or not. But, upon closer inquiry, we find that this is, in many cases, a very complex question, as the jurists know very well. They have cudgelled their brains in vain to discover a rational limit beyond which the killing of the child in its mother's womb is murder. It is just as impossible to determine absolutely the moment of death, for physiology proves that death is not an instantaneous momentary phenomenon, but a very protracted process. In like manner, every organic being is every moment the same and not the same, every moment it assimilates matter supplied from without, and gets rid of other matter; every moment some cells of its body die and others build themselves anew; in a longer or shorter time the matter of its body is completely renewed, and is replaced by other atoms of matter, so that every organic being is always itself, and yet something other than itself.

 

"Further, we find upon closer investigation that the two poles of an antithesis positive and negative, e.g., are as inseparable as they are opposed and that despite all their opposition, they mutually interpenetrate. And we find, in like manner, that cause and effect are conceptions which only hold good in their application to individual cases; but as soon as we consider the individual cases in their general connection with the universe as a whole, they run into each other, and they become confounded when we contemplate that universal action and reaction in which causes and effects are eternally changing places, so that what is effect here and now will be cause there and then, and vice versa. None of these processes and modes of thought enters into the framework of metaphysical reasoning. Dialectics, on the other hand, comprehends things and their representations, ideas, in their essential connection, concatenation, motion, origin, and ending. Such processes as those mentioned above are, therefore, so many corroborations of its own method of procedure." [Engels (1976), pp.26-27. Bold emphases added; several paragraphs merged.]

 

"In brief, dialectics can be defined as the doctrine of the unity of opposites. This embodies the essence of dialectics...." [Lenin (1961), pp.221-22. Bold emphases added.]

 

"The identity of opposites…is the recognition…of the contradictory, mutually exclusive, opposite tendencies in all phenomena and processes of nature…. The condition for the knowledge of all processes of the world in their 'self-movement', in their spontaneous development, in their real life, is the knowledge of them as a unity of opposites. Development is the 'struggle' of opposites…. [This] alone furnishes the key to the self-movement of everything existing….

 

"The unity…of opposites is conditional, temporary, transitory, relative. The struggle of mutually exclusive opposites is absolute, just as development and motion are absolute…." [Ibid., pp.357-58. Bold emphasis alone added. Paragraphs merged.]

 

"The Aristotelian logic of the simple syllogism starts from the proposition that 'A' is equal to 'A'…. In reality 'A' is not equal to 'A'. This is easy to prove if we observe these two letters under a lens -– they are quite different to each other. But one can object, the question is not the size or the form of the letters, since they are only symbols for equal quantities, for instance, a pound of sugar. The objection is beside the point; in reality a pound of sugar is never equal to a pound of sugar -– a more delicate scale always discloses a difference. Again one can object: but a pound of sugar is equal to itself. Neither is true (sic) -– all bodies change uninterruptedly in size, weight, colour etc. They are never equal to themselves." [Trotsky (1971), pp.63-64.]

 

"Marxist philosophy holds that the law of the unity of opposites is the fundamental law of the universe. This law operates universally, whether in the natural world, in human society, or in man's thinking. Between the opposites in a contradiction there is at once unity and struggle, and it is this that impels things to move and change. Contradictions exist everywhere, but their nature differs in accordance with the different nature of different things. In any given thing, the unity of opposites is conditional, temporary and transitory, and hence relative, whereas the struggle of opposites is absolute. Lenin gave a very clear exposition of this law. It has come to be understood by a growing number of people in our country." [Mao (1977b), pp.392-93. Bold emphases added.]

 

"The 'logic' that we have been discussing is very different from what commonly passes for logic, the formal logic which deals with syllogisms and is to be found in the text book. Formal logic is necessary for dealing with the abstractions which are formed in the first stage of thinking.... The essence of its technique is to keep apart, to prevent from confounding the distinctions which have been made. It is therefore based on a development of certain very fundamental principles about identity and contradiction, principles such as the famous 'law of the excluded middle' which states that a thing must be one thing (say 'A') or not that thing (say 'not A'). It can't be both 'A' and 'not A' at the same time. This logic, which may be termed the 'logic of common sense,' is perfectly justified and indeed essential within certain limits -- the same limits within which the abstractions it deals with are valid.  But just because it is based on taking these abstractions, for the time being, as absolute, and because it necessarily overlooks their inter-connections, and the development of one quality or thing into another, formal logic is unable to grasp the inner process of change, to show its dialectical character. For this we require dialectical logic...." [Guest (1939), pp.71-72. Bold emphases alone added. Paragraphs merged.]

 

"The laws of logic are based on two main propositions. The first is that of identity or of self-conformity. The proposition very simply states: 'A is A,' that is, every concept is equal to itself. A man is a man; a hen is a hen; a potato is a potato. This proposition forms one basis of logic. The second main proposition is the law of contradiction, or as it is also called, the law of the excluded middle. This proposition states: 'A is either A or not A.' It cannot be both at the same time. For example: Whatever is black is black; it cannot at the same time be black and white. A thing -- to put it in general terms -- cannot at the same time be itself and its opposite. In practice it therefore follows that if I draw certain conclusions from a given starting point and contradictions arise, then there are errors in thinking or my starting point was wrong. If from some correct premises I come to the conclusion that 4 is the same as 5, then I deduce from the law of contradiction that my conclusion is false.

 

"So far all appears to be clear and certain. What can be a clearer law than that man is man, a rooster a rooster, that a thing is always the same thing? It even appears to be absolutely certain that a thing is either large or small; either black or white, that it cannot be both at the same time, that contradictions cannot exist in one and the same thing.

 

"Let us now consider the matter from the standpoint of a higher doctrine of thought, from the standpoint of dialectics. Let us take the first law which we have developed as the foundation of logic: A is A. A thing is always the same thing. Without testing this law, let us consider another one which we have already mentioned, the law of Heraclitus which says 'Everything is in flux,' or 'One cannot ascend the same river twice.' Can we say that the river is always the same? No, the law of Heraclitus says the opposite. The river is at no moment the same. It is always changing. Thus one cannot twice nor, more exactly, even once ascend the same river. In short: the law 'A is A' in the last analysis is valid only if I assume that the thing does not change. As soon as I consider the thing in its change, then A is always A and something else; A is at the same time not-A. And this in the last analysis holds for all things and events." [Thalheimer (1936), pp.88-89. Bold emphases added.]

 

"There are three fundamental laws of formal logic. First and most important is the law of identity. This law can be stated in various ways such as: A thing is always equal to or identical with itself. In algebraic terms: A equals A.... If a thing is always and under all conditions equal to or identical with itself, it can never be unequal to or different from itself. This conclusion follows logically and inevitably from the law of identity. If A always equals A, it can never equal non-A." [Novack (1971), p.20. Paragraphs merged; bold added.]

 

"Formal Logic starts from the proposition that A is always equal to A. We know that this law of identity contains some measure of truth…. Now…when we go to reality and look for evidence of the truth of the proposition: A equals A…we find that the opposite of this axiom is far closer to the truth. Now what do we find when we go to reality and look for evidence of the truth of the proposition: A equals A? We discover that nothing in reality corresponds perfectly to the content of this proposition. On the contrary, we find that the opposite of this axiom is far closer to the truth. Wherever we encounter some really existing thing and examine its character, we find that A is never equal to A." [Ibid., pp.32-33.]

 

"This gives us a clue to the true nature of A. A is not the simple fellow, the fixed, unchangeable category the formal logicians make him out to be. That is only one of the appearances of A. In reality A is extremely complex and contradictory. It is not only A but also at the same time something else. That makes A very elusive and slippery. We can never quite catch hold of A because the minute we try to pin A down, it begins to change into something more or less different.

 

"What then, you may ask in exasperation, is A, if it's not simply and solely A? The dialectical answer is that A is both A and non-A. If you take A as simply A and nothing more, as the formal logician does, you see only one side of A and not its other side, its negative side. A, taken by itself as simply A and nothing more, is an abstraction that can never be fully realised or found in actuality. It is a useful abstraction so long as you understand its limits and do not take it or, better, mistake it, for the full and final truth about any given thing. This elementary law of identity holds good for most of the ordinary acts of everyday life and thinking, but it must be replaced by more deep-going and complex laws where more complicated and long-drawn-out processes are involved." [Ibid., p.37. Bold emphases added. Novack is particularly snotty about FL. I have subjected this rather smug comrade's work to searching and unflattering criticism in Essay Four Part One.]

 

"This law of identity of opposites, which so perplexes and horrifies addicts of formal logic, can be easily understood, not only when it is applied to actual processes of development and interrelations of events, but also when it is contrasted with the formal law of identity. It is logically true that A equals A, that John is John…. But it is far more profoundly true that A is also non-A. John is not simply John: John is a man. This correct proposition is not an affirmation of abstract identity, but an identification of opposites. The logical category or material class, mankind, with which John is one and the same is far more and other than John, the individual. Mankind is at the same time identical with, yet different from John." [Ibid., p.92. Bold emphasis added.]

 

"A moment's reflection will allow us to conclude that formal logic is characterised by the thought processes which consist of putting motion, change, into parenthesis. All the laws enumerated above are true, so long as we abstract from motion. A will remain A so long as it does not change. A is different from non-A so long as it is not transformed into its opposite. A and non-A exclude each other so long as there is no movement which combines A and non-A, etc. These laws are obviously insufficient if we consider the transformation of the chrysalid (sic) into the butterfly, the passage of the adolescent into the adult, the movement of life into death, the birth of a new species or a new social order, the combination of two cells into a new one, etc." [Mandel (1979), pp.160-61. Italics in the original. Bold emphasis added.]

 

"The basic principles of this Aristotelian or formal logic were the 'law of identity' and the 'law of non-contradiction'. The 'law of identity' stated, in symbolic terms, that A is equal to A, or an ounce of gold equals an ounce of gold, or, taking a unique object..., Leonardo da Vinci's Mona Lisa is equal to Leonardo da Vinci's Mona Lisa. The 'law of non-contradiction' stated that A cannot be equal to non-A, it makes no sense to say that an ounce of gold is not an ounce of gold or the Mona Lisa is not the Mona Lisa. On the basis of these apparently 'obvious' propositions a system of logic or sound reasoning was erected, exemplified by the syllogism." [Molyneux (2012), p.43. Quotation marks altered to conform with the conventions adopted at this site. Italic emphases in the original.]

 

"This matters because the dominant mode of thinking, based on the logic developed by Aristotle, is not founded on the principle of universal change, rather it deals with fixed states or 'things'. Its basic axioms are that A = A (a thing is equal to itself) and A does not = non-A (a thing is not equal to something other than itself), from which are derived sequences of sound reasoning known as syllogisms.... This formal logic was, and is, all well and good and very necessary for practical human affairs but it is limited -- it excludes change. Dialectical logic moves beyond formal logic by starting not with 'things' but with processes, processes of coming into being and passing out of being. The moment processes of change are fed into the equation it becomes necessary to deal with contradiction. If state A (e.g. day) changes into state B (night) it passes through a phase of A not being A or being both A and B (twilight)." [Molyneux, 'The Marxist Dialectic'. Paragraphs merged; bold emphasis added.]

 

"No two things are completely alike, no matter how seemingly identical, whether they are leaves of a tree, blades of grass, fingerprints, or any other thing. In having and identity, a thing has a sameness with other things (as well as with itself, despite all changes, during its lifetime) that stops short of complete identity, or sameness in all respects. Difference is always present.... Sameness and difference do not simply subsist side by side in mere conjunction. They cannot exist apart.... Every affirmation of a thing's features is simultaneously a denial of its possession of other features." [Gollobin (1986), pp.92-93. Bold emphases added; paragraphs merged.]

 

"In the whole world there is no developing object in which one cannot find opposite sides, elements or tendencies: stability and change, old and new, and so on. The dialectical principle of contradiction reflects a dualistic relationship within the whole: the unity of opposites and their struggle. Opposites may come into conflict only to the extent that they form a whole in which one element is as necessary as another. This necessity for opposing elements is what constitutes the life of the whole. Moreover, the unity of opposites, expressing the stability of an object, is relative and transient, while the struggle of opposites is absolute, expressing the infinity of the process of development. This is because contradiction is not only a relationship between opposite tendencies in an object or between opposite objects, but also the relationship of the object to itself, that is to say, its constant self-negation. The fabric of all life is woven out of two kinds of thread, positive and negative, new and old, progressive and reactionary. They are constantly in conflict, fighting each other.

 

"The ancients used to say that everything comes about through strife. If a phenomenon contains opposites, it must be in contradiction with itself. The same applies to the expression of this phenomenon in thought. There is an obvious contradiction in the fact that a phenomenon remains the same and at the same time constantly changes, that is, contains opposite tendencies.

 

"The opposite sides, elements and tendencies of a whole whose interaction forms a contradiction are not given in some eternally ready-made form. At the initial stage, while existing only as a possibility, contradiction appears as a unity containing an inessential difference. The next stage is an essential difference within this unity. Though possessing a common basis, certain essential properties or tendencies in the object do not correspond to each other. The essential difference produces opposites, which in negating each other grow into a contradiction. The extreme case of contradiction is an acute conflict. Opposites do not stand around in dismal inactivity; they are not something static, like two wrestlers in a photograph. They interact and are more like a live wrestling match. Every development produces contradictions, resolves them and at the same time gives birth to new ones. Life is an eternal overcoming of obstacles. Everything is interwoven in a network of contradictions." [Spirkin (1983), pp.144-45. Bold emphases added.]

 

"Identity means difference. Difference means identity. And now with a leap we can get into it. Hegel says that this principle becomes important, in fact decisive, when you watch, make a philosophical cognition, about a single object. Within the identity of an object, you have to establish the specific difference, and within its specific difference, you have to establish the identity. If you have established the specific difference, the difference which belongs to the object, which distinguishes it from all other objects and their differences, then you have the Other of the object. The other is the difference that matters, the essential difference. But as it is special (essential) difference to no other object, then [sic] Other is therefore identical with its object. To find that out is to find out what makes the object move. I look at bourgeois society and I see capital, but labour is its other. In capital is essential difference, but both capital and labour are one identity.... For Hegel, having established the uncertain character of Identity, moves on at once to Difference. And here he is equally bold but a little easier to follow. He says that if identity implies difference, then equally difference implies identity." [James (1980), pp.84-85. Bold emphases added; paragraphs merged.]

 

"For Marxism the world is characterized by interconnection and change. By interconnection is meant not only the external relations of things and processes to one another, but their internal relations; every thing, event, or process is therefore determined both by its external environment and its own internal processes. Further, by change is meant not merely a quantitative development but also, and fundamentally, qualitative change. Thus, in a world of such interconnection and change, any given thing is in process of becoming something other than what it has been; and it is, therefore, at any given time a conflict of what it was and what it is becoming -- of, say, a new content developing in an old form. The thing itself is nothing over and above this conflict which characterizes it and which makes it the thing it is. It is this which Marxists call the unity or interpenetration of opposites. The whole of dialectics is thus, for Marxism, the spelling out, in ever richer detail, of the essential features of such processes in their inherent contradictions and interconnections on endlessly varied levels -- levels being characterized by new internal contradictions and hence by new qualities and different modes of functioning. It is thus both an instrument for the knowledge of and control over natural and social processes, both an ontology and a logic, a theory of the nature of things and a method of thinking....

 

"Yet [the] principle of identity is the cornerstone of formal logic and of all static thinking, and so long as it is accepted it is impossible to make any sense of dialectics. Dialectics begins by calling into question the very idea that a thing is simply the thing it is; holding, on the contrary, that everything is in the process of becoming something else and hence is always a conflict between what it was and what it will be. Hence what we call a thing is a temporary unity of opposites.... An infant...is not a something...which has the property of infancy, but is a stage in the process from conception to maturity and death, of such a nature that every moment involves its being an infant and being a non-infant, that is, its moving away from infancy." [Selsam and Wells (1949), pp.155-56; bold emphases added, several paragraphs merged.]

 

"Dialectics is quite simply the logic of motion, or the logic of common sense to activists in the movement. We all know that things don't stand still, they change. But there is another form of logic which stands in contradiction to dialectics, which we call 'formal logic', which again is deeply embodied in capitalist society. It is perhaps necessary to begin by describing briefly what this method implies.

 

"Formal logic is based on what is known as the 'law of identity', which says that 'A' equals 'A' -- i.e. that things are what they are, and that they stand in definite relationships to each other. There are other derivative laws based on the law of identity; for example, if 'A' equals 'A', it follows that 'A' cannot equal 'B', nor 'C'.... Whereas the formal logician will say that 'A' equals 'A', the dialectician will say that 'A' does not necessarily equal 'A'. Or to take a practical example that Trotsky uses in his writings, one pound of sugar will not be precisely equal to another pound of sugar. It is a good enough approximation if you want to buy sugar in a shop, but if you look at it more carefully you will see that it's actually wrong." [John Pickard, quoted from here. Several paragraphs merged; bold emphasis added.]

 

"Classical, Aristotelian logic takes as its fundamental premise the Law of Identity, the statement that a thing is identical with itself. Expressed in a formula: A is A…. In Aristotle's formal logic A is A, and never non-A. In Hegel's dialectics A is A as well as non-A." [Baghavan (1987), pp.75-76. Bold added.]

 

From the above it would be difficult if not impossible to argue that DM-fans reject the claim that "A isn't identical with A" -- or, indeed, that they don't believe that "A is at one and the same time not-A". Those ideas are integral to their theory of change.

 

And yet, as soon as they allow A at the same time to be not-A, and inform their readers that everything is a "unity of opposites", the above fatal objection kicks in. And it is no good complaining that "the identity of A does not consist solely in its being not-A, there is a 'return' to A again", since that "return to A" is also a return to not-A, which is what we have just been told is what the identity of A consists in. Indeed, A would not develop fully into not-A unless A were also not-A.

 

With that observation, the entire 'dialectic' implodes.

 

Lawler sort of half recognises this when he says:

 

"The direct identity of A and not-A would constitute the annihilation of the beings involved." [Ibid.]

 

But that is precisely what he and Hegel have now done -- except it doesn't result in the annihilation of anything other than this theory (because of the aforementioned change in denotation of the letter "A").

 

The reason this doesn't result in the annihilation of anything other than this theory is that to imagine otherwise would be to confuse talk about talk with talk about the world -- as if what we do with letters, of itself, actually affects anything in reality.

 

Still less will it do to complain that the letters Hegel and Lawler employed refer to objects in reality, so that if A and not-A were identical -- that is, if what A refers to were identical to what not-A refers to --, A itself (in reality) would be annihilated. That isn't so. If a logical system uses a symbol (like "A") that is 'defined' in such a careless and sloppy way that it 'refers' to something and its supposed opposite (at the same time) -- or, to be charitable, if that symbol denotes two different referents (in this case A and not-A) -- then it ceases to be a symbol, and that logical system loses any right to be called a "logic". And such it will remain until the denotation of each 'symbol' it employs has been clearly and unambiguously established. So, it shouldn't surprise us when the sloppy 'logic' Hegel bequeathed to his gullible acolytes results in endless confusion and bogus 'contradictions'.

 

Nor will it do to argue that "A" refers to A and "not-A" refers to not-A, so that "A" does not refer to two distinct objects, contrary to the above assertion. That is because we are told that A is at the same time not-A, not that there are two symbols at work here. So, "A" does all the supposed symbolling on its own.

 

[For more on the above fatal defect at the heart of the 'dialectical criticism' of the LOI , see Note Two.]

 

Not A Tautology

 

Putting even this to one side for now, it was asserted earlier that identity 'propositions' aren't tautologies in any straight-forward sense. As far as FL is concerned, that is partly because identity 'statements' aren't molecular; i.e., identity 'propositions' purport to express a relation between an object and itself (or between its supposed names). Such 'propositions' aren't comprised of sub-clauses (except when they are paraphrased; on that see below), or simpler propositions. [On this, see Glock (1996), pp.164-69.] Identity 'statements' can't be expressed as tautologies in the truth tables, either. Of course, the identity sign is always given, or is defined as having, the value "true" in the truth tables, but that truth-value hasn't been derived from the truth-values of constituent propositions or clauses, since there are no constituent propositions or clauses in identity 'statements' (again, except when paraphrased; on that see the next few paragraphs). They are generally comprised of (i) nouns (common or Proper) linked by a copula, (ii) two noun phrases and a verb phrase, or (iii) a name (common or Proper) and a predicate expression, unlike genuine logical tautologies, such as, "p → q ¬p v q".

 

[Where "p" and "q" are propositional variables, "¬" is a negation operator, "" is a conditional sign standing for "if...then", and "" is a biconditional sign, standing for "if and only if". (There is more on this below.) Henceforth, in this section (and much of this site), I have put "proposition" and "statement" in 'scare' quotes when qualifying identity sentences in the indicative mood -- for reasons that will soon become apparent.]

 

It could be objected that in an identity 'statement', like "Cicero is identical with Tully" ("Tully" was Cicero's other name), there is a clause, namely "...is identical with Tully". But "Cicero is identical with Tully" is a paraphrase of "Cicero is Tully" into which a clause has been inserted in order to make clear that the "is" here is one of identity.

 

Even so, it could be replied that "Cicero is identical with Tully" is nevertheless a true "identity proposition". That is undeniable -- if we wave aside concerns about the nature of identity 'statements' and whether they can even be true or false --, but it still isn't a tautology, and that is for reasons suggested above and underlined further below.  

 

At a discursive level, even in 'predicative sentences', tautologies merely "say the same thing", or they involve the use of synonyms -- for example:

 

T1: A vixen is a female fox.

 

T2: A regicide is a king-killer.

 

Identity 'propositions' utilise what certainly appear to be relational expressions (e.g., "ξ is ζ", "ξ is identical with ζ", or even "ξ = ζ"), but such 'propositions' can't be tautological in the sense that the two noun phrases involved (i.e., two Proper Names or Definite/Indefinite Descriptions legitimately substituted for those Greek letters either side of the "is", or the "=" sign), "say the same thing". That is because noun phrases don't "say the same thing" since they don't say anything at all. The first A, in A = A, if it stands for a Proper Name or some other singular term/indefinite description, doesn't say the same thing as the second A since neither A says anything. Only clauses, propositions or indicative sentences can do that, or can be used to do it. On the other hand, if A is a propositional variable, it can't be put into a relation with itself, since it isn't an object, nor the Proper Name thereof. [Why that is so is covered in Note 2.]

 

[Elsewhere it will be explained why the following words or their equivalent have been used, "Propositions expressing identity utilise what certainly appear to be relational expressions...."; I have provided a hint why that is so, below.]

 

Discursively, T1 and T2 each express a rule of language (or, in Informal Logic, each would express a rule for the substitution of synonyms, salva veritate and salva congruitate), and so they can't be true or false (this point was argued at length in Essay Twelve Part One). Rules aren't the sort of thing that can be true or false; they can only be practical or impractical, useful or useless. [Why such sentences are rules will be explained shortly.]

 

[Here, salva veritate means such a substitution would preserve truth (in non-opaque contexts) -- i.e., it wouldn't turn a true proposition into a false one, nor vice versa. Salva congruitate is a little more complex, but refers to the substitution of grammatically conformable phrases, roughly: Proper Nouns for Proper Nouns, common nouns for common nouns, etc.]

 

We are also told that a tautology is true in virtue of "logical form alone". But that can't be the case. Briefly, here is why:

 

If, per impossible, such 'statements'/rules could be 'false', then the meaning of the terms involved will automatically have changed since such sentences/rules express or establish how certain words are to be used, and hence what they mean. For example, if a vixen isn't a female fox (which is what the supposed falsehood of T1 would seem to express), "vixen" will ipso facto have acquired a new meaning. In which case, the 'negation' of T1 would merely be recording that terminological fact (but, without revealing its new meaning). However, the same problems would now affect this new meaning, or, perhaps better, the status of any sentence recording that meaning. It couldn't be false, either. On the other hand, if T1 were 'true', and couldn't possibly be false, it couldn't be expressing a fact about the world (I have explained why that is so, here). In that case, T1 can't be true, either -- there is no fact of the matter that would make T1 true. If T1 were a fact about the world, it would make sense to check if it was indeed the case that vixens were female foxes. But, anyone who tried to ascertain whether it was true that vixens were female foxes would only have succeeded advertising their own lack of knowledge of English (or any other language that had similar uses of words). That shows T1 is prescriptive; it tells us how certain words are to be used, what their correct use is (which is why I called it a rule of language, or a "grammatical 'proposition'"). Moreover, neither T1 nor T2 are "true in virtue of logical form alone", since neither are true to begin with.

 

T1: A vixen is a female fox.

 

T2: A regicide is a king-killer.

 

Of course, such sentences record a fact about the English language. So, if someone were to say, "In English, 'vixen' means the same as 'female fox'", they would be speaking the truth, just as someone who said, "In English, 'vixen' doesn't mean the same as 'female fox'", or, "In English, 'vixen' means the same as 'female rabbit'", they would have spoken falsely. But those facts about English are a consequence of rules that establish the actual meaning of "vixen" (howsoever those rules emerged socially and historically), which rules themselves can be neither true nor false (and for the above reasons).

 

Some might object that a rule in English such as "A vixen is a female fox" is in fact true, despite what was argued earlier. But, if that were the case, "A vixen is a female fox" would then be descriptive not prescriptive, making it an assertion, which could be true or could be false, in relation to which supporting evidence would be appropriate. But, anyone who now claimed that such sentences were descriptive (and, in this case, were also true) would have no answer to someone else who retorted "Well, I'll use that word any way I like!". Other than an to appeal to tradition, to how the word has always been employed, they could make no response. So, in order to proscribe the antics of such maverick linguists, "A vixen is a female fox", and sentences like it, would have to be viewed prescriptively, and thus as rules, not descriptions. Rules are enforceable because they are prescriptive. It would make no sense to enforce a mere description.

 

Once again, "In English, 'vixen' means the same as 'female fox'" is a correct (or true) description of, or assertion about, a rule in English, in the sense that anyone who uttered it would be speaking truly about the rules themselves; but, the prescriptive nature of this rule doesn't depend on such truthful reports, but on the application of that rule, a rule which defines how certain words are to be used.

 

Naturally, individuals can employ words any which way they chose, and if they are consistent in that use, they will have laid down their own rules for such a novel use of language. But then, this new rule will attract the same constraints outlined above. It could be neither true nor false. On the other hand, if their use were inconsistent, they can't expect to be understood, nor expect anyone to believe they even understand themselves. [I have said more about such maverick speakers in Essays Twelve Part One and Thirteen Part Three.]

 

Hence, sentences like T1 and T2 express rules for the use of certain noun phrases. They aren't identity statements. If, for example, we were told that A is identical to B, and this were a supposed fact of the matter, it could be false that they were identical. But we have just seen that T1-type sentences can't be false. That being the case, T1-type sentences aren't even relational -- despite appearance to the contrary.

 

[Of course, logicians and grammarians might still want to treat such sentences as relational, but this is just another example where certain formal systems and ordinary language diverge.]

 

T1: A vixen is a female fox.

 

T2: A regicide is a king-killer.

 

By way of contrast, "A vixen is a vixen" and "A regicide is a regicide" aren't rules of language (except in special circumstances). No one would succeed in showing they knew how to use "vixen" by just saying "A vixen is a vixen", but they would if they showed they knew that a vixen was a female fox.

 

However, if a tautology just "says the same thing twice", or is an example of "needless repetition" (as some dictionaries inform us), and if "A vixen is a vixen" were interpreted predicatively, that is, if it were viewed as an interpretation of the linguistic function, "ξ is a vixen", that predicable can't be saying the same thing as "A vixen", since "A vixen" is plainly not of the form "ξ is a vixen" -- and, of course, "ξ is a vixen" isn't saying anything to begin with. That is because it is an uninterpreted predicable. In which case, in "A vixen is a vixen" the two halves can't be "saying the same thing" because "A vixen" and "ξ is a vixen" aren't saying anything at all, let alone "the same thing". If they were saying something, "ξ is a vixen is a vixen" would make sense, since, in that case, "ξ is a vixen" would "say the same thing" as "A vixen", and could be substituted for it in "A vixen is a vixen" to yield "ξ is a vixen is a vixen".

 

Hence, not even "A vixen is a vixen" is a tautology (if defined in the above sense)!

 

What is more, "...is identical with ξ" doesn't "say the same thing" as "ζ is identical with...", either!1

 

It could be objected that "A vixen" can be used to say the same thing as "A vixen" when it has been embedded in an appropriate sentential context, like T1. I will deal with that objection in the next few paragraphs.

 

T1: A vixen is a female fox.

 

We are also told that even in ordinary language a tautology is an "expression or phrase that says the same thing twice, just in a different way". In which case, it could be argued that the above would mean that "A vixen is a female fox" isn't a tautology, either, since "A vixen" and "ξ is a female fox" aren't "saying the same thing" (in the strict sense intended in the previous few paragraphs), which is absurd. The two halves of T1, for example, say the same thing; they are synonymous.

 

Indeed, and that is why such sentences were called rules (as opposed them being to tautologies, or even 'necessary truths'), since they express a rule for the substitution of synonymous terms in English (or in other languages with the same facility). In that way, anyone who used the phrase "A vixen" in a sentence would be saying the same as anyone using "a female fox" in the same, or a different, sentence (in non-opaque contexts).

 

For example, these two "say the same thing", or can be used to say it:

 

F1: A vixen turned the bins over last night.

 

F2: A female fox turned the bins over last night.

 

[Always assuming, of course, that the phrase "last night" referred to the same night in question, were talking about the same animal and the same bins!]

 

If that is what is meant by "tautology", no problem. But it is far from clear whether Hegel and/or Lawler meant this.

 

Even so, what about "A vixen is ζ" and "ξ is a female fox"? Aren't they saying the same thing (when embedded in an appropriate sentential context)?

 

If they were, "A vixen is a vixen" and "A vixen is a female fox" would also be same, where "A vixen" has been used to replace both Greek letters -- ζ and ξ -- which, plainly, they are not. 

 

It could be countered that the identity proposition, "Cicero is Tully", works in the same way, so that anyone who used "Cicero" in a sentence would be saying the same as anyone using "Tully" in the same (non-opaque) sentential context. For example:

 

F1a: Cicero turned the bins over last night.

 

F2a: Tully turned the bins over last night.

 

Of course, in such cases we would have co-referential terms that could be substituted for one another salva veritate (in non-opaque contexts), and salva congruitate -- that is, such a substitution wouldn't affect the truth value of the sentences involved, or render them ill-formed. Now, if that is what is meant by "tautology", again, all well and good, but it is certainly not what Hegel or Lawler meant.

 

[If anyone wants to claim they did, they will need to provide passages from the writings of one or both in order to substantiate that claim.]

 

However, as noted above, and again below, this isn't the case for paraphrases like "...is identical with ξ" and "ζ is identical with...", since they clearly don't "say the same thing", since neither saying anything outwith an appropriate sentential context.

 

[MFL = Modern Formal Logic.]

 

It could now be countered that F3 and F4 are identity statements, despite what was asserted earlier. As we have seen, that is controversial. But even if they were 'identity statements', that doesn't automatically make them tautologies -- not unless we re-cast, or re-interpret, that term along lines suggested above.

 

F3: A vixen is a female fox.

 

F4: A regicide is a king-killer.

 

It could be objected that identity statements are in fact predicative, or they can at least be paraphrased predicatively. Moreover, identity statements -- for example, "ξ is identical with ξ" --, always yield the value "true" for any legitimate substitution instance. Certainly, a case could be made for regarding them as tautologies, in this sense alone, and they would be so categorised in MFL (if "tautology" is defined as any wff that always yields the value "true" for any conformable or legitimate interpretation). But, and in addition to the points made earlier, this isn't a necessary part of logic, as Wittgenstein showed. In a properly constructed formal language, identity would be expressed by the use of the same sign, not a special sign for identity, so we don't in fact need this formal 'relation'. [More on that, here.] Moreover, and for reasons also outlined earlier, this would only be the case if we modified the word "true" to mean "logically true", not "empirically true".

 

[Wff = Well Formed Formula (pronounced "woof"); i.e., a string of letters or symbols that conform with the syntax of the formal language to which they belong.]

 

Anyway, and once again, this is certainly not what Hegel or Lawler were talking about.

 

However, even if identity 'statements' were to be interpreted as predicative 'propositions', they would still fail to be tautologies in the discursive sense that Lawler and Hegel require (i.e., in the sense that they "say the same thing"). That is because the predicable here would be a two-place linguistic function "ζ is identical with ξ" -- it can't be "ξ is identical with ξ", for that would prejudice its permissible substitutional instances --, which is in no way tautological. Once more, "...is identical with ξ" does not "say the same thing" as "ζ is identical with...".

 

[The term "linguistic function" is explained in Geach (1961). Basically, these functions are analogous to mathematical functions except they map linguistic expressions (of a certain sort) onto linguistic expressions (of another sort). For example, the linguistic function "ξ wrote Das Kapital" maps "Karl Marx" onto "Karl Marx wrote Das Kapital". (The use of Greek letters like "ξ" is explained here, and in Note 1. "Predicable" is explained here.)]

 

Even if the predicable here were "ξ is identical with ξ", that would be no use, either, for, as noted above, "...is identical with ξ" doesn't "say the same thing" as "ξ is identical with...".

 

Finally, as noted earlier, if we are told that A is identical to B, for instance, it could be false that they were identical. But we have seen that if propositions expressing identity are false, then the denotation of the "A" and "B" terms must be different. While that won't affect "A is identical to B" (i.e., a substitution instance of "ζ is identical with ξ"), it does affect "A is identical to A" (i.e., a substitution instance of "ξ is identical with ξ"). So, if "A is identical to A" were false, then there will be a problem with the denotation of those two "A"s, meaning that what we really have here is "A is identical to B" not "A is identical to A", after all! So, if "A is identical to A" can't be false, it can't be true, either (for reasons outlined earlier).

 

The Law Of Identity Mis-Identified

 

Remember: if you are viewing this with Mozilla Firefox, you might not be able to read all the symbols I have used. I have no idea whether other Browsers are similarly affected.

 

[LOC = Law of Noncontradiction; LEM = Law of Excluded Middle; LOI = Law of Identity.]

 

Nevertheless, for the sake of argument, let us concede that the LOI is something like the following:

 

L1a: p = p.

 

[Where "p" designates a proposition, statement or spoken token, or even type, declarative/indicative sentence, (etc.), depending on one's philosophy of logic.]

 

Or, perhaps even:

 

L1b: (x)[Fx = Fx].

 

[Where "(x)...x" is the universal quantifier, and "F(ξ)" is a one-place, first-level predicate expression (i.e., a predicable). The other symbols I have used below are explained here.]

 

Incidentally, L1b is ill-formed, and roughly 'says', "Everything true of an object is identical with every truth about that object." It should, of course, be:

 

L1c: (x)[Fx º Fx],

 

which roughly reads "For any object, whatever is true of it is equivalently true of that object." Indeed, a pointless 'proposition'!

 

Even then, neither of these would have any bearing on the relation they are imagined to have with their supposed 'dialectical opposite' -- as Lawler alleged. However, that might be the case with the following (as we will see):

 

L2: p cannot at the same time be p and not be p.

 

Nor would either have anything to do with any so-called "assertibility conditions":

 

L3: One cannot assert that p is true and at the same time, and in the same respect, assert that p is false.

 

That is because there are no rules for deriving either of L2 or L3 from L1a or L1b (or from less formal versions of each), or, indeed, from anything analogous. And it isn't hard to see why. [More about that presently. Anyway, restricting the LOC to assertibility conditions limits the 'law' to certain speech acts, when that 'law' is far more general.]

 

[Of course, L3 might itself prove to be acceptable for other reasons. Excepting the points made above (about a similar looking sentence), I will pass no opinion on this here; but L2 and L3 certainly do not follow from L1a or L1b, or from their alleged 'dialectical-negative' versions (or even from less from formal alternatives to one or both, as we will also soon see).]

 

However, as noted above, the real problem here is that if the negative particle attaches to singular terms (i.e., Proper Names and Definite Descriptions) so that it is interpreted as an operator mapping a singular term onto 'negative' singular term (whatever that means!), it can't also be a sentential operator mapping a sentence or proposition onto its negation, which is what it has to be in relation to both the LEM and the LOC. That is, if the following were the case:

 

P1: N*(A) º ¬*A.

 

Or even:

 

P2: N*(A) = ¬*A.

 

[Where "N*" is just such a general 'negative operator' (i.e.,  "Neg..."), which happily slides around between its role as a sentential operator and its role as an operator on Proper Names. "A" goes proxy for a Proper Noun (or maybe even for a Common Noun, in this non-standard, 'relaxed logic'), "¬*" is also a 'negative' particle in this 'novel logic', and "º" is the familiar logical equivalence sign and stands for "if and only if". (I have used asterisks to highlight the radically non-standard nature of the 'symbols' employed in P1 and P2.)]

 

Of course, given the above novel/artificial 'syntax', P1 is ill-formed, too. That is because neither N*(A) nor ¬*A are propositions, sentences, or clauses. [Negating a name (whether it is represented by a Proper or a Common Noun) on its own simply yields another Noun Phrase, not an indicative sentence or clause, while "º" can only operate on propositions, indicative sentences and clauses.] When actual names are inserted -- so that P1 yields, say, "Neg(Socrates) if and only if Not(Socrates)" -- the above can be seen for what they are, unvarnished nonsense. [As is also the case with "Neg(Socrates) is identical with Not(Socrates)".]

 

[Henceforth, I will omit reference to clauses when I am making points like those above; it should be assumed I also intend to include clauses, unless otherwise stated.]

 

On the other hand, if the negative particle (for example, in P3 and P4) is a sentential operator mapping an indicative sentence, or a proposition, onto its negation, it can't also be an operator mapping names in the above manner.

 

P3: N(A) º ¬A.

 

P4: N(A) = ¬A.

 

[Where "N" is a negative operator ("Neg..."), "A" is now a propositional variable, and "¬" is also a negative particle in standard logic (i.e., "It is not the case that..."), which maps an indicative sentence onto its negation.]

 

But, in that case, P4 would be ill-formed, too, since "=" can only be flanked by singular terms, not propositions. Once more, if we insert actual sentences into P4 --, so that it yields, for example, *"Neg(Paris is in France) is identical to it is not the case that Paris is in France" -- we can see that it, too, is no less nonsensical.

 

P3, on the other hand, looks alright as it is. While "Neg(Paris is in France) if and only if it is not the case that Paris is in France" is certainly odd, it isn't nonsense, but that is only because N now works as a surrogate for a standard sentential or propositional negation sign.

 

Once again, that is why it is so important to keep track of the denotation of each letter A (and, indeed, every other symbol) Hegel and/or Lawler used --, or rather, mis-used -- and why much was made of this point earlier. Incidentally, this is also why it is especially important to be clear about the precise logical role played by negative particles and what it is they are supposedly modifying.

 

Recall, Hegel thought he could derive the LOC from the LOI by claiming that the LOI "stated negatively" is, or implies, the LOC. To that end, he argued that while the LOI is "A = A", when stated (negatively) it is also "A cannot at the same time be A and not A" -- or, "¬(A & ¬A)".

 

[Of course, there might be other ways of expressing the 'negative form' of the LOI -- here, for instance, is one possibility: ¬[(A = A) & (A = ¬A)]. However, that version presents problems of its own, which will be explored again below, and in Note 2.]

But (and once more), as far as the LOC and the LEM are concerned, A can only stand for a proposition,
an indicative sentence, or a statement (depending on one's philosophical logic); i.e., it goes proxy for expressions that are capable of being true or false.

 

By way of contrast, when it features in the LOI, A should go proxy for a singular term; as such it can neither be a propositional nor a sentential, variable. So, for example, "Caesar" -- a singular term -- on its own isn't capable of being true or false. In which case, if "¬" is taken to be a propositional or sentential operator -- again, mapping truths onto falsehoods, or vice versa --, ¬A would make no sense. "It is not the case that Caesar" is, once more, nonsensical.

 

Alternatively, if A were a sentential or propositional variable, ¬(A & ¬A) would become "It is not the case that Caesar is identical with Caesar and Caesar is not identical with Caesar" (where, in this instance, "A" now stands for "Caesar is identical with Caesar" -- and not just "Caesar" on its own, as would be the case in relation to the LOI), which seems to make sense. But, as has already been pointed out, it can't stand for such sentence in relation to the LOI. Once again: that is because "A" can't go proxy for sentences like "Caesar is identical with Caesar" in connection with that 'law' because "Caesar is identical with Caesar" isn't a singular term.

 

The other form mentioned above -- i.e., ¬[(A = A) & (A = ¬A)] -- fares little better (even if it isn't patent nonsense), becoming, for example: "It is not the case that ((Caesar is identical with Caesar) and (Caesar is identical with not Caesar))" -- that is, if, per impossible, ¬ functions as both a sentential/propositional operator and an operator on singular terms! Who exactly is this "not Caesar" person?

 

[I have covered that particular issue -- the attachment of negative particles to Proper Names -- in more detail, here.]

 

That is quite apart from the fact that this example is susceptible to the fatal objection mentioned earlier.
 

On the other hand, if ¬ operates on Proper Names, or singular terms in general, then ¬(A & ¬A) would make no sense, either. In that case, "¬(A & ¬A)" would become "Not (Caesar and not Caesar)". But, what on earth does that mean? It isn't even a proposition! "Not Caesar" isn't an expression that is capable of being true or false, nor is "Not (Caesar and not Caesar)", on its own. In which case, given this use of ¬, ¬(A & ¬A) can't be the LOC -- "Not (Caesar and not Caesar)" isn't the LOC, nor is it even a contradiction. It is either plain gibberish or it isn't a proposition.

 

The other form (i.e., ¬[(A = A) & (A = ¬A)]) isn't much better, too, since it pans out (when interpreted) as: "Not ((Caesar is identical with Caesar) and (Caesar is identical with not Caesar))".

 

[This isn't to suggest that the negative particle can't attach to Noun Phrases in general (on that, see here), only that when it does, it has assumed an entirely different role -- and hence it takes on a new meaning -- distinct from the role it occupies when it operates on sentences or propositions. Indeed, as we have seen, when the negative particle attaches to a Proper Noun (in what appear to be relational expressions -- e.g., "Paris is no Vienna", or "Brutus is not Caesar" --, its function changes dramatically. These two sentences in effect become "Brutus is other than Caesar", or "Paris can't be compared with Vienna". Again, I have covered this particular topic in much more detail, here.]

 

The dilemma facing DM-fans is now quite stark:

 

(1) If ¬ operates on Proper Names, or singular terms in general, and if A is a singular term variable, then A = A certainly seems to make sense. But, in that case, the 'negative form' of the LOI -- ¬(A & ¬A), or even ¬[(A = A) & (A = ¬A)] -- turns out to be plain and unvarnished nonsense -- when Proper Names are substituted, yielding, for example: "Not (Caesar and not Caesar)", or even "Not ((Caesar is identical with Caesar) and (Caesar is identical with not Caesar))"!

 

(2) On the other hand, if ¬ operates on sentences, propositions or clauses, mapping them onto their negations, and if A is a sentential or propositional variable, then the LOI, (A = A), would become, for example, "Caesar is identical with Caesar is identical with Caesar is identical with Caesar"), which isn't the LOI! [Here interpreting the letter "A" in "A is identical with A" as the proposition "Caesar is identical with Caesar". Recall that in Option (2), A has to go proxy for a proposition, sentence or clause (in this case, "Caesar is identical with Caesar"), not a Proper Name.

 

Exception might be taken to the use of the letter "A" to stand for the proposition "Caesar is identical with Caesar". DM-fans can't in fact lodge that objection since, as we have seen, according to them and their sloppy syntax/semantics, these letter "A"s can stand for anything we please! In that case, take any randomly selected proposition and replace each letter "A" with it in the LOI. That having been done, not much will change: "Paris is in France is identical to Paris is in France" (interpreting the letter "A" in this instance as "Paris is in France"). Remember this doesn't yield "'Paris is in France' is identical to 'Paris is in France'", but  "Paris is in France is identical to Paris is in France". Is anyone prepared to accept that as an example of the LOI?

 

[In case someone is so prepared, I will consider that desperate and unwise move presently.]
 

So, Hegel was only able to 'derive' the LOC from the LOI by allowing A to slide effortlessly between two radically different semantic and syntactic roles: between (i) denoting singular terms and (ii) denoting propositions, 'judgements' or sentences (and, in fact, also denoting a whole host of other supposed referents besides -- such as processes, concepts, relations, relational expressions, etc., etc. -- on that, see an earlier section of this Essay). But, as soon that sloppy approach to syntax and semantics has been adopted the negative particle undergoes a change of meaning (in the above manner); that is, it changes from a sentential operator to a name modifier, and we almost invariably end up with unvarnished nonsense, as we have seen.

 

If a maverick logician now chooses to ignore the fatal defects that are now apparent in Hegel's argument, and if L2 had itself been:

 

L2a: p cannot at the same time be identical with p and not be identical with p,

 

it might be thought that things might work out differently (no pun intended).

 

[That is, if we allow the "A" above to be "p is identical with p" (or, as in the example considered earlier, we allow "A" to be something like "Paris is in France", and ¬ reverts to its role as a sentential operator, since p now goes proxy for a proposition or indicative sentence, etc.).]

 

Alas, even then, the above problems with Hegel's 'derivation' fail to evaporate. Quantifying across propositions (if that were possible, and if we could make sense of the use of an "=" sign between propositional variables/tokens), we might be able to obtain the following:

 

L4: (p) [(p = p) ® ¬(p ≠ p)].

 

[Here, "®" is short for "If...then", so L4 says: "If a proposition is identical with itself then it is not the case that it is not identical with itself." (A side note: some logicians are quite happy to quantify across propositions -- or sentences/statements. While this might be an interesting, or even fruitful formal device, it can't relate to anything in a natural language. On that see Glock (2003), pp.102-36, and Hacker (1996), p.288, n.65).]

 

Or, perhaps more simply:

 

L4a: [(p = p) ® ¬(p ≠ p)].

 

But, exactly how this implies the LOC, as Lawler says Hegel imagined, is still unclear.

 

Perhaps the following might work. From L4a, by well known rules, we can obtain:

 

L5: ¬(p = p) v ¬(p ≠ p),

 

and thus (by De Morgan's Rules) we have:

 

L6: ¬[(p = p) & (p ≠ p)].

 

If we now replace (p = p) with Γ and (p ≠ p) with ¬Γ, we could obtain the following from L6:

 

L7: ¬(Γ & ¬Γ).

 

[Again, these and other symbols were explained here. Γ is a metalogical symbol that allows us to talk about other symbols.]

 

Which, of course, looks like the LOC.

 

Unfortunately, we have as yet no rules for parsing the identity sign in the required manner, i.e., so that (p ≠ p) º ¬(p = p). Until we do, this derivation can't work. [There are, however, other serious problems with such a 'derivation'; on that see Note 2. Concerning the rules we do have, see Bostock (1997), pp.323-33 (this links to a PDF), Lemmon (1993), pp.159-67, and Quine (1974), pp.221-26. However, in order to cover every base I have introduced just such a rule, below.]

 

But, even if we had such rules, we can see that in order to obtain L7, the alleged LOI (i.e., in this case, p = p) had to be combined with its supposed Hegelian 'other' (i.e., ¬(p = p)) [or is it (p ≠ p)?]), and then with its double negation (i.e., perhaps, ¬(p ≠ p)) in a conditional. But, as we have also seen, it is far from clear how L7 can be derived from p = p on its own, or even from its alleged 'negative form'.

 

L7: ¬(Γ & ¬Γ).

 

Furthermore, it is also worth pointing out again that, because a proposition isn't an object, it isn't the sort of thing that could either possess or lack identity. In that case, if it were an object (and, per impossible, if it lacked identity), nothing could follow from it. On the other hand, if, per impossible, it were identical with itself, it would be an object, not a proposition, and, as indicated, nothing would follow from it. Quite apart from that, this 'alternative' also suffers from the fatal objection mentioned earlier.2

 

Either way, we hit a brick wall.

 

Nevertheless, it could be argued that in logical schemas like, say:

 

L9: (x)[Fx = Fx],

 

and:

 

L10: (x)(y)(F)[(Fx º Fy) ® (x = y)],

 

there is an unambiguous identity sign between propositions (or between two tokens of the propositional inscription, "Fx") in L9, and an equivalence sign between Fx and Fy in L10. If so, it could be argued that the counter-claims made earlier (against Hegel) are misguided.

 

[Incidentally, L10 is otherwise known as the "Identity of Indiscernibles", which we met in Essay Six. Loosely translated it reads: "Any two objects that share every property in common are identical."]

 

But, logicians who use either of these signs (between propositional variables/tokens) do not imagine that inscriptions on the page are identical. They variously interpret them as expressing a truth-functional relationship between the results of applying F(ξ), for example, to names (Proper or common), or to 'objects' (again, depending on the philosophy of logic to which they adhere), yielding an identity (or a stencil that expresses an equivalence relation) of some sort between abstract objects (i.e., sets, courses of values, graphs, ranges, classes, and the like), or between the truth-values of the interpreted sentences that finally emerge as a result, etc., etc.

 

So, these signs in effect express rules that are applicable to other signs/symbols; they don't express an identity (or an equivalence) between lifeless marks on the page, or even between propositions that exist in an ethereal realm somewhere. In which case, L9a or L9b are to be preferred over L9, and L10 over both:

 

L9a: (x)[Fx º Fx].

 

L9b: (x)(F)[Fx º Fx].

 

[Admittedly, there are, and have been, philosophers and logicians who hold, or who have held such views, but they, too, have simply confused propositions with propositional signs, or even with objects of some sort. On this, see Glock (2003), pp.102-36, and Hacker (1996), p.288, n.65, once more. A propositional sign is constituted by the physical marks on the page or the screen. A proposition is what is expressed by the use of such a sign. Unfortunately, however, L9b and L10 involve Second Order Quantification, which is no less controversial. I won't even try to translate L9a or L9b.]

 

Indeed, the second example from earlier pair (i.e., L10 -- reproduced below) underlines this by implicitly interpreting the equivalence sign as a symbol whose use in this particular stencil implies an identity between objects (or variables that take the Proper Names of objects as arguments -- in this case, x and y). So, schemas like L9 and L10 don't contradict what was maintained earlier -- which related to where the sign for identity can sensibly be used, since it focussed on a relation between objects (or between an object and itself -- or, even between its/their names), not 'concepts', predicables or propositions.

 

L9: (x)[Fx = Fx].

 

L9a: (x)[Fx º Fx].

 

L9b: ∀(x)(F)[Fx º Fx].

 

L10: (x)(y)(F)[(Fx º Fy) ® (x = y)].

 

L10a: (x)(y)[(Fx º Fy) ® (x = y)].

 

[Because of worries about Second Order Quantification, L10a might be preferable to the others!]

 

Sure, we can introduce a sign that is typographically identical to the identity sign (no pun intended), and insert it between concepts and propositions (in fact, some logicians and philosophers have done just that, especially when they have tried to recruit identity to other areas of philosophy, such as the alleged identity between 'mental'/psychological events and brain processes).

 

But, if this new sign is the same as the identity sign already in use, that would be to treat concepts and propositions as objects, once more. On the other hand, if this new sign isn't the same as the identity sign already in use, then it can't express identity, but must express 'identity', which would, of course, mean that the 'philosophical problem of identity' would remain unaffected by terminological tinkering like this. Unless, of course, we mean something different by "identity" in each case (irony intended). And, if that were so, we would need a different sign for each of these different meanings of "identity" --  double irony intended, too -- or risk confusion. At which point, we will have gone round in yet another circle.

 

L9: (x)[Fx = Fx].

 

L9a: (x)[Fx º Fx].

 

L10: (x)(y)(F)[(Fx º Fy) ® (x = y)].

 

L10a: (x)(y)[(Fx º Fy) ® (x = y)].

 

Whether or not these symbols capture the full range of meanings available to us in scientific contexts -- or even in ordinary language --, I will leave to one side for the present (but, it is worth noting that Essay Six returned a negative verdict in this regard).

 

Of course, in schematic sentences like L1b/L9, "="  would be replaced by "º", as we saw with respect to L9a/L1c (i.e., by a biconditional or equivalence symbol). That is because "=" operates in two-place first order linguistic functional expressions (i.e., "ξ = ζ") that takes Proper Names or other singular terms as arguments. So, as noted earlier, L1b and L9 are ill-formed as they stand. Once more, there are and have been philosophers and logicians who hold that the identity sign can be used between non-singular terms, but they have yet to explain why this doesn't imply that this novel use of such signs, or these variables/non-singular terms, thereby have a different meaning.

 

Indeed, we could now introduce a general 'identity' sign, and define it as follows:

 

Df: "Ω Ψ", where "Ω" and "Ψ" stand for singular terms or concept expressions of any level, and "" expresses a general identity relation between them.

 

Even then, it would require some sort of argument to show that the equal sign, =, is identical with this new sign, , and how might that be achieved, for goodness sake? That would, of course, leave it entirely mysterious whether or not the word "identical" in "= is identical with " is itself identical with the first or the second use of these two signs, prompting the very same question (no irony intended) about the word "identical" used to ask that very question -- and so on, ad infinitem!

 

And it is no use responding that is a general sign for identity which incorporates the meaning of the usual sign for identity, =, since that sign can only be flanked by singular terms, so its meaning isn't the same as the meaning of . In that case, can't incorporate the meaning of the usual sign for identity, =. Hence, they don't mean the same.

 

Nevertheless, one thing seems reasonably clear: MFL and ordinary language between them succeed in capturing the full range of words we have for identity (etc.) far better than the syntactic and semantic mess we inherited from Hegel's and his fractured 'logic' (now reflected in DL). In fact, as Essays Three through Eight show, DL can't handle the simplest of objects (such as a bag of sugar!), let alone anything more complex. Indeed, as Essay Seven Part Three amply demonstrates, if DM/DL were true, change would be impossible.

 

[DM= Dialectical Materialism/Materialist, depending on the context; DL = Dialectical Logic; LEM = Law of Excluded Middle; MFL = Modern Formal Logic.]

 

Hence, and yet again, the suggested Hegelian 'derivation' of the LOC (i.e., the one expounded by Lawler) can't work if those As are read as objects, or the Proper Names thereof (plainly, since objects/Proper Names can't be true or false) -- nor, indeed, can it work if propositions are viewed in the same way, as objects.

 

Once more, that is why it is so important to be clear about the denotation of the symbols we use in logic, and why such a fuss was made about it earlier.

 

Alas, there isn't much that can be done with this unfortunate passage:

 

"The principle of excluded middle is that something must either be A or not be A: there is no third possibility. By extension, the law of noncontradiction implies that 'A cannot be non-A', where 'non-A' is something that is not A, or some part or property of A." [Ibid.]

 

Here, A oscillates once again between its use standing for a predicable and its role and a name surrogate. If so, Lawler's characterisation of the LEM is as misconceived as his attempt to connect the LOI with the LOC. The LEM concerns the truth possibilities presented by propositions, or the truth possibilities of predicates as they are used to generate propositions (by mapping Proper Names, or sets of objects, onto indicative sentences -- depending once more on one's philosophy of logic). But, "Something must be Caesar or not Caesar" makes no sense (if, that is, the A here is taken to be a singular term variable, which it has to be in relation to the LOI), indeed, as we saw earlier.

 

Far less logically-challenged versions of the LEM run as follows:

 

E1: For any x, either x is F or x is not F.

 

E2: For any predicate, G, and any object, x, either G or its negation is true of x.

 

[These have been adapted from Geach (1956).]

 

Geach calls the first the "logical definition" and the second the "semantic definition". As he then notes, G, in E2, goes proxy for a predicate expression arbitrarily chosen (for example, "green"), while F, in E1, goes proxy for a predicate "used as such". So, any interpretation of E2 (such as E4, below) would have to use a quoted predicate expression in place of G:

 

E3: For any x, either x is green or x is not green.

 

E4: For any object x, either the predicate, "green", or its negation is true of x.

 

[Geach should, of course, have used "ξ is green" here!]

 

Now, if we treat only of propositions, then the LEM becomes:

 

E5: Either p or not p -- i.e., p v ¬p.

 

E6: Every proposition is either itself true or has a true negation.

 

[Naturally, E6 faces the not-inconsiderable problem of having to involve quantification over propositions.]

 

[Where "p" is a propositional variable. The problems even these face are outlined in Geach (1956); the reader is directed there for more details.]

 

Similarly, the LOC doesn't concern the predication of a 'negative Proper Name' applied to the same individual or object(!) (if "A" is now meant to go proxy for a singular term, as we will see is the case in relation to E7a/E7b, below), as Lawler would have us believe:

 

"...the law of noncontradiction implies that 'A cannot be non-A', where 'non-A' is something that is not A, or some part or property of A." [Ibid.]

 

However, I suspect the above should really have been:

 

"...the law of noncontradiction implies that 'A cannot be non-A', where 'non-A' is something that is not A, or isn't some part or property of A." [Corrected ibid.]

 

As we can now see, E7a makes little sense -- unless it is read along the lines suggested by E7b:

 

E7a: Caesar cannot be non-Caesar, where 'non-Caesar' is something that is not Caesar, or some part or property of Caesar.

 

E7b: Caesar cannot be non-Caesar, where 'non-Caesar' is something that is not Caesar, or isn't some part or property of Caesar.

 

Nevertheless, as with most topics in logic, things are never quite so simple. As we saw briefly above, we need to distinguish between sentential negation (i.e., "not p"), predicate negation (i.e., "not F"), predicate-term negation (i.e., "not-F" or "non-F"), and, for want of a better term, 'name modification' (i.e., "not A", as in "not Caesar"). [For well-known problems associated with the use of non-A type locutions -- especially those in quantified contexts -- see, Geach (1956). For a thorough discussion, see Horn (1989/2001).]

 

It is unclear, though, which of these Lawler intended in the above passage. His indiscriminate employment of "A", "not A", "not-A" and "non-A" suggests he is either unaware of this distinction or he considers it unimportant. The same unfortunately seems to be the case with many of Hegel's epigones (even though, for example, Redding (2007) informs us that Hegel himself was aware of some of these finer distinctions).

 

In which case, except where I have advanced two fatal objections to Hegel's attempt to 'derive' the LOC from the LOI ('stated negatively'), I have not dwelt on this form of negation at any length in the present Essay (nor on its alleged double negated form, "non-non-F"). These issues will, however, loom large in Essay Twelve where the deleterious effects of sloppy syntax and semantics like this will be exposed in all their glory.

 

[More details on this distinction can be found in Horn (1989/2001) pp.5-45, and Wansing (2001). (This links to a PDF.) See also Redding (2007), Chapters Two, Three, Seven and Eight.]

 

If A in the above passage were a predicable, or a property token/type (as the latter part of the last sentence in the quoted passage reproduced below clearly indicates), this version of the LOC could only be interpreted, for example, as:

 

B1: "…is red" cannot be "…is non-red",

 

that is, if we view predicate expressions (more traditionally) using gaps instead of functional place-holders --, or, as:

 

B2: "ξ is red" cannot be "ξ is non-red",

 

otherwise.

 

But, expressions like "ξ is red" aren't even sentences, so it isn't possible to make sense of them as they stand, let alone try to use them in (negated) identity statements, like B2!

 

"The principle of excluded middle is that something must either be A or not be A: there is no third possibility. By extension, the law of noncontradiction implies that 'A cannot be non-A', where 'non-A' is something that is not A, or some part or property of A." [Ibid. Bold emphasis added.]

 

As we saw earlier, this would only be 'true' if these expressions were interpreted as standing for Proper Names (or objects?), and not as predicate expressions or properties, property tokens/types -- or perhaps even as the names (general or Proper) of whatever it is that predicates (or property tokens/types) supposedly designate. Of course, "A cannot be non-A" has nothing to do with the LOC, as we have seen.

 

However, if we (charitably) assume Lawler's comments above were fully acceptable, in that case, his:

 

B3: "A cannot be non-A",

 

would in fact yield:

 

B4: "C cannot be D".

 

That is because Lawler clearly sees these As as proxies for the Proper Names of properties -- or, if the latter are represented by predicate expressions, they will now be the Proper Names of whatever those predicables supposedly designate. So, using C for the Proper Name of whatever "...is red" is supposed to represent, and D for whatever "...is non-red" is supposed to stand for, we would obtain "C cannot be D", in B4 -- but not B3.

 

And that is because, "...is red" must 'name' something different from "...is non-red", if Lawler is to be believed.

 

Of course, this would be the case unless "…is red" is to be viewed as the same Proper Name (say, "E") as "…is non-red" (which must then be "E", too!). In that case, Lawler's 'definition' would become "E cannot be E" -- but not "A cannot be non-A", after all!

 

Either way, we hit yet another brick wall, which is why it is impossible to make any clear sense of what Lawler and/or Hegel are trying to say.

 

That is plainly because Lawler's 'definition' attempts to relate a term to its supposed negated 'other', but his (sloppy) syntax and semantics prevent him from doing precisely that!

 

The reader will no doubt also note that at the beginning of the above passage (reproduced below), "A" functions as a predicate term letter, but by the end it has morphed into a Proper Name surrogate! That is clear from Lawler's own paraphrase, "where 'non-A' is something that is not A, or some part or property of A." [Bold added.] But, this is just another example of the tangled web of confusion that was highlighted earlier.

 

Now, there might be a way of reading these predicate expressions that allows them to be grafted onto the LEM in the way Lawler imagines. It is impossible to say since he doesn't. And, what is more, no one else has, either! Recall: DL-fans don't do detail. They simply label any attempt in that direction "pedantry" and then take their non-dialectical bat and ball home. Here is Lawler, again:

 

"The principle of excluded middle is that something must either be A or not be A: there is no third possibility. By extension, the law of noncontradiction implies that 'A cannot be non-A', where 'non-A' is something that is not A, or some part or property of A." [Ibid. Bold emphasis added.]

 

Moreover, when Lawler says that "non-A is something that is not A" (emphases added), it is far from clear what he means. It might be:

 

P1: Non-A is not A.

 

Or, it could be:

 

P2: Non-A is B which is not A.

 

Where B is the "something" that is not A.

 

However, Lawler immediately qualified his words by saying that "non-A" is "something that is not A, or some part or property of A" (emphases added, again). In which case, as noted above, he appears to mean:

 

P3: Non-A is not some part or property of A.

 

Or, perhaps even:

 

P4: Non-A is some part or property of A.

 

It is impossible to decide which of these represents his view. And this lack of clarity is, once again, a direct result of the impoverished logical and conceptual resources Hegel bequeathed to the poor unfortunates who look to him for guidance and inspiration.

 

As things stand it is reasonably clear that this logical sow's ear can't even be made into a plastic purse.

 

More Dark Declamations From Hegel's Dialectical Dungeon

 

Remember: if you are viewing this with Mozilla Firefox, you might not be able to read all the symbols I have used. I have no idea whether other Browsers are similarly affected.

 

Lawler now moves on to consider several other obscure ideas he unearthed in Hegel's Manichean Mausoleum:

 

"Recognition that the principle of noncontradiction is the principle of identity stated negatively, or is implied in the principle of identity, is central to Hegel's dialectical analysis." [Ibid., p.19.]

 

If so, Hegel's analysis is a non-starter. It could only 'work' if propositions, predicates and objects (and their Proper Names) are regularly confused with one another, as we have seen. This means that we may only make sense of a 'dialectical contradiction' if, like DM-fans, we pretend that the denotation of words and letters doesn't matter, and they can be interpreted any which way we like --, or, indeed, as the mood takes us. In that case, we should remove the word "logic" from the precarious toe-hold it now has on reality in Hegel's work and rename it "Dialectical Licence".

 

However, Lawler continues:

 

"Hegel's main objective is to show an integral connection between A and not-A, or, in categorical terms, between 'identity' and what is supposed to be the contradictory of identity, 'difference.' Hegel approaches this objective by considering the claim that 'identity' is 'held aloof from difference.' This is the claim that 'identity' is a concept that stands by itself and does not require its opposite or contradictory, 'difference,' in order to acquire its meaning." [Ibid., p.20. Italic emphases in the original.]

 

Unfortunately for Lawler, "identity" and "difference" can't be contradictories since they are Noun Phrases, not propositions, clauses, or indicative sentences. Of course, the use of words like "identity" and "difference" might turn out to be a confusing or obscure shorthand for "Propositions expressing identity are the contradictory of propositions expressing difference", but "A is identical to A" and "A is different from A" aren't contradictories. If A is indeed different from A then, at the very least, an error must have been made over the denotation of that letter, or its denotation must have changed. In that case, "A is different from A" must really be "A is different from B"!

 

But, why do we need to refer to "difference" in order to speak about, or give meaning to, "identity"? More to the point, why do we have to nominalise relational expressions in the first place -- turning, for example, a sentence like "London is different from Paris" into an indirect statement about something called "difference"?

 

As we saw in Essay Three Part One, this linguistic dodge -- i.e., the nominalisation of predicate and relational expressions -- was invented by Ancient Greek Philosophers who sought to do this across the board. In fact, they had to do it since that was the only way they could make their dogmatic 'theories' even so much as appear to work (which moves were ideologically-motivated, anyway -- a topic that will be explored in Essay Twelve Parts Two and Three (preview summary here)).

 

The problem is that these moves have the effect of changing a proposition into a list of names, which destroys its capacity to say anything at all. [Why that is so was explored at length in Essay Three Part One.] Any conclusions that 'follow' from this linguistic sleight-of-hand are, as a result, entirely bogus, since nothing can legitimately follow from the names (Proper or common) of abstract objects (such as "Identity", "Essence", "Difference", or even "Being"), nor from a list of the same. Conclusions, of course, can only follow from propositions, indicative sentences or clauses -- linguistic expressions capable of being true or false.2a

 

Well, perhaps Hegel meant that the practice of referring to, or using, identity statements tended to exclude any and all mention of relevant differences. In other words, he was merely speaking elliptically about one or both.

 

If so, that paraphrase still won't work since there is no such thing as Identity (i.e., it is isn't an object, but a purported relation between an object and itself -- or, in language, "identity" supposedly functions as a relational expression, in stencils such as "ξ is identical to ξ" and "ξ is identical to ζ" (where those Greek letters are gap holders for singular terms, Proper Names and Definite Descriptions).

 

[I have used "purported" and "supposedly" here, since, as we saw in Essay Six, the identity 'relation' -- or, at least, its linguistic form -- is best seen as the expression of a rule for the use of singular terms, as noted above. I have tended to gloss over that otherwise important point in this Essay (in order to avoid needless repetition), and so I have in general refrained from objecting to it being called a "law". Briefly put: calling the LOI a "law" implies it is such independent of human choice or convention. Calling it a "rule of language" does the exact opposite; it locates its origin in social practice.]

 

And yet, it is equally plain that Hegel and Lawler need this 'abstraction' to be an object so that it can serve as the denotation of those conveniently malleable letter "A"s we met earlier.

 

Of course, and once more, Hegel's talk about 'Identity' and/or 'Difference' could be an elliptical way of speaking about the identity relation itself and what it seems to imply, but the way Hegel and Lawler use these terms militates against that interpretation -- especially when they talk about "Identity held aloof from Difference." [On that, see below.]

 

However, if identity isn't an object (abstract or otherwise), then it isn't possible for Hegel or Lawler to extract a contradiction even from their own idiosyncratic version of the LOI:

 

"Hegel's main objective is to show an integral connection between A and not-A, or, in categorical terms, between 'identity' and what is supposed to be the contradictory of identity, 'difference.'" [Ibid.]

 

Here, plainly, "A" stands for "identity" and "not-A" for "difference", which of course, means once again that Lawler should have used "A and B", not "A and not-A" -- that is, until he or Hegel manage to show that "not identity" -- or whatever the "contradictory of identity" is supposed to be -- is synonymous with "difference". But, once again, the only thing that motivates talk like this is the sloppy syntax and semantics highlighted earlier. But, by no stretch of the imagination can "identity" be the contradictory of "difference". For a start, they aren't propositions or clauses. They might be antonyms, but that is a different matter. [No pun intended.]

 

The problems this now creates for Lawler's interpretation of Hegel become all the more obvious when we consider the last two sentences of a passage quoted earlier (along with the very next sentence from the same paragraph):

 

"Hegel approaches this objective by considering the claim that 'identity' is 'held aloof from difference.' This is the claim that 'identity' is a concept that stands by itself and does not require its opposite or contradictory, 'difference,' in order to acquire its meaning. This is also the claim that the identity of something can be determined without contrast to something that is not the thing we wish to define." [Ibid., p.20.]

 

Here, identity is many things all at once: a property (as in "identity of something"), a concept (as in "'identity' is a concept"), a word (as in "in order to acquire its meaning") as well as an object (as in "'identity' is 'held aloof…'"). As Bertrand Russell pointed out, it is no great mystery why Hegel thought he could derive all manner of 'interesting' results from logical goulash of this (in)consistency. But, there is more in the can:

 

"According to this 'philosophy of abstract identity,' meanings and objects (including processes, relations, etc.) are independently identifiable, standing on their own, atomistically. Against this claim, Hegel argues that it is impossible to say what one means by identity without bringing into the definition what it was supposed to exclude, namely difference." [Ibid., p.20. Italic emphasis in the original.]

 

However, if that were correct -- and if Hegel were the "genius" we have been led all along to believe -- he should have pointed out what is perfectly obvious to those who don't use language in such a peculiar way: 'abstract identity' can only be conjured into existence if relational expressions are transmogrified into singular terms that name 'abstract particulars'. This is indeed what apparently took place in the theoretical ruminations of the anonymous individuals Hegel was criticising, but neither he nor Lawler questioned those moves themselves. In fact, Hegel succeeded in compounding the problem by adding some novel confusions of his own. But, if we refuse to follow Hegel down this cul-de-sac (alongside those whom Hegel was targeting), and completely reject this way of talking, then the obverse conclusions should be repudiated, too -- i.e., the dialectical daydreams that originally motivated Hegel's dogmatic assertions, which were themselves based on similar moves (but in the opposite direction). Lawler and Hegel failed to question this odd way of talking (other than point out its limitations); they gladly use it to their own advantage. In which case, Hegel and Lawler are part of the problem, not the solution.

 

It could be objected that Hegel was fully aware that universals (and perhaps predicates) have been turned into abstract particulars (or the Proper Names thereof); in the following, for example:

 

"Now this is the very standpoint indicated above from which a universal first, considered in and for itself, shows itself to be the other of itself. Taken quite generally, this determination can be taken to mean that what is at first immediate now appears as mediated, related to an other, or that the universal appears as a particular. Hence the second term that has thereby come into being is the negative of the first, and if we anticipate the subsequent progress, the first negative. The immediate, from this negative side, has been extinguished in the other, but the other is essentially not the empty negative, the nothing, that is taken to be the usual result of dialectic; rather is it the other of the first, the negative of the immediate; it is therefore determined as the mediated -- contains in general the determination of the first within itself. Consequently the first is essentially preserved and retained even in the other. To hold fast to the positive in its negative, in the content of the presupposition, in the result, this is the most important feature in rational cognition; at the same time only the simplest reflection is needed to convince one of the absolute truth and necessity of this requirement and so far as examples of the proof of this are concerned, the whole of logic consists of such." [Hegel (1999), pp.833-34, §1795. Bold emphasis alone added.]

 

Hegel even used this fact to motivate his own argument -- or, so it could be maintained.

 

But, Hegel wasn't objecting to the fact that universals have been turned into abstract particulars; he is alluding to an argument we met in Essay Three Part One:

 

"One's first impression about the Judgment is the independence of the two extremes, the subject and the predicate. The former we take to be a thing or term per se, and the predicate a general term outside the said subject and somewhere in our heads. The next point is for us to bring the latter into combination with the former, and in this way frame a Judgment. The copula 'is', however, enunciates the predicate of the subject, and so that external subjective subsumption is again put in abeyance, and the Judgment taken as a determination of the object itself. The etymological meaning of the Judgment (Urtheil) in German goes deeper, as it were declaring the unity of the notion to be primary, and its distinction to be the original partition. And that is what the Judgment really is.

 

"In its abstract terms a Judgment is expressible in the proposition: 'The individual is the universal.' These are the terms under which the subject and the predicate first confront each other, when the functions of the notion are taken in their immediate character or first abstraction. (Propositions such as, 'The particular is the universal', and 'The individual is the particular', belong to the further specialisation of the judgment.) It shows a strange want of observation in the logic-books, that in none of them is the fact stated, that in every judgment there is still a statement made, as, The individual is the universal, or still more definitely, The subject is the predicate (e.g. God is absolute spirit). No doubt there is also a distinction between terms like individual and universal, subject and predicate: but it is none the less the universal fact, that every judgment states them to be identical.

 

"The copula 'is' springs from the nature of the notion, to be self-identical even in parting with its own. The individual and universal are its constituents, and therefore characters which cannot be isolated. The earlier categories (of reflection) in their correlations also refer to one another: but their interconnection is only 'having' and not 'being', i.e. it is not the identity which is realised as identity or universality. In the judgment, therefore, for the first time there is seen the genuine particularity of the notion: for it is the speciality or distinguishing of the latter, without thereby losing universality.... The Judgment is usually taken in a subjective sense as an operation and a form, occurring merely in self-conscious thought. This distinction, however, has no existence on purely logical principles, by which the judgment is taken in the quite universal signification that all things are a judgment. That is to say, they are individuals which are a universality or inner nature in themselves -- a universal which is individualised. Their universality and individuality are distinguished, but the one is at the same time identical with the other.

 

"The interpretation of the judgment, according to which it is assumed to be merely subjective, as if we ascribed a predicate to a subject is contradicted by the decidedly objective expression of the judgment. The rose is red; Gold is a metal. It is not by us that something is first ascribed to them. A judgment is however distinguished from a proposition. The latter contains a statement about the subject, which does not stand to it in any universal relationship, but expresses some single action, or some state, or the like. Thus, 'Caesar was born at Rome in such and such a year waged war in Gaul for ten years, crossed the Rubicon, etc.', are propositions, but not judgments. Again it is absurd to say that such statements as 'I slept well last night' or 'Present arms!' may be turned into the form of a judgment. 'A carriage is passing by' should be a judgment, and a subjective one at best, only if it were doubtful, whether the passing object was a carriage, or whether it and not rather the point of observation was in motion: in short, only if it were desired to specify a conception which was still short of appropriate specification....

 

"The abstract terms of the judgement, 'The individual is the universal', present the subject (as negatively self-relating) as what is immediately concrete, while the predicate is what is abstract, indeterminate, in short the universal. But the two elements are connected together by an 'is': and thus the predicate (in its universality) must also contain the speciality of the subject, must, in short, have particularity: and so is realised the identity between subject and predicate; which being thus unaffected by this difference in form, is the content." [Hegel (1975), pp.230-34, §§166-169. Italic emphasis in the original; bold emphases added. Some paragraphs merged.]

 

Hegel is here arguing that there is an identity between subject and predicate terms (the latter of which express a universal in the 'judgement'); that is, he is arguing that in such judgements the particular is the universal, which is, he thinks, a 'contradiction' -- as opposed to it being (what it plainly is), unvarnished nonsense.

 

He can only do this if both subject and predicate are regarded as singular terms.

 

This 'allowed' Hegel (just as it later 'allowed' Lenin) to generate 'contradictions' to order, which were then imposed on 'reality', true for all of space and time (as we saw in Essays Two and Three Part One).

 

This can be seen from the fact that Hegel makes that very point in the next two paragraphs to those quoted earlier:

 

"Accordingly, what we now have before us is the mediated, which to begin with, or, if it is likewise taken immediately, is also a simple determination; for as the first has been extinguished in it, only the second is present. Now since the first also is contained in the second, and the latter is the truth of the former, this unity can be expressed as a proposition in which the immediate is put as subject, and the mediated as its predicate; for example, the finite is infinite, one is many, the individual is the universal. However, the inadequate form of such propositions is at once obvious. In treating of the judgment it has been shown that its form in general, and most of all the immediate form of the positive judgment, is incapable of holding within its grasp speculative determinations and truth. The direct supplement to it, the negative judgment, would at least have to be added as well. In the judgment the first, as subject, has the illusory show of a self-dependent subsistence, whereas it is sublated in its predicate as in its other; this negation is indeed contained in the content of the above propositions, but their positive form contradicts the content; consequently what is contained in them is not posited -- which would be precisely the purpose of employing a proposition.

 

"The second determination, the negative or mediated, is at the same time also the mediating determination. It may be taken in the first instance as a simple determination, but in its truth it is a relation or relationship; for it is the negative, but the negative of the positive, and includes the positive within itself. It is therefore the other, but not the other of something to which it is indifferent -- in that case it would not be an other, nor a relation or relationship -- rather it is the other in its own self, the other of an other; therefore it includes its own other within it and is consequently as contradiction, the posited dialectic of itself. Because the first or the immediate is implicitly the Notion, and consequently is also only implicitly the negative, the dialectical moment with it consists in positing in it the difference that it implicitly contains. The second, on the contrary, is itself the determinate moment, the difference or relationship; therefore with it the dialectical moment consists in positing the unity that is contained in it. If then the negative, the determinate, relationship, judgment, and all the determinations falling under this second moment do not at once appear on their own account as contradiction and as dialectical, this is solely the fault of a thinking that does not bring its thoughts together. For the material, the opposed determinations in one relation, is already posited and at hand for thought. But formal thinking makes identity its law, and allows the contradictory content before it to sink into the sphere of ordinary conception, into space and time, in which the contradictories are held asunder in juxtaposition and temporal succession and so come before consciousness without reciprocal contact. On this point, formal thinking lays down for its principle that contradiction is unthinkable; but as a matter of fact the thinking of contradiction is the essential moment of the Notion. Formal thinking does in fact think contradiction, only it at once looks away from it, and in saying that it is unthinkable it merely passes over from it into abstract negation." [Hegel (1999), pp.834-35, §§1796-1798. Bold emphases alone added. I have used the on-line version here, correcting a few minor typos.]

 

As noted above, Hegel is here appealing to the Identity Theory Of Predication to motivate his argument. However, if predicates can't be tuned into singular terms, the entire dialectic short-circuits.

 

But, even if the volunteered objection from earlier were valid, and Hegel had anticipated the criticisms that have been levelled against him in these Essays, he nowhere repudiates this approach to predication. Quite the reverse. As we have just seen, he uses it to 'derive' several quirky results of his own, based solely on defective logic like this.

 

Be this as it may, can any sense be made of Hegel and Lawler's claims about 'abstract identity' (we met earlier)?

 

Not much, it seems, since the entire topic (indeed, the whole of Hegel's corpus) amounts to little more than a systematic capitulation to the misuse and distortion of language -- as Marx himself pointed out.

 

And, of course, it is possible to express identity (in the sense of the LOI) without having to involve "difference". Consider the following:

 

(1) (x)(y)((x = y) º (Fx ® Fy)).

 

(2) (x)(y)((F)(Fx º Fy) ® (x = y)).

 

(3) j(y) º [(x)((x = y) & j(x))].

 

(4) (x)(y)[(x = y) º (j)(j(x) º j(y))].

 

[Symbols that are often employed throughout this Essay: "" is the universal quantifier, equivalent to "All" or "Every"; "" is the existential quantifier, equivalent to "Some..." or "At least one..."; "º" is the sign for logical equivalence (i.e., "If and only if" -- "iff", for short); "j" and "F" are predicate letters; "®" is the implication arrow, equivalent to "if...then"; "x" and "y" are bound variables (often equivalent to "it", but that depends on the context); "¬" is the negation sign; "Γ" is a meta-logical symbol standing for any wff (i.e., "well formed formula", pronounced "woof"; wffs are strings of symbols that conform to the syntax of the system in which they are embedded); "p" and "q" are propositional variables; "&" is obviously "and"; "v" is the inclusive "or" (i.e., "and/or"). How these symbols are used is explained here.]

 

To be sure, different inscriptions (i.e., marks on the page or screen) were employed in the above, but many are equated.

 

Of course, someone could complain that that is precisely the point: all four of the above nonetheless involve "difference" -- they use different symbols. But that would be to misread what they actually say.

 

For example, (1) says: "Any two objects are identical if and only if they share the same properties", -- or, "…whatever is true of one is true of the other". No mention, or hint of "difference". It sets conditions on objects being the same, not different. The same applies to the other three -- they have all been translated here.

 

Moreover, it is worth adding that this 'problem' has been compounded by the fact that Hegel and Lawler slide effortlessly between the meaning two, dare I say it, different words, "identity" and "identify" -- that is, between (a) "identity" when it is used to provide an empty (or perhaps even significant) identity statement or criterion for any given object, and (b) "identify" when it is used to speak about the capacity the vast majority of us possess of being able to discriminate, pick out, point to, or recognise a person, property, location, smell, taste, sound, tune, process or object from moment to moment.

 

For example, if squaddie NN is asked whether or not he can identify Osama bin Laden in a line-up, and he replies, "Yes, Sarge! Osama is identical to Osama, Sarge!", he would risk being put on a charge. On the other hand, if he points to one of the suspects and says, "That's him, Sarge!", he wouldn't. [This was, of course, written before the US military executed Osama bin Laden extra-judicially.] So, identification isn't the same as identity (no pun intended).

 

Naturally, identification (i.e., option (b), above) could in some circumstances involve a capacity to differentiate among objects, but that isn't necessarily so in all circumstances -- as was argued here.

 

Would, for example, the rather dim squaddie above be able to identify Osama bin Laden only if he had first learnt to distinguish the latter from everything that Osama wasn't? Upon meeting someone for the first time, and being introduced to them, which one of us even so much as thinks "Hang on! Let me first distinguish this character from a bucket of fish, a corkscrew, a Rabbit Jelly Mould, a tidal estuary, a flock of geese, your recently deceased grandmother, a rusty old car, the Andromeda Galaxy, a self-adjoint operator, a pi-Meson, a Pulsar..., -- or even from everyone who has ever lived -- before you tell me who she is, otherwise I won't know who or what you are talking about!"

 

[I have also dealt with the objection that Hegel argued that we can't just use negation "arbitrarily" -- which some might take to mean that the comments in this Essay about 'determination', and later about "the SGP" (that term is explained below -- follow the link!) are thoroughly misguided --, here.]

 

By running these two words together, Hegel revealed once again that he was even more confused than this rather dim squaddie. Lawler might be advised, therefore, to resign from his role as Hegel's Dialectical Defence Counsel.

 

[To be sure, there are three uses of "identity" (indeed, in ordinary language, there are countless -- on that, see here), the third of which makes its appearance in more overtly 'philosophical' contexts, often connected with an attempt to provide a comprehensive description or definition of a substance, à la Leibniz.]

 

Of course, in order to perform the former (i.e., option (a) from earlier) we don't need to refer to, or allude to --, or even so much as vaguely hint at --, 'difference'. However, in order to do the latter (i.e., (b)), an ability to tell one object or human being from another clearly helps. But, the two skills (if such they may be called) are not at all the same (irony intended).

 

So, it looks like Hegel's criticism of "identity" can only get off the ground if we join him and become linguistic philistines -- or if we deliberately confuse our capacity to construct empty (or significant) identity statements with our ability to identify friends and relatives, or, indeed, discriminate among alleged miscreants.

 

Surely this is philosophy for Idiots, not just Idealists!

 

[For several examples of significant identity statements, see here. I have also given several examples where 'difference' can't be a factor. In Essay Three Part One -- here -- I have also neutralised the argument that different signs have to be used (even in an identity statement), a shaky argument Hegel and Lawler unwisely used in order to motivate their (unsuccessful) attempt to re-enchant the universe.]

 

Lawler now piles yet more confusion on his unfortunate readers:

 

"In fact, Hegel replies, when we want to identify something we assert in the predicate something different from what is in the subject. The subject of a proposition is in itself something (relatively) undifferentiated or unspecific and real thinking does not consist in simply repeating this." [Ibid., p.20. Italic emphasis in the original.]

 

We have already seen that 'subjects' (I assume Lawler is here alluding to the use of a Proper Name, or some other singular designating expression) assert nothing (nor can anything be asserted by the mere employment of a Proper Name, or any other singular term -- again: doubters should try 'asserting' "Plekhanov", or "The 42nd President of the United States of America" and only that). Hence, by the use of a Proper Name (or any other singular term) nothing different can be asserted from anything that can be asserted by the use of predicates. So, if Proper Names (and other singular terms) don't actually assert anything to begin with, they can hardly assert something different from predicates. [Once more, that point was covered extensively in Essay Three Part One.]

 

The idea that Proper Names on their own can assert something is based on the ancient (and early modern) doctrine that every particular -- each organic or non-organic body -- has associated with it its "complete/essential description", or concept, that 'God' alone knows, and which uniquely identifies it. This theory perhaps reached its most sophisticated form in Leibniz's work (this links to a PDF), whose ideas clearly influenced Hegel (as they do the latter's DM-acolytes).

 

If true, an 'essential' proposition about an individual would involve the correct predication of one or more of its 'internally-linked' properties [ILPs], ordained of 'god'. But, how many of these are there? Who knows? But, because ILPs are part of a given individual's 'complete notion', they are also supposed to be identical with their subject, or can so be linked by the expression of an alleged identity between that subject and (some of) its predicates.

 

"A notion that determines a certain individual Adam must contain absolutely all his predicates, and it is this complete notion that determines general considerations to the individual.... So: I hold that every true proposition is either immediate or mediate. An immediate proposition is one that is true by itself, i.e., a proposition whose predicate is explicitly contained in its subject; I call truths of this sort 'identical'. All other propositions are mediate; a true proposition is mediate when its predicate is included virtually in its subject, in such a way that analysis of the subject, or of both predicate and subject, can ultimately reduce the proposition to an identical truth. That's what Aristotle and the scholastics mean when they say 'the predicate is in the subject'." [Leibniz to Arnauld, 1686, quoted from here. See also here. Paragraphs merged.]

 

"The nature of an individual substance or of a complete being is to have a notion so complete that it is sufficient to contain and to allow us to deduce from it all the predicates of the subject to which this notion is attributed." [Leibniz, quoted from here.]

 

[This doctrine clearly conflates predication, which takes place uniquely in language, with what supposedly exists extra-linguistically, once again confusing talk about talk with talk about the world.]

 

According to this way of thinking, ILPs have to be identical with their subject since they express its 'essence' -- an assumption still in want of proof. For Hegel, they are also different from their subject, otherwise we couldn't discriminate among them, and, indeed, their concepts couldn't self-develop. So, because of that they possess "identity-in-difference'. It is out of this Mystical Mud that Hegel's confused and error-strewn 'theory' finally slithered.

 

[On this, see here and here. At a future date, I will publish a up-dated version of one of my undergraduate essays on this topic, which shows how and why this ancient idea gained traction among Traditional (Rationalist) Philosophers in Ancient Greece and then in Medieval Europe. This topic is also connected with several of the things I have said about a set of theological dogmas concerning the nature of 'God' and how they were intertwined with the scientific revolution of the 17th century (in Essay Eleven Part Two). Fortunately, this entire metaphysical line-of-thought falls foul of a fatal objection I also raised against all such 'essential' propositions (in Essay Twelve Part One, briefly summarised, here), namely, that they don't possess significant negations. This also means, for example, that there is no such thing as the 'Power of Negativity' beloved of many DM-fans. Hence, 'Spinoza's Greedy Principle'  [SGP, henceforth] -- as I have called it, i.e., 'Every determination is also a negation' -- upon which Hegel's dialectic was based turns out to be devoid of content, too. That drops a rather large spanner in the dialectical works, halting the DM-juggernaut in its tracks. (Apologies for that mixed metaphor!) I will explain in detail how and why that is so in Essay Twelve Part Five. Added on Edit: I have now posted several lengthy comments about SGP to Essay Three Part One, here and here, where I show it readily collapses into incoherence.]

 

Of course, and by default, it could be argued that this does in fact represent a 'difference': one of these (an ILP) can be used to assert something while the other (a singular term) can't.

 

That is undeniable, but it isn't Hegel's argument. And even if it were, it would have nothing to do with the alleged identity between predicate and subject (or their terms). That idea is based on the 'identity-and-difference' that supposedly exists between the two halves of a proposition ('subject' and 'predicate'), which are both said to assert the same thing, but at the same time assert something different. However, since only one is capable of being used to assert anything (the 'predicate part', but which on its own doesn't in fact assert anything), we can't even derive an 'identity' here between what is supposedly asserted, never mind a 'difference'. If both halves don't assert anything -- or even one half doesn't assert anything --, then they can hardly assert something different, can they?

 

Of course, it isn't easy to credit such a simple error to a leading Philosopher (whom many, strangely enough, regard as among the greatest ever), but if Hegel's argument does depend on the supposed physical, temporal or phenomenological differences between subject and predicate terms, then it is indeed based on the sort of confusion highlighted above. That is because it runs together these four items: "identity" and "being able to identify", "difference" (i.e., "lack of identity", or perhaps "non-identity") and "difference" (i.e., "being distinguishable from"). These four are not at all the same, and do not always depend upon each other, as noted above. [Irony intended. There is more on this in Essay Six.]

 

We also saw earlier that predicates needn't be physically different from 'subjects' (nor even separated from them temporally or spatially); so Lawler's 'argument' is defective from beginning to end.

 

Once again, it is only by blurring the distinction between subject and predicate expressions that defective logic like this is even capable of limping along.

 

'Difference' Rendered Unrecognisable

 

Unfortunately, there is more:

 

"Moreover, the defense of the theory of abstract unrelated identity leads proponents of such a theory unwittingly to assert the contrary of their original position. They must say that identity and difference are…different. Or, Hegel dialectically goads his opponents: identity is different…from difference. In this proposition identity has been 'identified' with difference, or difference is regarded as a property of identity. So much for 'identity held aloof from difference,' Hegel concludes." [Ibid., p.20.]

 

But, Lawler should have pointed out that this logically-benighted Hegelian riposte only works if the identity relation is nominalised and turned into the Proper Name of an abstract particular (which is capable of having properties). And the reason for doing this is so that the alleged contrast (or comparison) with "difference" is modelled on differences that might exist between two objects. Without this move, this linguistic dodge, Hegel's argument misfires.

 

That is quite apart from the fact that Lawler nowhere justifies this rather odd conclusion:

 

"In this proposition identity has been 'identified' with difference, or difference is regarded as a property of identity." [Ibid.]

 

The above supposedly follows from the following response Lawler volunteered from the (presumed) 'defenders' of 'abstract identity':

 

"Moreover, the defense of the theory of abstract unrelated identity leads proponents of such a theory unwittingly to assert the contrary of their original position. They must say that identity and difference are…different." [Ibid.]

 

It isn't clear why these 'defenders of identity' have to, or even might be tempted to, say this (or anything like it), but even if they were unwise enough to do so, the knock-down response they should come out with would go something like the following:

 

"There is no such thing as 'identity' for it to be the same as, or different from, anything else, comrade Lawler. If you think differently (no pun intended), can we see your proof?"

 

So, if there is no such thing as 'identity', 'it' can hardly have any properties -- at least, no more than the Tooth Fairy has. In which case, it makes no sense to assert sameness or difference of 'Identity' and 'Difference'. The 'defenders of abstract identity' can now sleep soundly in their beds; this Hegelian bogeyman is as real as the Tooth Fairy, and just as toothless.

 

Now, even though Lawler (and, as far as I can determine, Hegel) failed to identify (again, no irony intended) the 'simpletons' criticised in the above passage, it is quite easy to see what else 'they' could have said in reply to prove 'they' were more than a match for one or both:

 

"Mock all you like, Herr Hegel/Lawler, your 'argument' only works because you talk as if you think identity isn't a relation, but an object, or the Proper Name of an object. Now, this is about as crass an error as thinking that if someone were to say, '99 is nearly the same as 100' and '999,999,999 is nearly the same as 1,000,000,000', and that since 'nearly the same' names the same object in both cases (i.e., 'nearly the sameness', or perhaps 'approximate identity') '99 is thus nearly the same as 1,000,000,000'. If the relational term 'nearly the same' names the same abstract entity each time (as it must, given your crazy 'theory'), then we would be able to argue that any two numbers you care to mention (no matter how far apart they are on the number line) are nearly the same!"  [Any who object to the use of "nearly the same as", here, need only substitute for it "nearly equal to", and their qualms should happily melt away.]

 

As seems plain, this annoying riposte is effective only because it makes hay of Hegel's dim-witted confusion of relational expressions with singular terms, or, indeed, with abstract particulars (or the Proper Names thereof) --, a trick he learnt, of course, from equally confused Ancient Greek, ruling-class hacks.

 

In fact, this manoeuvre doesn't just relate to, it helped create and then further motivate a vacuous 2500 year-old puzzle over 'Subject-Object-Identity', which later became the main problematic of German Idealism. Hence, if Proper Names and predicates are both objects of some sort (or they designate objects), and if 'Being' turns out to be the 'Subject-Object-Predicate' par excellence, then the inter-identity (or lack of it) between these terms will 'naturally' become a 'philosophical problem'. But, if only Proper Names actually serve in this pairing as designators --, whereas predicates merely describe the objects so named, for example --, then all those centuries devoted to 'solving' this pseudo-problem can be seen for what they are: a monumental waste of time and effort.

 

To be sure, that peremptory accusation seems to consign several thousand works (and tens of thousands of commentaries on such works) to the 'dustbin of history'. In fact, there's no seeming about it; it does precisely that -- and good riddance, too.

 

Indeed, as we will see later (in Essay Twelve Part Six, when it is finished, and Thirteen Part Three (here and here)), this doctrine arose out of the Ancient Greek idea that there was something called "non-propositional thought" (a notion that surfaced in Aristotle and Plotinus, for example), which later revolved around the supposed relation between the Mystical Knower and the Neo-Platonic/Hermetic Unknown. This misbegotten doctrine not only provided the 'rationale' (if such it may be called) that motivated the nominalisations we have encountered many times throughout this Essay and this site, it also helped inspire the Identity Theory of Predication (the bogus validity of which was also required in order to initiate, it not enable, Hegel's complex dogmatic gyrations).

 

[On the Greek end of this sorry tale, see the Owen (1966/1986) -- particularly, pp.207-11 (i.e., of the 1986 version) --, Sorabji (2005), pp.90-93, Sorabji (1982), and Alfino (1988). On 'The Identity Theory of Predication', see here.]

 

So much philosophical hot air generated from a seemingly insignificant semantic/syntactic sleight-of-hand. A puddle of Metaphysics condensed from a cloudy use of grammar, to paraphrase Wittgenstein.

 

In that case, Marx didn't go far enough: ruling ideas don't just rule most minds, they ruin them into the bargain.

 

Hence, the following conclusion is so wide of the mark it is lodged in the next star system:

 

"Irrespective of the validity of this argument, it is clear that Hegel maintains that the defenders of the concept of abstract identity, or identity unrelated to difference, become prey to a logical self-contradiction, by affirming difference of identity, while at the same time trying to deny this." [Ibid., p.20. Italic emphasis in the original.]

 

Now, Hegel -- or one of his groupies -- can promulgate ideas like the above until the cows next evolve for all the good it will do. In which case, only those credulous enough to fall for the systematic nominalisation of relational expressions (outlined above) will be wrong-footed by the 'simpleton's' response, recorded earlier.

 

This misbegotten tale continues:

 

"Hegel points to another inconsistency to which defenders of the position of abstract identity are subject. Putting the concept of identity into practical application, as it is interpreted by abstract understanding, we are compelled to say that a cow is a cow, a man is man, white is white, spirit is spirit, etc. In attempting to express the principle of identity according to the spirit of abstract understanding, we end up paradoxically speaking of an endless number of different things. The category of difference asserts its right to exist despite the intent to banish it -- which Hegel attributes to his opponents -- and the two categories appear in a peculiar relationship in the cognate category of 'diversity.'" [Ibid., pp.20-21. Italic emphasis in the original.]

 

This isn't much better. If anything, it is worse. Exactly who it was that wanted to "banish" difference is somewhat unclear. How they might manage to pull that trick off is even less obvious. Organise a picket? Obtain an injunction? Utter a spell? Seek a Papal Interdiction? Issue a Fatwā? Cast it into Outer Darkness...? Kick it out of the party?

 

Nevertheless, the (conveniently) fictional characters to whom Hegel and Lawler refer, and their improbable philosophical antics, needn't bother us for much longer. What is more worrying is the uncritical way that Lawler accepts this lamentable 'argument'. Quite apart from the odd examples of identity Lawler quotes (for instance, his "white is white" can only work once more by nominalising the predicable "ξ is white", so that "white" is treated as the Proper Name of an abstract particular, and hence is no longer a predicate expression), appealing to the diversity allegedly involved here is no way to argue for the existence of the other nominalised entity in this mutant pair (i.e., "difference"), which is a creature of Hegel's (and now Lawler's) fevered imagination.

 

The most that can be milked from this egregious example of Diabolical Logic is that the five examples given above are all different from one another. Exactly how "Difference" (i.e., that abstract particular) can be conjured out of this banal observation Lawler and Hegel forgot to say.3

 

More to the point, even if it could be shown that the most ardent supporters of 'abstract identity' (and I assume Leibniz would be near the top of that list) were guilty of all the errors Hegel and Lawler lay at their door, then only if they could also show that anyone committed to a belief in 'abstract identity' also assented to the odd idea that everything was identical with everything else -- and thus that there is no such thing as 'difference' -- could they also substantiate the allegation that 'abstract identity' automatically excluded 'difference', which conclusion Hegel and Lawler pluck out of thin air. But has a single believer in 'abstract identity' ever held such an odd (and implausible) idea? Certainly not Leibniz. It is arguable that Parmenides, his disciples and other Absolute Monists (for instance, the Indian supporters of Advaita Vedanta, such as Adi Shankara) might have done so. But, few of the latter were around in Hegel's day and their ideas weren't influential in the 19th century (nor are they now, for that matter). Despite this, it is plain that even an unshakable commitment to 'abstract identity' doesn't deny, or even so much as hint at a denial of diversity. If it does, Hegel and Lawler unwisely omitted the proof (yet again!).

 

But, let us assume for the purposes of argument that an 'abstract entity' -- supposedly named by the word "difference" --, does indeed exist. If so, it must be a particular of some sort, which means that "difference" itself can't be a general term, but must be a singular designating expression. In that case, it can tell us absolutely nothing about the many and diverse relations that exist in nature and society. So, even if Hegel were right, there would be no need to appeal to this 'entity'/word -- in fact, we would be well advised to do the opposite, and ignore it --, in order to understand how to construct (or even reject) identity statements, let alone begin to study diversity.

 

Of course, it could be argued that when philosophers like Hegel use words like "identity" and "difference" (for instance, when they say things like "identity held aloof from difference") they aren't naming a 'abstract particular', as the above presumes, they are merely talking about a specific topic, or about certain topics. So, "identity held aloof from difference" is just shorthand for something like "Those who use identity statements forget (accidentally or deliberately) that they also indirectly involve statements of difference".

 

Unfortunately that contention sits rather awkwardly with what Lawler also had to say:

 

"Hegel's main objective is to show an integral connection between A and not-A, or, in categorical terms, between 'identity' and what is supposed to be the contradictory of identity, 'difference.' Hegel approaches this objective by considering the claim that 'identity' is 'held aloof from difference.' This is the claim that 'identity' is a concept that stands by itself and does not require its opposite or contradictory, 'difference,' in order to acquire its meaning." [Ibid., p.20. Italic emphases in the original.]

 

In that case, 'identity' appears to be a "concept" named by the word "identity", and by implication the same is the case with "difference". Furthermore, as I noted earlier:

 

Here, plainly, "A" stands for "identity" and "not-A" for "difference", which of course, means once again that Lawler should have used "A and B", not "A and not-A" -- that is, until he or Hegel manage to show that "not identity" -- or whatever the "contradictory of identity" is supposed to be -- is synonymous with "difference". But, once again, the only thing that motivates talk like this is the sloppy syntax and semantics highlighted earlier. But, by no stretch of the imagination can "identity" be the contradictory of "difference". For a start, they aren't propositions or clauses. They might be antonyms, but that is a different matter. [No pun intended.]

 

Lawler continues:

 

"Hegel approaches this objective by considering the claim that 'identity' is 'held aloof from difference.' This is the claim that 'identity' is a concept that stands by itself and does not require its opposite or contradictory, 'difference,' in order to acquire its meaning. This is also the claim that the identity of something can be determined without contrast to something that is not the thing we wish to define. According to this 'philosophy of abstract identity,' meanings and objects (including processes, relations, etc.) are independently identifiable, standing on their own, atomistically. Against this claim, Hegel argues that it is impossible to say what one means by identity without bringing into the definition what it was supposed to exclude, namely difference." [Ibid., p.20. Italic emphasis in the original.]

 

Plainly, Lawler and Hegel regard "identity" and "difference" as the Proper Names of two abstract particulars, precisely as argued earlier:

 

However, if that were correct -- and if Hegel were the "genius" we have been led all along to believe -- he should have pointed out what is perfectly obvious to those who don't use language in such a peculiar way: 'abstract identity' can only be conjured into existence if relational expressions are transmogrified into singular terms that name 'abstract particulars'. This is indeed what apparently took place in the theoretical ruminations of the anonymous individuals Hegel was criticising, but neither he nor Lawler questioned those moves themselves. In fact, Hegel succeeded in compounding the problem by adding some novel confusions of his own. But, if we refuse to follow Hegel down this cul-de-sac (alongside those whom Hegel was targeting), and completely reject this way of talking, then the obverse conclusions should be repudiated, too -- i.e., the dialectical daydreams that originally motivated Hegel's dogmatic assertions, which were themselves based on similar moves (but in the opposite direction). Lawler and Hegel failed to question this odd way of talking (other than point out its limitations); they gladly use it to their own advantage. In which case, Hegel and Lawler are part of the problem, not the solution.

 

Hence, it is clear that words like "Identity" and "Difference", as they are used by Hegel, aren't working as some sort of shorthand in the way surmised above.

 

[However, I covered such topics more extensively earlier; readers are referred back there for more details.]

 

So, we hit the same annoying, semantic brick wall yet again. Once particularised (à la Traditional Logic/Metaphysics), words like "Identity" and "Difference" lose all contact with the meaning of the words, concepts and exemplars from which they were supposedly abstracted. Hence they cease to have any meaning -- and that is because they no longer function as relational expressions.

 

The Fog Thickens

 

From here on in Lawler's attempt to clarify the meaning of the yet-to-be-explained, fogbound term "dialectical contradiction" only succeeds in lobbing a few more smoke bombs at it:

 

"'A is A' implies that A is not some other entity which is not-A. Thus a peculiar negative relation to not-A is implicitly asserted in the principle of identity and in the expression 'A is A.' It is easy enough to say that this is only a negative relation and to interpret the concept of negative relation as meaning no relation at all. If, however, it is a relation without which it it [sic; "is"? -- RL] impossible to establish the identity of A (any definite being or concept at all), then it cannot be 'nothing at all.' 'Abstract understanding' does not probe seriously into this problem, and in the abstract, undialectical understanding of identity, the relation of A to not-A (beings that are not A as well as A's own nonbeing) seems to 'vanish.'" [Ibid., p.22. Italic emphases in the original.]

 

In fact, and independently of the LOI, the normal use of A (as a Proper Name surrogate, perhaps) wouldn't imply that the item in question wasn't other than A. So, our use of such names contains no hidden reference, or even a faint allusion to a negative particle attached to a name -- as in "not A", or even "not-A".

 

That is so for at least two reasons:

 

(1) We have yet to be given (by Lawler, Hegel, or, for that matter, anyone else fond of this peculiar way of talking) a clear explanation of what, say, "not Caesar" could possibly mean. It can't be a 'negative name', for reasons outlined here.

 

(2) In ordinary life, if, when using a Proper Name to refer to or identify someone, and that person is mis-identified, the normal reaction would be to say, "I didn't mean Caesar, I meant Brutus". Here the negative particle would attach to the verb, not the Noun Phrase. Of course, this can be shortened to "Not Caesar, Brutus", but even then, the negative particle would attach to the implied verb (as in "I meant Brutus, not Caesar", which is in turn short for "I meant Brutus; I didn't mean Caesar"). If this weren't so, then the individual uttering this set of words would be taken to be referring to an odd character called "not Caesar", instead of "Caesar", as had been intended. So the phrase "not Caesar" in contexts like this can only mean "I am not referring to Caesar", rather than "I am referring to not Caesar." Hence, we can see once again that the negative particle attaches to the Verb Phrase, not the Noun Phrase. [More details were given at the above link.]

 

[Notice, it is our use of Proper Names that implies this, not the Noun Phrase itself. However, if Hegel and Lawler have a different understanding of our use of Proper Names, then their odd ideas would apply to the idiosyncratic term, 'Proper Name', and not to what we ordinarily call a Proper Name. (This comment, of course, assumes that Hegel and Lawler are interpreting A at this specific point in their argument -- whatever else they might be doing in other places -- as a Proper Name surrogate for an object or 'entity'. That might, of course, be an unsafe assumption given the carelessly profligate way they both tend to throw this letter at the page.)]

 

Of course, if A is meant to go proxy for a predicate expression, then it has no legitimate role to play in sentence like this, "A is A", as has been pointed out many times.

 

Be this as it may, and as we have also seen, the following can't be an implication of the use of A on its own (although it might be an implication of "A is A" -- more about that later):

 

"'A is A' implies that A is not some other entity which is not-A. Thus a peculiar negative relation to not-A is implicitly asserted in the principle of identity and in the expression 'A is A.' It is easy enough to say that this is only a negative relation and to interpret the concept of negative relation as meaning no relation at all." [Ibid.]

 

That is because, if A is an object, or the Proper Name thereof, no such implication is possible. Objects do not and cannot imply other objects, and neither can Proper Names, or expressions that have been nominalised. Implications primarily follow from propositions, indicative sentences and clauses, that is from linguistic expressions that are capable of being true or false. As I have pointed out elsewhere:

 

Only by confusing objects (or the names thereof) with propositions (or clauses) -- that is, by confusing objects or their names with what we say about them, confusing talk about talk with talk about things -- only by doing that was Hegel able to conjure the 'dialectic' into existence.

 

[His other 'arguments' are merely window dressing. They, too, will be demolished in Essay Twelve Parts Five and Six at my site, when they are published.]

 

We name objects and persons (among other things). Typically, only then can we say things about them, and we do that in sentences. These familiar features of language are quite distinct.

 

[Later on I'll explain why it is important that they stay that way. (Admittedly, we have other ways of referring to things, but they only complicate the picture, they don't alter it.)]

 

Furthermore, propositions aren't objects. Nor are they the names of anything, as Hegel appears to have assumed. If they were, they couldn't be used to say anything. Sure, we use various inscriptions (words, phrases, clauses, sentences, utterances) to articulate our thoughts -- that is, we write words on paper, type letters on computer screens, or simply say things --, but when we do any of these, the inscriptions we employ to that end work as symbols (i.e., they signify things for us, and to us, and convey meaning). We achieve this by the way we employ linguistic resources like these in accord with the grammatical complexity our ancestors built into language.

 

To see this, just look at any object or collection of objects, and, assuming they or their arrangement don't represent a coded message of some sort, ask yourself what it/they say to you. You might be tempted to reply that it/they say this or that, but in order to report what it/they allegedly say, you will be forced to articulate whatever that is in a proposition, or some other form of sentence. You couldn't do this by merely reproducing the original objects, or, indeed, any other objects. Nor could you do so by just naming them.

 

[This story taken from Jonathan Swift's Gulliver's Travels exposes the absurdity of the idea that it is possible to say things simply by using objects, or their names. More on this below. "Inscription" here applies to physical marks on a page/screen/wall/blackboard/whitescreen/cavewall that aren't considered random, but are held to be the product of intentionality, part of a natural-, or even a formal-language -- or perhaps even a work of art, no matter how 'primitive'.]

This isn't surprising since objects have no social history, intellect or language, whereas we do, and have.

 

Naming is like setting out the pieces on a chess board ready for a game. A move in a game is like a proposition (describing or explaining, for example). While both of these activities depend on each other, only someone intent on ruining a game (or who had a hidden agenda) would deliberately confuse the two.

 

Unfortunately, Engels and Lenin swallowed this spurious Hegelian word magic, hook, line and sinker -- and that is because neither of them were logicians. Despite this, they both had a wildly inflated opinion of Hegel's expertise in this area.

 

[This isn't to malign these two great revolutionaries; others, who should know better, have similarly allowed themselves to be duped. Exactly why they have all fallen for verbal con-tricks like this (and not just Hegel's sleight-of-hand) is explained in Essay Nine Part Two.]

 

However, because of their misguided respect for Hegel, Marxists ever since have been saddled with this garbled 'logic' (upside down, or 'the right way up').

 

Of course, as we have already seen, the employment of such names in a speech act (written or spoken), typically in a sentence, could imply all manner of things (by means of what has come to be known as "conversational implicature"), but Lawler and Hegel have yet to show that we do in fact use Proper Names in the idiosyncratic way that they imagine. Or, for that matter, show how it is even possible to use Proper Names in that way at all.

 

Independently of this, is it really the case that "'A is A' implies that A is not some other entity which is not-A" as Lawler says? Well, "A is A" doesn't in fact imply that A is not also not-A. Of course, it could be the case that, even while "A is A", A is also B (which is not-A).

 

Consider one of Lawler's own examples: while it is true that "A cow is a cow" -- "A is A" -- it is might also be true that "A cow is brown" -- "A is B" --, just as it is true that "Brown is not a cow", too -- "B is not-A".

 

Now, it is little use dialecticians objecting to the semantic 'looseness' of the above counter-example (with the terms there sliding between their role as nouns and adjectives), since the "A"s DM-fans use are subject to no little dialectical double-dealing themselves. Hence, they have no more right to complain about 'sloppy semantics' when it is used against them than Donald Trump has any right to moan about 'fake news'. If the above counter-example is to be ruled out-of-court on semantic grounds alone, then much of Lawler's (and hence Hegel's) argument would soon follow it out of the window.

 

On similar lines, someone could argue that brown is not an "entity", so the above example is misguided. But, anyone who accepts Lawler's argument has no room to complain on that score, either, since, as we have seen, Lawler's "A"s can be anything he pleases.

 

Indeed, Lawler himself calls a colour term a "thing":

 

"Hegel points to another inconsistency to which defenders of the position of abstract identity are subject. Putting the concept of identity into practical application, as it is interpreted by abstract understanding, we are compelled to say that a cow is a cow, a man is man, white is white, spirit is spirit, etc. In attempting to express the principle of identity according to the spirit of abstract understanding, we end up paradoxically speaking of an endless number of different things. The category of difference asserts its right to exist despite the intent to banish it -- which Hegel attributes to his opponents -- and the two categories appear in a peculiar relationship in the cognate category of 'diversity.'" [Ibid., pp.20-21. Italic emphasis in the original. Bold emphases added.]

 

Once more, someone could object that even if the above were correct, it is still the case that B is not A, so there is a negative relation here, after all. But, as we have seen, the required relation can only be manufactured if key expressions are nominalised. As we have also seen, even if the diminutive verb employed here is viewed as an "is" of identity, and not of predication, the argument still hits a brick wall. [Follow the above link for more details.]

 

In that case, if it is indeed the case that "abstract understanding" ignores this 'problem', it would be well-advised to continue to do so, for there was no problem here to begin with.

 

More-or-less the same comment applies to this example of dialectical casuistry:

 

"Looking one step further into this matter, Hegel suggests that the relation of A to not-A is doubly negative. Identity is established (not immediately given) through a negative relation to not-A. A is itself in not being not-A. But this negative relation to not-A is itself negated. That is, the identity of A does not consist solely in its being not-A, there is a 'return' to A again -- which Hegel calls 'reflection.' Thus 'A is A' is not a tautologous (sic) repetition of A (as 'abstract understanding' would have it) but an affirmation that has been made possible only through a doubly negative movement, a 'negation of the negation.'" [Ibid., p.22. Italic emphases in the original.]

 

Again, these 'inferences' only work if the letter "A"s used here stand for propositions, while the relations they supposedly express only apply if they do not.

 

However, there is no "negative relation" of A to not-A (since predicates aren't objects nor the Proper Names thereof), and that means that it isn't the case that "A is itself in not being not-A". Hence, the entire passage is about as accurate as one of Tony Blair's Iraq WMD dossiers.

 

In which case, the NON is just as fabulous a beast as the Jabberwocky ever was.

 

On the one hand, if the NON were a viable principle, it couldn't apply to negation, on the other, if the NON does apply to negation, it can't be viable.

 

[NON = Negation of the Negation.]

 

Zeno -- No Help At All

 

We are now in a position to see how Lawler employs the results of the reconstructive linguistic surgery he learnt from Hegel as he turns to the latter's use of "contradiction", beginning with a consideration of Zeno's 'Paradox of Motion':

 

"Hegel's statement [i.e., 'that something moves because "it at once is and is not"' -- quoted from the previous paragraph to this one -- RL]  is made in response to Zeno's famous paradox. Zeno's paradox, according to Hegel, is that since motion involves both A and not-A, and since this violates the principle of noncontradiction, it follows that motion is impossible. What should probably be called 'Hegel's paradox' is the assertion that since motion occurs, there must be in some sense both the A and not-A of Zeno's position. It is clear that this assertion cannot be taken in the sense of a strict logical contradiction. Not-A in a purely formal sense means only the denial of A, and is compatible with saying that the object is both 'here' and 'anywhere else,' perhaps also on the moon. Not-A can also mean the simple denial of 'here' -– an assertion that clearly leaves us nowhere. Is there any possible sense to be made out of Hegel's statement.

 

"The value of a paradox is that it makes us rethink the position which we originally held, if this positions leads to a 'self-contradiction.' Hegel's line of thought here is similar to his approach to the problem of 'abstract identity' or 'identity held aloof from difference.' The paradox arises if we begin with an abstract notion of place, a 'here' which is totally discrete and unrelated to any other place. The common-sense definition of motion as 'change of place' or as a passage of an object through a succession of places runs into insuperable intellectual difficulties if 'place' is understood in this manner. For one thing 'place' is defined as 'fixed place,' i.e., as motionless place. Can motion be explained in terms of a concept which excludes motion? On the other hand, it does not seem possible to eliminate some notion of definite place from our concept of motion, but such a notion must be that of a 'relative place,' a place which is both 'here' and 'there' or, paradoxically, 'here' and 'not-here.' This is an example of the way in which terms which play a useful role at the level of common sense and everyday practice, the proper domain, according to Hegel, of the 'abstract understanding,' fail to work on the strictly theoretical plane. The result cannot be their total abandonment, according to Hegel, but must involve their 'remodelling' by a dialectical understanding of the systematic interrelation of categories which 'abstract understanding' takes to be self-contained, possibly self-evidence units of thought." [Ibid., pp.28-29. Italic emphases in the original.]

 

But, this is no use at all helping the bemused reader understand the term "dialectical contradiction" since Zeno's 'paradox' isn't a paradox, and neither is there such a thing as the "common sense" notion of place, or even of motion -- as we saw in Essay Five. Or, rather, motion is only paradoxical for those Idealists who are determined to think and speak like linguistic Philistines. Our ordinary words for location and movement are far more complex than Hegel imagined (that is, in his 'theoretical deliberations'; in his ordinary, everyday use of language he will have been aware of this or he couldn't have functioned efficiently, again, as we saw in Essay Five).

 

But what about these words:

 

"On the other hand, it does not seem possible to eliminate some notion of definite place from our concept of motion, but such a notion must be that of a 'relative place,' a place which is both 'here' and 'there' or, paradoxically, 'here' and 'not-here.'" [Ibid.]

 

One might well wonder how places themselves can move -- how, for instance, they can be "here" and "not here" --, and what the dickens they could possibly move into! What "places" do places occupy? [I have also explored these odd ideas in Essay Five, here, and shown how no sense can be made of them.]

 

In passing it is worth pointing out that Hegel admits that 'dialectics' only works if ordinary language (which he calls the province of 'abstract understanding') is 'remodelled' -- or, and more honestly, if we use Marx's term, "distorted" -- exactly as alleged throughout this Essay and this site:

 

"This is an example of the way in which terms which play a useful role at the level of common sense and everyday practice, the proper domain, according to Hegel, of the 'abstract understanding,' fail to work on the strictly theoretical plane. The result cannot be their total abandonment, according to Hegel, but must involve their 'remodelling' by a dialectical understanding of the systematic interrelation of categories which 'abstract understanding' takes to be self-contained, possibly self-evidence units of thought." [Ibid.]

 

Nor does Lawler even consider another, far more obvious tactic when faced with a 'paradox that leads to self contradiction': take Marx's advice seriously and re-examine the distorted language upon which Hegel and Zeno relied to spin their fantasies. Once more, I have done just that in Essay Five (link above).

 

But, is this being a little too hasty, if not unfair, to Hegel and Lawler? The latter seems to think so, and for the following reasons:

 

"The solution to the paradox, which is expressed in the form of a logical contradiction, is the 'dialectical contradiction.' Thus in the case of motion the logical contradiction arises for the 'natural' mode of thought, based on common sense and practical life requirements, that argues 'either continuity or discontinuity.' Since place is classified as an instance of discontinuity, while movement implies continuity, the notion of motion as 'change of place' leads to a logical contradiction, and to Zeno's paradox. The dialectical solution involves the recognition of the relative nature of the basic categories involved in thinking about motion as 'change of place.' Motion must be understood as involving a 'unity of opposites,' 'discontinuity' which is relative to 'continuity' (or, perhaps, space that is relative to time)." [Ibid., p.29. Italic emphases in the original.]

 

This 'problem' appears to arise because we supposedly regard 'place' as a discrete concept at the same time as viewing motion as continuous. Hence, "change of place" automatically generates 'contradictions'. But, it is unclear what it might mean to say that "place" is "discrete", especially if it is defined as the location of a moving body. As I pointed out in Essay Five, "place" can be as continuous as we care to make it, since even a moving body occupies a region of space large enough to contain it. So, a worker can move about in her place of work (an entire factory) and hence remain in the same place even as she moves. Here is how I made that point in Essay Five (slightly edited):

 

Several of the points raised above require further elaboration -- in the course of which we will discover once again that Engels was in fact saying nothing at all intelligible.

 

As we have seen, Engels asserted the following:

 

"[A]s soon as we consider things in their motion, their change, their life, their reciprocal influence…[t]hen we immediately become involved in contradictions. Motion itself is a contradiction; even simple mechanical change of place can only come about through a body being both in one place and in another place at one and the same moment of time, being in one and the same place and also not in it. And the continual assertion and simultaneous solution of this contradiction is precisely what motion is." [Engels (1976), p.152.]

 

However, in so doing he was clearly appealing to what he regarded as the established, inter-subjective meaning of terms like "motion", "change", "place", "moment", and "time". This can be seen from the fact that he didn't even think to define or explain what he meant by these words.

 

Engels did, however, offer an aside (in the above comment) to the effect that motion is a "simple mechanical change of place", an idea he reiterated in DN:

 

"All motion is bound up with some change of place, whether it be change of place of heavenly bodies, terrestrial masses, molecules, atoms, or ether particles. The higher the form of motion, the smaller this change of place. It in no way exhausts the nature of the motion concerned, but it is inseparable from the motion. It, therefore, has to be investigated before anything else." [Engels (1954), p.70. Italic emphasis added.]

 

I will re-examine what Engels had to say above, later in this Essay.

 

Ordinarily, this lack of precision wouldn't be a problem in itself since we understand words like these perfectly well in our day-to-day affairs, and typically without a need to check any definitions, etc. But, in such specialised areas of philosophy or science -- especially those associated with an attempt to revise or correct the way we understand, or even perceive, objects and processes --, a sloppy approach to theory like this isn't just unacceptable, it is counter-productive. Indeed, this cavalier attitude to ordinary language has a tendency to backfire on anyone foolish enough to allow it to direct their thinking. Again, this is especially true of those who try to press the vernacular into service way beyond its prosaic remit.

 

The ability to manoeuvre one's way around linguistic conundrums like this with ease is supposedly what dialecticians mean by "grasping a contradiction". This seems to imply that when confronted with the many 'contradictions' that nature allegedly throws our way, dialecticians merely have to "grasp" them, and all is well. This neat trick then 'allows' such serial 'graspers' to ignore the internal contradictions this approach introduces into their own theory. [The fatal problems that tactic brings in its train have been explored here and here.]

 

However, as we will see in Essay Seven (as well as here), DM-theorists are highly selective when it comes to deciding which 'contradictions' they should "grasp", which they should simply drop (or, and far more likely, just ignore), or which they try to blame on the defective nature of a rival theory. Hence, when dialecticians "grasp" the 'contradictions' they claim to see in motion and change, they attribute them to nature itself -- failing to blame them on Hegel's logical incompetence, on Engels's lack of clarity, or, indeed, on Zeno's confused fantasies.

 

On the other hand, when a contradiction is detected in a rival theory, that becomes a handy excuse for berating those who still promote or accept it, and hence a reason for rejecting it, root-and-branch. By way of contrast, DM-theorists are remarkably forgiving and accepting of the contradictions implied by their own ideas, which aren't allowed to suggest, under any circumstances, that their theories are defective or in need of revision.

 

So, for example, they tell us that by 'resolving' certain contradictions science has been able to progress. However, if science advances by rejecting or 'resolving' contradictions in and between theories, or in and between a theory and observation, then, plainly, kinematics itself can't advance unless or until this 'dialectical contradiction' has also been resolved (as, indeed, it will be by the end of this Essay --, except that will be done by dissolving it). However, just as soon as that has been done dialecticians will surely have to abandon their belief in the 'contradictory' nature of motion -- or, of course, risk holding up the progress of science.

 

This self-inflicted quandary I have called "The Dialecticians' Dilemma".

 

As seems obvious, 'dialectically grasping' a 'contradiction' doesn't make it disappear. Even if we grant for the moment the veracity of DM, motion would still be 'contradictory' whether or not anyone else viewed this phenomenon the same way. Hence, the significance of "grasping a contradiction" appears to be little more than this: Certain processes in nature and society, which might seem puzzling or paradoxical (to some), suddenly stop bothering dialecticians -- that is, if ever they did bother them. They have "grasped" these oddities and can now move on (no pun intended). But, this tactic only works if it is accepted that this is the way the world actually is, that it is indeed contradictory. In that case, and on this basis, DM-theorists seem to think they can stop worrying about the contradictions their world-view places at the heart of their own theory. They accept the fact that even though nature is deeply perplexing, a pair of well-adjusted DM-spectacles allows it to be viewed correctly -- where "viewed correctly" in fact appears to mean "Ignore what you can't explain and then accuse critics of not understanding dialectics".

 

Despite the DM-spin, this nevertheless implies that it is impossible to explain what it could possibly mean for something to be in two different places at once (save in the ambiguous manner described earlier in this Essay, and again below). If that is so, the dialectical 'analysis' of motion is of little use to anyone, least of all dialecticians. That is because it is clear that not even they can explain motion, since all their theory does is re-describe it in a perplexing form. All that Engels's 'analysis' seems to have achieved, therefore, is to stop dialecticians worrying about their own defective theory, all the while leaving motion, as they see it, no less of a 'paradox'.

 

We have also seen that, even if DM were a correct description of, or theory about, 'reality', this view of motion does no real work. How does it help anyone change the world to be told that motion is contradictory? How does it help scientists to be told motion is a contradiction? Can they use it to predict anything? Can technologists and engineers use it to help control nature? How many bridges can be built on the basis of the belief that motion is a contradiction? How many strikes won? Or even leaflets printed? What dialectical -- or any -- use is this?

 

In that case, if there is in fact a rational solution to this 'paradox' -- if we but knew what it was --, it is no good looking to dialecticians for an answer. They gave up on that score the moment they leafed through Hegel's 'Logic', and began "grasping" 'contradictions'.

 

Left to DM-fans, the advance this branch of Physics and Applied Mathematics would come to a grinding halt.

 

[Irony intended.]

 

However, Engels did at least make some attempt to use everyday terms in his effort to show that they, or what they supposedly reflected, weren't all they seemed -- i.e., that when considered 'dialectically' the vernacular reveals more about reality than might otherwise have been apparent, especially to those who are mesmerised by 'commonsense' or 'formal thinking'. Or, indeed, those who have been bamboozled by that 'inner fifth-columnist', the "abstract understanding" (very helpfully identified for us by Hegel without the use of a single consulting couch -- or even a brain scan).

 

Nevertheless, anyone who disagrees with the 'dialectical' conclusions Engels drew would no doubt be reminded that these few words -- or, the 'concepts', objects and processes they supposedly 'represent' -- clearly and unambiguously imply the 'contradictions' that Engels and Hegel said they did. In that case, defenders of the 'dialectical view' of 'reality' could claim that Hegel and Engels had actually made explicit what were in fact implicit 'contradictions' in our knowledge of the world and how it works, and not just the language we use to express that assumed fact.

 

Intentionally or not, by arguing this way Engels succeeded in situating his paradoxical theses in an ancient metaphysical tradition stretching back to Zeno, Parmenides and Heraclitus -– a tradition which ordinary working people had no hand in building, but which is (demonstrably) based on ruling-class priorities, forms-of-thought, and, not uncoincidentally, on a distortion of the vernacular, the only language that links humanity directly with the material world, as Marx himself pointed out:

 

"One of the most difficult tasks confronting philosophers is to descend from the world of thought to the actual world. Language is the immediate actuality of thought. Just as philosophers have given thought an independent existence, so they were bound to make language into an independent realm. This is the secret of philosophical language, in which thoughts in the form of words have their own content. The problem of descending from the world of thoughts to the actual world is turned into the problem of descending from language to life....

 

"The philosophers have only to dissolve their language into the ordinary language, from which it is abstracted, in order to recognise it, as the distorted language of the actual world, and to realise that neither thoughts nor language in themselves form a realm of their own, that they are only manifestations of actual life." [Marx and Engels (1970), p.118. Bold emphases alone added.]

 

Indeed, Engels's approach in this area began to falter the moment he attempted to squeeze some metaphysical juice out of such desiccated philosophical raisins; that is, when he tried to extract 'paradoxical' conclusions from a few rather innocent-looking words, suitably doctored.

 

Naturally, only those who have already accepted the view that reality is fundamentally 'contradictory' will agree with the conclusions Engels drew. Others, however, might be forgiven for remaining sceptical -- particularly those who (not unreasonably) think that Engels's 'solution' is far more puzzling than the original 'problem' had ever been. Indeed, if the nature of motion is problematic, calling it "contradictory", while making no attempt to explain how that actually accounts for anything, or even explains anything, is worse than useless.

 

If these 'contradictions' do no work (again, as was argued above), then their presence here is, at best, unhelpful. That is because we can now see that they are the product of an over-active imagination, compounded by a naive acceptance of the Idealist gobbledygook Hegel and Zeno inflicted on their audience.

 

In that case, Engels's 'analysis' is an obstacle to our understanding, which will, of course, need to be removed if science (let alone Marxism) is to advance.

 

In fact, Engels failed to consider other, far more likely possibilities; indeed, it looks like it never even occurred to him that his 'contradictory' conclusions might fail to follow if he had instead given consideration to the full range of words, or meanings, available to ordinary language users. To be sure, these are easily accessed by those determined to use the vernacular with far a greater concern for consistency, honesty and sensitivity than Engels, Hegel, or Zeno ever managed.

 

Engels clearly wanted to make a specific point about the paradoxical implications of a handful of seemingly innocent-looking ordinary words. As we will see, he did this by unwittingly altering their everyday use/meaning while imagining that the meaning of several other ordinary terms intimately associated with them remained unaffected.

 

In so doing he wasn't, of course, alone. Semantic sleight-of-hand has been the sport of choice throughout the entire history of Traditional Philosophy; and the practice continues to this day. Even careful philosophers often fail to notice that their own work involves what can only be called "piecemeal selectivity" over the use of certain words. Indeed, they have invariably assumed it is possible to tinker around with a handful of specially-chosen expressions while the meaning of any other words normally associated with them remain unaffected. Selectivity like this is, alas, double-edged. In fact, these associated words -- whose meanings in this case Engels also simply took for granted -- prove to be equally (if not more) problematic than those he finally latched onto.

 

As we are about to see, this unexpected turn of events will not only undermine Engels's 'analysis' of motion, it will vitiate every single classical theory, too.

 

If, according to Hegel and Engels, an ordinary word like "motion" possess 'contradictory' implications, then perhaps other terms these two failed to consider might have analogously paradoxical connotations, especially given this perverse way of viewing language. What about the word "place", for instance? What if it turns out to be just as 'problematic'? In such circumstances, could we continue to accept the validity of Engels's conclusions about "motion" if the interplay between these two intimately connected words is more complex than he imagined, and an alteration to one only succeeded in changing the other?

 

More pointedly: What if certain uses of the word "place" neutralise Engels's interpretation of the word "move"?

 

Clearly, Engels's argument relies on the meaning of "place" remaining fixed while he tinkered around with "move". But, if "place" itself has no single meaning, then any conclusions based on the supposition that it has just one meaning will automatically come under suspicion. Worse still, any argument based on one aspect of the ordinary meaning of "place", which undercuts the supposed 'philosophical' implications of "motion", will be thrown into even greater doubt. That is because, if connotations of the latter are compromised by the slippery nature of the former (or, indeed, vice versa), the meaning of neither will emerge unscathed in view of their intimate connection.

 

In fact, as we are about to see, these close connections have the salutary effect of deflating the philosophically grandiose conclusions Engels and others thought they could derive from a handful of mundane marks on the page -- when, for example, they employed a non-standard application of "motion" in parallel with what they took to be a standard use of "place", and vice versa.

 

Many of the ambiguities mentioned earlier (in relation to Engels's analysis of "motion") actually depend on systematic vagueness in the meaning of the word "place" and its cognates. Even when translated into the precise language of coordinate algebra, or even geometry, the meaning of this particular word doesn't become any clearer (when used in such contexts), as we are about to find out. [Added on edit: I have omitted that part of Essay Five -- it can be accessed here.]

 

Of course, this isn't to criticise the vernacular; imprecision is one of its strengths. Nor is it to malign mathematics! However, when ordinary words are imported into Philosophy, where it is almost invariably assumed -- implicitly or explicitly -- that they have a single unique (or 'essential') meaning, problems invariably arise, as Wittgenstein noted:

 

"I think that essentially we have only one language, and that is our everyday language.... [O]ur everyday language is the language, provided we rid it of the obscurities that lie hidden in it. Our language is completely in order, as long as we are clear about what it symbolizes." [Waismann (1979), pp.45-46. Paragraphs merged.]

 

"You ask why grammatical problems are so tough and seemingly ineradicable. -- Because they are connected with the oldest thought habits, i.e., with the oldest images that are engraved into our language itself (Lichtenberg).... Language has the same traps ready for everyone; the immense network of easily trodden false paths. And thus we see one person after another walking down the same paths....

 

"One keeps hearing the remark that philosophy really doesn't make any progress, that the same philosophical problems that occupied the Greeks keep occupying us. But those who say that don't understand the reason this must be so. The reason is that our language has remained constant and keeps seducing us into asking the same questions. So long as there is a verb 'be' that seems to function like 'eat' and 'drink', so long as there are the adjectives 'identical', 'true', 'false', 'possible', so long as there is talk about a flow of time and an expanse of space, etc., etc. humans will continue to bump up against the same mysterious difficulties, and stare at something that no explanation seems able to remove....

 

"I read '...philosophers are no nearer to the meaning of 'Reality' than Plato got...'. What a strange state of affairs. How strange in that case that Plato could get that far in the first place! Or that after him we were not able to get further. Was it because Plato was so clever?" [Wittgenstein (2013), pp.311-12e. Italic emphases in the original; quotation marks altered to conform with the conventions adopted at this site. Some paragraphs merged.]

 

Indeed, as it turns out, there is no such thing as the meaning of the word "place" -- or, for that matter, of "move".

 

This lack of clarity also spills over into our use of technical terms associated with either word; the application of coordinate systems, for example, requires the use of rules, none of which is self-interpreting. [The point of that comment will emerge presently.]

 

Nevertheless, it is relatively easy to show -- by means of the sort of selective linguistic 'adjustment' beloved of metaphysicians, but applied in areas and contexts they generally fail to consider, or, rather, which they choose to ignore -- that ordinary objects and people are quite capable of doing the 'metaphysically impossible'. The flexibility built into the vernacular actually 'enables' the mundane to do the magical, and on an alarmingly regular basis. Such everyday 'prodigies' don't normally bother us -- well, not until some bright spark tries to do a little 'philosophising' with them.

 

[Added in a Note: Needless to say, the alleged fact "that ordinary objects and people are quite capable of doing the metaphysically impossible" is meant to be taken ironically! Such 'prodigies' are only 'possible' if we insist on using the vernacular in the same crass way as metaphysicians and DM-fans.]

 

If the ordinary word "place" is now employed in one or more of its usual senses, it is easy to show that much of what Engels had to say about motion becomes either false or uninteresting. Otherwise, we should be forced to concede that ordinary people and objects can behave in extraordinary -- if not miraculous -- ways.

 

Consider, therefore, the following example:

 

L41: The strikers refused to leave their place of work and busied themselves building another barricade.

 

Assuming that the reference of "place" is clear from the context (that it is, say, a factory), L41 depicts objects moving while they remain in the same place -- contrary to what Engels said (or implied) was possible. Indeed, if this sort of motion is interpreted metaphysically, it would involve ordinary workers doing the impossible -- moving while staying still!

 

Of course, an obvious objection to the above would be that L41 is a highly contentious example, and not at all the sort of thing that Engels (or other metaphysicians) had in mind by their use of the word "place". [That was indeed the point I made a few paragraphs back.]

 

But, Engels didn't tell us what he meant by this term; he simply assumed we would 'understand' his use of it. [Again, that was the point of that earlier preamble.] Here is what he did say:

 

"Motion in the most general sense, conceived as the mode of existence, the inherent attribute, of matter, comprehends all changes and processes occurring in the universe, from mere change of place right up to thinking....

 

"All motion is bound up with some change of place, whether it be change of place of heavenly bodies, terrestrial masses, molecules, atoms, or ether particles. The higher the form of motion, the smaller this change of place. It in no way exhausts the nature of the motion concerned, but it is inseparable from the motion." [Engels (1954), pp.69-70. Bold emphasis added.]

 

"[A]s soon as we consider things in their motion, their change, their life, their reciprocal influence…[t]hen we immediately become involved in contradictions. Motion itself is a contradiction; even simple mechanical change of place can only come about through a body being both in one place and in another place at one and the same moment of time, being in one and the same place and also not in it. And the continual assertion and simultaneous solution of this contradiction is precisely what motion is." [Engels (1976), p.152.]

 

There is nowhere in there that tells us what Engels meant by "place". [I have been checking for more years that I care to count, but he nowhere tells us what he meant by this word. If anyone thinks differently, please e-mail me.]

 

It could be countered that it is perfectly clear what he meant by his use of this word -- but as we are about to see, that isn't so.

 

If, however, it is now claimed that he didn't mean by "place" a sort of vague "general location" (such as the factory used in the above example), then that would confirm the point being made in this part of the Essay: Engels didn't say what he meant by "place" since there was nothing he could have said that wouldn't also have ruined his entire argument. Tinker around with the word "place" and the meaning of "motion" can't fail to be compromised (again, as noted above). That can be seen by considering the following highly informal 'argument':

 

L42: Nothing that moves can stay in the same place.

 

L43: If anything stays in the same place, it can't move. [L42 contraposed.]

 

L44: A factory is one place in which workers work.

 

L45: Workers move about in factories.

 

L46: Any worker who moves can't stay in the same place (by L43 and modus tollens).

 

L47: Hence, if workers move they can't do so in factories (by L44 and L45).

 

L48: But, some workers remain in factories while they work; hence, while they are there either they can't move or they can't work (by L43).

 

L49: Therefore, either workers work and do not work in factories -- or they move and they do not move.

 

As soon as one meaning of "place" is altered (as it was in L44), one connotation of "move" is automatically affected (in L45 and L46), and vice versa (in both L47 and L48). In one sense of "place", things can't move (in another sense of "move") while staying in one place (in yet another sense of "place"). But, in still another sense of both they can, and what is more, they typically do both. Failure to notice this produces 'contradictions' to order, and everywhere (as in L49).

 

If the above example confuses anyone, think about moving around your flat or house. It is quite clear that while doing that you move but remain in the same place. In that case, if moving means you have to change place, then you must move and not move at the same time. Here a looser use of "place" undermines one meaning of move, for it seems you have moved while remaining still, while remaining in the same place.

 

That appears to contradict Engels:

 

"All motion is bound up with some change of place, whether it be change of place of heavenly bodies, terrestrial masses, molecules, atoms, or ether particles. The higher the form of motion, the smaller this change of place. It in no way exhausts the nature of the motion concerned, but it is inseparable from the motion." [Engels (1954), pp.69-70. Bold emphases added.]

 

Even so, who believes that workers work and do not work in factories? Or, that they move and do not move while staying in the same place? Who believes that you move around your house or flat while remaining still? That is, you move and do not move at the same time?

 

Perhaps only those who 'understand' dialectics...?

 

Clearly, Engels's 'theory' of motion has to be able to take account of ordinary objects if it is to apply to the real world and not just philosophical abstractions, or, indeed, physically meaningless mathematical 'points'. But, that is precisely what his 'theory' can't do, as we are about to find out.

 

It could be objected that it would be possible to understand what Engels and Hegel were trying to say if "place" is defined precisely without altering the meaning of "move", contrary to the points raised in the last few sub-sections of this Essay. In that case, it could be argued that if "place" is defined by the use of precise spatial coordinates (henceforth, SCs), Engels's account of motion would become viable again.

 

Or, so some might like to think.

 

Of course, the problem here is that in the example given above (concerning those contradictory mobile/stationary workers), if we try to define the meaning of the word "place" a little more precisely, it will start to mean something like:

 

F1: Df. Place: A finite three-dimensional region (of space) large enough to contain the required object.

 

Well, plainly, in that sense things can and do move about while they remain in the same region (i.e., "place") -- since, by default, any object occupies such a region as it moves -- that is, it must always occupy a three-dimensional region of space large enough to contain it as it moves. They certainly don't occupy larger or smaller spaces (unless they expand or contract)! Moreover, objects occupy finite regions as they move (or they wouldn't be able to move).

 

Hence, if defined this way, moving objects always occupy the same space -- and, if we are to believe Engels, they don't move while they are doing so! That is, if they always stay in the same space, they can't move -- if we insist on characterising "motion" the way Engels and Hegel thought they could and we define space along lines suggested by F1 above.

 

As we have just seen, objects always occupy the same space, even as they move. So, they both move and don't move! Plainly, in order to circumvent these problems, we need to be even more precise.

 

Of the countless problems about motion and place that confront us the following seem to be most relevant to the issues at hand, at least at present:

 

(1) If an object always occupies the same space (which fits it like a glove, as it moves), then it can't actually move!

 

(2) If an object occupies a larger space as it moves, it must expand.

 

(3) If an object moves about in the same region of space (such as a factory), it still can't move!

 

[(4) However, if an object successively occupies spaces equal to its own volume as it moves, the situation is even worse, as we will soon see.]

 

So, if the 'region' concerned (in which, by means of which, or even through which) an object is said to move is constrained too much, nothing would be able to move -- this is Option (1). Put each worker in a tightly-fitting steel box that exactly fits him or her and watch all locomotion grind to a halt.

 

On the other hand, put that worker in a larger region of space, and he/she still won't be able to move -- this is Option (3). That is because if we define motion as successive occupancy of regions of space within a broader region, then this worker can't move since he/she is always in the same broader region, the same space -- for example, a factory. [Or you as you move around your house or flat.]

 

The difficulty here is plainly one of relaxing the definition of the required region that an object is allowed to occupy sufficiently enough to enable it to move from one place to another without stopping it moving altogether. Hence, this problem revolves around preventing Option (3) from undermining what we might ordinarily want to call motion -- the successive occupancy of certain regions of space; i.e., the first half of (4) --, all the while providing an account that accommodates the movement of medium-sized objects in the real world.

 

(3) If an object moves about in the same region of space (such as a factory), it still can't move!

 

(4) However, if an object successively occupies spaces equal to its own volume as it moves, the situation is even worse....

 

But, once this has been done (if we, say, relax the definition of the space, or the place concerned, making it larger, for example) the above difficulties soon re-appear; for it is quite clear that such objects will still move while staying in the same place -- i.e., if the place allowed for this is big enough for them to do just that! [Option (3), again!]

 

Indeed, this fact probably accounts for, or permits, most (if not all) of the locomotion in the entire universe. Clearly, in the limit, if anything moves in nature it must remain in the same place, i.e., it must remain in the universe! Unless an object travels beyond the confines of the universe (if there were such a thing!), this must always be the case: the said object moves while remaining in the same place -- i.e., it remains in the universe! Of course, this relaxes the definition of "same place" far too much. But, the problem now is how we are to tighten the definition of "place" so that objects aren't put in straight-jackets once more. [I.e., Option (1).]

 

(1) If an object always occupies the same space (which fits it like a glove, as it moves), then it can't actually move!

 

At first sight, the above objection (concerning a precise enough definition of "place") seems reasonable enough. Engels clearly meant something a little more specific than a vague or general sort of location (like a factory). But what? He didn't say, and his epigones haven't, either. Well over a century of silence on this issue! Indeed, it is quite clear that they don't even recognise this as a problem, so sloppy has their thought become. [And good luck finding a clear definition in Hegel! Even more luck getting an answer out of DM-fans! I have been trying for over thirty years!]

 

It might seem possible to rescue Engels's argument if tighter protocols for "place" were prescribed --, perhaps those involving a reference to "a (zero volume) mathematical point in three-dimensional space, located by the use of precise SCs". But, that option would embroil Engels's account in far more intractable problems. That is because it would (plainly!) involve mathematical point locations, or even the movement of mathematical points themselves -- and, as we saw earlier, that is itself a non-starter.

 

[SC = Spatial Co-ordinate.]

 

Clearly, things can't move about in such points -- but that has nothing to do with the supposed nature of reality. Mathematical points can't contain anything. That is because mathematical points aren't containers. They have no volume, no shape, no circumference, no diameter and are made of nothing. If that weren't the case, they wouldn't be mathematical points, they would be regions, or volume intervals. [More on those presently.]

 

As noted above, if Engels meant something like this by his use of "place", his account would fail to explain (or accommodate) the movement of gross material bodies in nature, for the latter don't occupy mathematical points.

 

And, it is no use appealing to larger numbers, or sets, of such points located by SCs (or by means of other technical devices); no material body can occupy an arbitrary number of points, since points aren't containers.

 

Perhaps we could define a region (or a finite volume interval) by the use of SCs? Maybe so, but that would only introduce another classical conundrum (which is itself a variation on several of Zeno's other paradoxes): how it is possible for a region (or a volume interval) to be composed of points that have no volume. Even an infinite number of zero volume mathematical points adds up to zero. Now, there are those who think this conundrum has a solution (just as there are those who think it doesn't), but it would seem reasonably clear that the difficulties surrounding Engels's 'theory' aren't likely to be helped by importing several more 'problems' from another set of paradoxes -- especially when those paradoxes gain purchase from the same linguistic ambiguities and vagaries about "space" that bedevilled "motion"!

 

We seem to be going round in circles.

 

[No irony or pun intended.]

 

Be this as it may, it is far more likely that Engels's use of the word "place" is itself an implicit reference to a finite three-dimensional volume interval (whose limits can be defined by the application of well-understood rules in Real and Complex Analysis, Vector Calculus, Coordinate Algebra and Differential Geometry, etc.).

 

Clearly, such volume intervals must be large enough to hold (even temporarily) a given material object. If so, this use of "volume interval" would in principle be no different from the earlier use of "place" to depict the movement of those workers! If objects can move about in locations big enough to contain them, and remain in the same place while doing so, Engels's moving objects must be able to do likewise -- except they would now have a more precise "place" or region in which to do it.

 

However, and alas, this sense of "place" is no use at all, for, as noted, when objects (such as workers) move, they will, by definition, stay in the same place! So, it seems this must be the case with Engels's moving objects, if we try to depict "place" this way. But, this is just Option (3), again!

 

(3) If an object moves about in the same region of space (such as a factory), it still can't move!

 

Naturally, the only way to avoid this latest difficulty would be to argue that:

 

F2: The location of any object must be a region of space (i.e., volume interval) equal to that object's own volume.

 

This is in effect one of the classical definitions. In that case, as the said object moves, its own exact volume interval would move with it; the latter would follow each moving object around more faithfully than its own shadow, and more doggedly than a world-champion bloodhound. But, plainly, if that were the case, it would mean that any such object would still move while staying in the same place -- since, plainly, any object always occupies a space equal to its own volume, which would, on this view, travel everywhere with it like a sort of metaphysical glove.

 

But that is just Option (1), again!

 

(1) If an object always occupies the same space (which fits it like a glove, as it moves), then it can't actually move!

 

As should now seem plain: we now have two problems where once there was only one, for we should now have to explain not only how bodies can move, but how it is also possible for volume intervals to move so that they can faithfully shadow the objects they contain!

 

Moreover, and far worse: not only would we have to explain how locations (i.e., these volume intervals) are themselves capable of moving, we would also have to explain what on earth they could possibly move into!

 

What sort of ghostly regions of space could we appeal to in order to allow regions of space themselves to move into them?

 

Even worse still: these 'moving volume intervals' must also occupy volumes equal to their own volume, if they are to move (given this 'tighter' way of characterising motion, expressed in F2, repeated below). And, if they do that, then these new 'extra' volume intervals (containing the original volume intervals which also contain the moving body!) must now act as secondary 'metaphysical containers', as it were, to the original 'ontological gloves' we met earlier. Metaphorically speaking, this theory, if it took such a turn, would be moving backwards, since an infinite regress would soon confront us as spatial mittens, inside containing gloves, inside holding gauntlets, pile up alarmingly to account for each successive spatial container, and how each of them could possibly move without another one to enable it to do just that!

 

F2: The location of any object must be a region of space (i.e., volume interval) equal to that object's own volume.

 

As seems reasonably clear, we would only be able to account for locomotion this way if each moving object were situated at the centre of some sort of 'metaphysical onion', each with a potentially infinite number of 'skins'!

 

[Iterated version of Option (1)!]

 

It could be countered that even though objects occupy spaces equal to their own volumes, as they move (locomote) they then proceed to occupy successive spaces of this sort (located in the surrounding region, for example), all of which are of precisely the right volume to contain the moving object that now occupies them, and which can be located or defined precisely. On this revised scenario, moving objects would leave their old volume intervals (their old containers) behind, successively occupying new volume intervals along their trajectories, as they barrelled along.

 

Perhaps this is the direction we need to take?

 

[No pun intended.]

 

This now brings us to a consideration of Option (2), and/or Option (4) -- now modified to (4a) --, from earlier:

 

(2) If an object occupies a larger space as it moves, it must expand.

 

(4a) An object successively occupies spaces (or volume intervals) equal to its own volume as it moves.

 

I will reject (2) as absurd. If anyone wants to defend it, they are welcome to all the headaches it will bring in its train.

 

Consider, then, Option (4a):

 

Even if (4a) were a correct interpretation of what Engels meant, and it proved to be a viable alternative -- and, indeed, if sense could be made of these new, and accommodating successive locations without re-duplicating the very same problem noted above --, no DM-theorist could afford to adopt it. That is because dialecticians claim that moving bodies occupy at least two such "places" at the same time, being in one of them and not in it at the same moment. Clearly, if motion were defined in such terms (that is, if it were characterised as involving objects successively occupying spaces equal to their own volumes), then moving objects would occupy at least two of these volume intervals at once.

 

In that case, 'dialectical objects' would not so much move as stretch or expand!

 

[Modified Option (2)!]

 

To see this point more clearly (again, no pun intended!), it might be useful to examine the above argument a little more closely.

 

If the centre of mass (COM) of a 'dialectically moving' object, D, were located at, say, (Xk, Yk, Zk) and (Xk+1, Yk+1, Zk+1), at the same time (to satisfy the requirement that moving bodies occupy at least two such "places" at the same time, being in one of them and not in it), it would have to occupy a space larger than its own volume while doing so.

 

Let us call such a space, "S", and let the volume interval containing (Xk, Yk, Zk) and (Xk+1, Yk+1, Zk+1) be δV1, leaving it open for the time being whether S and δV1 are the same or are different. Thus, if the COM of D is in two such places (i.e., (Xk, Yk, Zk) and (Xk+1, Yk+1, Zk+1)) at once, it would plainly be in S, and would occupy δV1.

 

But, once again, that would mean that D would move while remaining in the same place -- i.e., it would remain inside S, or inside δV1 (whichever is preferred), as its COM moved from (Xk, Yk, Zk) to (Xk+1, Yk+1, Zk+1), in the same 'moment'. [Option (3), again!]

 

[Except, we can't speak of a 'dialectal object' moving from one point to the next since that would imply it was in the first before it was in the second, and that it was in the second after it was in the first. As we have seen, if such an object is in both places at the same time, there can be no "before" and no "after", here, and hence no "moving from (Xk, Yk, Zk) to (Xk+1, Yk+1, Zk+1)", either!]

 

This is perhaps better: D would move while remaining in the same place -- i.e., it would remain inside S, or inside δV1 (whichever is preferred), as its COM is located at both (Xk, Yk, Zk) and (Xk+1, Yk+1, Zk+1), in the same 'moment'. [Option (3), again!]

 

Now, the only way to avoid the conclusion that D moves while occupying the same place, or space, S and/or δV1 --, and hence that it appears to stay still while it moves, just like the 'mobile/stationary' workers we encountered earlier -- would be to argue that such spaces remain where they are while D moves into successively new locations or spaces. This seems to be the import of Option (4a):

 

(4a) An object successively occupies spaces (or volume intervals) equal to its own volume as it moves.

 

But, as D moves it still occupies δV1, only we would now have to argue that as it does so it also moves into a new δV each time -- say, δV2 -- except this new δV2 must now contain (Xk+1, Yk+1, Zk+1) and (Xk+2, Yk+2, Zk+2) -- otherwise it wouldn't be a new containing volume interval that satisfied the requirement that moving bodies occupy at least two such "places" at the same time, being in one of them and not in it.

 

Plainly, all objects have to occupy some volume interval or other at all times (or they would 'disappear'). However, in D's case it has to do this while also occupying a new volume interval as it locomotes -- otherwise, as we saw, it would move while being in the same place, which would imply that it didn't move, after all!

 

[Except, of course, we have already seen that there is no "while" applicable to moving DM-objects. I will, however, ignore that fatal glitch for now.]

 

So, if D occupies only one S, or only one δV, at once, it would be at rest there. [This is Option (1) and/or Option (3).] Hence, it must occupy at least two of these at the same time (if, that is, we accept the 'dialectical' view of motion).

 

(1) If an object always occupies the same space (which fits it like a glove, as it moves), then it can't actually move!

 

(3) If an object moves about in the same region of space (such as a factory), it still can't move!

 

That being so, the only apparent way of avoiding the conclusion that D-like objects move while staying still is to argue that they occupy two successive Ss, or two successive δVs (perhaps these partially 'overlap', perhaps they don't), at once. Unfortunately, this would now mean that D-like objects would have to occupy a volume, or a volume interval, bigger than either one of S or δV on their own, at once, and hence: they must expand or stretch!

 

It could be objected that two successive δVs would contain (Xk, Yk, Zk) and (Xk+1, Yk+1, Zk+1) each between them -- that is, δV1 would contain (Xk, Yk, Zk) and δV2 would contain (Xk+1, Yk+1, Zk+1) --, so the above objection is misguided. Maybe so, but the point is that dialectical objects must occupy two δVs at once, and if that is so, both δVs will contain (Xk, Yk, Zk) and (Xk+1, Yk+1, Zk+1), jointly or severally, otherwise moving objects couldn't occupy two spaces (two δVs) at the same time.

 

If that were so, and D wasn't stationary while it occupied δV2, as we saw above in an analogous context, it must also occupy δV3 at the same time, otherwise it will be stationary while in δV2, and so on. Successive applications of this argument would have D occupying bigger and bigger volume intervals (i.e., δV1 + δV2 + δV3 + δV4 +..., + δVn), all at the same time. In the limit, D could fill the entire universe (or, at least, the entire volume interval encompassing its own trajectory), all at the same time -- if it moves, and if Hegel were to be believed! [Added on edit: this conclusion is based on a detailed argument not reproduced here. In order fully to understand the point being made, readers are encouraged to follow the link posted at the beginning of this paragraph.]

 

There thus seems to be no way to depict the motion of D-like objects that prevents them from either (i) Moving while staying still, or, (ii) Expanding alarmingly like some sort of metaphysical Puffer Fish.

 

 

Figure One: At Last! An Organism That

'Understands' Dialectics

 

Either way, Engels's theory has dropped itself into yet another Hermetic Hole.

 

The reader should now be able to see for herself what mindless mystical mayhem is introduced into our reasoning by this cavalier use of (contradictory) metaphysical language. When one sense of "move" is altered, one sense of "place" can't remain the same, nor vice versa.

 

Of course, no one believes these ridiculous conclusions, but there appears to be no way of avoiding them if all we have to hand are the radically defective, recklessly meagre conceptual and logical resources DL supplies its unfortunate victims -- compounded by a cavalier misuse of ordinary language.

 

[DL = Dialectical Logic.]

 

[Added on Edit: In Essay Five I then proceed to list and explain several even more absurd consequences of this theory, here and here, as well as demonstrate that not only can ordinary objects move while remaining in the same place, they can also change places while remaining stationary -- i.e., they can move while they aren't moving! Any who harbour doubts: check out the above links.]

 

Back to the main feature...

 

However, it now seems we may only grasp this terminally obscure notion (i.e., "dialectical contradiction") if we make use of another equally obscure concept -- "unity of opposites".

 

We should also note in passing that what Lawler calls a "dialectical solution" to this alleged conundrum turns out to be even more problematic than the original paradox ever was! He nowhere explains what "the relative nature of the basic categories involved in thinking about motion", or what "a 'unity of opposites,' 'discontinuity' which is relative to 'continuity' (or, perhaps, space that is relative to time)" could possibly mean. Unfortunately, Hegel fans have an annoying habit of stitching obscure phrases together as if they meant something when separated, or even if they work as a job lot -- or, indeed, if these tactics solve anything.

 

[Once again, I have tried to give some sense to an appeal to the 'relativity' of the relevant terms used in this respect in Essay Five (links above) -- i.e., connecting notions of space, location, time and movement. Unfortunately, every attempt to do so only succeeded in generating even worse paradoxes!]

 

As might be expected of a Christian mystic like Hegel -- but surely not of an atheist/materialist like Lawler (if he is one) -- his 'solution' to this paradox is no more helpful than the 'solution' to the equally intractable 'problem' of the precise nature of Christ in the Christian Doctrine of The Incarnation. That 'solution' also comes in the form of even more paradoxical word combinations (wherein Christ is a 'unity of opposites', too, 'God' and 'Man'). Any who harbour doubts are invited to make sense of passages like the following:

 

"One of the most important effects of the union of the Divine nature and human nature in One Person is a mutual interchange of attributes, Divine and human, between God and man, the Communicatio Idiomatum. The God-Man is one Person, and to Him in the concrete may be applied the predicates that refer to the Divinity as well as those that refer to the Humanity of Christ. We may say God is man, was born, died, was buried. These predicates refer to the Person Whose nature is human, as well as Divine; to the Person Who is man, as well as God. We do not mean to say that God, as God, was born; but God, Who is man, was born. We may not predicate the abstract Divinity of the abstract humanity, nor the abstract Divinity of the concrete man, nor vice versa; nor the concrete God of the abstract humanity, nor vice versa. We predicate the concrete of the concrete: Jesus is God; Jesus is man; the God-Man was sad; the Man-God was killed. Some ways of speaking should not be used, not that they may not be rightly explained, but that they may easily be misunderstood in an heretical sense." [Catholic Encyclopaedia, quoted from here.]

 

Well, that clears things up nicely, and no mistake!

 

Nevertheless, at the risk of annoying further those who, even now, are content to stumble about in this Hegelian Haze, the alleged 'unity of opposites' can only be cobbled-together if the predicates "ξ is continuous" and "ξ is discontinuous" are nominalised once more into "continuity" and "discontinuity". Only then can these abstract particulars be put in any sort of relation with one another. But, just as soon as that has been done, these 'terms' cease to be predicates -- either that, or they are no longer general in form (depending, of course, on how this Idealist fairy-tale is finally unpacked; that is, whether it is interpreted as applying to 'things', or only to the Proper Names of 'things').

 

[It is also worth pointing out here that I am not arguing that nothing should be nominalised, only that once that has been done, the logic of any modified terms that are involved changes dramatically. Traditional theorists in general ignored this glaringly obvious fact. They still do. Of course, the problem with nominalised expressions is that they can't be true or false (of anything), whereas predicates can (or, rather, they can be used to generate true or false indicative sentences). In which case, nominalisation in philosophy is invariably a backward step if we want to understand how language works, or we want to draw any valid conclusions.]

 

As noted in Essay Three Part One, and again above, this 'remarkable' a priori 'revelation' about motion is 'true' solely because Hegel's system depends on a 'logical' method he imported from an ancient ruling-class tradition, which systematically distorted ordinary language (and logic) in order to concoct such 'interesting' results -- as Marx noted:

 

"The philosophers have only to dissolve their language into the ordinary language, from which it is abstracted, in order to recognise it, as the distorted language of the actual world, and to realise that neither thoughts nor language in themselves form a realm of their own, that they are only manifestations of actual life." [Marx and Engels (1970), p.118. Bold emphases added.]

 

[On this in general, see here.]

 

Lawler then notes that Hegel's analysis of 'dialectical contradictions' begins with the 'common sense' view of movement and place and proceeds from there (p.29). He adds that it isn't relevant to argue that modern, mathematical definitions of motion are more precise. Or, to be more accurate: that approach would constitute an effective response if it could be shown that:

 

"(1)…there was no valid use of the common-sense categories of place and motion from which the paradox arises; and (2) that no new paradoxes arise from the categories involved in more advanced mathematical interpretations of motion." [Lawler (1982), p.30.]

 

But, (1) above fails to apply since ordinary language doesn't collapse into paradox -– not unless it is bent out of shape, à la Hegel, or à la Zeno -- indeed, as we saw in Essay Five. And (2) only applies if the terminology that mathematicians use is deliberately twisted in like manner, whereby functional expressions are transmogrified, for example, into the Proper Names of 'categories' (so that they now appear to designate 'abstract particulars').

 

Every Magic Trick Requires A Diversion Of Some Sort

 

Lawler then proceeds to divert his readers' attention (once more) with a detour into 'diversity' (no pun intended):

 

"The next step in the development of Hegel's argument in the Logic consists in the 'passage' from the category of 'diversity' to the elementary scientific level of comparison and contrast. Hegel maintains that the (paradoxical) unity of identity and difference in the category of diversity is unstable. The 'tranquil' coexistence of a multiplicity of different things or concepts that appear indifferent to each other is itself untenable. In thinking of reality under the category of diversity, the mind now asserts identity and forgets difference, and then asserts difference and forgets identity. These categories have not yet been satisfactorily grasped in explicit relation to each other. (Scientific) thought, accordingly, is dissatisfied with mere diversity and attempts to find identity in different things (comparison) and differences among 'identical' things (contrast).

 

"Here we see clearly the correlative, and still opposite character of the categories 'identity' and 'difference,' 'at work' in a more productive process of thought than was the case earlier when empty tautological identification seemed to follow from the way in which the category 'identity' was understood. The inadequacy of this method of relating these categories should nevertheless become evident. Although comparison and contrast are two sides of a single movement of scientific thought involved in the classification of objects or concepts, it is again possible to overlook this connection by forgetting that comparison is implicit in contrasting, and conversely. A more serious criticism is that without some objective connection in the objects which are related and opposed, the operation of comparison and contrast may appear to be only a subjective necessity for thought with no real objective content. However, to understand that real content, it is necessary, according to Hegel, to go beyond the level of thoughts involved in comparison and contrast." [Ibid., pp.30-31. Italic emphases in the original.]

 

Again, this argument only appears to work because the (supposed) 'identity' relation and its alleged opposite, 'difference', have been nominalised and turned into 'abstract particulars' (or the Proper Names thereof). They are then unceremoniously lumped together in the 'category' of 'diversity'. But, if these relational expressions aren't 'abstract particulars' (or their supposed names), and can only be turned into them by yet more linguistic 'remodelling', they can't be lumped together in the way Lawler imagines. Conversely, if they are lumped together, then they cease to be relational expressions. Either way, this entire way of looking at these two 'relations' falls apart.

 

While we are at it, how does Lawler know what 'the mind' does or doesn't do? Has he consulted a single psychologist on this? Or is he content merely to be told by that non-psychologist, Hegel, what allegedly goes on 'in our heads'?

 

At this point it could be objected that if we gave some thought to the similarities that exist between objects then we must of necessity forget about their differences, and vice versa, which is all Lawler and Hegel need. [That response was in fact considered earlier.]

 

But, this is just hand-waving in advance of the genuinely magical moves soon to be performed (and from which they serve to distract). But, they aren't even convincing moves. While Empiricist Philosophers -- who, it seems, are perhaps the real target of this impressive display of verbal prestidigitation -- might be guilty of emphasising diversity, attributing 'identity' to a mere 'habit of the mind', no scientist (that is, those who aren't in the grip of a 'philosophical theory' of some sort) would forget about the similarity between the diverse objects of their study. For example, when they are classifying animals into the various genera in the Canidae family, for instance, no competent zoologist would itemise the characteristics that unite them all in that family while forgetting what distinguishes them from other genera, deciding which species are to be collected in the genus Alopex, the genus Lycalopex, or the genus Vulpes, and so on. Hegel might forget this (or develop a bad case of selective blindness, once again), and Lawler's memory could even be a little less secure in this respect, too. That might be why both failed to choose science as a career, but one suspects Carl Linnaeus wasn't quite so anamnetically-challenged.

 

In which case, this isn't even remotely correct:

 

"Although comparison and contrast are two sides of a single movement of scientific thought involved in the classification of objects or concepts, it is again possible to overlook this connection by forgetting that comparison is implicit in contrasting, and conversely." [Ibid.]

 

Be this as it may, and as noted above, all this hand waving is no more than elaborate stage-setting for the main event to come: some sort of description of and justification for the 'logic' underlying Hegel's 'theory of causation', which will 'ratify' an appeal to 'contradictions' as the 'motive force' behind all change and movement in the entire universe. As it turns out, that was the point of this remark:

 

"A more serious criticism is that without some objective connection in the objects which are related and opposed, the operation of comparison and contrast may appear to be only a subjective necessity for thought with no real objective content. However, to understand that real content, it is necessary, according to Hegel, to go beyond the level of thoughts involved in comparison and contrast." [Ibid. Bold emphasis added.]

 

This supposed "connection" will perhaps become a little clearer if we review what I argued in Part Two of this Essay:

 

Exactly why this view of causation depends on necessitation is connected with the points raised in Essay Seven Part Three (concerning Kant and Hegel's response to Hume's criticisms of rationalist theories of causation). There, it was demonstrated that in order to defuse Hume's attack, Hegel had to find a dialectical-logical, and therefore necessary, link between a cause and its effects:

 

Hume had argued that there is no logical or conceptual connection between cause and effect. This struck right at the heart of Rationalism, and Hegel was keen to show that Hume and the Empiricists were radically mistaken. Kant had already attempted to answer Hume, but his solution pushed necessitating causation off into the Noumenon, about which we can know nothing. That approach was totally unacceptable to Hegel, so he looked for a logical connection between cause and effect; he found it in (1) Spinoza's claim that determination is also negation (which, Hegel rendered "Every determination is negation" -- by the way, neither Spinoza nor Hegel even so much as attempted to justify this 'principle' -- more about that in Essay Twelve; on this, see Melamed (2015)), and in (2) His argument that the LOI "stated negatively" implies the LOC (which, unfortunately for Hegel, it doesn't).

 

[LOI = Law of Identity; LOC = Law of Non-contradiction.]

 

Based on this, Hegel was 'able' to argue that for any concept A, "determinate negation" implies it is also not-A, and then not-not-A. [I am, of course, simplifying greatly here! I have reproduced Hegel's argument below for those who think I might have misrepresented him.]
 

This then 'allowed' Hegel to conclude that every concept has development built into it as A transforms into not-A, and then into not-not-A. This move provided him with the logical/conceptual link he sought in causation. Hence, when A changes it doesn't just do so accidentally into this or that; what it changes into is not-A, which is logically connected with A and is thus a rational consequence of the overall development of reality. This led him to postulate that for every concept A, there must also be its paired "other" (as he called it), not-A, its 'internal' and hence its unique 'opposite'. Hegel was forced to derive this consequence since, plainly, everything (else) in the universe is also not-A, which would mean that A could change into anything whatsoever if he hadn't introduced this limiting factor, this unique "other".

 

From these moves was born the "unity of opposites". So, the link between cause and effect was now given by a 'logical' unity, and causation and change were the result of the interaction between these logically-linked "opposites".

 

Plainly, this paired, unique opposite, not-A, was essential to Hegel's theory, otherwise, he could provide his readers with no explanation why A should be followed by a unique not-A as opposed to just any old not-A -- say, B, or, indeed, something else, C, for example -- all of which would also be not-A.

 

So, since B and C (and an indefinite number of other objects and processes) are all manifestly not-A, Hegel had to find some way of eliminating these, and all the rest, as candidates for the development of A, otherwise he would have had no effective answer to Hume.

 

[Hume, of course, wouldn't have denied that A changes into "what it is not", into not-A, he would merely have pointed out that this can't provide the conceptual link that rationalists require unless all the other (potentially infinite) not-As could be ruled out in some way. He concluded that it is only a habit of the mind that prompts us to expect A to change into what we have always, or what we have in general, experienced before. There is no logical link, however, between A and what it develops into since there is no contradiction in supposing A to change into B or C, or, indeed, something else. (In saying this the reader shouldn't conclude that I agree with Hume, or that Hume's reply is successful!)]

 

Hence, as an integral part of his reply, Hegel introduced this unique "other" with which each object and process was conceptually linked -- a unique "other" that was 'internally' connected to A --, something he claimed could be derived by 'determinate negation' from A.

 

[How he in fact derived this "other" will be examined in Essay Twelve Part Five, but a DM-'explanation' -- and my criticism of it -- can be found in Essay Eight Part Three.]

 

This special not-A was now the unique "other" of A. Without it Hegel's reply to Hume falls flat.

 

Engels, Lenin, Mao, and Plekhanov (and a host of other Marxist dialecticians) bought into this spurious 'logic' (several of them possibly unaware of the above 'rationale'; although, as far as I can see, of the DM-classicists, only Lenin seems to be explicitly aware of it!), and attempted to give it a 'materialist make-over'. And, that is why this Hegelian theory (albeit "put back on its feet") is integral to classical DM. It supplied Engels, Lenin and Mao (and all the rest) with a materialist answer to Hume.

 

[There are in fact far better ways than this to neutralise Hume's criticisms, as well as those of more recent Humeans, which do not thereby make change impossible. More details will be given in Essay Three Part Five. Until then, the reader is directed to Hacker (2007), and Essay Thirteen Part Three.]

 

Here is Lenin's open acknowledgement and endorsement of this theory:

 

"'This harmony is precisely absolute Becoming change, -- not becoming other, now this and then another. The essential thing is that each different thing [tone], each particular, is different from another, not abstractly so from any other, but from its other. Each particular only is, insofar as its other is implicitly contained in its Notion....' Quite right and important: the 'other' as its other, development into its opposite." [Lenin (1961), p.260. Lenin is here commenting on Hegel (1995a), pp.278-98; this particular quotation coming from p.285. Bold emphasis added; quotation marks altered to conform with the conventions adopted at this site.]

 

"But the Other is essentially not the empty negative or Nothing which is commonly taken as the result of dialectics, it is the Other of the first, the negative of the immediate; it is thus determined as mediated, -- and altogether contains the determination of the first. The first is thus essentially contained and preserved in the Other. -- To hold fast the positive in its negative, and the content of the presupposition in the result, is the most important part of rational cognition; also only the simplest reflection is needed to furnish conviction of the absolute truth and necessity of this requirement, while with regard to the examples of proofs, the whole of Logic consists of these." [Lenin (1961), p.225, quoting Hegel (1999), pp.833-34, §1795. Emphases in the original.]

 

Lenin wrote in the margin:

 

"This is very important for understanding dialectics." [Lenin (1961), p.225.]

 

To which he added:

 

"Marxists criticised (at the beginning of the twentieth century) the Kantians and Humists [Humeans -- RL] more in the manner of Feuerbach (and Büchner) than of Hegel." [Ibid., p.179.]

 

This shows that Lenin understood this to be a reply to Hume, and that it was integral to comprehending dialectics.

 

It is worth quoting the entire passage from Hegel's Logic (much of which Lenin approvingly copied into the above Notebooks -- pp.225-28):

 

Now this is the very standpoint indicated above from which a universal first, considered in and for itself, shows itself to be the other of itself. Taken quite generally, this determination can be taken to mean that what is at first immediate now appears as mediated, related to an other, or that the universal appears as a particular. Hence the second term that has thereby come into being is the negative of the first, and if we anticipate the subsequent progress, the first negative. The immediate, from this negative side, has been extinguished in the other, but the other is essentially not the empty negative, the nothing, that is taken to be the usual result of dialectic; rather is it the other of the first, the negative of the immediate; it is therefore determined as the mediated -- contains in general the determination of the first within itself. Consequently the first is essentially preserved and retained even in the other. To hold fast to the positive in its negative, in the content of the presupposition, in the result, this is the most important feature in rational cognition; at the same time only the simplest reflection is needed to convince one of the absolute truth and necessity of this requirement and so far as examples of the proof of this are concerned, the whole of logic consists of such.

 

"Accordingly, what we now have before us is the mediated, which to begin with, or, if it is likewise taken immediately, is also a simple determination; for as the first has been extinguished in it, only the second is present. Now since the first also is contained in the second, and the latter is the truth of the former, this unity can be expressed as a proposition in which the immediate is put as subject, and the mediated as its predicate; for example, the finite is infinite, one is many, the individual is the universal. However, the inadequate form of such propositions is at once obvious. In treating of the judgment it has been shown that its form in general, and most of all the immediate form of the positive judgment, is incapable of holding within its grasp speculative determinations and truth. The direct supplement to it, the negative judgment, would at least have to be added as well. In the judgment the first, as subject, has the illusory show of a self-dependent subsistence, whereas it is sublated in its predicate as in its other; this negation is indeed contained in the content of the above propositions, but their positive form contradicts the content; consequently what is contained in them is not posited -- which would be precisely the purpose of employing a proposition.

 

"The second determination, the negative or mediated, is at the same time also the mediating determination. It may be taken in the first instance as a simple determination, but in its truth it is a relation or relationship; for it is the negative, but the negative of the positive, and includes the positive within itself. It is therefore the other, but not the other of something to which it is indifferent -- in that case it would not be an other, nor a relation or relationship -- rather it is the other in its own self, the other of an other; therefore it includes its own other within it and is consequently as contradiction, the posited dialectic of itself. Because the first or the immediate is implicitly the Notion, and consequently is also only implicitly the negative, the dialectical moment with it consists in positing in it the difference that it implicitly contains. The second, on the contrary, is itself the determinate moment, the difference or relationship; therefore with it the dialectical moment consists in positing the unity that is contained in it. If then the negative, the determinate, relationship, judgment, and all the determinations falling under this second moment do not at once appear on their own account as contradiction and as dialectical, this is solely the fault of a thinking that does not bring its thoughts together. For the material, the opposed determinations in one relation, is already posited and at hand for thought. But formal thinking makes identity its law, and allows the contradictory content before it to sink into the sphere of ordinary conception, into space and time, in which the contradictories are held asunder in juxtaposition and temporal succession and so come before consciousness without reciprocal contact. On this point, formal thinking lays down for its principle that contradiction is unthinkable; but as a matter of fact the thinking of contradiction is the essential moment of the Notion. Formal thinking does in fact think contradiction, only it at once looks away from it, and in saying that it is unthinkable it merely passes over from it into abstract negation." [Hegel (1999), pp.833-35, §§1795-1798. Bold emphases alone added. I have used the on-line version here, correcting a few minor typos.]

 

The most relevant and important part of which is this:

 

"It is therefore the other, but not the other of something to which it is indifferent -- in that case it would not be an other, nor a relation or relationship -- rather it is the other in its own self, the other of an other; therefore it includes its own other within it and is consequently as contradiction, the posited dialectic of itself." [Ibid. Bold emphases alone added.]

 

This "reflection", as Hegel elsewhere calls it, of the "other in its own self", a unique "other", provides the logical link his theory required. Any other "other" would be "indifferent", and not the logical reflection he sought. It is from this that 'dialectical contradictions' arise, as Hegel notes. Hence, Lenin was absolutely right, this "other" is essential for "understanding" dialectics -- except he forgot to mention that dialectics is in fact rendered incomprehensible and unworkable as a result!

 

Hegel underlined this point (but perhaps less obscurely) in the Shorter Logic:

 

"Instead of speaking by the maxim of Excluded Middle (which is the maxim of abstract understanding) we should rather say: Everything is opposite. Neither in heaven nor in Earth, neither in the world of mind nor of nature, is there anywhere such an abstract 'either-or' as the understanding maintains. Whatever exists is concrete, with difference and opposition in itself. The finitude of things will then lie in the want of correspondence between their immediate being, and what they essentially are. Thus, in inorganic nature, the acid is implicitly at the same time the base: in other words, its only being consists in its relation to its other. Hence also the acid is not something that persists quietly in the contrast: it is always in effort to realise what it potentially is." [Hegel (1975), p.174; Essence as Ground of Existence, §119. Bold emphases added.]

 

[The problems these rather odd ideas in fact create for Hegel have been highlighted here.]

 

Hence, any attempt to (1) Eliminate the idea that change results from a 'struggle of opposites', or (2) Deny that objects and processes change into these 'opposites', or even (3) Reject the idea that these 'opposites' are 'internally'-related as one "other" to another specific "other", will leave DM-fans with no answer to Hume, and thus with no viable theory of change.

 

[For Hegel's comments on Hume, see Hegel (1995b), pp.369-75.]

 

In which case, Hegel's theory (coupled with the part-whole dialectic) was at least a theory of causation, change and of the supposed logical development of history; so the above dialecticians were absolutely right (as they saw things) to incorporate it into DM. It allowed them to argue that, among other things, history isn't accidental -- i.e., it isn't just 'one thing after another' -- it has an inner logic to it. Hence, Hegel's 'logical' theory enabled them to argue, for example, that capitalism must give way to the dictatorship of the proletariat, and to nothing else. Hume's criticisms -- or, rather, more recent incarnations of them (which, combined with contemporary versions of Adam Smith's economic theory (Smith was, of course, a close friend and collaborator of Hume's) in essence feature in much of modern economic theory and large swathes of contemporary philosophy, and thus in criticisms of Marx's economic and political theory) -- are a direct threat to this idea. If these bourgeois critics are right, we can't predict what the class struggle will produce. Or, rather, if Hume is right, the course of history is contingent, not necessary, not "rational" -- and there is no 'inner logic' to capitalism.

 

[This dependency on Hegel's theory of causation and change also supplies us with an explanation for the implicit teleology and determinism apparent in DM, providing its acolytes with hope in a hopeless world. More on this in Essays Nine Part Two and Fourteen Part Two. The mystical and rationalist foundations of this approach to change are outlined here, here, here and here.]

 

As far as I can tell, other than Lenin, very few dialecticians have discussed (or have even noticed!) this aspect of their own theory. The only authors that I am aware of who take this aspect of DM into consideration are Ruben (1979), Lawler (1982), and Fisk (1973, 1979). I will examine Fisk's arguments, which are the most sophisticated I have so far seen (on this topic), in other Essays published at this site. Lawler's analysis is the subject of Essay Eight Part Three. [However, since writing this I have also come across some of Charles Bettelheim's comments that suggest he, too, understood this point.]

 

Incidentally, this puts paid to the idea that there can be such things as 'external contradictions' (a notion beloved of STDs and MISTs). If there were any of these oddities, they couldn't be 'logically' connected as 'one-other-linked-with-another-unique-other' required by Hegel's theory. For Hegel, upside down or the 'right way up', this would fragment the rational order of reality, introducing contingency where once there had been 'logico-conceptual' or 'necessary' development. Hence, any DM-fan reckless enough to introduce 'external contradictions' into his or her system/theory would in effect be 're-Hume-ing' Hegel, not putting him 'back on his feet'! In which case, it is no surprise to find that 'external contradictions' were unknown to Hegel, Marx, Engels, Lenin and Plekhanov.

 

[STD = Stalinist Dialectician; MIST = Maoist Dialectician.]

 

[I have analysed several other fatal defects implicit in the idea that there can be 'external' and/or 'internal contradictions' (in nature or society) in Essay Eleven Part Two, here and here. See also here, where I develop the above argument in response to a 'Marxist-Leninist' who seems not to know his own theory.]

 

The above helps explain why Lawler then went on to make the following point, which, it seems to me, is aimed directly at empiricists like Hume -- hence his comment about "correlational methodology" --, who wanted to turn the 'objective' relations (that were presumed by Rationalists to be "necessary" and to exist in 'external reality') into subjective impressions:

 

"The relations implicit in scientific thought, if they are not to be simply arbitrary, must be founded on relations in reality. Definitions in thought can only be real definitions if they are based on 'definitions' in reality. The most fundamental level of scientific thought is reached when we grasp how things determine themselves, or, the real interconnections and processes in which things become what they are. Hegel essentially distinguishes here between correlational methodology, which aims at finding regular relations between separate phenomena, and theoretical explanation, which attempts to discover the actual 'mechanisms' whereby real interacting phenomena occur.

 

"Just as thought is not content with enumerating a diversity of things, so the process of comparison and contrast cannot be satisfactory if the relations are between any objects. Such comparison and contrast of a thing with any other thing, as is implied by the abstract concept of identity, will not do for real thought, which, Hegel says, attempts to banish the apparent indifference of one thing to another and to discover necessary relations in which things in fact 'define themselves' and relate to their own determinate 'other'. The object, Hegel writes,

 

'is seen to stand over against its other. Thus, for example, inorganic nature is not to be considered merely something else than organic nature, but the necessary antithesis to it. Both are in essential relation to one another; and the one of the two is, only in so far as it excludes the other from it, and thus relates itself thereto.'" [Lawler (1982), p.31. Bold emphasis alone added. Lawler is in fact quoting Hegel (1975), p.174, §119 and not Hegel (1999), as Lawler mistakenly asserts!]

 

Here, at last, we see the point of the whole exercise; all that has gone before was good old-fashioned window dressing.

 

Even so, it is worth noting that the antithesis Hegel drew between organic and inorganic matter/nature is surely invalid. If he were right, inorganic matter/nature can't have existed before organic molecules evolved -- otherwise there would have been on such antithesis! Moreover, the currently postulated 'heat-death of the universe', must also mean that inorganic and organic matter must survive, since they would otherwise have no unique 'other'! With or without this 'heat death', inorganic and organic matter/nature must be eternal, and for the same reason.

 

[I will return to make a similar point, below.]

 

The Real Main Feature

 

Hey Presto! A Non-Hat Out Of A Non-Rabbit

 

As we approach the denouement of this elaborately staged stage act -- i.e., the attempt to supply some sense to the Noun Phrase "dialectical contradiction" -- Lawler confronts those who think that Hegel:

 

"…illicitly passed from the fact that an object relates to some other object, and the consequent need to include this relation to another object in either the definition or the description of the first object, to a theory that the being of the first object includes the being of the second. And if the second is something that is not-A, the definition of the relating being should be expressed in the logically contradictory form, 'A and not-A.'" [Lawler (1982), p.32. Italic emphases in the original. Bold added.]

 

Well, how does Lawler answer sceptical questions about this non-contradiction?

 

[Yes, you read that correctly; "A and not-A" isn't a contradiction -- unless, that is, Lawler abandons the idea that "A" is an "object", or the Proper Name thereof, and decides to interpret it as a proposition or propositional variable. But, as soon as he does that, it can stand in no relation to anything, least of all itself, since propositions aren't objects nor yet their Proper Names.]

 

He does so as follows:

 

"One might readily grant that the definition of A includes A's relating to something that is not A (some non-A which is not-A). This does not mean that non-A or what is not-A is a part of A or part of A's identity. Such a position would lead to regarding all interacting beings as constituting essentially one being. Only the relation to non-A (not-A) seems to be a property of A -- not non-A or not-A itself. Hegel clearly wants to claim more than this. To understand dialectical 'identity' it is necessary to recognize the insufficiency of the abstract concept of 'identity'. Despite Hegel's detailed critique of this category, critics commonly persist in interpreting dialectical contradiction as the assertion of the undialectical identity of A and not-A." [Ibid., p.32. Italic emphases in the original; bold added. We have already seen that Hegel and Lawler's sloppy use of language does indeed imply this, and that this is how subsequent Marxists have interpreted him. After all what else is the DM-doctrine, 'the identity of opposites'? Even Lawler half-recognises that this is an implication of this theory. On that, see the next section]

 

We note once again that none of this works without the Hegelian/traditional confusion of relations with properties, names, predicables and propositions.

 

And, while we are at it, what exactly is the difference between "not A" and "not-A" (or even "non-A")? If the first "not" is (or expresses) a sentence-forming operator, which maps a sentence onto its 'negation', we are surely on firmer ground. But, that can't be the case with "not-A", which Lawler clearly sees as an object of some sort --, an "entity" --, but this "entity" he also regards as somehow the 'same as' "not A". Unfortunately, this now means that the second "not" (in "not A") can't now be a sentence forming operator, as was originally surmised. In fact, and to be honest, one suspects that Lawler has confused a sentential use of these letter "A"s with a phrasal (or predicate term) operator -- or worse, he sees no problem with sliding effortlessly between the two. [On that, see here.]

 

Unity Of Opposites?

 

Now, as Lawler proceeds to 'explain', Hegel rejects the open insertion of "not-A" for "A" (which, if that were correct, would in fact be bad news for Diabolical Logicians -- as we saw in Essay Four), and he quotes in support a quintessentially obscure passage (from Hegel's Shorter Logic) that seems to be devoid of all earthly sense:

 

"Substance, as the universal negative power, is as it were a dark shapeless abyss which engulfs all definite content as radically null, and produces from itself nothing that has a positive subsistence of its own." [Hegel (1975), p.215, §151.]

 

Well, as we saw in connection with the Christian doctrine of the Incarnation of Christ, that sorts things out nicely!

 

[In fact, the above passage is clearly an echo of Hegel's infamous attempt to derive 'nothing' from 'being', which will be taken apart in Essay Twelve Part Five.]

 

Lawler continues:

 

"If we grant that A's identity involves its necessary relation to what is not-A, and that this not-A is 'its own other' -- a definite other being and not any being whatsoever -- and that this relation to some definite other is necessary for the existence of A or is essential to the constitution of A (A's identity), it seems reasonable to look for some 'imprint' of this 'other' in A, so that in some sense not-A is internally constitutive of A. The internal structure of an entity should be investigated, according to this schema, not as something that stands alone, in isolation, but as 'reflecting' in various forms its necessary relations to its environment. In other words, to understand the internal nature of A it is necessary to study the determinate not-A not only as a necessary external condition but as 'reflected' in A. This is not to say that one should expect to find in A some direct or immediate duplication of not-A. The direct identity of A and not-A would constitute the annihilation of the beings involved. Short of this 'abstract identity,' however, the dialectical theory of the unity of identity and difference suggests a different general schema for understanding things in their necessary relations. A is not to be conceived of as already formed, but as coming into being through its relation to not-A. The necessary relation of A to not-A is thus 'internal' to the constitution of A and should be regarded as necessarily reflected in A's identity." [Lawler (1982), pp.32-33. Bold emphases alone added.]

 

This represents Hegel's way of:

 

"[D]iscover[ing] necessary relations in which things in fact 'define themselves' and relate to their own determinate 'other'." [Ibid., p.31. Italic emphases in the original.]

 

Bemused readers will no doubt wonder how "The necessary relation of A to not-A is...'internal' to the constitution of A and should be regarded as necessarily reflected in A's identity" fails to imply the "identity of A and not-A." Again, as we have seen, that is precisely how leading DM-theorists have understood Hegel. Lawler appears to think that if he plasters the magical words "dialectical"/"undialectical" all over this conundrum that that will be an effective response to Hegel's critics, in the following way: "critics commonly persist in interpreting dialectical contradiction as the assertion of the undialectical identity of A and not-A".

 

This is uncannily reminiscent of the way that heroes of yesteryear used to escape impossible, life-threatening predicaments: all a lazy author had to do was add a "With one leap Jack was free" comment, and with that wave of the hand our hero escaped.

 

In relation to that we read:

 

"The title of this article refers to what's generally considered sloppy story telling. Your characters end up in some seemingly impossible situation and then with no explanation beyond saying something like 'and suddenly they were free' they manage to get away unscathed. This is a really good way to annoy your readers as they're left wondering what actually happened, but it's an easy trap to slip into if you're not careful. A similar situation arises when a character picks up an essential tool or weapon which has never been mentioned before, or suddenly reveals a key skill the reader never knew they had until the very moment they need to use it to escape." [Quoted from here; accessed 29/05/2022.]

 

But that is precisely what Lawler's sleigh-of-hand sought to achieve when he deployed the secret weapon, "dialectical contradiction" -- and so "With one bound Hegel was free!" But, even if sceptical readers were prepared to give handy escape scenarios like this a pass, the magical phrase itself is still in want of explanation and so can't be used to explain anything else.

 

Even so, is there any evidence that nature itself sees things this way? Lawler thinks there is:

 

"...At any rate, it seems obvious that living beings, which are normally contrasted with nonliving beings, are nevertheless internally composed of non-living elements, transform nonliving sources of energy into living forms and break down ultimately into nonliving components. Thus, beyond contrastive opposition in thought, and a corresponding (external) 'interaction in reality', there appears to be room for 'inner interconnections' which do not amount to dissolving all definite entities into one dark abyss." [Lawler (1982), p.33. Italic emphases in the original.]

 

Now, as we saw earlier and in Essay Seven Part One, this example of homespun, neo-Romantic pseudo-science won't wash -- but note here the confusion Lawler shares with other DM-theorists between "internal" (meaning "logically internal") and "internal (meaning "spatially internal") highlighted in Essay Eight Part One. Unfortunately for Lawler and Hegel, there is no intrinsic difference between living and non-living matter, so the alleged contrast he draws is entirely bogus. In fact, the above words are more an expression of the obscure ideas found in mystical vitalism -- which were, of course, prominent in Hegel's day -- than they are an accurate reflection of living things themselves.

 

But, what should we say of lifeless matter as it was before life evolved? Back then there was nothing with which it could be 'contrasted'; it had no "other". Did that mean lifeless matter had no 'identity', no 'Being'? Did it gain an 'identity' only when the first living things evolved? In that case, was life (logically?) bound to evolve just to help provide an 'identity', a unique "other", for non-living things? (But how could that have happened if change can only occur because there exist such 'dialectical opposites', which, as we have just seen, don't exist yet?) Indeed, does this classic example of a priori superscience mean that life in the universe can't (logically can't) ever cease, otherwise lifeless matter will once again lose its 'identity'?

 

Taking this a step further, should we not now postulate the existence of non-material beings (spirits) to help identify material beings? Surely, on this view, 'spirit-matter'/'spirit-substance' must exist somewhere if all things, including ordinary matter, are to have an 'identity' only in and because of such a unique "other"? Have we not now found a perfect argument for the existence of 'God'?

 

And we had better not ask what the "other" of the universe is. [To be sure, Hegel thought he had an answer to this pointless conundrum, but the hot air will be let out of that metaphysical balloon in Essay Twelve.]

 

However, it is plain that none of this make a blind bit of sense if 'conscious minds' are removed from the equation. Even if it were admitted for the purposes of the argument that the following is 100% correct:

 

"If we grant that A's identity involves its necessary relation to what is not-A, and that this not-A is 'its own other' -- a definite other being and not any being whatsoever -- and that this relation to some definite other is necessary for the existence of A or is essential to the constitution of A (A's identity), it seems reasonable to look for some 'imprint' of this 'other' in A, so that in some sense not-A is internally constitutive of A," [Ibid.]

 

it would still be unclear how any of it affects what happens extra-mentally? Even lf it were true that in order to specify A's identity, its "other" -- a unique and logically connected not-A -- must be taken into account, how does that effect what happens in nature? Does the universe itself have to do any of this 'identifying'? Do any of the objects and events in nature have to do any? If not, precisely who does all this identifying? And who did it before sentient life evolved?  From those questions alone it becomes plain that this entire argument gains what limited plausibility if might appear (to some) to have -- and only if we wave aside all the objections aired above and below -- if what happens in the mind has ontological implications for what occurs in nature. That is, if we accept some form of 'objective idealism'.

 

Now, this might have made sense to a mystic like Hegel, but it can surely make no sense to a historical materialist.

 

At this point, it could be objected that Marx in fact had an answer:

 

"My dialectic method is not only different from the Hegelian, but is its direct opposite. To Hegel, the life process of the human brain, i.e., the process of thinking, which, under the name of 'the Idea,' he even transforms into an independent subject, is the demiurgos of the real world, and the real world is only the external, phenomenal form of 'the Idea.' With me, on the contrary, the ideal is nothing else than the material world reflected by the human mind, and translated into forms of thought." [Marx (1976). p.102. Quotation marks altered to conform with the conventions adopted at this site. Link and bold emphasis added.]

 

And yet, how are dialecticians going to show there is a logical connection between events in the real world without giving ground to some form of Idealism? If what takes place in the mind, according to Marx, is but a reflection of what happens in the material world (one presumes these 'reflections' must be processed in some way, since no one before Hegel spilled the beans saw things this way, and relatively few have done so since!), then there must be necessary connections out there, first, in the material world, if they are to be 'reflected' internally, second. However, as we will see in Essay Thirteen Part Three, DM-fans have yet to come up with convincing reasons to suppose this is the case, that there are any such logical or 'necessary' connections between events. [Readers are referred to that Essay for more details.]

 

In that case, we might need to understand 'dialectical negation' a little better so that the above materialist impertinences might safely be ruled out. Fortunately, Lawler is ready to help (which he does in more detail in the next sub-section where he attempts to show there are just such 'necessities' in 'extra-mental reality'):

 

"The crucial issue does not seem to be how necessary relations to specific entities involve some form of 'reflection' of the 'other' in the relating entity. It is the problem of understanding this necessary relation and internal constituting activity as one involving negativity. This is the respect in which 'interaction' becomes 'contradiction.'" [Ibid., p.35.]

 

At last we are beginning to see a little less darkness at the end of the tunnel, for now we are in a position to understand how "negativity" and "interaction" relate to those elusive 'dialectical contradictions':

 

"It is one thing to say that to understand organic processes one must understand their systematic connection with and 'internalization' of inorganic processes, and another thing to argue that this relationship involves opposition or 'contradiction.' Starting with a picture of the world as consisting of 'diversity' -- the juxtaposition of A and indifferent non-A's -- Hegel attempts to arrive at a view of interconnecting beings in which the negativity reflected in our mental distinctions, contrasts, and comparisons is regarded as a real feature of the entities themselves." [Ibid., p.35. Italic emphases in the original.]

 

Maybe so, but it would have been an even better idea if Hegel had made a more concerted attempt to consider how we actually speak about medium sized dry goods and the like (indeed, as he himself must have spoken about them in his day-to-day affairs), instead of imposing on 'thought' a form which is really only of interest to members of the ruling-class and their hangers-on.

 

Well, maybe not Hegel, but certainly Lawler should.

 

Except, had Hegel done that he wouldn't have been able to spin any of his convoluted dialectical fairy-tales since ordinary speakers don't confuse predicate expressions with 'beings', sentences with objects, objects with relations, or "not" with 'negativity', in their everyday use of language.

 

But, even if they were to do so (but, on that, see here), this would only have ontological implications for Idealists.

 

The Magical Use Of 'Negation'

 

But, is this once again being a little too hasty? We are about to find out:

 

"In the first place, negation cannot be understood in the formal sense, according to which the existence of some entity implies the nonexistence, pure and simple, of another." [Ibid., p.35. Bold added.]

 

The ripe old fun we had at the expense of assorted LCDs (in Essay Four) was perhaps a little too hard on them, for here we find an HCD like Lawler committing all the usual sophomoric errors we have come to associate with this backwater of sub-Aristotelian 'logic'. What the dialectics has the "formal" sense of negation got to do with 'nonexistence'? Precisely what non-existence of which entity does the following pair of sentences imply: "Blair owns a copy of Hegel's Logic" and "Blair doesn't own a copy of Hegel's Logic"?

 

With such 'logic', when someone, for instance, says you don't own the Taj Mahal, they must mean that amazing building has just disappeared. Indeed, if you want to get shut of your neighbour's tall trees (that are maybe blocking your daylight), just try saying to yourself that you don't own those trees. If that doesn't inspire you, then maybe reflect on the fact that Tony Blair isn't a socialist.

 

Problem solved...

 

Would that it were quite that easy to consign Hegel's confused book (or, indeed, Blair) to Logical Limbo!

 

But, the above use of "not" isn't an example of "formal negation", I hear someone say. That is undeniable. In that case, we should perhaps consider the following question: What 'non-existence' is implied by ¬p? Of course, it is impossible to say before symbols like this have been interpreted. But, as soon as that has been done, the negative particle ceases to be formal! In which case, it is impossible to make sense of Lawler's "negation cannot be understood in the formal sense".

 

It could now be objected that if Blair doesn't own a copy of the said book then it doesn't exist on his shelves, or in his possession. So, non-existence is implied after all.

 

But, is it? Isn't it possible that even though Blair doesn't own a copy of the said book, it still sits on his shelves because he borrowed one from the library or from a friend, or he was sent a copy by the publishers for him to review? Even if it were true that Blair doesn't own that book, it doesn't imply it isn't on his shelves or in his possession. So, the proposition "Blair does not own a copy of Hegel's Logic" does not of itself imply the non-existence of anything.

 

Someone could now object that the sentence "There is no copy of Hegel's Logic anywhere in Blair's house, office, car, garage, potting shed, or any property he owns" --  this use of negation does imply nonexistence, the nonexistence of a copy of that book in any property owned by Blair.

 

Not so fast! Nonexistence here is built into that sentence by the use of a quantifier expression qualifying a general noun -- i.e., "no copy" -- not the use of the negative particle itself. So, no wonder it is implied by that sentence -- which we can see when it is expanded into what it is really saying: "There isn't a copy of Hegel's Logic in any property owned by Blair." The use of a quantifier expression that explicitly implies non-existence hardly shows that non-existence is implied by negation as such! Indeed, we can achieve the same result by using a sentence with no negative particle anywhere in that sentence. For example: "Everything Blair owns has just been blown to pieces." That sentence implies the non-existence of the said book in anything Blair owns, but there is no negative particle anywhere in sight.

 

And while we are at it, the non-existence of precisely what is implied by the actual existence of, say, the Eiffel Tower? Of course, it could be argued that had the Eiffel Tower never been built, something else would occupy its place, which, of course, 'it' now does not. So that 'it' does not exist. But, this "something else" could still exist somewhere else. The very best such an argument could establish is that the presence of the Eiffel Tower where it is in Paris prevents anything else occupying the same space, not that 'it' (this vague 'something') cannot, or does not, exist.

 

However, given the complexities involved in our use of the word "place" (on that, see Essay Five), not even this is as secure an inference as it might seem at first sight. For example, someone could itemise the Eiffel Tower first in their list of favourite structures, and then The Great Pyramid first in their list of places to visit. Here, these two structures, or their names, would then occupy the same place in both columns -- namely, first in each list -- at the same time. And this doesn't even involve the use of their names (i.e., their physically written names), since both lists could be committed to memory. In that case, we would have two things in the same place at the same time.

 

Someone could object that the above example in fact concerns the appearance of two names in two lists (wherever those lists were situated), not the structures themselves. Maybe so, but this example was quoted merely to show that two objects (names, or whatever) can occupy the same place at the same time; hence the occupancy of one does not always imply the non-occupancy of the other. That being so, Lawler's argument is defective.

 

Someone could still object, arguing that no two items could occupy the same place in the same list at the same time. [Unfortunately, only those who accept the validity of the LOI are allowed to advance that objection, and thus use the phrase "same list" or "same time"!] But, even if that were the case (and there is good reason to suppose it isn't, but I will let that pass for now), it is worth recalling that the above counter-example (concerning those two names) was only cited to show that Lawler's inference isn't safe, since there are examples where one object doesn't always imply the non-existence of others (using his way of expressing things). For his argument to work, it must always do this.

 

It could be countered that the material that constitutes the Eiffel Tower -- in that it has been used to make this structure -- could have been used to make something else, which, as a result does not now exist. Indeed, but then that "something else" could have been made by other materials. Now, we could go on like this for some time, arguing that the material constituting this "something else" -- in that it has been used to make this "something else" -- denies the existence of yet another "something else", and so on..., but that won't save Hegel, or Lawler. That is because, concerning any object that is allegedly denied existence in this way, we can always substitute another that might have existed in its place, ad infinitem. With such airy-fairy fancies, after all, anything goes -- not just in the construction of such fancies, but in their repudiation, too.

 

[LOI = Law of Identity.]

 

And, even if two contradictory sentences could be found that did imply that something or other did not exist (if something else did), what would that have to do with formal negation in general, as opposed merely to a particular instance of ordinary negation?

 

Of course, ordinary negation is very complex -- on that, see Horn (1989/2001) -- but, formal negation is the result of either (i) the use of sentence-forming or (ii) clause-forming, operators, both in a formal language. That's it! Anything else ain't formal negation, howsoever much this "anything else" allows this virulent strain of Hermetic Herpes to proliferate. [So-called "predicate term negation" will be ruled out of court in Essay Twelve Part Five -- but even if that ruling were quashed on appeal for some reason, it isn't too clear how it might be of assistance to Hegel, or Lawler.]3a

 

However, Lawler doesn't appear to mean the exclusion of other objects (in this way). He has in mind something a little more specific, and inter-active:

 

"In the first place, negation cannot be understood in the formal sense, according to which the existence of some entity implies the nonexistence, pure and simple, of another. [We have just seen that neither 'formal negation' nor ordinary negation imply this -- RL.] And yet intuitively we recognize in real life some entities do destroy others, or less radically, they 'clash,' collide or struggle. It is common to regard such practical negativity as external or accidental to the nature of the entity or entities involved. The entities are regarded as in themselves self-subsistent 'positives' which may 'interact,' modify, and sometimes interfere with or destroy one another." [Ibid., pp.35-36. Bold added.]

 

If so, the mere existence of one object does not automatically imply the non-existence of another. If it did, there would be nothing for A to struggle against or interfere with, would there? So, it would seem that this odd form of negation would make the existence of 'dialectical opposites' (i.e., 'not-A', where the 'not' here is understood 'dialectically') impossible. [I return to this topic again, below.]

 

Lawler continues:

 

"To place negativity within the framework of necessarily related beings, however, it is necessary to conceptualise negativity differently and paradoxically. It is necessary to say that the negative or destructive tendency is not extrinsic to the connections that positively constitute the beings involved, but are (sic) (also) intrinsic to that constitution. The negativity is not an unfortunate by-product, which one might possibly eliminate, of the positive relations necessary for the thing's development. It is intrinsic to that positive connection." [Ibid., p.36. Bold added.]

 

There are so many things here that Lawler simply takes for granted he stands in danger of being indicted on a conceptual robbery charge.

 

What has a "clash" got to do with 'negativity', or even with negation? And what has 'intuition' got to do with recognising the destructive aspects of nature? And do we really have to accept the idea that such features are internal (intrinsic), but reject the claim that they are external (extrinsic)? All we are given here (by Lawler) are a few manufactured terms-of-art that he (following Hegel) says mean that objects are related to their significant "others" in a quirky, 'dialectical' sort of way. On examination, all of them turn out to be part of a motley collection of words with an ill-defined "not" attached to them, and nothing more. So, apart from an appeal to yet more sloppy logic, there is nothing to indicate that these 'internal relations' are any more real than Gryphons and Harpies.

 

Perhaps because he recognises the bogus nature of this derived-out-of-thin-air sort of 'necessity', Lawler now retreats into the subjunctive mood:

 

"Hegel's procedure in advancing this position may be open to criticism to the extent that he attempts to deduce (idealistically) necessary 'inner negation' in reality from an analogous process in thought. However, such dialectical negation may nevertheless be real and the dialectical negativity characteristic of certain thought processes may also characterise extra-mental processes." [Ibid., p.36. Bold emphasis added.]

 

But, the "dialectical negativity" of "certain thought processes" is about as genuine as a $17 bill (even if we knew what the obscure phrase, "dialectical negativity", meant!). So, unless the universe is itself as logically-challenged as this passage clearly is, such 'innovative' reasoning will find no easy correlate in nature.

 

[Perhaps Lawler has access to the missing container-loads of evidence that went 'walk-about' soon after Lenin made similar, but even more grandiose claims over a century ago, and that lend 'support' to such hyper-bold claims?]

 

Well, here it is; here is the missing 'evidence' -- and, surprise, surprise --, it is just as watery-thin and unimpressive as the 'data' produced in support of the sort of Mickey Mouse Dialectical Superscience we met in Essay Seven Part One (much of it having been scraped-together by Engels and the aforementioned conceptually-'challenged' LCDs):

 

"Thus we intuit a negative side to the relation of living beings to the non-living environment. Gravitational, electromagnetic, geological, meteorological, solar, etc. forces constitute obstacles to the development of life as well as necessary conditions. The fact that certain optimal conditions of inorganic processes are required for life to evolve does not mean that the negative forces which otherwise would have prevented the appearance of life have simply ceased to exist. Rather, the optimal conditions permit them to be 'surmounted' or 'overcome,' but not eliminated. Moreover, this 'surmounting' of the negative life-destroying forces of the environment is intrinsic to the development of life. Life can only develop by 'repelling' the negative forces of its environment -- by 'negating its negation.'" [Ibid., p.36. Bold emphases added.]

 

We have already seen (in Essay Eight Part Two) that this way of depicting forces doesn't work howsoever they are re-packaged. Even so -- and flowery language to one side --, the forces at work here are all manifestly external. There are no 'internal relations' (except, of course, those conjured into existence by yet more Hegelian Hocus Pocus and dogmatic imposition).

 

And, like it or not, life arose because of the operation of real material, causal factors at work in nature, not logical principles inherent in Hegel's 'concepts' (upside down or 'the right way up').

 

But what, we might ask, has become of those eternally-malleable letter "A"s, which were said to have one, and only one, "other"? Wonder no more:

 

"A's identity involves its necessary relation to what is not-A, and that this not-A is 'its own other' -- a definite other being and not any being whatsoever -- and that this relation to some definite other is necessary for the existence of A or is essential to the constitution of A (A's identity)…." [Ibid., p.32. Italic emphases in the original; bold added.]

 

That is puzzling, to say the least. We have just been informed there are numerous "forces" that oppose life. So it seems that life must be exempt from the Hegelian caveat -- that each object or event has a 'unique other' --, since it appears to have hundreds, if not thousands, of them. Of course, that depends on how we differentiate or count forces. For example, is each molecule of Carbon Monoxide, or Ozone, or Chlorine, or Phosgene, or Hydrogen Cyanide a single opposing force, or do they count as many? Perhaps they work in gangs? Is every poison a separate force that opposes life? Or are they all to be lumped together as a sort of collective 'unique other'? What about other lethal forces, like extreme cold or a raging fire? What about tsunamis, avalanches, earthquakes, landslides, icebergs, volcanoes and meteor strikes (like the one that we are told wiped out the dinosaurs)? What of the countless bacteria and viruses that can cause death (and not just to humans)? What of diseases like cancer, heart attacks, strokes, diabetes, and multiple sclerosis? Are car crashes part of this 'dialectical assault' on life? If so, what about other accidental causes of death, like falling off a ladder, drowning, electrocution or medical incompetence? What about the deliberate taking of life, say, by the cops, the US Marines, the Saudi execution machine, or a drone strike? Is each natural predator (wolves, lions, tigers, sharks, etc.) to be counted? If so, are herbivores to be lumped in or left out? Or is plant life exempt? Do serial killers count as 'dialectical enemies' of life? And, what about suicide? Do successful attempts imply that those who take their own lives are their own 'unique others'?

 

Once more: so many questions, so few answers...

 

Of course, we mustn't be foolish and expect answers to such impertinent questions. After all, we are dealing here with Mickey Mouse Superscience, where any request for detail is labelled "pedantry", "semantics" or "academic nit-picking".

 

Fortunately, Lawler does have an answer (of sorts):

 

"For the same reasons that we argued for the 'imprint' of the 'other' in an entity chosen for study, we should expect to find an imprint within the entity of this opposition that exists between entities. For example, the internal process of growth is opposed by excessive heat -- a physical or inorganic force. Growth must surmount this force which tends to inhibit or suppress growth. Extreme temperatures would prevent life altogether. At the same time, growth is dependent upon heat. Systems of temperature self-regulation develop whereby the negative effects of heat are, within limits, negated while the positive effects are absorbed. Normally we think of heat as having positive effects within certain ranges and negative effects outside of those ranges. But even within the 'positive' range, heat would still be destructive without the heat-regulating mechanism of the organism.... Thus, even within optimal ranges heat tends to negate life." [Ibid., pp.36-37. Italic emphasis in the original; bold added.]

 

But, what "imprint" does a meteor strike imply? Or an earthquake? And is there a different "imprint" for each virus type? If so, there must be countless trillions of such "imprints" now that we know there are more (vastly more!) different strains of virus out there than there are stars in the entire universe:

 

"An estimated 10 nonillion (10 to the 31st power) individual viruses exist on our planet -- enough to assign one to every star in the universe 100 million times over." [Quoted from here; accessed 30/05/2022. Link in the original.]

 

Of course, not all those viruses are lethal or a threat to life (human, animal or plant), but that is surely because life can fend them off because it has an "imprint" for each. Why then do we need vaccines?

 

But, where is heat itself (not its regulation), heat itself "imprinted" in a cell? And, where are cells "imprinted" in heat? Or, does "imprinting" only work one way? Where, indeed, is the cell's 'regulation force' "imprinted" inside heat? And what has happened to heat's own "other", cold?

 

Of course, heat isn't a force; the word is, in such contexts, merely shorthand for the energy we accredit to certain molecules. Hence, it is even more difficult to see how the vibrational energy of, say, a Carbon-Carbon bond could be the unique "other" of..., well what? And, isn't heat simply our subjective impression of molecular motion (which was unknown in Hegel's day)? Shouldn't, therefore, its opposite, its 'other' be no motion at all? Disappointingly, Lawler is silent on this important issue, as, indeed, are other DM-fans -- perhaps wisely so.

 

Furthermore, cells have to regulate more than just heat; homeostasis is maintained inside cells by a variety of processes. In that case, we are forced to ask: Do cells have several (perhaps countless) significant ('internal') "others"?

 

Despite this, the processes Lawler describes are all causal. So, there are no Hegelian concepts here for Biophysicists to study. Even less surprising in the fact that, as far as is known, no PhD thesis has ever been commissioned to study these Hegelian fantasies scientifically -- not even by Haldane, Bernal, Levins, Lewontin or Rose. [If anyone knows of one, please e-mail me with the details!]

 

Nevertheless, this might be to miss the point:

 

"The expression 'tends to' has been used advisedly, since 'full' realisation of a dialectical negation would amount to the destruction of both external and internal conditions of existence, and hence total self-suppression. Dialectical negation is not abstract or formal negation of the 'other,' but is 'mediated' by the other itself. (This is not to deny 'relatively immediate' forms of negation, such as destructive 'clashes'; these can often be understood, however, in terms of the underlying necessary dialectical relations of which they constitute a 'form of expression.') In a dialectical negation, what is negated is at the same time a necessary condition of existence. For example, life is maintained both through and in opposition to non-living conditions -- both externally and internally. The opposition must be relative, not absolute, however, because the 'full' realisation of the negation (corresponding to 'abstract negation' in thought) would mean self-destruction. Thus, dialectical negation falls short of the 'full' negativity of logical negation or logical contradiction." [Ibid., p.37. I have added a missing right parenthesis that was omitted from the original. Bold emphasis added.]

 

So, how precisely does heat 'mediate' here? Unfortunately, Lawler neglected to say, just as he neglected to say how organisms know when, where or how it is possible to dial-down the negations they encounter so that they don't experience the full fury of these nasty, destructive 'contradictions'. Maybe they know more logic than Hegel?

 

[Incidentally, Lawler also forgot to include so much as a vague demonstration -- or even a weak argument -- that made some attempt to show that logical contradictions have anything to do with destruction (which they don't). (On that, see above, and again, below.)]

 

To be sure, Hegel did offer his readers this rather weak argument:

 

"If the contradiction in motion, instinctive urge, and the like, is masked for ordinary thinking, in the simplicity of these determinations, contradiction is, on the other hand, immediately represented in the determinations of relationship. The most trivial examples of above and below, right and left, father and son, and so on ad infinitum, all contain opposition in each term. That is above, which is not below; 'above' is specifically just this, not to be 'below', and only is, in so far as there is a 'below'; and conversely, each determination implies its opposite. Father is the other of son, and the son the other of father, and each only is as this other of the other; and at the same time, the one determination only is, in relation to the other; their being is a single subsistence. The father also has an existence of his own apart from the son-relationship; but then he is not father but simply man; just as above and below, right and left, are each also a reflection-into-self and are something apart from their relationship, but then only places in general. Opposites, therefore, contain contradiction in so far as they are, in the same respect, negatively related to one another or sublate each other and are indifferent to one another. Ordinary thinking when it passes over to the moment of the indifference of the determinations, forgets their negative unity and so retains them merely as 'differents' in general, in which determination right is no longer right, nor left left, etc. But since it has, in fact, right and left before it, these determinations are before it as self-negating, the one being in the other, and each in this unity being not self-negating but indifferently for itself." [Hegel (1999), p.441; §960. Italic emphases in the original; bold added.]

 

The above paragraph quite nicely highlights Hegel's warped thought processes compounded by his tunnel vision. This was neatly summed up by Rosenthal:

 

"...[D]espite Hegel's obvious preference for patrilineal forms of descent -- 'father is the other of son,' he writes, 'and son the other of father, and each only is as this other of the other'... -- reality...is burdened with two biological sexes. Clearly, a father can still be a father, even if his 'other' happens to be a daughter, and a son cannot be a son without another 'other' besides his father." [Rosenthal (1998), p.218.]

 

And if a man were to reproduce with his daughter (surely not an uncommon occurrence, at least among royalty), then her son will also be her brother (and that child's mother will be his sister), as well as being son and grandson, all in one go, to the father.

 

Of course, the situation is even worse than this, for Hegel seemed to be fixated only on alleged binary relations -- but what is so 'contradictory' about right and left, or above and below? "Not above" used in sentences doesn't imply below, but "on a level with or below". Something similar occurs with right and left. So, if you aren't stood to the right or left of someone, you could be in front or behind, or even above or below, them.

 

What about tripartite relations (like speed, distance and time, or mass, density and volume)? Or, the three "colour charges" belonging to Quarks in Quantum Chromodynamics? What about multivariate analysis in statistics, or relations like the points on a compass?

 

 

Figure Two: Has Hegel Lost His Bearings?

 

If this particular example is regarded as a little too 'abstract' (but those who think so should check out the next 'abstract compass' they use on a hike in the mountains, say, or when they are at sea in, for instance, a yacht; a compass will then seem pretty material), think of the same figure, but now representing people sat around a circular table. Each individual will be sat next to at least two contingent 'others', while sat opposite many 'others'. And, worse still, none of them will "transition" into any of those 'others' (as Hegel imagined), and they will still be "opposite" one another (even if they aren't "diametrically opposite"). So, for example, if NN were sat at 12 o'clock (if we view the table from above as a clock face) and two others, NM and MN, were seated at 05:30 and 06:30, respectively, they will both be sat opposite NN even though neither is directly opposite her. Certainly neither will "[sublate] itself and [make] itself into its opposite":

 

"The self-contradictory, self-subsistent opposition was therefore already itself ground; all that was added to it was the determination of unity-with-self, which results from the fact that each of the self-subsistent opposites sublates itself and makes itself into its opposite, thus falling to the ground...; but in this process it at the same time only unites with itself; therefore, it is only in falling to the ground..., that is, in its positedness or negation, that the opposite is really the essence that is reflected into and identical with itself." [Hegel (1999)., §945, p.435. Bold emphasis added.]

 

"In the perception of the movement of force, consciousness becomes aware that the extremes, in both these aspects, are nothing per se, that rather these sides, in which their distinction of nature was meant to consist, are merely vanishing moments, an immediate transition of each into its opposite." [Hegel (1977), §140, p.85. Bold emphasis added. I have used the in-line version here, which is different from the published version I have cited.]

 

Maybe that is because those sat around a table aren't 'dialectical opposites'? That seems to be a valid objection, but until we are told with far greater clarity what one of these fabulous beasts is, they will have to do. [I have said more about 'dialectic opposites' in Essays Eight Part Two and Seven Part One. Readers are directed there for more details.]

 

Do fathers really change into sons? Does anything on the right always change into something on the left (or vice versa)? They should if Hegel is to be believed. And if those sat around the table mentioned above (including those are diametrically opposite one another) aren't 'dialectical opposites', one wonders how they might ever be able to interact. Maybe there is total silence around 'dialectical tables' since conversation (i.e., verbal interaction) must be totally non-existent. Or are some changes in Hegel's quirky universe not governed by these 'logical' principles?

 

It could be argued that a father must also be somebody's son, or he wouldn't exist. That is undeniable, but when will any of them change ("transition") into a son, as opposed merely to being a son at the same time as being a father? What are we to say of those who die childless? And, what about your right hand? Is it about to become your left hand? A bird flies above your head. According this genius, Hegel, that animal is about to "transition" into a bird flying below your head!

 

If we now 'transition' into three dimensions, and consider objects placed around a globe, Hegel's 'logic' will begin to look even more ridiculous. [Of course, these can all be translated into Relational Algebra, so this isn't an 'abstract' counter-example. Of course, this last point might be criticised as being a little unfair since formal systems like this were only invented after Hegel's demise. Maybe so, but that just shows once again how hopelessly parochial and dogmatic Hegel's 'logic' really is.]

 

It could be objected once more that individuals sat around a table aren't dialectically linked, and neither are birds flying above or below anyone's head, so those earlier counter-examples are misguided. Perhaps so, but the point of raising them is still relevant. Many things in nature and society have plenty of 'others'. Hegel was fixated on binary relations and completely ignored multivariate cases.

 

Undeniably, it could be argued that by "opposite" in such circumstances Hegel meant "diametrically opposite". So North, for example, is the opposite of South in that case. Even then, there will still be a problem for anyone sat at the centre of the aforementioned table (or in the middle of the group, if we remove the table but maintain the seating arrangement). That individual will have many such 'opposites'. Moreover, each individual, or direction, will have two other individuals or directions next to it/them. These would still be multivariate relations that Hegel ignored. [On that, see below.] Of course, if we move into three dimensions (again, see below) there will be even more such 'opposites'.

 

Once more it could be argued that Hegel is interested in negation:

 

"If the contradiction in motion, instinctive urge, and the like, is masked for ordinary thinking, in the simplicity of these determinations, contradiction is, on the other hand, immediately represented in the determinations of relationship. The most trivial examples of above and below, right and left, father and son, and so on ad infinitum, all contain opposition in each term. That is above, which is not below; 'above' is specifically just this, not to be 'below', and only is, in so far as there is a 'below'; and conversely, each determination implies its opposite. Father is the other of son, and the son the other of father, and each only is as this other of the other; and at the same time, the one determination only is, in relation to the other; their being is a single subsistence. The father also has an existence of his own apart from the son-relationship; but then he is not father but simply man; just as above and below, right and left, are each also a reflection-into-self and are something apart from their relationship, but then only places in general. Opposites, therefore, contain contradiction in so far as they are, in the same respect, negatively related to one another or sublate each other and are indifferent to one another. Ordinary thinking when it passes over to the moment of the indifference of the determinations, forgets their negative unity and so retains them merely as 'differents' in general, in which determination right is no longer right, nor left left, etc. But since it has, in fact, right and left before it, these determinations are before it as self-negating, the one being in the other, and each in this unity being not self-negating but indifferently for itself." [Hegel (1999), p.441; §960. Italic emphases in the original; bold added.]

 

The point is that right is not left, below is not above, and so on. This implies binary opposites linked by negation, which rules out the above objections based on other types of relation. But, a father is not not-a-son. All fathers are sons of somebody. And we have already seen that not right does not imply left, since something not on the right could be in front or behind.

 

The absurdity of Hegel's remarks become all the more obvious if begin to think about large finite relationships, such as "The millionth woman to give birth to a child in the USA since January 1st 1967", or "The ten thousandth individual to visit the USA in April 2011", which have been counted as such because of the ordering relations in our numbering system and their relationship to individuals to whom they are so connected (as well as what they might have done). Each one is only what he or she is because of the 999,999 or the 9999 individuals-- 'others'(?) -- who preceded them. And we needn't refer to such 'unlikely examples' -- but are these really all that unlikely? We encounter such things all the time -- as in "You're the fourth person who has asked that question today", "That's the tenth paper we've sold this morning", and so on. [If there are such things as 'internal relations', they would surely apply here!] In such cases, what is the 'dialectical opposite' of what? What is the 'dialectical opposite' of the tenth paper sold on any one morning? Or, the third person to climb Mt Everest? If there isn't one, they must be changeless -- that is, if we were foolish enough to believe Hegel and Lawler.

 

Hegel's other examples are no less defective. Sure, in two dimensions, something can be to the right only if some 'other' is to the left, but what about a third object between the two? It would only be between because it has at least two 'others'. And if we move into three dimensions, once more, while something will be to the right and left of the very same 'other' (if it is located on a sphere, this 'other' will lie to the West and the East), it will lie between at most eight 'others', which would be located on the vertices of an imaginary cube which surrounds it. There will be even more options if we consider other Polyhedra. Of course, the same observations apply to "above" and "below". On a globe, Scotland is both above and below England -- if by that we mean north of, or south of. Travel far enough along a line of longitude (say, 3 Degrees West) in both directions ('up' or 'down', north or south), and you will reach Scotland from England. And that also applies if you travel far enough North North West or South South East (for example) from some point in England to some point in Scotland. And, if we are allowed to leave the surface of the sphere, one could travel from one point to any other point in the Solar System, or beyond, in a potentially infinite number of different ways.

 

So, just as three-, or even n-dimensional geometry has shown that Euclid's system was rather parochial, it seems it has had the same effect on DM-Superscience.

 

Indeed, as Wittgenstein pointed out, metaphysics is a disease of the intellect brought on by an unbalanced diet of too few examples.

 

Hegel's Hermetic House Of Horrors

 

Before we weave our way into the final chamber in Lawler's guided tour of Hegel's Hermetic House of Horrors he helpfully summarised the story so far:

 

"But perhaps it would be better to say that logical negation or the law of noncontradiction is an abstract representation of a certain limit of dialectical negations in reality. The ontological significance of the law of noncontradiction would be found in the nature of dialectical contradiction, with the impossibility of fully realising relative negations without the suppression of the entity that negates." [Lawler (1982), p.37.]

 

Earlier we met this comment:

 

"…in the abstract, undialectical understanding of identity, the relation of A to not-A (beings that are not A as well as A's own nonbeing) seems to 'vanish.'" [Ibid., p.22. Italic emphasis in the original.]

 

But, while we are reasonably clear about the nature of contradictions (at least in ordinary language and FL), we still remain in the dark about these mysterious 'dialectical contradictions' -- that is, other than their merely being the product of Hegel's insecure grasp even of the primitive logic of his day, compounded by his cavalier distortion of ordinary language, balanced, of course, by an all too secure grasp of Christian and Hermetic Mysticism.

 

Unfortunately for Lawler (and, indeed, for Hegel), the LOC has no ontological implications (i.e., it isn't about "non-being"): in its simplest form, all it says -- once more! -- is that a proposition and its negation can't both be true and can't both be false at once, in the same respect. [This characterisation can even be found in Aristotle's famous "Square of Opposition".] There is nothing in there about what must or must not exist, or about "non-being".

 

Admittedly, some propositions are 'about' existence, or about what does or does not exist, but that is an entirely separate matter (as we are about to discover).

 

However, when such propositions are combined by a conjunction, even that observation is controversial. Consider this example (and assuming there is no figurative meaning either to "exists" or "...does not exist", for example):

 

C1: Tony Blair exists and Tony Blair does not exist.

 

Of course, C1 is already about what does or does not exist, so it can hardly be used to try to show that the LOC exclusively involves, or is only about, existence or "non-being".

 

Putting that 'quibble' to one side for now, in many systems of logic, if there isn't now and has never been a Tony Blair, then "Tony Blair does not exist" is truth-valueless. On the other hand, if there is a Tony Blair, "Tony Blair exists" is a logical truth! In such systems "Tony Blair exists" is in effect shorthand for "The existent Tony Blair exists"! Hence, in such systems C1 isn't a contradiction, since the second half lacks a truth value. In that case, even this 'contradiction' isn't about "non-being", since it isn't a contradiction to begin with.

 

Of course, as indicated, that itself will depend on what is meant by "Tony Blair does not exist." Depending on the system of logic: if there isn't now, and has never been a Tony Blair, then "Tony Blair does not exist" is either truth-valueless or it, too, as a logic truth. If the Proper Name, "Tony Blair", doesn't refer to anyone, then the set of Proper Names over which "ξ does not exist" ranges lacks at least one input value -- i.e., "Tony Blair" --, so there can be no output, true or false, in that case. On the other hand if the sentence "Tony Blair does not exist" is deemed to be short for "The non-existent Tony Blair does not exist", then it, too, will be a logical truth.

 

Either way, C1 fails to be a contradiction.

 

And, even if we reject the above characterisation of  "Tony Blair does not exist", along with the above systems of logic, and insist that C1 is a contradiction -- as noted above -- it would have no implications for the LOC in general. Not every proposition and its negation are about what does or does not exist.

 

[There will be more about this in Essay Twelve. Until then, readers are directed to Williams (1981), and Nelson (2020), for further details.]

 

In other systems of logic, existential implications are built into the formal structure and so aren't the result of an alleged 'ontological form of contradiction'; they are 'baked in', as it were. However, it is reasonably clear that the existential implications of a formal system have nothing to do with what does or doesn't actually exist in the physical universe. In which case, these are plainly 'existential implications', not existential implications; that is they relate to what 'exists' in that formal system, or in a formal model, not 'reality'.

 

C1: Tony Blair exists and Tony Blair does not exist.

 

Returning to C1, above. In ordinary discourse, if it is clear that this Tony Blair person is the individual who used to be the UK Prime Minister (and is the husband of Cherie Blair, the son of..., the father of..., etc., etc.), then the denotation of the two occurrences of the name "Tony Blair" in C1 will automatically be called into question by C1 itself. In that case, C1 can't be a contradiction, whatever system we might be using. That is because, if Blair exists, his name will have a denotation; if he doesn't, the name "Tony Blair" must have a different denotation in the second half to what it had in the first. So, if Blair is indeed the individual mentioned above, and if he does exist, then the second occurrence of "Tony Blair" can't be about him (since that Tony Blair, the one in the first half, is still alive, he still exists). That means the second half of C1 will either lack a denotation, or the Noun Phrase, "Tony Blair", in that second half must name someone else called "Tony Blair", who has perhaps passed away. The converse will be the case if the second half is true; that would imply the first occurrence of "Tony Blair" denoted a different individual from typographically the same name used in second half. Either way, the two halves of C1 will be about two different individuals, which means C1 can't be a contradiction, to begin with -- any more than this is: "George W Bush exists and George H W Bush does not exist".

 

In that case, C1 should be read as follows:

 

C1a: Tony Blair1 exists and Tony Blair2 does not exist.

 

To be sure, in certain forms of traditional logic, a non-empty universe must be assumed if the Square of Opposition is to work. But, even then, the LOC itself doesn't concern what exists, nor is it about "non-being" (since existence has already been assumed).

 

Of course, there are many different characterisations of contradictions in MFL. For example, Grimm (2004) -- pp.51-55 -- lists 19 different definitions of the LOC, and when he combines these with other factors, he tells us that there are at least 240 different ways of depicting this 'law' (p.55)!

 

It is worth pointing out, however, that not only are most of these definitions virtually indistinguishable, but with respect to many of them it is clear that their originators have confused contradictions with inconsistencies. Indeed, in his opening sentence, Grimm does just that!

 

Of those that Grimm lists, only a handful are described by him as 'ontological' (i.e., about 'existence', etc.).

 

"On an ontological outline, a contradiction would be neither a single statement nor a pair of statements, neither a proposition nor a pair of propositions, but a state of affairs. A contradictory state of affairs would be one in which something had a particular property and also an incompatible property, or in which something both had a particular property and lacked that property." [Grimm (2004), p.53.]

 

However, Grimm nowhere explains why this alleged contradiction doesn't concern the language about these states of affairs, as opposed to those states themselves (I will return to this specific point again presently). Still less does he tell us why they should be called "states of affairs" to begin with!

 

Just because two sentences say the following:

 

G1: "The Nile is a river and the Nile isn't a river", or,

 

G2: "This football is red all over and the same football is green all over",

 

(where it is made clear that these alleged 'properties' (if that is what they are!) apply in the same respect and at the same time, and it is also clear that the use of G1 refers to the River Nile, and G2 to a given football, which had perhaps been made clear by a pointing gesture),

 

that doesn't imply they concern certain 'states of affairs', and aren't merely contradictions in the language used -- assuming for the moment that "incompatible properties" (used in this way in relation to G2, for example) does imply a contradiction, as per the hypothesis.

 

However, if in G1 the Nile is indeed a river, then the denotation of the second occurrence of the phrase, "the Nile", is automatically thrown into doubt, as we saw was the case in relation to C1 and "Tony Blair". Hence, "The Nile isn't a river" will lack a truth value until the denotation of "the Nile" in the second half of G1 has been made clear. But, it can't have the same denotation as "the Nile" had in the first half, since the Nile is a river in that half, while in the second half the Nile isn't a river. So, this, too, can't be a contradiction, 'ontological' or otherwise. And, as we have seen, that is because either (i) one half lacks a truth-value, (ii) both halves have different subject terms, or (iii) their subject terms have different denotations. [The same applies, mutatis mutandis, if the Nile isn't actually a river.]

 

Someone could object that the above strictures would apply to all contradictions of the form, "The a is the F and the a is not the F", or "a is F and a is not F". Wouldn't that mean there are in fact no actual contradictions! In some cases, it does indeed mean this. Wittgenstein classified all contradictions as "senseless" -- i.e., they lacked a truth-value and represent a breakdown in the expressive capacity of language. But there are different kinds of contradiction depending on what F above stands for. [I will return to this again below.]

 

[Of course, that admission alone might appear to have serious (negative) implications for much that is argued at this site about contradictions in ordinary language, FL and indirect proofs. But, that would be a mistake. In most cases, what has been argued at this site has centred on traditional interpretations of contradiction (as always false), which supposed fact has then been used against DM-theorists. Other examples of alleged contradictions have in fact been analysed to show that many are based on the ambiguous use of certain words. As far as indirect proofs (in FL and mathematics) are concerned, contradictions are defined differently, once again, as always false, not senseless. In many places in this Essay I have reverted to Wittgenstein's characterisation of contradictions (as senseless, that is they lack a truth-value) in order to highlight a fatal objection to the DM-view of them, as well as their traditional interpretation. Once more, I will return to discuss this topic below.]

 

But, what are we to do with the phrase "incompatible property", as it supposedly applies to sentences like G2?

 

G2: "This football is red all over and the same football is green all over".

 

First of all, how can we ascertain if there are any such properties?

 

There are only two possible answers to such questions. Either:

 

(a) It is up to science to find out;

 

Or:

 

(b) We establish a convention and decide to classify any sentence ascribing at least two such properties to the same object (in this case, say, the same football) -- or, perhaps better still, we classify any sentence where at least two such predicates are attached to the same subject term -- as a contradiction, either because of (i) what we consider to be incompatible properties/predicate expressions, or (ii) what we think certain words 'really' mean.

 

In the first place, if it is the job of science to determine such things then, plainly, logic has no obvious role to play. So, this would now be an empirical question and so no contradiction ('ontological' or otherwise) will be implied. In the unlikely circumstance that a scientific investigation does determine that an object (such as that football) can be red all over and green all over at the same time, it can't be a contradiction, let alone an 'ontological' one. That is because both of these would be true if G2 were itself the case:

 

G2a: "This football is read all over",

 

and:

 

G2b: "This football is green all over".

 

But for two indicative sentences to be contradictory, both can't be true and both can't be false. That isn't the case here.

 

G2: "This football is red all over and the same football is green all over."

 

On the other hand, if scientific research is unable (at present) to show that no such object is in fact red all over and green all over at the same time and in the same respect, then this will always be an open question, but it still isn't a contradiction.

 

Some might complain that this isn't a question about whether or not we know there are any such properties, hence, it isn't up to science to decide in such cases.

 

But, sentences like this can only be counted as contradictory if the indicative sentences involved are capable of being assigned a truth-value, and in that case, it is relevant to raise the following question: how do we know there are any such properties instantiated by the same object at the same time anywhere in the universe? How do we know there are any incompatible properties, to begin with? That is a scientific, not a philosophical, question. A football that is partially covered in one colour and partially in another isn't at issue here. What is at issue is whether it is physically possible for the said ball to be completely covered by both colours at the same time and in the same respect. This could only ever be a scientific question if an actual truth-value is to be assigned to one or both of the two propositions (G2a and G2b) expressing either possibility.

 

On the other hand, and despite the above, if it is still maintained that it isn't the job of science to decide in such cases, then this can't be a matter of fact, which in turn means it can't be an empirical question. In that case, this must be a linguistic or conceptual, but not an ontological, question. However, just as soon as it is deemed ontological (about what exists!), scientific enquiry becomes relevant again, and we are back where we were a paragraph or so ago.

 

Some might object to the above claim that an ontological question automatically means it becomes something for science to deal with. But, as noted above, we have only two valid methods of enquiry here: scientific or conceptual. If it is a question about what does or doesn't exist, science is the only legitimate line of enquiry open to us. On the other hand, if this is a question of what can or can't possibly exist, or it is about the nature of existence itself, that would make it a conceptual enquiry and hence it would become a question about the use of language. An appeal to 'intuition', or some other mysterious 'source of knowledge', would therefore amount either to a cop out, an admission that it is up to each individual to decide for themselves what certain words mean or imply, or it would suggest that there are other legitimate ways to find out what does or doesn't exist that aren't the province of science to decide. So, what are these other legitimate ways? [Email me if you know.]

 

Returning to the language used in G2 (reproduced below): let it now further be stipulated that the phrases "red all over" and "green all over" are taken to mean "completely covered in or by red" and "completely covered in or by green", respectively, such that, in each case, the other colour doesn't show through, or can't be seen anywhere on the surface of the football in question. Let it also be stipulated that G2 doesn't mean that the said football was painted red and then when the paint had dried it was painted green, so that it is still covered in red paint but that colour can no longer be seen because there is now a coat of green on top of it -- nor vice versa. Finally, let it further be stipulated that this doesn't mean that since red and green paint, when mixed, create the colour brown, the football isn't coloured brown all over. Those appear to be the only three complicating factors here, which I have now ruled out of contention.

 

So, apparently what is really implied by G2 is that, despite the above, the football in question was painted red all over and likewise green all over, but that both colours show through and are visible (to any suitably placed viewer) over its entire surface, at the same time and in the same respect.

 

In that case, wouldn't G2 -- or maybe what G2 means (expressed by G2c) --, be a legitimate example of an 'ontological contradiction'?

 

G2: "This football is red all over and the same football is green all over."

 

G2c: "This football is completely covered in red and the same football is completely covered in green."

 

It seems not. Given how the predicable, "ξ is completely covered by F", is employed to generate indicative sentences (where "F" is a variable going proxy for a conformable general noun phrase that is used to describe colours), its employment to form sentences like G2 and G2c (understood in the way indicated above) would constitute its misuse. So, G2 isn't an 'ontological contradiction' since it isn't a contradiction to begin with; it is a clear example of the misuse of a specific predicable. A confused use of language is no way to set the stage for an ontological enquiry, scientific or philosophical. So, for example, it isn't part of an ontological or empirical enquiry to find out if the Queen in chess can move like the Knight in chess. Such an 'enquiry' would be based on a clear misunderstanding of the rules of chess and the role that certain pieces occupy in the game. So a sentence like the following:

 

Q1: "The Queen can move like the Knight and the Queen can't move like the Knight,"

 

isn't a contradiction, since the first half isn't actually about the Queen in chess, while the second half looks like it is. "The Queen can move like the Knight" plainly isn't about the Queen in chess.

 

The same applies if someone says:

 

Q2: "The Rook in chess moves like this and it does not move like this",

 

(where "this" is made clear by demonstration and means both times that the said piece moves in straight lines normal (perpendicular) to any edge of the board, back and forth). That would throw into question not just that individual's grasp of the game but of language itself.

 

But, couldn't someone show a novice what how the Rook moves in chess by demonstrating how it doesn't move (diagonally, for example)? Indeed, but they wouldn't do that in the way suggested by Q2 (again, where "this" in Q2 means both times that the said piece moves in straight lines normal to any edge of the board, back and forth).

 

It could be objected that a chess analogy is in appropriate since chess is a game with clear cut rules. Maybe so, but it is still an apt analogy since it is legitimate to ask whether the use of predicables like those above amounts to their misuse. Anyone who used "ξ is completely covered in/by F and completely covered in/by G" (where "G" is also a variable going proxy for a conformable general noun phrase as before), with the relevant substitution instances generating something like G2/G2c -- or, indeed, any of the predicables to be considered presently -- would be deemed not to understand how to use language, and who doesn't know what "red", "green", or "completely covered" mean. They certainly wouldn't be viewed as an intrepid, 'edgy' metaphysician.

 

G2: "This football is red all over and the same football is green all over."

 

G2c: "This football is completely covered in red and the same football is completely covered in green."

 

It won't do now to argue that this is still an ontological contradiction involving incompatible properties because it is physically impossible for an object such as this to be red all over and green all over (in the manner specified above).

 

But, how do we know it is 'physically impossible'? It is no good replying that it is physically impossible because these properties are incompatible for that would be to argue in a circle. It would be to reason as follows: "These are incompatible properties because it is physically impossible for an object like this to be red all over and green all over..., and that is because they are incompatible properties!" Anyone arguing in that circle will merely have shown that they know how to use the predicable "ξ is completely covered by F", not that they were a superscientist who had examined every football that ever there was, or ever could be, and had painted them all accordingly (even those that don't yet exist!) to check if it was, indeed, physically impossible. They might judge or deem it to be physically impossible, but that conclusion can't follow even from a hundred trillion such 'experiments' -- as, indeed, Engels himself pointed out. Such a conclusion would have been based on their understanding how to use the language involved, how to use predicables like "ξ is completely covered in/by F" correctly.

 

So, this isn't an 'ontological' or even a scientific question, it is conceptual, and the points made in the previous few paragraphs still apply.

 

[It won't be shown here, but it is a corollary of the above comments that the phrase "ontological contradiction" is incoherent, so any sentence using it will be non-sensical. That will be left to Essay Twelve Part Five to establish.]

 

Despite the above -- according to Grimm -- the following is an example of an 'ontological contradiction':

 

G3: "This football is red and it isn't red (in the same respect and at the same time)."

 

[Of course, this assumes once again that it is clear to which football we are referring. I haven't reverted to using the phrase "completely covered" since I want to consider every conceivable possibility. Here, the said football could be completely red or even partially red (and the same applies to any other colour). All that matters is that it is said to have one property and lack the very same property at the same time and in the same respect.]

 

In this case, we are dealing with the predicable "ξ is F" alongside the alleged contradictory form, "ξ is F and ξ isn't F" (with the same caveats applying here as were the case with G2/G2c, where "F" goes proxy for a conformable noun phrase, once more). Of course, it still has to be shown (it can't simply be assumed) that G3 isn't a contradiction de dicto, but is a contradiction de re. That is, it still has to be shown that this isn't merely a contradiction in language, but is an 'ontological contradiction' according to Grimm's use of that phrase -- not that he is at all clear about what he means by it! In general, this 'difficulty' has generally been sidestepped by philosophers who use the word "property" in such circumstances; this is what is supposed to imply such examples are 'ontological'. So, G3 now becomes something like the following:

 

G4: This football has, or instantiates, the property of being red and it hasn't, or doesn't insatiate, the property of being red (in the same respect, at the same time).

 

Alternatively:

 

G5: This football has, or instantiates, the property of being red and has, or instantiates, the property of being not red (in the same respect, at the same time).

 

[In which case, these involve the following predicables: "ξ is F and ξ isn't F", or even "ξ is F and ξ is not F", where "F" will now be a 'property token'.]

 

But, the same problems confront the above as they did G2/G2c. Once more: anyone who used "ξ is F and ξ is not F", with the relevant substitution instances generating something like G4 or G5, would be deemed not to understand how to use language, or who doesn't know what "red" means, not an intrepid metaphysician. Hence, these examples represent a breakdown in the use of language not an 'ontological contradiction'.

 

It could now be objected that if the above examples represent a breakdown in the use of language, it would mean that there could be no contradictions whatsoever. Again, that introduces issues raised by Wittgenstein in the Tractatus where he classified all contradictions as Sinnloss -- i.e., they were said to be senseless (4.461), lacking a bi-polar truth-value (that is, G4 and G5 look like indicative, fact-stating sentences, but neither of them is true or false). There is nothing in our use of language that prevents us from using or considering one sentence that contradicts another (absence of this facility would in fact cripple language). Problems arise when we try to use sentences like these -- where we conjoin a proposition with its negation. For Wittgenstein, contradictions in language like this represent a breakdown in the expressive capacity of language (4.466). Aristotle held a somewhat similar view. This means that characters like Hegel who think contradictions are somehow the driving force of conceptual development, and hence development in general, clearly want to employ language that has already broken down, (indeed, as Marx noted, they use distorted language upon which they wish to construct metaphysical systems or upon which they base an 'ontology'. As such, they are no better than those who want to make up the rules of chess or baseball as they go along -- or, in this case, the rules we have for using predicables like those mentioned above. So, while we might utter sentences like G4 and G5, no sense can be made of them.

 

In which case, the view advanced in these Essays isn't that there can't be any contradictory sentences, only that anyone who wants to construct an ontology out of 'contradictions' is like someone who wants to move the Queen in chess anyway they please while still thinking they are playing chess.

 

For those who don't like that analogy, such individuals resemble this character:

 

"'When I use a word,' Humpty Dumpty said, in a rather scornful tone, 'it means just what I choose it to mean, neither more nor less.'

 

"'The question is,' said Alice, 'whether you can make words mean so many different things.'

 

"'The question is,' said Humpty Dumpty, 'which is to be master -- that's all.'

 

"Alice was too much puzzled to say anything; so after a minute Humpty Dumpty began again. 'They've a temper, some of them -- particularly verbs: they're the proudest -- adjectives you can do anything with, but not verbs -- however, I can manage the whole lot of them! Impenetrability! That's what I say!'

 

"'Would you tell me, please,' said Alice, 'what that means?'

 

"'Now you talk like a reasonable child,' said Humpty Dumpty, looking very much pleased. 'I meant by "impenetrability" that we've had enough of that subject, and it would be just as well if you'd mention what you mean to do next, as I suppose you don't mean to stop here all the rest of your life.'

 

"'That's a great deal to make one word mean,' Alice said in a thoughtful tone.

 

"'When I make a word do a lot of work like that,' said Humpty Dumpty, 'I always pay it extra.'

 

"'Oh!' said Alice. She was too much puzzled to make any other remark.

 

"'Ah, you should see 'em come round me of a Saturday night,' Humpty Dumpty went on, wagging his head gravely from side to side, 'for to get their wages, you know.'

 

"(Alice didn't venture to ask what he paid them with; so you see I can't tell you.)

 

"'You seem very clever at explaining words, Sir' said Alice. 'Would you kindly tell me the meaning of the poem called "Jabberwocky"?'

 

"'Let's hear it,' said Humpty Dumpty. 'I can explain all the poems that ever were invented just yet.'

 

"This sounded very hopeful, so Alice repeated the first verse:

 

'Twas brillig, and the slithy toves,

Did gyre and gimble in the wabe:

All mimsy were the borogroves,

And the mome raths outgrabe.'


"'That's enough to begin with,' Humpty Dumpty interrupted: 'there are plenty of hard words there. 'Brillig' means four o'clock in the afternoon -- the time when you begin broiling things for dinner.'

 

"'That'll do very well,' said Alice: 'and 'slithy'?'

 

"'Well, 'slithy' means 'lithe and slimy.' 'Lithe' is the same as 'active.' You see it's like a portmanteau -- there are two meanings packed up into one word.'

 

"'I see it now,' Alice remarked thoughtfully: 'and what are 'toves'?'

 

"'Well, 'toves' are something like badgers -- they're something like lizards -- and they're something like corkscrews.'

 

"'They must be very curious-looking creatures.'

 

"'They are that,' said Humpty Dumpty: 'also they make their nests under sundials -- also they live on cheese.'

 

"'And what's to 'gyre' and to 'gimble'?'

 

"'To 'gyre' is to go round and round like a gyroscope. To 'gimble' is to make holes like a gimlet.'

 

"'And 'the wabe' is the grass-plot round a sundial, I suppose?' said Alice, surprised at her own ingenuity.

 

"'Of course it is. It's called 'wabe,' you know, because it goes a long way before it, and a long way behind it-----'

 

"'And a long way beyond it on each side,' Alice added.

 

"'Exactly so. Well then, 'mimsy' is 'flimsy and miserable' (there's another portmanteau for you). And a 'borogove' is a thin shabby-looking bird with its feathers sticking out all around -- something like a live mop.'

 

"'And then 'mome raths'?' said Alice. 'I'm afraid I'm giving you a great deal of trouble.'

 

"'Well, a 'rath' is a sort of green pig: but 'mome' I'm not certain about. I think it's short for 'from home' -- meaning that they'd lost their way, you know.'

 

"'And what does 'outgrabe' mean?'

 

"'Well, 'outgrabing' is something between bellowing and whistling, with a kind of sneeze in the middle; however you'll hear it done, maybe -- down in the wood yonder -- and, when you've once heard it, you'll be quite content. Who's been repeating all that hard stuff to you?'

 

"'I read it in a book,' said Alice." [Lewis Carroll, Alice Through The Looking Glass. Quotation marks altered to conform with the conventions used at this site.]

 

Marxists should be wary of such moves, especially since Marx himself warned us about them, never mind Lewis Carroll. Here he is again:

 

"The philosophers have only to dissolve their language into the ordinary language, from which it is abstracted, in order to recognise it, as the distorted language of the actual world, and to realise that neither thoughts nor language in themselves form a realm of their own, that they are only manifestations of actual life." [Marx and Engels (1970), p.118. Bold emphasis alone added.]

 

Nevertheless, the only modern logicians Grimm references to illustrate the 'ontological' definition are Arthur Prior and the two Routleys (p.52) -- i.e., the late Richard and Val Routley, who later changed their names to Richard Sylvan and Val Plumwood. Their definition goes as follows:

 

"A contradictory situation is one where both B and ¬B (it is not the case that B) hold for some B". [Quoted from Grimm (2004), p.52. I have used a different sign for negation here.]

 

But, this is just a variation on G4 and G5 from earlier, so no more need be said about it.

 

Putting that 'difficulty' to one side for now, it would need to be made clear what the two Routleys meant by "situation" before a decision could be made whether or not their example was to be deemed "ontological". For instance, if "situation" means "formulae in the context of a theory", then this wouldn't be "ontological". Unfortunately, the original article in which this 'definition' appears was published in an obscure Colombian mathematics journal (Revista Colombiana de matemáticas), to which I do not have access, so I can't say much more about it. Anyway, as should seem obvious, even this unfortunate 'definition' isn't about "non-being". In the absence of access to that article, if "situation" means something like "real word scenario depicted by a true (or a false) proposition", then the comments made above apply here, too.

 

Independently of that, the two Routleys were both radical activists, and Sylvan himself was also a Paraconsistent logician who collaborated with Graham Priest in inventing that discipline. Hence, it isn't hard to see that Hegel's baleful influence already lies behind this persuasive definition of theirs.

 

[That suspicion is confirmed by the existence of Routley and Meyer (1976) (no irony intended). On this, see Graham Priest and Dominic Hyde's brief biography of Sylvan in Hyde and Priest (2000), pp.1-3. Indeed, in the same biography (p.13), Sylvan pointedly recommends 'dialethic logic' (often spelt "dialetheic logic", a family of non-standard logics which is overtly dependent on Hegel), and the many essays published in Priest, Routley and Norman (1989). Background material can be found in Franklin (2003).]

 

Prior's 'ontological' definition went as follows:

 

"The law of contradiction asserts that a statement and its direct denial cannot be true together ('not both p and not-p') or, as applied to terms, that nothing can both be and not be the same thing at the same time ('Nothing is at once A and not-A')." [Prior (1967). I have relied on the quotation found in Grimm, p.50.]

 

This is an appallingly bad definition from a leading logician,. It first of all confuses inconsistency with contradiction (and is therefore on a par with the lamentably poor 'dialectical definitions' we met in Essay Four Part One). I won't try to defend it. Even so, there is nothing here about what must exist, or about "non-being", and Prior's 'definition' doesn't seem to conform to Grimm's typology, anyway.

 

Now, I suspect Prior would have paraphrased this definition (maybe in a longer article) in terms of modern quantification theory, thus removing the apparent existential implications it seems to have. Indeed, this guess is partially confirmed by the other definition Grimm quotes from Prior (1967) [on p.51], which is far superior, and much closer to the one adopted at this site.

 

Grimm also quotes Aristotle's own alleged 'ontological' definition (pp.49-50):

 

"For a principle which every one must have who understands anything that is, is not a hypothesis; and that which every one must know who knows anything, he must already have when he comes to a special study. Evidently then such a principle is the most certain of all; which principle this is, let us proceed to say. It is, that the same attribute cannot at the same time belong and not belong to the same subject and in the same respect; we must presuppose, to guard against dialectical objections, any further qualifications which might be added. This, then, is the most certain of all principles, since it answers to the definition given above. For it is impossible for any one to believe the same thing to be and not to be, as some think Heraclitus says. For what a man says, he does not necessarily believe; and if it is impossible that contrary attributes should belong at the same time to the same subject (the usual qualifications must be presupposed in this premiss too), and if an opinion which contradicts another is contrary to it, obviously it is impossible for the same man at the same time to believe the same thing to be and not to be; for if a man were mistaken on this point he would have contrary opinions at the same time. It is for this reason that all who are carrying out a demonstration reduce it to this as an ultimate belief; for this is naturally the starting-point even for all the other axioms." [Aristotle (1984b), p.1588. In the internet version, this can be found in Book IV, at the end of section 3. Bold emphases added.]

 

This isn't much better than Prior's first attempt above and won't be defended here, either. The only thing that can be said in Aristotle's defence is that he was writing 2400 years ago and was attempting to kick-start the study of logic, beginning almost from scratch. The same excuse can't be extended to Hegel and his coterie of faithful 'dialectical echoes'. Even so, Aristotle's 'definition' doesn't mention "non-being", either. To be sure, Aristotle says: "For it is impossible for any one to believe the same thing to be and not to be", but this is far too vague to co-opt in Hegel's defence since Aristotle might have meant: "For it is impossible for any one to believe the same thing to be and not to be true of a man/a cat/a number...". This interpretation is confirmed by the next sentence in the above passage:

 

"For what a man says, he does not necessarily believe; and if it is impossible that contrary attributes should belong at the same time to the same subject...." [Ibid. Bold added.]

 

That would also mean this example is just a variant of one or more of G1-G5 above. Readers are therefore referred back to that discussion.

 

In any case, even if (per impossible) it were clear what 'dialectical contradictions' actually were, FL would neither need them nor seek to recruit DL in order to help understand, or even apply, the LOC.

 

After all, does Hydrodynamics need assistance from Dousing? Does Medical Science need Crystal Healing? Does Astronomy need Astrology?

 

The Dialectical Denouement Looms Large

 

At last we are nearing the dialectical denouement:

 

"For our purposes, this illustration is sufficient to show that while the term 'contradiction' as used here does not have the seemingly 'full' sense of logical contradiction, nevertheless it is not reducible to some 'clash' of externally related 'positives.' Nor is it equivalent to some 'tranquil' association of mutually exclusive logical contraries, such as odd and even numbers, male and female persons, or north and south poles of a magnet -- unless these are in fact understood dialectically…. It is necessary to understand the mutual relation and opposition that constitutes the inner dynamic of the terms in opposition. This opposition may contain the possibility of developing into 'full' contradiction, i.e., into real destruction. However, the real potentiality for the development of dialectical contradiction is not to be seen in this possibility of destruction, but in a potentiality for transformation where only the 'immediate forms' of opposing phenomena are suppressed -- while other, often more developed forms are realised through essential 'internal' interconnections." [Lawler (1982), pp.37-38. Bold emphases added.]

 

Unfortunately, obscure jargon like this is standard fare in HCD circles, but that doesn't mean it makes any sense. Indeed, it is a sure sign of the opposite. [Irony intended.]

 

No less a DM-fan than Lenin agreed about the use of such language (even as he quoted page-after-page of it from Hegel!):

 

"The flaunting of high-sounding phrases is characteristic of the declassed petty-bourgeois intellectuals." ["Left-Wing" Childishness.]

 

As did this long-dead sociologist -- noted by the following commentator:

 

"Sociologist C. Wright Mills, in critically examining 'grand theorists' in his field who used verbosity to cover for a lack of profundity, pointed out that people respond positively to this kind of writing because they see it as 'a wondrous maze, fascinating precisely because of its often splendid lack of intelligibility.' But, Mills said, such writers are 'so rigidly confined to such high levels of abstraction that the "typologies" they make up -- and the work they do to make them up -- seem more often an arid game of Concepts than an effort to define systematically -- which is to say, in a clear and orderly way, the problems at hand, and to guide our efforts to solve them.'

 

"Obscurantism is more than a desperate attempt to feign novelty, though. It's also a tactic for badgering readers into deference to the writer's authority. Nobody can be sure they are comprehending the author's meaning, which has the effect of making the reader feel deeply inferior and in awe of the writer's towering knowledge, knowledge that must exist on a level so much higher than that of ordinary mortals that we are incapable of even beginning to appreciate it.... The harder people have to work to figure out what you're saying, the more accomplished they'll feel when they figure it out, and the more sophisticated you will appear. Everybody wins." [Quoted from here. Quotation marks altered to conform with the conventions adopted at this site. One link added; some paragraphs merged.]

 

More to the point, in what way does it help to interpret, say, the relation between numbers 'dialectically'? Do they struggle with and then change into one another, as the DM-classics assure us they must? If so, that will be news to most of us.

 

But, why has "full contradiction" been equated with "real destruction" by Lawler, here? The LOC was (and still is) connected with a gamut of odd ideas that surfaced in the bad old (pre-modern) logic. Lawler himself seems to think it has something to do with "cancelling out" -- although he doesn't use those exact words, as far as I can ascertain (but Hegel certainly does -- he copied this way of talking from Kant), and yet he does speak of negatives in mathematics cancelling. [On this see below. Lawler uses terms like "self-nullifying" (for instance, on p.16). As we will see in Essay Twelve (as well as, here), card-carrying HCDs also think likewise.]

 

However, neither the contradictions of FL nor those of ordinary language have anything to do with "cancelling out", or "nullifying" (a widely held belief, even among Analytic Philosophers). If a proposition, "p", is true, its contradictory, "not p", is simply false, not "cancelled out".

 

Look, it is still there on the page/screen, unharmed!

 

This weird idea is connected with the equally bizarre notion that 'negative' propositions are all false (or are 'defective', or 'non-existent' in some unspecified way). But, 'negative' propositions can be, and often are, true. For example, "Blair isn't a socialist" is true, as is "Anyone who reads the Daily Mail and doesn't reject much of what it says is no Marxist."

 

Furthermore, not even "the content" of "not p" is "cancelled", for whatever it is that "not p" expresses is still up for consideration. "Not p" is just false if "p" is true -- true if "p" is false. Nor is it "nullified", for (and once more) "not p" could one day become true and "p" itself false, and vice versa. For example, "Boris Johnson hasn't resigned" is the contradictory of "Boris Johnson has resigned". The first is currently false, but, hopefully, it will become true one day; it could hardly do that if it had been "cancelled", or "nullified".

 

Moreover, every proposition/indicative sentence is paired, or is pairable, with its negation; does that mean that they have all been "cancelled"/"nullified"?

 

Anyway, what would count as the "nullification" of, say, "Johnson has resigned"? One could try to nullify his actual resignation (or its effects), but what could one do to nullify "Johnson has resigned"? Prevent this message getting out? Silence whoever might want to utter it? Of course, if that sentence were false, then what it says hasn't even happened, so nothing can nullify it. Even so, that proposition is still there, on your screen, silently mocking any and all attempts to "nullify" it.

 

Those who talk this way have clearly confused FL-contradictions with what seem to be contradictory orders or instructions, like "Stand up!"/"Sit down!", which, if acted upon, undo each other, etc. But, the propositions of FL and ordinary language are neither instructions nor orders.

 

[Of course, "Stand up!" and "Sit down!" aren't even contradictory orders! There is a third possibly here that would nullify the other two if acted upon --, namely, "Don't move!", said to someone crouching or lying down.]

 

Lawler does, however, try to illustrate this sort of negation by appealing to negatives in mathematics (a popular ploy used by, among others, Engels), not noticing the difference between negative numbers (which are still numbers; their negativity doesn't prevent them from being numbers!) and the negative particle as it is used in language (for example, where it can be used to deny certain properties of sundry objects; negativity in relation to numbers denies nothing of anything):

 

"From the 'thoughtless' viewpoint of abstract understanding, A is conceived of as simply given, and the implicit relation to not-A does not get the trouble of a serious consideration. Just as in mathematics two negatives make a positive, in which they are thought of as cancelling out, here abstract understanding makes the journey from A to not-A and back again without noticing that any movement has taken place." [Ibid., p.22. Italic emphases in the original.]

 

Lawler then proceeds to sort of reject this view (or, rather, he aims to transcend it since it is 'formalistic'), but he doesn't repudiate the idea that it is somehow correct to regard formal negation as a sort of "cancelling-out". He then uses this 'analysis' -- beloved of the ever-present, "abstract understanding" -- to develop a higher, 'dialectical' account of negation. So, for Lawler, this sort of 'negation' isn't just "cancelling-out", it has moved beyond it.

 

However, if formal negation is not and never has been a "cancelling-out", then the dialectical moves that allegedly follow from (or seek to transcend) it can't use it as a launch pad for such an aimless 'logical' journey to nowhere, since it isn't a launch pad to begin with.

 

But, and to spoil the fun, not even in mathematics -- if we adopt for the moment this primitive way of talking -- is it always true that two negatives give a positive. For example: -1 + -2 = -3. [Notice, no "cancelling-out" here, either!]

 

It isn't clear here whether Lawler is only considering multiplication (and perhaps also, by implication, division) in order to illustrate this obscure point. But, if so even here the results aren't always as he imagines: in the Complex Plane, -i x -i = i2 = -1, which is still a negative integer!

 

Of course, it could be objected that i2 isn't negative (even though it is equal to -1(!)), but what about -(i1/2)/-i = i-1/2; is that negative? Maybe so, maybe not. Well then what about -(a - b) x -1 = (b - a), where b>a? Or -a x -a = a, where a<0? Or, (x2 - 3x - 1) x -1 = 1 + 3x - x2. Are any of these 'negative'?

 

[I have highlighted "x" in bold when it represents a letter in order to distinguish it from its use as a multiplication sign.]

 

In which case, it seems reasonably clear that this quasi-Hegelian 'rule' is far too crude to use even in lower mathematics. But, when we turn to more complex areas (such as matrices and their inverses, groups or infinite series), the whole idea becomes more obviously ridiculous.

 

Anyway, negatives in mathematics don't "cancel-out"; what happens is that certain functions take negative numbers as arguments and yield positives as images, but, the domain set of negatives still exists -- it hasn't been "cancelled-out", or even "nullified". So, for example, -2 x -3 = 6, but -2 and -3 are still both there on your screen, ready to be used over and over again.

 

On the other hand, Lawler might have had something like this in mind: -8 --3 = -5, which turns out to be the equivalent of -8 + 3 = -5, where the double "-" supposedly cancels and becomes a "+". But, my double use of "-" obscures what is actually going on here, since those two minus signs signify differently. As I have pointed out in Part Two of Essay Eight (in relation to Kant's attempt to explain what he meant by "real negation":

 

Kant has plainly confused positive and negative integers with the operations of addition and subtraction. 7, for example, is a positive integer; adding 7 is what we do with it. Running the two together would be like confusing, say, a pencil with what can be done with it. This muddle hasn't been helped either by mathematicians using "−", for instance, to indicate both an operation and a sign attached to a numeral to map it onto an element in the set of negative integers. Hence, in order to distinguish these two different uses of what look like the same sign, novices in arithmetic are often taught to distinguish a number from an operation by the use of brackets. Hence, the integer 7 would be written as "(+7)", and the integer -5 as "(-5)"; so, when the latter is subtracted from the former that would be written as "(+7)-(-5)". However, even this is far from perspicuous, and often causes confusions of its own. In which case, I will henceforth distinguish the operation of subtraction from the negative integer sign itself in the following way: "─" (a long dash) signifies the operation of subtraction, and "-" (a short dash) the negative sign used to signify elements of the set of negative integers. 

 

[Of course, Kant wrote at a time when mathematicians themselves were unclear what they meant by numbers in general --, or, indeed, operations and functions. Subsequent philosophers who uncritically draw on Kant's ideas are less easy to absolve.]

 

Now, it isn't too clear how Kant would classify, for instance, the following: -8 ─ -3 = -5. Is this subtraction or addition? Well, according to Kant's comments above, since there is no '+' and '-' sign together, it can't be a subtraction!

 

Consider an overdraft of £8. Suppose the bank manager discovers an error of £3 in the said account and wipes £3 off that overdraft in order to correct this mistake. The overdraft will now be £5. Plainly, the owner of that account won't have any more money in her account as a result (she is still overdrawn!) -- so, nothing has been added. All that has happened is that some of the debt has been subtracted -- taken away or removed.

 

This nicely illustrates what happens when operations are conflated with numbers --, or, for that matter, mathematical operations are muddled with cancellation (or, indeed, with "opposition"). "Mighty thinker" though he was, Kant's thought is confused from beginning to end on these issues. Hegel's doubly so.

 

Someone might object that the above bank manager did in fact cancel part of the debt, but that isn't so. An error was rectified, that is all. Of course, debts can be cancelled, but the cancellation of a debt isn't itself a mathematical operation (you don't learn your 'cancellation tables' at school, nor are there 'cancellation theorems' in Number Theory). The cancellation of a debt involves one or more of the following: an act of goodwill, or of charity, a rectification, a humiliation, or, indeed, a host of other incidental social or interpersonal actions/relations. We can certainly work out the mathematic result or consequences of a cancellation, but that doesn't remove the clear distinction between how we calculate and how we describe the causes or the results of such moves socially, should we choose to do so. If someone pays off a debt, that is different from cancelling it, and the same applies to errors that are put right -- although the end result in each case might be the same.

 

Finally, if a debt is cancelled simpliciter, then someone else will have lost out (willingly or otherwise), which isn't the case with debts that have been paid off, or where an error has been rectified. So, let us assume that NN has $100 in his bank account and that he also owes MM $25; if MM cancels NN's debt, then someone other than NN will lose out (in this case, MM will have lost $25). But if NN pays the $25, only NN will lose out. The result in each case for NN will be the same in some respects but not others. It will be the same in that NN will now no longer owe that money (this being the result whether the debt is paid or wiped), but it will be different in that in the second instance (if the debt is paid), NN will be $25 worse off, not MM. In the first instance, however, if the debt is wiped, NN will be free of the debt, but nothing will have been added to his bank balance, which remains at $100. The debt will just be forgotten and it is MM who will have lost out. So, as we can see, paying off a debt is significantly different from that debt being cancelled.

 

The reader is referred back to the rest of that discussion for more details.

 

Of course, teachers of mathematics will often say that two minuses "cancel", but we don't have two minuses, here. We have an operation (subtraction) performed on a negative number that is the equivalent of adding a positive integer (i.e., mapping that negative number to another number to its right on the number line). This can be illustrated by imagining eight marbles all labelled with "-" signs. If three of those marbles are removed then there will only be five of those labelled marbles left: -8 ─ -3 = -5. Nothing has been cancelled.

 

In that case, there is no good reason to connect the "full" contradictions of FL with "destruction".

 

Well, not for us materialists.

 

Lawler continues:

 

"Real opposition must be understood as dialectical contradiction." [Ibid., p.38. Italic emphasis added.]

 

And that's it! All the bemused reader is offered by way of justification is a plain and simple "must" -- and this after a lengthy detour and trek across the arid wastelands of sub-Aristotelian/Hegelian gobbledygook.

 

The rest of Lawler's article is simply more window-dressing. We are left with a counterfeit "must" here, backed neither by logic nor fact. Exactly why we "must" see these obscure creations of Hegel's Hermetic Hallucinations in this way remains entirely mysterious.

 

To be sure, there is no problem with the phrase "real opposition". But, the phrase "dialectical contradiction" is still lost in the same impenetrable fog in which Hegel left it 200 years ago. Precisely why the word "contradiction" has to be super-glued to the other term ("dialectical") is still shrouded in mist -- except, Lawler might have hoped that some of the clarity associated with the word "contradiction" might rub off on the word "dialectical".

 

Perhaps fittingly, the opposite is the case.

 

[However, I have offered a historical materialist explanation for Hegel's decidedly odd conclusions in Essay Twelve (summary here), just as I have advanced similar reasons for their acceptance by DM-fans, in Essay Nine Part Two.]

 

As noted above, Kant introduced into Philosophy the concept of "real opposition" and "real negation" (an idea that was also embryonic in Aristotle):

 

"Two things are opposed to each other if one thing cancels that which is posited by the other. This opposition is two-fold: it is either logical through contradiction, or it is real, that is to say, without contradiction." [Kant (1763), p.211. Emphasis in the original.]

 

However, as we have seen in this Essay, the idea that these 'cancel' each other is completely misguided. [Again, I have said much more about this idea of Kant's in Essay Eight Part Two, here.]

 

Lawler then quotes the following prime example of a priori Superscience, taken from Hegel's Shorter Logic:

 

"Instead of speaking by the maxim of Excluded Middle (which is the maxim of abstract understanding) we should rather say: Everything is opposite. Neither in heaven nor in earth, neither in the world of mind nor nature, is there anywhere an abstract 'either-or' as the understanding maintains. Whatever exists is concrete, with difference and opposition in itself. The finitude of things with then lie in the want of correspondence between their immediate being and what they essentially are. Thus, in inorganic nature, the acid is implicitly at the same time the base: in other words its only being consists in its relation to its other. Hence the acid is not something that persists quietly in the contrast: it is always in effort to realize what it potentially is. Contradiction is the very moving principle of the world: and it is ridiculous to say that contradiction is unthinkable. The only thing correct in that statement is that contradiction is not the end of the matter, but cancels itself. But contradiction, when cancelled, does not leave abstract identity; for that is itself only one side of the contrariety. The proximate result of opposition (when realised as contradiction) is the Ground, which contains identity as well as difference superseded and deposited to elements in the completer notion." [Lawler (1982), p.38; partially quoting Hegel (1975), p.174, §119. I have used the online version and given a fuller quotation than Lawler.]

 

Considering this famous (but no less dogmatic) assertion: it is nevertheless true that either Hegel wrote it or he didn't. If either (but not both) of these is the case, then Hegel was mistaken since there is just such an "either-or", thanks to Hegel himself -- namely, right here!

 

Worse: in heaven, hell (or high water) there either is an "either-or" or there isn't. So, if Hegel were right (and there isn't an "either-or"), he was thereby wrong, since one of these options would be the case, not both, nor neither. On the other hand, if he was wrong, then he was wrong anyway.

 

Either way, he was wrong.

 

[A longer and perhaps more perspicuous version of this argument can be accessed here.]

 

How did Lawler miss this obvious inference? Has the bad old logic "nullified" his brain? Has Hermetic Hype "cancelled" his ability to use/understand a simple "either-or"?

 

The rest of what Hegel says should now be introduced to of one of Hume's bonfires.

 

I'll fetch the matches...

 

[I am, of course, joking!]

 

Acid Finally Corrodes Hegel's 'Logic'

 

Remember: if you are viewing this with Mozilla Firefox, you might not be able to read all the symbols I have used. I have no idea whether other Browsers are similarly affected.

 

Hegel's acid example isn't too clever, either. Lawler commented on it as follows:

 

"…the acid is only an acid through its implicit relation to what negates it…." [Ibid., p.38.]

 

A sentiment echoed by this dusty old Stalinist textbook:

 

"An acid has many properties, but the most essential is its ability to combine with an alkali or a metal and form a salt. In a word the most essential qualities are those which a thing manifests in relation to 'its other,' to its opposite." [Shirokov (1937), p.272. Quotation marks altered to conform with the conventions adopted at this site.]

 

That old textbook, or rather its authors, failed to notice that if both bases and metals are the 'other' of acids, then acids don't have a unique 'other', which in turn means Hegel, Lenin and Lawler were/are mistaken.

 

Ignoring that awkward fact for now, acids burn the skin, not because a base exists (which negates nothing, since a base isn't a sentential/phrasal operator; neutralise is not negate) -- which would counteract it if they came into contact --, but because of its corrosive properties. And, if there were no bases anywhere in existence, acids would still do what acids do. Or are we supposed to conclude that individuals can protect themselves from, say, the burning effect of concentrated Nitric Acid on unprotected skin by making sure there are no bases anywhere in their vicinity?

 

Anyway, in what sense is a base (like NaOH -- Sodium Hydroxide) the opposite (the 'other') of an acid (like HNO3 -- Nitric Acid)?

 

   

 

Figure Three: A Match Made In Hegelian Heaven?

 

But, Nitric acid is 'neutralised' by countless bases, and not just Sodium Hydroxide. The same is true of other acids. Do they all have countless 'others', as well, contrary to what Hegel assured us must be the case? Of course, if these were genuine 'dialectical opposites', they would turn into each other as the DM-Classics assure us they must. Does Nitric Acid turn into Sodium Hydroxide? Or vice versa? If they do, Inorganic Chemistry textbooks have been remarkably quiet about it.

 

It could be argued that Hegel is making a generic point here, that in general acids and bases are dialectical 'opposites'. But, modern definitions of acids don't characterise acids in such a simplistic way. The Brønsted-Lowry definition says that acids are proton donators, while the Lewisian definition tells us that an acid is an electron-pair acceptor. Admittedly, bases are still defined as the 'opposite' of each of these, but acids and alkali's are no longer defined in terms of each other, but in terms of a third item (or, rather, a third and a fourth term, if we lump the lot together). [On this, see Zumdahl (1989), pp.654-56 and Shriver and Atkins (2001), pp.143-76.]

 

So, it seems that Chemistry has taken a decidedly 'reactionary' turn since Hegel attempted to pontificate on the subject.

 

But, this is a specially-chosen example. It won't work in cases that DM-fans conveniently ignore. Many of those were listed in Essay Seven; others were itemised above. Here are several additional examples for readers to ponder: voltage, current and resistance are all interlinked, but no single one has its 'being' defined in terms of any one "other" (but two "others"); this is also true of pressure, volume and temperature in an ideal gas, just as it is true of the four separate entries in the traditional Square of Opposition (where implications, contraries (two propositions which can't both be true but can both be false), subcontraries (two propositions which can't both be false but can both be true) and contradictories (two propositions which can't both be true and can't both be false) are interdefined among these three "others"). What are we to say of the US Constitution (and of many other countries), which sees the State separated into three main branches: The Executive, The Legislature and The Judiciary?

 

Lest these be rejected as 'abstract' (a fine accusation to be levelled by anyone who looks to Hegel for inspiration!), consider this: in the Periodic Table, none of the Halides (Chlorine, Bromine, Fluorine, Iodine, etc.) are defined in terms of a significant "other", and neither are salts, proteins, enzymes, catalysts, alcohols, and aldehydes.

 

Finally, what are we to say of "buffer solutions", which can be both acid and alkaline?

 

Infinitely Confused

 

This entire topic was further muddled by Hegel's confused and obscure musings about "finitude" and "infinity". Lawler quotes him as follows:

 

"Thus essentially relative to another, [something -- Lawler's addition, RL] is virtually against it: and since what is passed into is quite the same as what passes over, since both have one and the same attribute, viz., to be another, it follows that something in its passage into other only joins with itself. To be thus self-related in the passage, in the other, is the genuine Infinity." [Lawler (1982), p.39, quoting Hegel (1975), p.139, §95; Lawler's italics. Again, I have used the on-line version of Hegel's text.]

 

Well, that certainly clears things up!

 

But, how is self-relation a "genuine Infinity"? Lawler just accepts this mystical morsel and fails to explain why his readers should match his gullibility, except he expands on it with another barrage of obscure language:

 

"…[I]n speaking of the chemical relation of an acid and an alkali, where he notes that 'the negation of the negation is not a neutralization: the infinite is the affirmative, and it is only the finite that is absorbed' [Lawler is quoting Hegel, taken from here -- RL]. The 'absorption' of finite objects consists in the transition implicit in the 'want of correspondence between their immediate being and what they essentially are,' which leads to the realization of that essential being or to the 'genuine Infinite' which Hegel calls being 'self-related in the passage' into the other. In other words, since the other is essential to the original being, there is a form of relating to that other which is not a relation to something 'alien' but a 'self-relation' -- a relation in which the being, at first seemingly self-sufficient, finds its 'self' in and through the other (its other, some definite other)." [Ibid., p.39. Italic emphasis in the original.]

 

I think I have posted enough derogatory remarks about verbal knotweed like this, but what is a materialist like Lawler -- I am assuming, of course, that he is a materialist! -- doing helping spread this Idealist pest, as if it helps account for anything?

 

We seem, therefore, to be going backwards; our "passage" away from the clarity to be found in FL (and, potentially, in ordinary language) appears to be accelerating toward the 'infinite non-sense' of dialectics.

 

Surprisingly, we now encounter another puzzling passage as Engels connects this mysterious 'infinity' with "law":

 

"'[F]undamentally we can know only the infinite.' In fact all real, exhaustive knowledge consists solely in raising the individual thing in thought from individuality into particularity and from this into universality, in seeking and establishing the infinite in the finite, the eternal in the transitory. The form of universality, however, is the form of self-completeness, hence of infinity; it is the comprehension of the many finites in the infinite. We know that chlorine and hydrogen, within certain limits of temperature and pressure and under the influence of light, combine with an explosion to form hydrochloric acid gas, and as soon as we know this, we know also, that this takes place everywhere and at all times where the above conditions are present, and it can be a matter of indifference, whether this occurs once or is repeated a million times, or on how many heavenly bodies. The form of universality in nature is law, and no one talks more of the eternal character of the laws of nature than the natural scientists." [Engels (1954), pp.234; quoted in Lawler, pp.39-40. Italic emphases in the original. I have used the on-line version, again.]

 

Lawler comments on this idea as follows:

 

"While rejecting Hegel's ultimately idealist interpretation of 'self-relation' or 'reflection' in the other as 'ideality,' Engels' treatment of 'infinite' as law-governed process, 'absorbing' finite moments into itself, is faithful to Hegel." [Lawler (1982), p.40.]

 

At the risk of repeating myself, how is it possible to equate the word "infinite" with "law-governed process"? Are the rest of us using the wrong Mystical Gobbledygook Into Plain English dictionary?

 

Now, Engels certainly tried to connect, or even equate, these two terms, but, for those of us who are still in command of the language, neither an "always" nor an "at all times" is an "infinite". Natural selection is now "always" working, but it isn't 'infinite'. Capitalists are "always" trying to maximise profit, but that isn't an 'infinite', either.

 

[In Essay Thirteen Part Two, we will see that this view of scientific or physical law developed out of ancient, animistic ideas about nature and causation, so it is no surprise to find this doctrine re-surfacing here in such mystically-compromised company. (On this, see here and here; the first is Swartz (2009), the second Swartz (2003). See also Guy Robinson's Essays.) Certainly, a weak case could be made for linking "general" with "law-governed" -- but, given the fact that Hegel's 'logic' destroys generality, no Hegelian (drawn either from the 'orthodox upside-down' wing, or the 'renegade right-way-up' tendency) is free to make that connection. Of course, the real problem here is the fondness traditional theorists have for the use of the word "infinite", a notoriously difficult term and one whose many 'attempted definitions' have so far created more 'problems' than the introduction of this word (in these contexts) was meant to resolve. I will say more about that in Essay Twelve.]

 

As noted in Essay Three Part One, from simple sentences like "John is a man" (and now, in Lawler's case, "Socrates is mortal") we can -- if we were so minded -- 'derive' the idea that the world is a 'law-governed' "Totality" alongside the theory that knowledge is an 'infinite' asymptotic journey into the eternally 'unknown'. As Lawler explains (beginning with a quotation from Hegel):

 

"'Outside one another as the phenomena in this phenomenal world are, they form a totality, and are wholly contained in their self-relatedness. In this way the self-relation of the phenomenon is completely specified, it has Form in itself: and because it is in this identity, has it as essential subsistence. So it comes about that the form is Content: and in its mature phase is the Law of the Phenomenon.'

 

"It is clear from these passages that 'ideality' is not derived by Hegel from the simple suppression of distinct phenomena but from the interaction and dialectically negative interpenetrations which result in their law-governed transformations. The explosive combination of hydrogen and chlorine is more than the 'clash' of two externally related beings. It is the negation of their 'immediate' form as self-subsistent 'free' entities, and the realization of their inner or essential connectedness with each other (under the necessary conditions). The result is not their mutual annihilation, but their transformation." [Ibid., p.40, quoting Hegel (1975), p.189, §133. Lawler's version has italic emphases; the original has bold. I have used the original.]

 

But, this rather poetic description of a chemical reaction is far from being even 'metaphorically true'. Since when has Chlorine ever been a 'free entity'? At the very least, as a gas under normal temperature and pressure, each atom of Chlorine exists as a diatomic molecule, bound to another atom, and in aqueous solution, it whiles away the hours as an ion. Nowhere in nature does it subsist as a 'pure' element, as far as we know, and certainly as far as Lawler or Hegel knew/know. [If it does so exist, Lawler cited no authoritative source in support of that assumed 'fact'.]4

 

And, we note once again that the Mystical and Hermetic typology of the "other" has now been quietly dropped, since Chlorine reacts with practically everything. Indeed, it has more "others" than the number of times Trump has been caught lying.

 

By way of contrast, if we choose a far less 'dialectically-accommodating' element -- say one of the 'Noble gases' (Helium, Neon, Krypton, Xenon, etc.), which seem in comparison to be rather stand-offish loners, 'rugged individuals' if you please, with no willing "others" to speak of -- the above comments become all the more apposite. That is because, except under the most extreme of conditions these gases react with nothing at all, and have to be dragged, kicking and screaming down the "passage".

 

"[O]ne might describe the noble gases as aloof. Because they're reluctant to share electrons from their filled outer electron shells, noble gases are generally considered unreactive. But it is possible to wrestle reactivity from these elements, as...Neil Bartlett showed in 1962, when he made the first noble-gas compound, Xe[PtF6], by mixing xenon with platinum hexafluoride.

 

"Making noble-gas compounds is not for the faint of heart, however. Because the electrons in the noble gases' outer shells are comfortable where they are, it requires extremes -- like reactive reagents, low temperatures, or high pressures -- to get them to budge. When compounds do form, the results are seldom practical: most noble-gas compounds are too fleeting or unstable to be useful. But the few chemists who take on the challenge of coaxing reactivity from these recalcitrant elements say the true rewards are finding new insights into the nature of reactivity and chemical bonding." [Quoted from here; accessed 08/03/2022. See also Shriver and Atkins (2001), pp.428-32. Bold emphases added.]

 

So, even the reluctant 'logical' object, Fluorine -- this "other" that appears to be the only Halogen that will react with a Noble Gas, and then only with Xenon -- (Shriver and Atkins (2001), pp.430-32) -- will have to be forced into accepting to its 'dialectically-determined fate' with respect to these inert elements, these Noble Gases, by reacting with them. [If so, are the "others" of the Noble Gases dependent on human -- i.e., external -- intervention? Does the dialectic in nature really need a helping hand? Did these "others" only begin to exist when human beings with advanced technology and expert knowledge appeared on the scene?]

 

But, even if the above 'mystical fairytale' (about the formation of HCL) were correct, exactly how this is an internally-driven process is still far from clear. Surely, Chlorine isn't to be regarded as not-Hydrogen? If it were, then everything in the universe that is not Hydrogen (or not-Hydrogen) would be Chlorine, or, at least, its "other"! Conversely, everything that is not-Chlorine would be Hydrogen, or, perhaps, its "other". [In which case, dear reader, in so far as you are 'not Hydrogen', you must be Chlorine, as well as Zinc, and pencil shavings, and poisonous reptiles, and used bus tickets, and interstellar gas, and..., since all of these are 'not-Hydrogen', too!]

 

Of course, that is why Hegel invented the myth of a unique, significant "other" (supposedly identified by 'determinate negation') in order to block this impertinent, but rather obvious, objection -- as well as exclude the above 'others' as legitimate 'others', to begin with. However, we have already seen that Chlorine reacts with so many things we would have to use a veritable via negativa to 'identify' it -- when, for example, Chlorine is declared not-this, not-that, not-this, not-...; indeed, in the limit, it would be not-anything. Trapped in this Hermetic Hell Hole, Chlorine would disappear about as relentlessly as the Cheshire Cat's smile! The same is true, only more so, of Fluorine, and even more so of Hydrofluoric Acid.

 

Furthermore. as we saw in Essay Eight Part One, these obscure 'internal relations' in the end turn out to be mis-identified or mis-described 'external relations'. It is little wonder then that we need the timely and welcome assistance of Hegel's Super-Duper 'Logic' in order to appreciate more fully such cosmic verities, so effortlessly discovered by the simple expedient of fiddling around with a few words --, or, even easier, by gluing a negative particle to a convenient Noun Phrase. That is because, ordinary language, FL, and the good old-fashioned material universe are most unhelpful in this regard, with anti-dialectical counter-examples around every corner, including corners.

 

[After all, what is the 'dialectical opposite' of a corner? If they have none, are corners unchanging, eternal beings?]

 

We now encounter the following passage, which attempts to resolve the above 'difficulties':

 

"However, if their identity is narrowly or abstractly defined by the superficial features of their original phenomenal form, the result appears to be annihilation. And this annihilation seems to 'realize' a formal contradiction: for example, 'hydrogen exists independently of chlorine' and 'hydrogen does not exist independently of chlorine.' Following the law of noncontradiction, both of these statements can only be true if we distinguish the 'different respects' in which independence of chlorine can be asserted and then denied of hydrogen. Thus, in the original free state hydrogen is independent of chlorine, while in the chemical reaction or in the hydrochloric acid gas it is not. The logical contradiction in the original crude statements seems to be resolved by qualification of the different respects or conditions in which the seemingly contradictory assertions hold." [Ibid., p.40.]

 

The first example (i.e., "Hydrogen exists independently of chlorine") is apparently of the form:

 

L11: E(x)E(y)[(Hx & Cy) & Fxy].

 

Or perhaps even:

 

L12: ∀(x)∀(y)[(Hx & Cy) ® Fxy].

 

L13: ∀(x)E(y)[(Hx & Cy) ® Fxy].

 

[Where "E" is the existential quantifier, "" is the universal quantifier; "®" is the implication arrow (i.e., "if...then"); "H(ξ)" and "C(ζ)" go proxy for one-place, first level predicate expressions/predicables, in this case standing for "ξ is Hydrogen" and "ζ is Chlorine", respectively; "F(ξζ)" is a first level, two-place predicable (in this case, a binary relation), standing for "ξ is independent of ζ"; and "x" and "y" are bound variables, ranging over elements, in the above examples.]

 

L11 roughly reads: "There are two elements, Hydrogen and Chlorine, which are independent of each other". In that event, its contradictory would be: "No two elements, which are Hydrogen and Chlorine, are independent of each other".

 

L12 translates approximately as: "Take any two elements, if they are Hydrogen and Chlorine, then they are independent of each other". If so, the contradictory would be something like: "For any two elements, if the first is Hydrogen and the second is Chlorine, then there is at least one instance where they are not independent of each other."

 

L13 is roughly: "For any element which is Hydrogen, if there is a second element which is Chlorine, then they are independent of each other". The contradictory here would be something like: "For any element which is Hydrogen, there is no second element which is Chlorine that is independent of it."

 

If, on the other, hand Lawler's example were of the following form:

 

L14: E(x)E(y)[(Hx & Cy) & Fxy],

 

where "F(ξζ)" is a first-level two-place predicate, standing for "ξ exists independently of ζ", not much would change. [No pun intended.]

 

L14 is roughly: "There are two elements Hydrogen and Chlorine and they are independent of one another". Its contradictory would be something like "There are no two elements, Hydrogen and Chlorine, that are independent of one another."

 

Of course, it is unlikely that this way of analysing propositions will find ready acceptance among dialecticians. Indeed, there is nothing that forces any of us to adopt this method, or logic, or even both (except perhaps the fact that it prevents this mystical sort of a priori Idealism and Superscience from establishing even so much as a slender toe-hold in our brains, as was pointed out in Essay Three Part One, here and here). Anyway, if for some reason this more precise and contemporary method of analysis is rejected, then Lawler's example would be a contradiction only if someone asserted both conjuncts, held both to be true at once, and who then denied both could be false at once. But, who on earth would want to do that?

 

[In all his talk about "respects", I suspect Lawler half realised this, but also seemed to want to ignore it.]

 

In that case, this latest example is yet another logical flop. It certainly doesn't resolve the above 'difficulties'.

 

Two Meanings  Of "Independent" Conflated

 

On second thoughts, maybe it does, for Lawler continues:

 

"We should first of all note that the above reformulation of the apparent contradiction implicitly depends on the general proposition, formulated according to the law of noncontradiction, that something, at any one time or in one respect, is either independent or not independent (dependent). But for something which is independent to become dependent, it must have within it the potential to become dependent. It was therefore relatively, not absolutely independent. The potentiality for the chemical reaction was present in the hydrogen in its free state. To follow Hegel's form of expression, in its free state hydrogen was all the while 'repelling' or negating possible reactions with other elements with which it was nevertheless related. Its 'independence' was maintained in its state of interdependence under certain conditions where this was possible." [Ibid., pp.40-41.]

 

Unsurprisingly, there are several highly dubious moves in the above argument. The original claim that "Hydrogen is independent of Chlorine" has now morphed into "Hydrogen is independent, period" -- that is, it now seems to be independent of everything. Moreover, the meaning of the word "independent" has altered in like manner. From "independent" implying "not linked to" (or "isolated from"), it has become "does not depend on", and it is this slide that allows the conclusion that one item both can and does depend on the other to be smuggled in while no one was paying close attention.

 

But, it is surely possible for Hydrogen to exist totally isolated from Chlorine (this is the first sense of "independent") and for it still to be capable of reacting with it if and when its quarantine-like status has ended.

 

Indeed, scientists invent new compounds all the time (about which they might initially know very little), that have to be isolated from other compounds (some of which they will never encounter), but with which they would/could react if given the chance.

 

Let us assume, therefore, that one day a team of scientists create a new compound called "Hegelase" (a new form of poison -- apparently it blocks certain "passages" and cripples a victim's powers of reason before brain death finally sets in), which they keep isolated from everything else as best they can, for obvious reasons. However, let us further imagine that some of this compound escapes and kills a dialectician, who, for the sake of mischief, we will call "Lawless".

 

Now, did Hegelase have the potential to kill Lawless before it reached him? Was Hegelase's significant "other" Lawless himself? Well, in the sense that this poison will kill him if it reaches him, it most certainly had that potential, which is why it had to be isolated (and not just from Lawless). On the other hand, in the sense that Lawler (not Lawless) requires, the answer must be: "No, it doesn't because it isn't Lawless's 'other'". If it were, then we would be forced to conclude that Hegelase has seven billion or so "others" out there (i.e., the rest of the human race currently alive), which it has the potential to kill 'programmed' into it. And if we now assume that Hegelase is able to kill every living thing on the planet, then those seven billion "others" would in comparison amount to a tiny fraction of all of those countless "others" out there.

 

Does this one chemical have so much 'programmed' into it? So many significant "others"?

 

For those who regard "potentialities" as "actualities" in disguise --, or, at least, who view them as very well hidden "actualities" just waiting to pounce --, the above example presents several serious problems. Every time a new life comes into the world, Hegelase would gain a new "potentiality", for free, without breaking into a sweat.

 

Let us now imagine that a new strain of bacteria comes into existence (which, for the sake of further mischief, we will christen "Grantococcus Woodsonii B#2", or "GWB2", for short), by means of whatever processes such cells have for evolving. Let us further suppose that Hegelase can (i.e., has the potential to) kill GWB2. When GWB2 came into existence, Hegelase thus gained a new potential, an ability to kill GWB2 (let us call this potential, PGWB2, for short). But, to do that it must have had the potential to develop this new potential (or it wouldn't have happened, given the traditional way of looking at such potentialities). So, before PGWB2 came into existence, GWB2 must have also had a potential to develop PGWB2 (call this meta-potentiality, PPGWB2). But, once more, in order for that to happen, PGWB2 must have had a further potential to develop PPGWB2 (say, PPPGWB2), too. Well, it doesn't take very much Diabolical Logic to see where this is going if we insist on regarding potentialities as the disguised, or as the hidden properties of bodies (perhaps under the auspices of those ubiquitous, but ill-defined, 'dialectical negations'), and not just our way of describing, not necessarily explaining, what they do or can do.

 

We are forced to conclude this or imagine that Hegelase has an (actual?) potential to kill things that do not now exist (and perhaps might never exist). But, what kind of 'potential' is that? This is a blank metaphysical cheque that surely threatens to break the ontological bank.

 

However, even if the above conclusions are rejected for some reason (perhaps, by the use of a complex counterfactual, or a crafty deployment of the Nixon defence), what is all this "repelling" that Hegel thinks atoms engage in?

 

"To follow Hegel's form of expression, in its free state hydrogen was all the while 'repelling' or negating possible reactions with other elements with which it was nevertheless related. Its 'independence' was maintained in its state of interdependence under certain conditions where this was possible." [Ibid., p.41. Bold emphasis added.]

 

It is worth noting that in the highlighted parts of the above passage Lawler implicitly admits that Hydrogen, for example, has no single significant "other", it has many such "others". With that (unforced) admission/faux pas we can see that Hegel's account of change "repels" even his own 'logic', and collapses under the weight of its 'internal contradictions', once more.

 

A rather ironic but no less fitting fate for so confused a 'theory' to have to experience.

 

Independently of this (no pun intended), Lawler nowhere explains how Hydrogen is able to ward off all its many unwanted suitors. Does it have bad breath? Does it bathe only once a year? Maybe it behaves obnoxiously? Perhaps it has a couple of vicious dogs guarding it? Maybe it fends them of with a copy of Hegel's 'Logic', or something written by Zizek or a contemporary French 'philosopher'?

 

As the point of asking facetious questions like these suggests, it isn't easy to take Lawler seriously, here. In fact, this looks like yet another example of DM-special pleading. Anyone using Hegel's sub-Aristotelian 'logic' has no way of explaining how elements like Hydrogen do not have countless "others". Smuggling in a bogus mechanism by which Hydrogen is able to 'repel' all but one of these other "others", which mechanism is left forever unexplained (except with yet more word-juggling), might impress the easily impressed, but that is about all it will achieve. In effect, it is the dialectical equivalent of all those ad hoc appeals to 'divine miracle' and convenient 'mysteries' (in order to explain every apparent suspension of the course of nature), which Christians are fond of doing. For what else is a verbal trick that would see Hydrogen not interact with anything else -- all those 'others'?

 

It could be argued that this is unfair. All Hegel requires is that while a Hydrogen atom is reacting in one particular way, it can't be reacting in any other way. So, for example, while one such atom is reacting with Oxygen to produce water it can't also be reacting with Chlorine to produce Hydrochloric Acid.

 

Of course Hydrogen atoms don't exist for long as single atoms, but readily form diatomic molecules. [Shriver and Atkins (2001), pp.256ff.] But, even if for the moment we accept the details rehearsed in the above volunteered DM-response -- i.e., that a Hydrogen atom can react with only one other atom at a time --, that Hydrogen atom will in fact react with another Hydrogen atom and an oxygen atom to produce water. So, it will have two "opposites" given the above view of the formation of water. [This doesn't mean I accept that rather idealised 'explanation' of the formation of water!] However, when we turn our attention to another element, Carbon, we see that it will react with many other atoms at the same time (for example, Hydrogen and Oxygen). In that case, the above volunteered DM-response doesn't in general work, even if we assumed it were viable to begin with.

 

[Again, as we have seen so many times (in other Essays published at the site), I am forced to try to make sense of these DM-fantasies by offering counter-examples to my own argument, or, as here, offer a volunteered DM-explanation that tries to defend DM, or present what might be considered a plausible DM-interpretation/'clean-up', since DM-fans don't ask the sort of questions I do. And even when they are confronted with them they tend to reject detailed enquiry/analysis as "pedantry". (I have said more about that, here.)]

 

Be this as it may, is Hydrogen really that intelligent or, indeed, single-mined? Can it really "repel" each and every "possible" reaction -- even those on the far side of the universe? [This mighty atom is clearly master of all it can't survey.] Anyway, why describe such a constraint (i.e., that a single atom can only react with another atom, one at a time) as "repelling". If you, dear reader, are doing something (such cooking a meal), which prevents you from doing something else (such as mowing the lawn), in what way would you be "repelling" mowing the lawn? More to the point how does any of this imply that Hydrogen doesn't have countless "others"?

 

Apart from sounding profound, what sense can be made of the above rather odd claim?

 

Maybe this?

 

"Within this analysis, the concept of independence and nonindependence as mutually exclusive states applies primarily or most adequately to the surface distinction between the phenomenal states of hydrogen (classification of phenomena) but does not apply, at least with the same ease, to the law of hydrogen's development and its internal structure. In this deeper analysis it is necessary to see 'independence' as a form of interdependence ('nonindependence'). The conception of the categories 'independence' and 'dependence' as mutually exclusive and so not applicable to the same thing -- in the same respect -- is more difficult to defend." [Ibid., p.41.]

 

And yet, this only works because of the ambiguous way that the words "independence" and "dependence" have been used. As noted earlier: one minute the word "independent" means "isolated", or "free and unconnected", the next it means "not dependent on".

 

Lawler then proceeds to ruminate on a few technical notions connected with "form" and "essence":

 

"One might argue that Hydrogen in its free state is independent 'in respect to' its actual form and dependent 'in respect to' its essential relations (or its potential). But this analysis only postpones the problem, for it implies that 'form' and 'essence' or 'actuality' and 'potentiality' can be distinguished as 'respects' [sic] of the object -- in a manner at least analogous to the way we can distinguish the two distinct states of Hydrogen.  But 'phenomenal form' cannot be distinguished from 'essence' in the way in which two phenomenal states can be distinguished. The form is the form only through the essence and vice versa -- but the one is not the other. Although 'essence' and 'form' are mutually exclusive categories there is no possibility of adequately separating the phenomenal 'respect' from the essential 'respect' -- so as to permit one to say, unproblematically, that hydrogen in its phenomenal form is independent while in its essential properties it is not independent. Such a distinction of respects superficially applies to the two phenomenal states of hydrogen ('superficially' in the sense that it is necessary to go on from the distinction to understanding the law relating to the phases of hydrogen's transformations). But in understanding the essential nature of hydrogen there can be no comparable distinguishing of 'respects' -- except as an abstract or formal approximation of the dialectical unity of opposites." [Ibid., pp.41-42. Italic emphasis in the original.]

 

What exactly the "unity of opposites" amounts to here is left annoyingly vague, hence the whole passage is about as clear as a good old-fashioned London smog. [We have already seen that there is no such thing as "essential nature" -- or rather, it makes no sense to suppose there are any such --, a fiction invented by card-carrying mystics and ruling-class ideologues. So, as one might have predicted, this idea was bound to re-surface in DM! The "ideas of the ruling class", etc., etc....]

 

 

Figure Four: Dialectical 'Clarity', At Last!

 

A Few Loose Threads Left

 

Mercifully, we are nearing the end of Lawler's losing battle with the English language. He now tries to draw several seemingly disconnected threads together:

 

"Thus the process of chemical reaction demonstrates the inner connectedness as well as relative opposition of hydrogen and chlorine which must be taken into account and explained in a scientific theory of the law of chemical reactions and in an understanding of the particular properties of these elements. The 'finitude' that is suppressed is the particular state of the element as 'free,' as existing (relatively) independently of other elements while being essentially related to them. Realisation of the reaction constitutes at least some approximation to the 'self-relatedness' which Hegel calls 'genuine infinity'. (This amounts to the claim that the essential nature of elements consists in their reactions and combinations rather than in their relative independence in a free state.)" [Ibid., p.42. I have yet to see a single Chemistry textbook that has gone down this route and used Hegel's obscure ideas to advance our knowledge of the world and all the elements and compounds it contains -- and that includes those written in 'communist' countries. If anyone knows of one (or more) such, let me know.]

 

However, all that Lawler has done here is interconnect certain elements (Hydrogen and Chlorine) with talk about potentialities, which, because of the problems rehearsed earlier, they can in no way be regarded as physically real. Of course, they could perhaps be viewed as a metaphorical or poetic way of depicting the capacity these elements have to react with other substances (under certain circumstances). In addition, we have seen that this entire approach was predicated on the random juggling of a few letter "A"s, themselves of a somewhat 'mercurial' disposition (or, indeed, "potential"). [Irony intended.]

 

[As we will see in Essay Twelve Part Four (when it is published), all this dialectical talk about 'independence' and 'relatedness' (relative or otherwise) is no less confused. Discussion will therefore be postponed until then (since it is far from clear what the above comments have got to do with 'dialectical contradictions').]

 

As far as the laws that 'govern' nature are concerned, they can't be viewed as literal decrees written into, or superimposed on, matter that everything has to obey (as Lawler seems to imply). To be sure, Hegel himself might (consistently) have been able to adopt that animistic way of viewing things/'concepts'/'laws' (given his overt devotion to Mystical Christianity), but no materialist can or should -- unless, of course, they capitulate and subscribe to the non-materialist dogma that the universe is governed by a 'Cosmic Will' or 'Mind' of some sort. [Again, on that, see here and here.]

 

In fact, Lawler admits as much in his final paragraph:

 

"It seems that the main reason why Hegel terms the essential relatedness of one element to another and their lawful connectedness as their 'ideality' is that Hegel regards matter as inherently incapable of such relations and transformations. Matter is conceived of as the embodiment of the principles of abstract understanding. In other words, Hegel accepts the mechanistic or atomistic theory of matter, and so any discovery nonmechanistic, nonatomistic properties of reality is interpreted as evidence of the operation of a nonmaterial force -- the Idea." [Ibid., p.42. Bold added.]

 

And there we have it in a nutshell! Hegel's Mysticism and  Idealism prevented him from seeing the material world as sufficient to itself, or capable of doing all the things we have seen Idealists deny it is capable of doing, unaided -- since, according to them, the contrary supposition wouldn't be 'rational'. This is where their Theism (or, in Hegel's case, perhaps, his Panentheism) rears its ugly head. Earlier we saw Lenin take the side of the Idealists against the materialists on this very issue (here and here), just as we have seen other dialecticians tell us that matter is merely an abstraction, in need of help from countless other 'abstractions' for it to work! That alone explains all the convoluted word-magic and symbol-juggling -- overtly or covertly aimed at re-enchanting nature -- in order to view the world as, in effect, the development of Idea, since plain-and-simple, common-or-garden, boring old matter isn't quite up to scratch if left to its own devices, as far as these mystics are concerned. Which is, of course, why they have always hated and opposed us materialists.

 

But, how does Lawler square all this with HM? Disappointingly, like this:

 

"But the fact that Hegel sees in natural laws a manifestation of this Idea makes possible materialistic interpretations which reverse this scheme -- interpreting the 'idea' as the subjective image of the material law. This reinterpretation requires a rejection of the mechanistic form of materialism and the development of a more advanced theory of matter." [Ibid., p.42.]

 

And yet, how could this possibly work if the belief that there are laws in nature (which in fact turn out to have been derived from misconstrued, garbled 'laws' of 'logic') is itself based on an Ideal view of reality? We have seen how the quirky 'logic' that Hegel employed helped conjure these mythical beings (these "laws") into existence from a range of specially-selected words and concepts -- which were then distorted -- and nothing else. Simply reversing our perspective (putting Hegel back 'on his feet') in no way transforms bogus moves like these into valid inferences. Without the Ideal background that Hegel attempted to concoct these (allegedly) materialist 'laws' have no ontological basis, no rationale (except perhaps in a more deflationary sense as integral to the way we try to make sense of nature -- a sort of 'materialist' and watered-down version of Positivism, a "subjective image of the material law").5

 

What A Dialectical Dog's Dinner!

 

And that's it! This article is the best explanation and defence of the obscure doctrine that there are such things as 'dialectical contradictions' I have read in over 30 years picking my way through the conceptual rubble left behind by Hegel!

 

Read it again if you must, dear reader, and scratch your rather 'inadequate' materialist head (alongside yours truly).

 

WTF is a 'dialectical contradiction'?

 

Are you any the wiser?

 

If you are, please help me out, for I am, if anything, even more in the dark!

 

On several occasions throughout this site I have claimed that the objection that dialectical mystics often throw in the faces of us genuine materialists (i.e., that we don't "understand dialectics") in fact applies in reverse, to these very same mystics, since they clearly don't understand the phrase, "dialectical contradiction". What is worse, these mystics have shown time and again they are totally incapable of explaining (with any clarity) what a single 'dialectical' concept amounts to (in over 150 years of not trying too hard) -- even to one another. If the very best attempt to explain what a 'dialectical contradiction' is, is itself hoplessly vague, confused and shrouded in mist, readers can perhaps now see why I have repeatedly asserted such things.

 

Finally: reading through the many papers and books written by Dialectical Marxists (who still think we can learn anything from Hegel) one is struck by the similarities between their approach to knowledge and that adopted by, for example, Roman Catholic Philosophers and Theologians. Nearly a thousand years ago they began the unenviable task of trying to render Aristotle's theories consistent with Church Dogma, then later with science -- and who are still trying to do it, and who, even now, attempt to defend Papal Infallibility (in the face of the countless screw-ups emanating from the Pontiff himself we have witnessed over the last fifteen or more centuries).

 

The 'logical' distortions DM-fans are thereby forced to inflict on language and thought are eerily reminiscent of the linguistic gyrations perfected by the above theologians and casuists. Indeed, the verbal somersaults dialecticians perform surely merit some sort of International Gymnastics award. Dialectically double-jointed comrades should, in my opinion, receive Gold every time.

 

Lawler is no exception. In order to make Hegel's obscure jargon 'work' he has to twist language way beyond even the knotted pretzel stage, rather like the aforementioned Roman Catholic Contortionists.

 

 

Figure Five: Compared With Dialectics, This Pretzel

Is Remarkably Straight And True!

 

Now, I don't expect hardboiled dialecticians to accept the validity of the above criticisms since they are still committed to the ancient idea that human discourse, or 'thought', at some level contains or possesses a key to the inner secrets of 'Being', but only if it is 'processed' enough and in the 'right' way. Given this archaic view of language and 'thought', all that an aspiring Philosophical Alchemist has to do is find the right formula -- the right key --, and 'linguistic dirt' can be turned into Philosophical Gold, this impressive transformation achieved without leaving the non-dialectical armchair. As Lenin (inadvertently) admitted:

 

"Hegel brilliantly divined the dialectics of things (phenomena, the world, nature) in the dialectics of concepts…. This aphorism should be expressed more popularly, without the word dialectics: approximately as follows: In the alternation, reciprocal dependence of all notions, in the identity of their opposites, in the transitions of one notion into another, in the eternal change, movement of notions, Hegel brilliantly divined precisely this relation of things to nature…. [W]hat constitutes dialectics?…. [M]utual dependence of notions all without exception…. Every notion occurs in a certain relation, in a certain connection with all the others." [Lenin (1961), pp.196-97. Italic emphases in the original. First bold emphases alone added.]

 

"The identity of opposites…is the recognition…of the contradictory, mutually exclusive, opposite tendencies in all phenomena and processes of nature…. The condition for the knowledge of all processes of the world in their 'self-movement', in their spontaneous development, in their real life, is the knowledge of them as a unity of opposites. Development is the 'struggle' of opposites…. [This] alone furnishes the key to the self-movement of everything existing…." [Ibid., pp.357-58. Bold emphases alone added.]

 

"Flexibility, applied objectively, i.e., reflecting the all-sidedness of the material process and its unity, is dialectics, is the correct reflection of the eternal development of the world." [Ibid., p.110. Bold emphasis added.]

 

As I pointed out in Essay Two:

 

Lenin is quite open about the origin of his ideas in these private notebooks: dialectics derives its 'evidential' support -- not from a "patient empirical examination of the facts" -- but from studying Hegel! As far as evidence goes that is it! That's all there is! The search for evidence begins and ends with dialecticians leafing through Hegel's Logic. That is the extent of the 'evidence' Lenin offered in support of his assertions about "all notions" without exception, about "all phenomena and processes in nature", and about nature's "eternal development", etc., etc.

 

As we will discover in the next two Essays (Nine Parts One and Two), 'dialectics' can't even be based on the revolutionary practice of the party -- never mind everyday experience or the development of science.

 

Dialecticians are indeed the philosophical equivalent of those whom Marx called revolutionary alchemists -- except these dialectical casuists are looking for the right verbal formula, the right combination of words that will 'allow' them to unlock the 'doors of perception', giving access to the hidden mysteries of 'Being', thus enabling them to construct an Ideal world as political expediency requires. Up to now, they have manifestly failed to transform the class structure of the planet, but, not to worry, they have compensated for that fiasco by withdrawing into an Ideal World where they can juggle with 'reality' to their class-compromised hearts' content, ignoring both criticism and long-term failure in equal measure.

 

And that is partly why they cling to this mystical theory for dear life -- resisting all attempts to prize their fingers loose. Indeed, they do this for reasons Feuerbach exposed nearly two centuries ago: it is because this theory 'allows' them to view the world as the opposite of the way it really is -- consolation derived from linguistic contortion.

 

There is no arguing with Hermetic Faith like this. As I have pointed out elsewhere:

 

The founders of this quasi-religion weren't workers; they came from a class that educated their children in the classics and in philosophy. This tradition taught that behind appearances there is a hidden world, accessible to thought alone, which is more real than the material universe we see around us.

This way of seeing things was concocted by ideologues of the ruling-class, who viewed reality this way. They invented this world-view because if you belong to, benefit from or help run a society which is based on gross inequality, oppression and exploitation, you can keep order in several ways.

The first and most obvious way is through violence. This will work for a time, but it is not only fraught with danger, it is costly and it stifles innovation (among other things).

Another way is to persuade the majority (or a significant section of "opinion formers", administrators, bishops, 'intellectuals', editors, teachers, lawyers, philosophers, and the like) that the present order either works for their benefit, is ordained of the 'gods', or is 'natural' and cannot be fought against, reformed or negotiated with.

Hence, a world-view is necessary for the ruling-class to carry on ruling in the same old way. While the content of this ruling ideology may have altered with each change in the mode of production, its form has remained largely the same for thousands of years: Ultimate Truth can be accessed by thought alone, and can therefore be imposed on reality dogmatically.

So, these non-worker founders of our movement, who had been educated as children to believe there was just such a hidden world that governed everything, when they became revolutionaries, looked for principles in that invisible world that told them that change was inevitable and part of the cosmic order. Enter dialectics, courtesy of the dogmatic ideas of that ruling-class mystic, Hegel.

That allowed the founders of this quasi-religion to think of themselves as special, as prophets of the new order, which workers, alas, couldn't quite grasp because of their defective education and reliance on ordinary language, 'abstract understanding', and the 'banalities of commonsense'.

Fortunately, history has predisposed these prophets to ascertain the truth about reality on their behalf, which means they are their 'naturally-ordained' leaders. That in turn means these 'leaders' are the rightful teachers of the 'ignorant masses', who could thus legitimately substitute themselves for the unwashed majority -- in 'their own best interests', you understand.

And that is why 'Materialist Dialectics' is a world-view.

It is also why dialecticians cling to this theory like grim death (and become very emotional (
and abusive!) when it is attacked (by yours truly)), since it provides them with a source of consolation that, despite appearances to the contrary, and because this hidden world tells them that Dialectical Marxism will one day be a success, everything is in fact peachy, and nothing in the core theory needs changing -- in spite of the fact that the core theory tells them that everything changes!

 

Hence, this 'theory' is ossified into dogma, and imposed on reality. A rather nice unity of opposites for you to ponder.

And that is how this 'theory' insulates the militant mind from reality.

In which case (to paraphrase Marx): Dialectics is the sigh of the depressed dialectician, the heart of a heartless world. It is the opiate of the party. The abolition of dialectics as the illusory happiness of the party hack is required for their real happiness. The demand to give up the illusion about its condition is the demand to give up a condition which needs illusions.

Unfortunately, these sad characters will need revolutionary workers to rescue them from their folly.

 

Changing the material conditions that gave rise to such alienated thought-forms is the only way that Dialectical Day-Dreaming like this will be brought to an end.

 

I stand no chance!

 

Dialectical Mystics are just going to have to rely on the material force provided by the working class to save them from the consequences of their unwise, regressive and disastrous decision to allow this virus-of-the-mind to corrupt their thought -- which is why Max Eastman has been quoted several times at this site:

 

"Hegelism is like a mental disease -- you can't know what it is until you get it, and then you can't know because you have got it." [Eastman (1926), p.22.]6

 

Neo-Hegelian, Non-Marxist Attempts To Dispel The Fog

 

In a future re-write of this Essay I will focus on Hahn (2007) and her valiant (but vain) attempt to make what Hegel had to say about 'contradictions' comprehensible. After that, I will trawl through the tangled mess that passes for Hegel scholarship/commentary to see if anyone has managed to translate Hegel's fluent Martian into English, or, indeed, some other language that has ever been spoken on this planet.

 

Kosok's Kooky 'Logic'

 

Preliminary Points

 

Remember: If you are viewing this with Mozilla Firefox, you might not be able to read all the symbols I have used -- Mozilla often replaces them with an "°". I do not know whether other browsers are similarly affected. And, if you are using Internet Explorer 10 (or later), you need to follow the advice given at the top of this page, otherwise many of the links I have included below won't work properly.

 

Kosok (1966) represents what many regard as a bold and path-breaking attempt to 'formalise' Hegel's dialectical 'logic' -- and one that has been recommended to me by various Marxist dialecticians, perhaps in order to help 'put me straight'. Here, for example, is Chris Arthur's advice to that end. But, before I examine this 'formalisation' in detail I need to make four preliminary points:

 

[1] Kosok's article consists of little other than page-after-page of dogmatic pronouncements (most of which are in fact non-sequiturs), of the sort that were shown to be both non-sensical and incoherent in Essay Twelve Part One. In which case, I won't be examining his more substantive 'philosophical' ideas in this Essay. Most of my comments would have overlapped anyway with what will appear in Essay Twelve Parts Five and Six -- when they are published -- where I will be subjecting many of Hegel's core ideas to prolonged and destructive criticism.

 

So, in what follows I will largely be concerned with Kosok's claim to have formalised Hegel's 'logic'. To that end I will be subjecting his work to detailed logical scrutiny. As far as can be determined, this will be the very first meticulous examination (of this sort) it has ever received. Some readers might regard what follows as excessively tedious and 'pedantic'. Any who do so think are encouraged to read this first, and then perhaps think again.

 

Or, of course, proceed no further!

 

Recall, Kosok claimed he had formalised Hegel's 'logic', so it is appropriate to test that claim to the limit. In which case, only a detailed, logical analysis would be the only appropriate way to do that.

 

It goes without saying that critiques like this don't make for easy reading -- certainly no more than Kosok's original article is itself bedtime fodder. In fact, any who can stomach that article should find my critique a veritable 'walk in the park' in comparison.

 

Incidentally, in what follows, I have used the on-line version of Kosok's article. Unfortunately, when the latter is compared with the published version it soon becomes obvious that it contains scores of minor typos as well as several more serious transcription errors, all of which have been corrected in what follows.

 

[2] In order to show how far short even of a sophomoric attempt at formalisation Kosok's rendition falls, it might be useful to remind ourselves what a formalisation in genuine logic or mathematics actually looks like.

 

[A far more competent (but no less incomprehensible) attempt to formalise Hegel's Logic can be found in McCumber (1993), pp.123-78. I will examine McCumber's version in a later re-write of this Essay.]

 

The following relatively simple formalisation has been adapted from Hunter (1996), pp.54-62 (but, for an on-line example, see Shapiro and Kouri Kissel (2018)); but what follows only represents the initial stages of a formalisation of the Propositional Calculus. I won't provide a full formalisation since my aim here is merely to show how lamentable Kosok's rather pathetic gesture in that direction actually is. Indeed, Kosok's work falls short to such an extent that the only honest way to describe it would be to call it a joke.

 

Any who deem that allegation itself rather harsh, if not downright impertinent, should read on where they will soon find their qualms laid to rest.

 

[Finally, in what follows I have included one or two comments that wouldn't normally appear in a formalisation. This has been done in order to assist those who may not be too familiar with modern logic, and which might therefore help them understand what is going on.]

 

Formal Language, L:

 

Symbols of L:

 

1. Propositional variables:

 

a. 'p', 'q', 'r'.

 

2. Connectives of L:

 

a. '¬' -- negation (interpreted below);

b. '®' -- 'if...then'.

 

3. Punctuation for L:

 

a. Left and Right brackets: '(' and ')', full stops, ".", commas, "," and single quotation marks, "'". [These all mean the same as they do in ordinary language.]

 

4. Meta-symbols of L:

 

a. 'Γ', 'Δ', 'Ω'. [These stand for any wff of L ("wff" is short for "well formed formula" -- that is, they are inscriptions that conform with the formalisation rules --, pronounced 'woof'. Inscriptions are physical marks on the page or screen, i.e., in this case, the letters and symbols associated with this formal language).]   

 

Formulae (wffs) of L:

 

a. Any propositional symbol on its own is a wff of L.

b. ¬Γ is a wff of L.

c. (Γ® Δ) is a wff of L.

d. Nothing else is a wff of L.

 

Semantics of L:

 

1. An interpretation, I, of L is an assignment to each propositional symbol of L one or other (not both, nor neither) of the truth-values T (true) or F (false), and an assignment of truth-functional meanings to the connectives of L. [In other formal languages, naturally, these stipulations might vary.]

 

2. For one proposition there are only two (i.e., 21) distinct interpretations:

 

a. p is assigned T, or,

b. p is assigned F.

 

For two propositions, p and q, there are four (i.e., 22) possible interpretations:

 

c. p is assigned T and q is assigned T.

d. p is assigned T and q is assigned F.

e. p is assigned F and q is assigned T.

f. p is assigned F and q is assigned F.

 

For three there are eight interpretations (i.e., 23), for four there are sixteen (i.e., 24)..., so, for n propositions, there are 2n distinct possible interpretations.

 

3. If Γ is true in I then ¬Γ is false in I, and vice versa.

 

[In other words, in L, "¬" is a truth-functional operator mapping a proposition onto its negation. Normally, one would also stipulate that in L, "false" means the same as "not true", and vice versa. In other formal languages, naturally, that, too, could vary.]

 

4. (Γ® Δ) is true in I iff (i.e., if and only if) either Γ is false in some I of L, or Δ is true in some I of L.

 

[That might seem somewhat counter-intuitive, but it follows from something we want to rule out: the case where Γ is true and Δ is false. Condition 4, above, achieves this. (Why that is so I won't enter into here; recall, this isn't meant to be a logic lesson!)]

 

A formalisation would normally add more detail, but for present purposes that is as far as I need go.

 

[For more on formalisation, see, for example, here -- or even better, here and here (the second links to a PDF) -- or, indeed, the rest of Hunter (1996). See also Sider (2010), Mates (1972), and Bostock (1997) -- this also links to a PDF.]

 

An Elaborate Hegelian Hoax?

 

[3] It is highly unusual for the vast bulk of a formalisation to consist of prose (with a few ill-defined, or even undefined) 'symbols' thrown in for good measure). In fact, in the 45 years I have been studying logic, I have never seen a formalisation like Kosok's, and I doubt anyone else has, either.

 

[Recall: much of the prose I added to the above formalisation was aimed at assisting those who are unfamiliar with Pure Mathematics or Symbolic Logic. Normally, most of it would be omitted.]

 

Indeed, when I first read Kosok's article (back in the early 1990s), and I encountered page-after-page of dense prose, peppered with an idiosyncratic and wildly inconsistent use of 'symbols', my first reaction was one of complete incredulity. To be honest, I had to resist the temptation to conclude this 'formalisation' was a deliberate hoax. I even wondered whether Kosok wasn't trying to see how many Hegel-fans ignorant of genuine logic would buy into this convoluted con-trick, as a sort of dialectical version of the parable of The Emperor's New Clothes.

 

After all, another mischievous Mathematician/Physicist, Alan Sokal, published a similar hoax only a few years back. [Of course, he owned up to it soon after, otherwise he might never have been found out.]

 

Anyway, Kosok has apparently disappeared, according to his leading disciple, the 'Marxist' mystic, Peter Wilberg:

 

"The larger-than-life man to whom this essay is dedicated and without whose genius and inspiration it could not possibly have been written, is in all likelihood long dead. I first encountered Michael Kosok in 1975, when he was still professor of physics and mathematics at Fairleigh Dickinson University, New Jersey. For over two decades now he has disappeared from trace, his extraordinary writings on philosophy and science now seemingly consigned to oblivion -- never published save for a few articles in the journal Telos." [Quoted from here.]

 

Otherwise, I would have asked Professor Kosok directly whether or not his 'formalisation' was genuine. In fact, I tried to e-mail him using the address given at his site, but my message was returned "undeliverable". I have been unable to ascertain any more details about this maverick 'logician' (although Peter Wilberg's hagiographical site tells us that Kosok passed away in 2015, and this appears to be a notice of his death).

 

In what follows I will, however, assume that Kosok's 'formalisation' wasn't meant either as a convoluted hoax or an elaborate joke.

 

[4] Finally, to date I have found only a handful of attempts made by Marxist Dialecticians and others to appropriate or appeal to Kosok's work. For example, Roy Bhaskar [Bhaskar (1993), pp.30ff] describes Kosok's article as a "path-breaking study". Clearly, Bhaskar failed to notice the glaring errors and confusions in Kosok's 'formalisation' -- exposed in extensive detail in what follows. In which case, one can only assume he didn't read it with due care, or maybe at all! Even so, Bhaskar himself attempted to construct a quasi-formalisation of his own (although I don't think he actually used that term to describe the results), making use of a number diagrams and symbols (of dubious import) throughout his impenetrable and largely unreadable book -- a tome that fellow mystic, Terry Eagleton, called a "massively important work". I am reasonably sure Eagleton wasn't joking.6a

 

[I have now added several comments (to Note 6a) about Bhaskar's attempt to develop his own version of Kosok's "path-breaking study".]

 

Others have (approvingly) referred their readers to this 'formalisation'; for example, James E Hansen -- Hansen (1977), p.105 (footnote 11). As was the case with Bhaskar, Hansen plainly either failed to read this 'formalisation' with due care, or he doesn't know the difference between formalisation and Shinola. Susan Hahn (see below) also referred to it, but only to point out that Hegel's logic shouldn't be formalised, all the while failing to tell her readers what a lamentably poor job Kosok had actually made of it, anyway!

 

Petru Ioan also referenced Kosok's work (calling it a "generalisation of Hegelian dialectics" -- Ioan (1990), p.141 -- unfortunately, mis-spelling Kosok's name as "Korok"!), but he, too, failed to notice the egregiously glaring errors and confusions in Kosok's article (again, exposed below). Might he be yet another DM-fan who failed to read Kosok's work with due care -- or at all? Elsewhere, Ioan's book suggests he is a competent logician, but anyone who can reference and indirectly recommend this dialectical dog's dinner has only succeeded in raising serious doubts about their own competence in this area -- or, indeed, their honesty.