Essay Four Part One: Formal Logic And Change

I am currently adding detailed comments about a brand new book -- Smith and Hayslip (2025) -- which among many other things, tries to advance several rather familiar (and by now decidedly shop-worn) Dialectical Marxist criticisms of Formal Logic.

This new material is being uploaded, continually edited and modified as it is being written.

As of January 2nd 2026 the update is 100% complete.

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Visitors are encouraged to read this Essay in conjunction with Essays Five and Six.

Technical Preliminaries

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Preface

[DM = Dialectical Materialism/Materialist, depending on the context; HM = Historical Materialism/Materialist, also depending on the context.]

As is the case with all my Essays, nothing here should be read as an attack either on HM -- a scientific 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 thirty-eight years ago. The difference between DM and HM, as I see it, is explained here.

Some readers might wonder why I have quoted extensively from a wide variety of DM-sources in the Essays published at this site. In fact a good 10-20% of the material in many of them is comprised of just such quotations. Apologies are therefore owed the reader in advance for the length and extremely repetitive nature of most of these passages. The reason for their inclusion is as follows: Long experience has taught me that Dialectical Marxists simply refuse to accept that their own classicists -- e.g., Engels, Plekhanov, Lenin, Trotsky and Mao --, alongside countless 'lesser' DM-theorists actually said the things I have attributed to them. That is especially the case after they are confronted with the absurd consequences that follow from their words. That remains the case unless they are shown chapter and verse and in extensive detail. Partial quotes, paraphrases and summaries in my own words they reject as "distortions", "mis-interpretations", "mis-representations", and even "manipulations".  Furthermore, in debate when I quote only one or two passages in support of what I allege they are simply brushed off as "outliers" or "atypical". Indeed, in the absence of dozens of proof texts drawn from a wide range of sources (drawn from all areas of Dialectical Marxism), and reproduced in full, they tend to regard anything that a particular theorist has to say -- regardless of who they are, even if they turn out to be one of the aforementioned classicists -- as either "far too crude", "unrepresentative" or even(!) unreliable. Failing that they often complain that any such quotes have been "taken out of context". Many in fact object since -- surprising and sad though this is to say --, they are largely ignorant of the fine detail of their own theory, or, perhaps even worse, they simply haven't read the DM-classics! The only way to counter such attempts to deflect, reject and deny is to quote DM-material frequently and at length.

But even that doesn't always work!

Furthermore, because of the highly sectarian and partisan nature of Dialectical Marxism I have also found it necessary to quote a wide range of sources from across the entire 'dialectical spectrum'. Trotskyists object if I quote Stalin or Mao; Maoists and Stalinists complain if I reference Trotsky -- or even if I cite "Brezhnev era revisionists". Non-Leninist Marxists bemoan the fact that I haven't confined my remarks solely to what Marx or Hegel had to say, advising me to ignore the confused, even "simplistic", ideas expressed by Engels, Plekhanov, Lenin, Stalin, Mao and Trotsky! This often means I have to quote the lot!

That itself has had the (indirect) benefit of revealing how much and to what extent they (the classicists and subsequent epigones across all areas of Dialectical Marxism) largely agree with each other (despite sectarian rhetoric to the contrary), at least with respect to DM (but not so much over how to apply it)!

Some critics 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 related to the vast majority of topics I could link to other than Wikipedia. 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 most of the old Wikipedia links with links to these other sources. Having said that, I haven't done so for some of the Wikipedia links -- for instance, those that are connected with geographical, historical, scientific, biographical (etc.) topics where the latter aren't deemed controversial, at least among fellow Marxists. In every case, I have endeavoured to avoid linking to Wikipedia in relation to key areas of my arguments against DM so that at no point does my criticisms depend exclusively on such links. [However, it will take several years to complete this change-over!]

In addition to the above (as readers can easily check if they consult the Bibliography and End Notes attached to each Essay), I have provided copious references to other published academic and non-academic books and articles (posted on-line or printed in hard copy) that further develop, amplify or substantiate anything I argue, claim, allege or propose.

Several others have complained about the sheer number of links there are attached to these Essays, because they say it makes them very difficult to read. Of course, DM-supporters can hardly grumble about that since they believe everything is inter-connected, which must surely apply to Essays that attempt to debunk that very idea. However, to those who find this does make these Essays difficult to read I say this: ignore the links(!) -- unless, of course, you want to access further supporting evidence and argument related to a particular point, or a specific topic fires your interest.

Still others wonder why I have linked to familiar subjects and topics that are part of common knowledge -- such as the names of recent US Presidents, UK Prime Ministers, the names of rivers and mountains, the titles of popular films or the definition of certain words in common usage. I have done so for the following reason: My Essays are read all over the world by people from all 'walks of life', so I can't assume that something which is part of common knowledge in 'the west' is equally well-known across the planet -- or, indeed, by those who haven't had the benefit of the sort of education that is generally available in the 'advanced economies', or any at all. Many of my readers aren't native English speakers, either, so any help I can give them I will continue to provide.

Finally on this specific issue, several of the aforementioned links connect to web-pages that regularly change their URLs or which even vanish from the Internet altogether. While I try to update them when it becomes apparent that they have changed or have disappeared, I can't possibly keep on top of this. I would greatly appreciate it, therefore, if readers informed me of any dead or incorrect links they happen to notice. 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.

In what follows, at least 30% of my case against DM and Traditional Philosophy has been relegated to the End Notes (link above). This has been done to allow the Essay itself to flow a little more smoothly. Naturally, this means that if readers want to appreciate more fully my case against DM (and Metaphysics), they should also consult this material. In many cases, I have added numerous qualifications, clarifications, and considerably more detail to what I have argued in the main body. In addition, I have raised several objections (some obvious, many not -- and some that might even have occurred to the reader) to my own arguments and assertions, to which I have then responded. [I explain why I have adopted this tactic in Essay One.]

If readers skip this material, then my reply to any qualms or objections some readers might have will be missed, as will my expanded comments, references and clarifications.

I have also linked to Woods and Grant's book, Reason in Revolt, many times in this Essay, but the link I used now only takes the reader to parts of the second edition instead of the entire book, as used to be the case. However, anyone who wants to access a complete version of that edition can now do so here. I haven't changed the scores of links to the old site that I have inserted in what follows since they used to take the reader to specific chapters of that book, but that faculty is no longer available.

It is also important to add 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. 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 issue will become the central topic of Parts Two and Three of Essay Twelve (when they are published); until then, the reader is directed here, here and here for more details.

[**Exactly how this applies to DM has been explained in several 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 in this case aimed at absolute beginners) here.]

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Finally, Formal Logic [FL] is a highly technical subject, but since the vast majority of revolutionaries know little of no FL (that isn't to put them down, one can know zero FL and still be an excellent revolutionary!) in what follows I have had to keep such complexities totally at bay. What little FL I have used has deliberately been kept simple and straightforward. Any technical terms I have used I have endeavoured to explain or provide links to where they are explained. If there is anything I have left obscure, unclear or unexplained, please let me know and I will do my best to rectify the problem.

Because of that I have endeavoured to keep this Essay as simple and straight-forward as possible, minimising the sort of technicalities normally found in modern logic, since -- as noted above -- most dialecticians appear to know little or no logic. That can be seen from the crass things they say about it. Even Marxist Academics (who should know better!) are guilty in this regard; on that, see here. In which case, the indulgence (and patience!) of those trained in logic (some of whom might read the material presented below) is required.

Anyone who wants to read more substantial accounts of the sort of logic that forms a background to this Essay should consult the numerous books and articles referenced in the End Notes (as well as in other Essays published at this site).

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Two final points:

First of all, throughout this site I have used the term "Dialectical Marxism"; I have done so in order to distinguish Marxism from the 'dialectical aberration' that has completely dominated (and I claim has helped cripple) revolutionary socialism for over 150 years. So, the terms 'Dialectical Marxism' and 'Dialectical Marxist' refer to the mainstream 'Marxist' tradition that has accepted, in one form or another, the validity of DM and as a result has either applied it to all of 'reality' or has restricted it to social and historical development (i.e., where it has largely or even exclusively been inserted into HM). However, I distance Marx himself from this toxic amalgam -- to which conclusion many Dialectical Marxists have taken great exception (perhaps more so than anything else at this site!). Why that is so has been explained here and here. Furthermore, why this Hegelianised Hybrid (but not Marxism itself) has been an abject failure for well over a century is explained here and here. [That argument has been summarised here and here.]

Second: Anyone puzzled by the unremittingly hostile tone I have adopted toward DM and Dialectical Marxism might find it instructive to read this first.

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As of January 2026, this Essay is just under 155,000 words long; a much shorter summary of some of its main ideas can be accessed here.

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

[Latest Update: 10/01/26.]

Quick Links

Anyone using these links must remember that they will be skipping past supporting argument and evidence set out in earlier sections.

If your Firewall/Browser has a pop-up blocker, you will need to press the "Ctrl" key at the same time or these and the other links here won't work!

I have adjusted the font size used at this site to ensure that even those with impaired vision can read what I have to say. However, if the text is still either too big or too small for you, please adjust your browser settings!

(1) Formal Logic [FL] Versus Dialectical Logic [DL]

(a) A 'Troubled' Relationship

(2) FL And Change

(a) Unfounded Allegations

(b) Validity And Truth

(3) FL Allegedly Uses 'Fixed' Definitions And Categories

(a) Variables And Change

(b) Static Terms Or Slippery Arguments?

(c) Change Of Denotation

(d) An Annoying Counter-Example

(e) Other Systems Of Logic Unknown To Dialecticians

(4) Conceptual Change

(a) 'Dialectical Change': Is It Conceptual Or Material?

(b) Conceptual Change -- Or Conceptual Distortion?

(c) Logic And Change

(d) Real Material Change

(5) Merely Academic?

(6) 'Unconscious' Dialecticians?

(a) Seriously?

(b) Russian Scientists' Disastrous, Conscious Application Of DM

(c) The 'Dialectical Biologist'

(7) Is DL A 'Higher Form' Of Logic?

(a) Judge For Yourself

(b) The Inane Things Dialectical Marxists Say About FL (In No Particular Order)

(i)       George Novack

(ii)      Clifford Conner

(iii)     Woods And Grant - 01

(iv)     Robin Clapp

(v)      Plekhanov

(vi)     Joseph Dietzgen

(vii)    John Molyneux

(viii)   Robin Hirsch

(ix)     Camilla Royle

(x)      Ernest Mandel

(xi)     David Hayden-Guest

(xii)    August Thalheimer

(xiii)   John Somerville

(xiv)   Ira Gollobin

(xv)    John Pickard

(xvi)    Fred Casey

(xvii)   Sean Sayers

(xviii)  Hyman Cohen

(xix)    Herbert Marcuse

(xx)     Henri Lefebvre

(xxi)    Erwin Marquit

(xxii)   Interlude 1 -- 'Dialectical Logic' Collapses Into Nonsense

(xxiii)  James Lawler

(xxiv)  Interlude 2 -- 'Dialectical Logic' Explodes

(xxv)   Woods And Grant 2

(xxvi)  Murray Smith And Tim Hayslip

(xxvii) R S Baghavan (under construction)

(xxviii) Miscellaneous Internet Examples

(xxix)  Serial DM-Confusion

(c) Ordinary Language, 'Commonsense' And Change

(i)     Mistaken Assumptions

(ii)    Descent Into Hegelian Confusion

(iii)   Ordinary Language Isn't A Theory -- 1

(iv)   Ordinary Language Isn't A Theory -- 2 -- Nor Does It 'Assume' Things Are Static

(v)    Ordinary Language Different From 'Commonsense'

(vi)   Ordinary Language Isn't Ideological

(vii)  High Church Vs Low Church Dialectics

(viii) Low Church Dialectics

(ix)   High Church Dialectics

(8)   Was There Any Logic After Aristotle?

(9)   Explaining Change

(10) 'Thesis, Antithesis, Synthesis' -- Debunked

(11) Conclusions

(12) Notes

(13) References

Summary Of My Main Objections To Dialectical Materialism

Abbreviations Used At This Site

Return To The Main Index Page

Contact Me

Formal Logic [FL] Vs Dialectical Logic [DL]

A 'Troubled' Relationship

The relationship between DL and FL hasn't been a happy one. Nevertheless, Dialectical Marxists (in general) take great pains to make it clear that while they don't reject FL, they certainly regard its scope as seriously limited, especially in relation to motion and change. For example, John Rees commented as follows:

"[T]he dialectic is not an alternative to 'normal' scientific methods or formal logic. These methods are perfectly valid within certain limits…. [But] formal logic…has proved inadequate to deal with the 'more complicated and drawn out processes'." [Rees (1998), p.271. Quotation marks altered to conform with the conventions adopted at this site.]

"The old logic has fallen into Verachtung [disrepute]. It requires transformation.... The old, formal logic is exactly like a child's game, making pictures out of jig-saw pieces.... In the old logic there is no transition, development (of concept and thought), there is not 'eines inneren, notwen-digen Zusammenhangs' [an inner, necessary connection] of all the parts and 'Übergang' [transition] of some parts into others." [Lenin (1961), pp.96-97. Quotation marks altered to conform with the conventions adopted at this site; paragraphs merged. Bold emphasis added.]

FL And Change

Unfounded Allegations

[FL  = Formal Logic; AFL = Aristotelian FL; MFL = Modern FL.]

In fact, as is well known, the criticisms DM-fans level against FL echo Hegel's critique of the FL of his day, which was in fact a garbled and bowdlerized version of AFL.¹

The reasoning behind their approach was outlined for us by Rees:

"Formal categories, putting things in labelled boxes, will always be an inadequate way of looking at change and development…because a static definition can't cope with the way in which a new content emerges from old conditions." [Rees (1998), p.59.]

"The reason why formal logic is often forced to abandon its own procedures in the face of the facts is that it attempts to analyze a living, evolving reality with static concepts. Formally things are defined statically, according to certain fixed properties -- colour, weight, size, and so on…. [This] is satisfactory only under conditions where the scale of change is not vital to our understanding…. But for more complex tasks in politics, history, and science generally, this will not do. Common sense and formal logic are agreed on static definitions…. But 'dialectical thinking analyzes all phenomena in their continuous change'….'" [Ibid., pp.272-73. Quotation marks altered to conform with the conventions adopted at this site. Rees is here quoting Trotsky (1971), p.65. (Rees cites the latter as p.50, but that might be because he is using the Pathfinder edition, which I haven't consulted.)]

"You, however, serve up to us only a stale re-hash of Engels. The latest scientist admitted to your pages is -- Darwin; apart from Aristotle, the only 'logic worthy of attention' is that of -- Hegel, the century-dead arch-muddler of human thought. Comrade Trotsky, as we Americans ask: where have you been all these years? During the 125 years since Hegel wrote, science has progressed more than during the entire preceding history of mankind. During that same period, after 2300 years of stability, logic has undergone a revolutionary transformation: a transformation in which Hegel and his ideas have had an influence of exactly zero.... In a most sarcastic vein, you keep asking me to 'take the trouble to inform us just who following Aristotle analysed and systematised the subsequent progress of logic', 'perhaps you will call my attention to those works which should supplant the system of dialectic materialism for the proletariat...' as if this demand were so obviously impossible of fulfillment (sic) that I must collapse like a pricked balloon before it. The sarcasm is misplaced, for the demand is the easiest in the world to fulfil. Do you wish me to prepare a reading list, Comrade Trotsky? It would be long, ranging from the work of the brilliant mathematicians and logicians of the middle of the last century to one climax in the monumental Principia Mathematica of Russell and Whitehead (the historic turning point in modern logic), and then spreading out in many directions -- one of the most fruitful represented by the scientists, mathematicians and logicians now cooperating in the new Encyclopedia of Unified Science. For logic in its narrower sense, C. I. Lewis' Survey of Symbolic Logic is an excellent, though not easy, introduction. I am afraid, however, that in all of these works you will find scarcely a single reference to Hegelian (or Marxian) dialectics; nor will you in those of a single reputable contemporary scientist -- except the Soviet scientists, whose necks depend upon such references, or one or two Kremlin hangers-on, like J. B. S. Haldane, in other nations. The study of these works would be not uninteresting; but I am afraid that when we finished we would be not much nearer the solution of the question of the role of Russia in the war." [Trotsky (1971), pp.236-37. Burnham's response hasn't been published alongside the on-line edition of Trotsky (1971), but it has been posted as a separate entry at the James Burnham archive. Italic emphases are those in the published edition, but were omitted from the on-line version. Links added; paragraphs merged.]

Even worse, after another eighty years, DM-fans still refuse to be told; many of them remain fixated on the idea that FL began and ended with Aristotle!

Admittedly, throughout its history Logic has been conflated with a wide range of unrelated disciplines -- for example, Metaphysics, Epistemology, Ontology, Theology, Psychology (including the so-called "Laws Of Thought"), Mathematics, and, indeed, with Science itself. In such circumstances, it is understandable that the only legitimate role that FL can occupy -- the study of inference -- was all too easily lost. Unfortunately, that is just one more tradition DM-fans have been only too eager to emulate.³

Validity And Truth

[DM = Dialectical Materialism/Materialist, depending n the context; HM = Historical Materialism/Materialist, also depending on the context; FL = Formal Logic; DL = Dialectical Logic; LOI = Law of Identity.]

One explanation for this sorry state of affairs is that DM-theorists have allowed themselves to be led astray by what turns out to be an elementary mistake -- an error novices often make --, that is, they confuse validity with truth. As will soon become apparent, the limitations DM-theorists attribute to FL arise out of their misidentification of rules of inference with logical, or even empirical, truths, but not from the supposed inability of FL to accommodate change.⁴

"This objective thinking, then, is the content of pure science. Consequently, far from it being formal, far from it standing in need of a matter to constitute an actual and true cognition, it is its content alone which has absolute truth, or, if one still wanted to employ the word matter, it is the veritable matter -- but a matter which is not external to the form, since this matter is rather pure thought and hence the absolute form itself. Accordingly, logic is to be understood as the system of pure reason, as the realm of pure thought. This realm is truth as it is without veil and in its own absolute nature. It can therefore be said that this content is the exposition of God as he is in his eternal essence before the creation of nature and a finite mind. Anaxagoras is praised as the man who first declared that Nous, thought, is the principle of the world, that the essence of the world is to be defined as thought. In so doing he laid the foundation for an intellectual view of the universe, the pure form of which must be logic. What we are dealing with in logic is not a thinking about something which exists independently as a base for our thinking and apart from it, nor forms which are supposed to provide mere signs or distinguishing marks of truth; on the contrary, the necessary forms and self-determinations of thought are the content and the ultimate truth itself." [Hegel (1999), pp.50-51, §§53-54. Bold emphases and link added. Italic emphases in the original. I have reproduced the published version since the on-line version differs from it; I have informed the editors over at the Marxist Internet Archive about this. (They have now corrected the on-line version!) Paragraphs merged.]

"Philosophy misses an advantage enjoyed by the other sciences. It cannot like them rest the existence of its objects on the natural admissions of consciousness, nor can it assume that its method of cognition, either for starting or for continuing, is one already accepted. The objects of philosophy, it is true, are upon the whole the same as those of religion. In both the object is Truth, in that supreme sense in which God and God only is the Truth. Both in like manner go on to treat of the finite worlds of Nature and the human Mind, with their relation to each other and to their truth in God. Some acquaintance with its objects, therefore, philosophy may and even must presume, that and a certain interest in them to boot, were it for no other reason than this: that in point of time the mind makes general images of objects, long before it makes notions of them, and that it is only through these mental images, and by recourse to them, that the thinking mind rises to know and comprehend thinkingly. But with the rise of this thinking study of things, it soon becomes evident that thought will be satisfied with nothing short of showing the necessity of its facts, of demonstrating the existence of its objects, as well as their nature and qualities. Our original acquaintance with them is thus discovered to be inadequate. We can assume nothing and assert nothing dogmatically; nor can we accept the assertions and assumptions of others. And yet we must make a beginning: and a beginning, as primary and underived, makes an assumption, or rather is an assumption. It seems as if it were impossible to make a beginning at all." [Hegel (1975), p.3., §1. Bold emphases alone added; links in the on-line version. Paragraphs merged.]

As pointed out above, the histories of Philosophy, Theology and Mysticism reveal that from such esoteric assumptions it is but a short step to the derivation of 'philosophical truths' from thought/language alone. Dogmatic, a priori theory-mongering and Idealism thus go hand-in-hand. If Nature is Ideal, then it would seem perfectly legitimate to derive 'philosophical truths' solely from language/thought -- a conclusion once again highlighted by George Novack:

"A consistent materialism cannot proceed from principles which are validated by appeal to abstract reason, intuition, self-evidence or some other subjective or purely theoretical source. Idealisms may do this. But the materialist philosophy has to be based upon evidence taken from objective material sources and verified by demonstration in practice...." [Novack (1965), p.17.]

In several Essays posted at this site (for example, this one and this) we will see that that is a step DM-theorists and metaphysicians in general were only too eager to take -- and, many times over, too.

Nevertheless, there is precious little evidence that Dialectical Marxists have given much thought to the above untoward implications of the theory that DL reflects the 'underlying structure of reality'. That is, they have given little or no thought to the fact that their 'logic' actually implies 'Reality' is Ideal. If logic does indeed 'reflect the structure of Being', then 'Being' must be 'Mind', or mind-dependent, after all.

[DL = Dialectical Logic.]

[On this, see Essay Twelve Part Four (to be published in 2026) -- a partial summary of which can be accessed here.]

Anyway, since the aim of this sub-section is to examine the specific allegations that DM-theorists level against FL, the above issues will be addressed more fully in other Essays posted at this site (for example, Essays Three Part One and Twelve Parts One and Four).

FL And "Static" Definitions

As it turns out, despite the dearth of evidence offered in support of the allegations examined in an earlier sub-section, there is good reason to question the perennial accusation advanced by Dialectical Marxists that FL deals only with "static" definitions, and hence that it can't cope with change.

Variables And Change

As we have seen, DM-theorists regularly advance the following, consistently unsupported, allegations about FL:

"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.]

"Logic involves unchanging qualities (a = a) and fixed quantities of these qualities. Dialectics is constructed on the transition of quantity into quality and the reverse." [Trotsky (1986), p.87.]

"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 (1971a), p.20. Paragraphs merged.]

"Dialectics is a way of studying the phenomena of the world in a way that is quite a bit different than formal logic. Logic is undoubtedly very useful in many instances, but it has its limitations. Even the fundamental axioms of logic, which often seem intuitively obvious to western thinkers (e.g. A = A), only really hold when looking at the world at fixed moments in time." [Quoted from here. Bold emphasis added.]

Attentive readers will no doubt have noticed that every single one of the above dialecticians failed to quote or cite any evidence that FL is guilty in the way they allege. [Any who think I might have misrepresented these individuals are invited to re-check the references I have given, as well as the dozens more cited elsewhere in this Essay and at this site.] What is more, DM-fans continue to assert such things despite being asked (repeatedly, and by yours truly!) to provide evidence and proof (here is just the latest example -- from May 2015 --, and here is my request for this comrade to provide the 'missing' evidence -- which, predictably, was simply ignored). [Unfortunately, these links are now dead!]

[FL = Formal Logic; AFL = Aristotelian FL.]

However, far from it being the case that FL depends on 'changeless categories', even traditional AFL employed variables to stand for propositions and predicates (i.e., general terms) long before they were used in mathematics. This fact alone shows that traditional AFL was no more incapable of handling change than is modern Mathematics.⁷

Here is what the late Professor Nidditch had to say about AFL:

"One has to give Aristotle great credit for being fully conscious of this [i.e., of the need for a general account of inference -- RL] and for seeing that the way to general laws is by the use of variables, that is letters which are signs for every and any thing whatever in a certain range of things: a range of qualities, substances, relations, numbers or of any other sort or form of existence.... If one keeps in mind that the Greeks were very uncertain about and very far from letting variables take the place of numbers or number words in algebra, which is why they made little headway in that branch of mathematics...then there will be less danger of Aristotle's invention of variables for use in Syllogistic being overlooked or undervalued. Because of this idea of his, logic was sent off from the very start on the right lines." [Nidditch (1998), pp.8-9. Italic emphasis in the original. Paragraphs merged.]

As Engels himself pointed out, the introduction of variables into Algebra allowed mathematicians to cope with change. That being the case, it is difficult to understand why DM-theorists believe that traditional FL can't cope with change, either. If mathematicians are fully able to depict change by their use of variables, why deny this of formal logicians who have employed the very same device for at least 2400 years?

Of course, it could always be argued that the variables that designate quantities in mathematics aren't at all the same as the variables that relate to concepts, properties or qualities employed in FL. That is undeniable, but not relevant. The point is that both sorts of variable allow for change, even if they do so in different ways.

[I will return to that specific point in the next sub-section.]

Static Terms -- Or Slippery Arguments?

Despite this, does the charge that FL can't cope with change itself hold water? In order to answer that question, consider one particular valid argument form taken from AFL:

L1: Premise 1: No As are B.

L2: Premise 2: All Cs are B.

L3: Ergo: No As are C.⁸

[Where "A", "B" and "C" can stand for noun phrases, such as "mammal", "mortal", or "rational". Where I use capital letters in the above way in this Essay I will highlight them in bold to distinguish them from the ordinary use of capital letters -- except where I am directly quoting DM-sources that don't do this. I will also do the same for small case variable letters.]

With respect to this argument schema, the only condition validity requires is the following: if, for a given interpretation (concerning that word, see the next but one paragraph), the premises are true then the conclusion is true. This is a necessary condition for validity, but it isn't sufficient. For it to be sufficient, another necessary condition must apply: the conclusion must follow from the premises by the rules of inference of that formal system.

This characterisation of validity isn't affected by the fact that schematic premises can't themselves be true or false -- plainly, since they are schematic sentences, not propositions. [Any who doubt this need only ask themselves "Is it true that all As are C?"] The point is that for any legitimate interpretation of these schematic sentences, if the premises are true, the conclusion is true -- again, providing the latter follows from the premises according to the aforementioned rules of inference. But, it will automatically follow from them if the original schematic argument is valid. Below, I have given an interpretation of the above syllogistic form, and it is one that validly argues from false premises to a true conclusion, a condition many novices find hard to accept. In this specific case, had the premises been true, the conclusion would be true. [A clear explanation of this counter-intuitive fact about validity, with many more examples, can be found here.]

It is also important to add that the word "Interpretation" doesn't mean the same in logic as it does in the vernacular. It relates to the legitimate substitution instances that result from the systematic replacement of variable letters with suitable words drawn from some lexicon or other (often these terms are taken from ordinary language, but they can also be from technical, scientific or mathematical languages), according to the syntax and the semantics of the formal system involved. "Legitimate" means "substitution instances that comply with the syntactic rules of the given system". So, for example, a Proper Name (Proper Noun) can't be substituted for a schematic predicate expression or propositional variable, nor vice versa.

[Semantics: what words or symbols are supposed to designate, refer to, signify, or mean -- rules that help us determine which sentences are true or are false. Syntax: formal or discursive rules that underlie the construction of legitimate strings of words/schemas in a formal or natural language.]

One interpretation of L1 that might illustrate the above form is the following:

L1a: Premise 1: No moving object is stationary.

L2a: Premise 2: All objects with zero velocity are stationary.

L3a: Ergo: No moving object has zero velocity.

[L1: Premise 1: No As are B.

L2: Premise 2: All Cs are B.

L3: Ergo: No As are C.]

[Certain stylistic modifications were required above in order to prevent the ordinary language interpretation from becoming somewhat stilted. It is also assumed that L1a-L3a relate to the same inertial frame.]

The above syllogism is valid, and would remain valid even if all motion ceased. But, it also copes with movement, and hence with change, as is clear from what it says.

And we don't have to employ what seem to be 'necessarily true' premises (or, indeed, use this particular argument form) to make the same point:

Premise 1: All human beings are aging.

Premise 2: All Londoners are human beings.

Ergo: All Londoners are aging.

[Premise 1: All As are B.

[Premise 2: All Cs are A.

[Ergo: All Cs are B.]

Admittedly, phrases like "aging" and "one with zero velocity" aren't of the sort that Aristotle himself would have countenanced in a syllogism, so far as can be determined. However, if we free Aristotle's logic from his metaphysics, the above inferences are clearly valid, based on a syllogistic form. Anyway, the term "aging" can easily be replaced by a bona fide universal term (such as "the class of aging animals"), to create the following stilted, but genuine, syllogism:

Premise 1: All human beings are members of the class of aging animals.

Premise 2: All Londoners are human beings.

Ergo: All Londoners are members of the class of aging animals.

[Except, of course, Aristotle would have employed "All men" in place of "All human beings".]

Finally, here is an (interpreted) argument that depends on change:

Premise 1: All rivers flow to the sea.

Premise 2: The Mississippi is a river.

Ergo: The Mississippi flows to the sea.

A couple of points are worth making about that argument:

(a) In order for the conclusion to follow, the premises of an argument don't have to be true -- clearly Premise 1 is false.

(b) The above argument isn't of the classic syllogistic form, although it parallels it.

(c) Anyone who understands English will already know that rivers are changeable, and that they flow; this example alone shows that logic can not only cope with changeable 'concepts' (or, rather, general nouns that can be employed to express change), it actually uses them. Hence, logic is capable of employing countless words that express change in a far more varied and complex form than anything Hegel (or his latter-day DM-epigones) imagined. [On that, see here. I have listed several such words, here.]

Here are two more examples:

Premise 1: All fires will release heat.

Premise 2: I have just lit a fire.

Ergo: That fire will release heat.

And:

Premise 1: All sound waves transmit energy.

Premise 2: Thunder is a sound wave.

Ergo: Thunder transmits energy.

The above examples are perhaps more akin to argument patterns found in IF, but that is also true of many interpretations of argument schemas drawn from FL.

To be sure, the above changes aren't of the sort that interest dialecticians, but, as I pointed out above, examples like this have only been given in order to refute the claim that FL can't cope with change. Combine this with the additional thought that dialectics can't cope with change anyway (on that, see here) and the alleged 'superiority of DL over FL turns into its own opposite.

[Which is yet another rather ironic 'dialectical' inversion.]

Someone could object that while the above examples might appear to cope with some of the changes we experience in nature and society, they ignore conceptual change, and as such show once again that FL is inferior to DL. I have dealt with conceptual change elsewhere in this Essay.

It could further be objected that this fails to show how FL can cope with complex or extended changes, or with inter-connected development.

However, I have been studying DM for more years than I care to mention, but I have yet to see a single example of these 'complex drawn-out' changes that DM-fans continually bang on about. Perhaps the following example might allay their qualms:

Premise 1: All fertilised chicken eggs will hatch in about 21 days.

Premise 2: This egg is a fertilised egg.

Ergo: This egg will hatch in about 21 days.

[Premise 1: All As are B.

[Premise 2: All Cs are A.

[Ergo: All Cs are B.]

[Try saying any of the above just using Hegel-speak.]

It wouldn't be difficult to replace eggs with tectonic plates that move slowly over millions of years, and in complex ways, too. How much more 'drawn-out' do DM-fans need? Of course, what they are looking for are changes expressed in 'dialectical language', not the language of FL (or even IF). Well, they are welcome to it, especially since 'dialectical language' would in fact make change impossible. Nevertheless, the only point worth making here is that it is now perfectly clear that both FL and IF can easily cope with 'drawn-out' change.

[IF = Informal Logic.]

Returning to the above schema:

L1: Premise 1: No As are B.

L2: Premise 2: All Cs are B.

L3: Ergo: No As are C.

In this rather uninspiring valid argument schema the conclusion follows from the premises no matter what legitimate substitution instances replace the variable letters. So, L3 follows from the premises no matter what. But, the argument pattern this schema expresses is transparent to change; that is, while it can cope with change, it takes no stance on it (since it is comprised of schematic sentences that are incapable of being assigned a truth-value until they have been interpreted). Some might regard this as a serious defect, but it is no more a failing than it would be, say, for Electronics to take no stance on the evolution of Angiosperms -- even though electronic devices may be used to assist in their study. Otherwise, one might just as well complain that FL can't launder clothes or paint a wall. What FL supplies us with are the conceptual tools that enable scientists theorise about change, and much else besides. That is especially true in Mathematics and Computer Science.

As noted above, the possible truth-values of each of the above schematic sentences depend on the interpretation assigned to the variables (i.e., "A", "B" and "C"). So, as noted above, the premises of L1 aren't actually about anything until they have been interpreted; before this they are neither true nor false (which is why I referred to possible truth-values). Not only that, but the indefinite number of ways there are of interpreting schematic letters like these means that it is possible for 'changeless' and 'changeable' items to feature in any of its concrete instances (indeed, as we have just seen).

[That was the point behind the observation made earlier that dialecticians and logical novices often confuse validity with truth; the above schema is valid, but its schematic propositions can't be true or false, for obvious reasons. The words "changeless" and "changeable" are in ;'scare quotes' since it is the use of words capable of expressing change, or the lack of it, that is meant here.]

Of course, where truth-tables are used (in MFL), truth-values are assigned to such schemas, but, in that case, what is being considered are the truth-values of interpreted propositions, should any be assigned.

[I have given an elementary example of the use of truth tables, here.]

To illustrate further the absurdity of the idea that just because FL uses certain words or letters it can't handle change (or that it uses nothing but 'rigid' terms), consider this parallel argument:

(1) If x = 2 and f(x) = 2x + 1, then if y = f(x), y = 5.

(2) Therefore, x and y can never change or become any other number.

No one would be foolish enough to argue like this in mathematics since that would be to confuse variables with constants. If so, then DM-inspired allegations about the supposed limitations of FL are all the more bizarre -- to say the least.

Of course, and once more, it would be naïve to suppose that the above considerations address issues of concern to DM-theorists. As John Rees himself pointed out:

"Formal categories, putting things in labelled boxes, will always be an inadequate way of looking at change and development…because a static definition can't cope with the way in which a new content emerges from old conditions." [Rees (1998), p.59.]

But, as a criticism of FL, this is entirely misguided. FL doesn't put anything in "boxes", and its practitioners don't deny change as a result.

[Sure, some logicians might have metaphysical reasons for denying change, but that can't be blamed on logic, any more than the belief in three persons in one 'god' (as part the Christian Doctrine of the Trinity) can be blamed on mathematics.]

Indeed, without an ability to reason discursively (along lines that have been systematised in FL -- and which have been explored more extensively in Informal Logic), dialecticians would themselves find it impossible to argue rationally.

[TAR = The Algebra of Revolution; i.e., Rees (1998).]

For example, the argument above (from TAR) appears to draw certain conclusions from apparently 'fixed definitions' (or a 'fixed'/'relatively fixed' use) of certain words -- like "change" and "static" -- in order to make a point about change itself. If, however, Rees's argument is now deliberately and uncharitably mis-interpreted (that is, if we emulate the tactics used by Dialectical Marxists when they deliberately misconstrue FL), it would soon turn into a self-refutation. In that case, in order to point out the supposed limitations of FL, Rees found he had to use the very things he accused FL of employing -- i.e., "static" terms. Of course, if this unsympathetic way of reading Rees's book were correct, or even fair, it would mean that if he and other DM-theorists want to argue validly about the limitations of FL using "static" categories such as these, their arguments would promptly self-destruct (along these lines).

On the other hand, if Dialectical Marxists were to employ 'non-static categories' consistent with their own precepts, then that would rapidly undermine any conclusions they hoped to derive. That is because such categories (having no fixed meanings) would sanction no inferences, for it isn't possible to decide what follows from what if the meaning of the terms employed is indeterminate or is liable to change. So, while it is unwise of DM-theorists to criticize FL for employing supposedly changeless categories, it would be even more inept of them to do this while using terms whose meanings alter unpredictably. Hence, in practice, DM-theorists must either ignore their own principles and argue from 'fixed categories' about the limitations of FL, or they will have to construct a case against FL using 'slippery' terms, which would establish nothing at all.

Like it or not, rational criticism of FL can't succeed, or even proceed, if either tactic were adopted.⁹

Some might feel that there is a contradiction here between what was said earlier about variables that can stand for things that change, and the objection above to the effect that changeable terms would prevent a conclusion following from its premises. So, it could be objected that while the following had been claimed earlier about the variables used in FL:

RL1: "...the indefinite number of ways there are of interpreting schematic letters like these [re-quoted below] means that it is possible for 'changeless' and 'changeable' items to feature in any of its concrete instances...",

the following point was also made:

RL2: "If, on the other hand, Dialectical Marxists were to employ 'non-static categories' consistent with their own precepts, then that would rapidly undermine any conclusions they hoped to derive. That is because such categories (having no fixed meanings) would sanction no inferences, for it isn't possible to decide what follows from what if the meaning of the terms employed is indeterminate or is liable to change. So, while it is unwise of DM-theorists to criticize FL for employing supposedly changeless categories, it would be even more inept of them to do this while using terms whose meanings alter unpredictably. Hence, in practice, DM-theorists must either ignore their own principles and argue from 'fixed categories' about the limitations of FL, or they will have to construct a case against FL using 'slippery' terms, which would establish nothing at all."

One minute we are being told that these variables stand for things that can change, the next that the idea that they can change would undermine any conclusion DM-theorists wanted to derive. Which is it to be? Are these variables, or are they constants? Do they change within the body of an argument, or do they remain 'fixed' as DM-theorists allege?

Of course, the point of RL2 was to bring out the imprecise nature of the allegations levelled by DM-fans. If the denotations of the terms used in FL change within an argument, then L1-L3 might just as well become:

L1b: Premise 1: No As are B.

L2b: Premise 2: All Cs are D.

L3b: Ergo: No Es are F.

[L1: Premise 1: No As are B.

L2: Premise 2: All Cs are B.

L3: Ergo: No As are C.]

Here, B changes into D in L2b, A into E, and C into F, and/or whatever they supposedly stand for in L3b, which means that L3b no longer follows from L1b or L2b (or even L1 and L2).

But this is to misread these variables. In order to make this clearer it might help if we translate L1-L3 into hypothetical form:

RL3: If it is the case that no A, or whatever they become, is whatever B is, or becomes, and if it is the case that all Cs, or whatever they become, are whatever B is, or becomes, then it is the case that no A, or whatever they become, is whatever C is, or becomes.

This shows that AFL can cope with change.

However, the point being made in RL2 (repeated below) is that the above constraints don't apply. The nondescript 'changes' referred to by DM-theorists mean that their arguments more closely resemble L1b-L3b, not RL3, and so the point made in RL2 still stands.

RL2: "If, on the other hand, Dialectical Marxists were to employ 'non-static categories' consistent with their own precepts, then that would rapidly undermine any conclusions they hoped to derive. That is because such categories (having no fixed meanings) would sanction no inferences, for it isn't possible to decide what follows from what if the meaning of the terms employed is indeterminate or is liable to change. So, while it is unwise of DM-theorists to criticize FL for employing supposedly changeless categories, it would be even more inept of them to do this while using terms whose meanings alter unpredictably. Hence, in practice, DM-theorists must either ignore their own principles and argue from 'fixed categories' about the limitations of FL, or they will have to construct a case against FL using 'slippery' terms, which would establish nothing at all."

[I am not suggesting that this is how Aristotle would have viewed any of this (in fact, he probably wouldn't!); L1-L3 have only been expanded to show that AFL can cope with change.]

Of course, concerning the examples of interpreted arguments given earlier, words like "river" or "fire" don't change their meaning in the course of an argument, but their meaning shows that logic can deal with concepts that express change in nature and society.

Finally it could be argued that the syllogism is a categorical, not a hypothetical argument form (although Aristotle hinted at hypothetical syllogism when arguing from a hypothesis, later developed into a system by Theophrastus (c.371-287 BCE) and Alexander of Aphrodisias (fl.200CE) -- Kneale and Kneale (1962), pp.105, 110).

Indeed, but RL3 was only referenced to make the point clear: syllogisms can be interpreted so that they can cope easily with change.

Anyway, here is a categorical version of RL3 to show that it, too, can be interpreted along the same lines:

L1c: Premise 1: No As (or whatever they become) are Bs (or whatever they become).

L2c: Premise 2: All Cs (or whatever they become) are Bs (or whatever they become).

L3c: Ergo: No As (or whatever they become) are Cs (or whatever they become).

And, here is an interpretation that might make the point clearer still:

L1d: Premise 1: No salmon (or whatever they become) are mammals (or whatever they become).

L2d: Premise 2: All cats (or whatever they become) are mammals (or whatever they become).

L3d: Ergo: No salmon (or whatever they become) are cats (or whatever they become).

Now, it isn't to the point to argue that L1d and L2d might very well turn out to be false (if evolution takes, or had taken, an odd turn, for example), thus making L3d false. That is because it once again confuses truth/falsehood with validity. The hypothetical form in RL3 brings this out a little better: Whether or not L1 and L2 are false, if they were true, the conclusion would follow.

RL3: If it is the case that no A, or whatever they become, is whatever B is, or becomes, and if it is the case that all Cs, or whatever they become, are whatever B is, or becomes, then it is the case that no A, or whatever they become, is whatever C is, or becomes.

Again, another interpreted argument might show this to be so -- here using two unambiguously false premises that imply a true conclusion:

L1e: Premise 1: No roses are plants. [False]

L2e: Premise 2: All frogs are plants. [False]

L3e: Ergo: No roses are frogs. [True]

Change Of Denotation

Furthermore, the schematic letters employed earlier don't in fact possess "definitions" only interpretations; hence, questions about the 'fixity' of those 'definitions' or otherwise are entirely misplaced. The flexibility of interpretation permitted here -- even with respect to traditional schematic argument patterns, like the one given above -- enables change to be accommodated by the simple expedient of choosing appropriate substitution instances for each schema. Moves like this will have the effect of re-distributing truth-values among the constituent sentences without affecting the associated inference.

Unfortunately, even this might still fail to address the worry exercising DM-theorists, which seems to centre on the alleged superiority of DL over FL, especially with respect to its (supposed) ability to depict complex change through 'internal contradiction'.

[DL = Dialectical Logic.]

Admittedly, whatever one thinks of the ability or inability of classical FL to handle change, few question its intolerance of 'true contradictions'. However, since this section of the Essay is largely concerned with a narrow range of logical issues, I will postpone the examination of DM-theorists' appeal to 'dialectical change' through 'contradiction' until several later Essays.¹⁰

An Annoying Counterexample

Nevertheless, a more effective way of rebutting the claim that FL can't handle change would be to provide a counterexample (in addition to those given earlier!). The example below is based on a very simple pattern drawn from MFL, which employs a valid argument form despite the changes it records when interpreted. This is in fact an example of the schema known as Modus Ponendo Ponens (MPP):

In the above, the arrow stands for "If...then", so premise (1) reads "If P then Q". The following is therefore a legitimate interpretation of MPP:

[The numbers, letters and terms used above have all been explained in Note 11 (link above).]

This simple interpretation of MPP (and one involving reasonably rapid change) is perhaps as good a counterexample as one could wish to find, which refutes the claim that FL can't handle change. Moreover, there are countless other inferences that MPP itself can instantiate, and many inferential forms other than MPP, all capable of depicting change equally well, when suitably interpreted.^11a

This indicates that the accusations levelled by DM-theorists against MFL are even less accurate than those they direct against AFL. Of course, the example above will hardly satisfy dialecticians, since no "new content" has been added in the conclusion. Fortunately, that 'defect' is relatively easy to fix. Consider this valid, one premise argument:

Premise 1: All dialecticians are human beings.

Ergo: The refutation of a dialectician is the refutation of a human being.

Here, the conclusion 'contains' more than the premise, so new content has 'emerged', and, mercifully, with no 'dialectics' anywhere in sight. [And, perhaps as an additional bonus, it depicts change to our dialectical friends, too!] This argument form is used in mathematics and the sciences all the time to derive results not available to those who are still super-glued to the old logic -- and, of course, DM-fans who are blissfully unaware of this.

However, dialecticians might still wonder if the changes depicted above are at all relevant to their concerns. They tell us that DL is superior in the way it accounts for social change; that is, it handles developments of far greater complexity than the above rather trivial examples could possibly countenance.

Nevertheless, those examples were simply aimed at countering the specific claim that FL can't handle change. In later Essays we will see that it is DL itself can't account for changes of any sort -- simple or complex, whether they occur in nature or society. In that case, no matter how poorly FL copes with change (if that is indeed the case), DL fares far, far worse. Even worse still, if DM were true, change would be impossible.

Other Systems Of FL

Perhaps of greater significance is the fact that over the last hundred years or so theorists have developed several post-classical systems of logic, which include Modal, Temporal, Deontic, Imperative, Epistemic and Fuzzy Logic (among many others). Several of these systems sanction even more sophisticated depictions of change than are available in AFL, or even MFL (i.e., so-called 'Classical Logic').¹²

Conceptual Change

Notwithstanding the above, the feeling may perhaps persist that the examples rehearsed earlier still employ "fixed concepts" and "static definitions". Unfortunately, because DM-theorists seldom (if ever) provide examples of what they mean by a "fixed concept" -- or even what they imagine Logicians take these to be (rightly or wrongly) -- it isn't easy to make much sense of their complaints.^12a

[In Note 12a (link above), I have responded to the objection that Dialectical Marxists have in fact presented a few examples of 'fixed concepts'.]

However, there are several confusions that might lie behind, or, indeed, which might motivate, this odd belief in 'changeable', or even 'changeless', concepts.

Change In DM -- Is It Conceptual Or Material?

The first confusion revolves around DM-theorists' own concept of material change. They frequently depict it in terms that are reminiscent of the Hegelian doctrine, which holds that change is fundamentally conceptual. How else are we to interpret John Rees's words that any account of change must explain how: "…new content emerges from old conditions"? [Rees (1998), p.59.] How else are we to interpret the following remarks by Lenin?

"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. Emphases in the original.]

"[Among the elements of dialectics are the following:]…internally contradictory tendencies…in this [totality]…and unity of opposites…. [E]ach thing…is connected with every other…[this involves] not only the unity of opposites, but the transitions of every determination, quality, feature, side, property into every other…." [Ibid., pp.221-22. Emphases in the original.]

Or, indeed, this from Trotsky?

"Cognizing thought begins with differentiation, with the instantaneous photograph, with the establishment of terms -- conceptions in which the separate moments of a process are placed from which the process as a whole escapes. These terms-conceptions, created by cognizing thought, are then transformed into its fetters. Dialectics removes these fetters, revealing the relativity of motionless concepts, their transition into each other. (S. Logik, I. 26-27)." [Trotsky (1986), p.97-98.]

[Or, the many other passages quoted here?]

Admittedly, Rees did appeal to the 'materialist inversion' that has allegedly been imposed on Hegel's system (to turn it into "materialist dialectics", and hence put "back on its feet"), as, indeed, did Lenin and Trotsky. But, all three pointedly failed to explain how conceptual change is related to material change, upside down or 'the right way up'. Or, indeed, how the one can become the other merely by the expedient of flipping them, or the entire system, upside-down. Precisely how is it possible for a concept, or a category, to change if neither of them is material? And it won't do to suggest that concepts, for example, change because the objects they 'reflect' change, since that would be to confuse concepts with objects, once more. Does the concept of colour, for example, change every time a leaf turns from green to brown? Or, a traffic light from red to green, and then back again? [In fact, in Essay Three Part One we saw that this approach to concepts is a dead end. We will have occasion to examine it again in more detail presently.] Nor will it do to argue that concepts change because we reflect on them (that is, if we employ the 'sophisticated' version of the RTK, here), since that would be to treat concepts as objects, again.

It might be thought that concepts are somehow formed, or are reflected, 'in each head' as objects of "cognition". In that case, the question becomes: does the concept of colour change when, say, someone thinks about a traffic light altering from red to green, and then back again? Indeed, does the concept of colour -- as a concept, once it had been, or might have been, apprehended by an individual apprehender -- change in such circumstances? But, how could anyone possibly tell whether or not it had? If we have lost touch with the old 'concept' of colour (since it will have changed), with what could anyone compare the new 'concept' of colour so that they were able to declare it had in fact changed? No good appealing to memory, since the concept itself has (allegedly) changed -- unless we are to suppose there are now two concepts of colour: one that has changed, and one (in the memory?) that hasn't, thus allowing a comparison to be made. And how might that be confirmed? Any response here that tried to argue that these concepts must have changed since everything does will simply have confirmed earlier allegations that this theory only appears to work because it has been imposed on nature and society -- or, here, on human cognition. In this case, these moves will have assumed -- and then imposed on thought -- a view of concepts that has yet to be justified or confirmed.

Even worse, how might it be decided whether or not our memories haven't also changed?

Or has memory been given a pass so that the Heraclitean Flux holds no power over it?

[That intriguing possibility will be left dangling for the time being. I return to it again, below.]

The problem now facing DM-theorists is how to explain 'mental objects' like this (i.e., 'images', 'reflections', 'representations', and/or 'concepts' that are supposedly located in our heads, brains, or in 'consciousness') while successfully avoiding reductionism -- or, indeed, bourgeois individualism.^12b

[RTK = Reflection Theory of Knowledge. The 'sophisticated' version involves the active input of human "cognition" and practice, as opposed to the 'naive' version which (apparently) doesn't -- but which merely stresses the passive 'subject' of perception or knowledge. Both theories will be criticised in Essays Three Part Six and Twelve Part Four.]

[It is worth pointing out here that I am not denying conceptual change, merely questioning what dialecticians could possibly mean by "fixed" compared to "developing" concepts.]

Furthermore, how might it be possible for changes that material objects undergo even to be recorded by our use of concepts? In DM-writings the impression is given that these two sorts of change are simply the same, or, at least, that one is a 'reflection' of the other. To be more honest, the impression is that little thought has actually gone into either sort of change -- that is, over and above the regurgitation of the obscure (and sanitised) ideas Dialectical Marxists have borrowed from Hegel.

[The word "sanitised" was used here because of the way that DM-theorists have appropriated the Christian/Hermetic concepts Hegel inflicted on his readers, which they tell us they have flipped so that they are now 'the right way up', in order to render them 'consistent' with materialism. This ploy is reminiscent of the way that Christian theologians, for example, re-interpret the scientifically 'unacceptable' passages in the Book of Genesis (as 'allegorical' or 'figurative'), 'sanitising' them in order to render them 'consistent' with post-Enlightenment 'sensibilities' and modern science.]

It could be objected that the above comments ignore the dialectical relation between the "knower and the known", just as it fails to take note of the fact that our concepts change in accord with the development of material and social reality, as well as in response to practice.

Admittedly, DM-theorists have made an attempt (of sorts) to explain the relationship between material and conceptual change along such lines, but, as noted earlier, they have invariably tried to do so by means of a detour into the RTK, buttressed by an appeal to practice -- both of these they then connect with a materialist analysis of the dialectical relationship between the abstract and the concrete. Since these topics are have been addressed in other Essays at this site, no more will be said about them here.

Conceptual Change -- Or Conceptual Distortion?

A second (perhaps hidden) source of confusion might be because conceptual change isn't at all easy to depict -- if we rely on Traditional Philosophy to guide our way. Indeed, if it should emerge that conceptual change can't be pictured using traditional-, or even DM-terminology -- as it is just about to! --, then the alleged superiority of DL over FL would become even more difficult to sustain.

In order to motivate this unexpected turn of events a brief digression into a consideration of some of the problems involved in any attempt to express conceptual change (along traditional lines) might be in order. Consider, therefore, the following sentence:

C1: Green has changed.

The word "green" in such circumstances would normally be understood as the Proper Name (i.e., the surname or family name) of an individual (perhaps this guy) -- as opposed to signifying a concept. On the other hand, if it were made clear that C1 was actually speaking about the colour green itself, and not someone called "Green", it would probably be re-interpreted along the following lines:

C2: This patch of green has changed.

That is because little sense can be made of the idea that the concept green (expressed in C3 below) could have changed like this (for reasons that will be explored presently). In which case, C1 (re-interpreted as C2) would perhaps be understood as an allusion to a change in the colour of a material object, or part of an object -- but not to the concept green itself. That can be seen if the following sentence were substituted for C1:

C3: The concept green has changed.

Despite what C3 seems to say, the phrase "The concept green" is longer an expression for a concept; it is a singular term designating an object! Concept expressions are expressed by a specific use of general terms (often signified by the employment of the indefinite article and common nouns). But, C3 transforms the supposed concept expression into one designating an object of some sort.

As noted earlier, if the concept itself had changed, or if it were asserted that it had changed -- and we understood this concept to be a 'mental entity' of some sort, apprehended somehow by each individual (in their own way?), which is often how it is viewed in Traditional Philosophy and now in DM -- then it would be impossible to decide whether or not it had actually changed. With what could we (as individuals) compare our supposedly subjective apprehension of the concept green if it had indeed changed? All we would have is a fading memory of the 'old concept green', which, ex hypothesi, would also have changed! Otherwise, the concept green, as we 'individually apprehend it', won't actually have changed. Any attempt to access the 'old concept green' (again, perhaps via memory) will of necessity have to appeal to, or employ, the current apprehension of the concept green!

Hence, in order to recall the 'old concept green' (labelled in G2 below, "green_n", which refers to the n^th instantiation of 'the concept green', either in the memory or via a contemporaneous 'act of cognition'), something like the following would have to be 'cognised':

G1: My memory of the concept green₁ is such and such, which tells me my current apprehension of the concept green₂ has changed.

Or, more generally:

G2: My memory of the concept green_n is such and such, which tells me my current apprehension of the concept green_(n+1) has changed. 

But if is so, it is reasonably clear that in order for this to be of any use to the individual concerned, the concept green_n can't itself have changed, for if it had, then it wouldn't be possible to decide if it had indeed changed! Plainly, that is because it would no longer be the concept green_n, it would be the concept green_(n+1) -- or maybe even the concept green_k, which would be what the old concept green_n had changed into. Of course, any such 'act of intellection' would simply have changed the subject, or the target, of this supposed 'mental concept search'. Unless, of course, the individual concerned had access to an even older 'concept of green' (or an even older memory of 'the concept green') that hadn't itself changed, pushing this 'search' one stage further back. In that case, the following would have to be the case:

G3: My memory of the concept green_(n-1) is such and such, which tells me my past apprehension of the concept green_n has changed. 

And so on...

Of course, if that were so, there would be no such thing as "the concept green" to change, just a potentially infinite set of fading memories of something that now no longer resembled the 'current concept green' as apprehended by the said individual!

[The 'relative stability of language' response (that is, as it has been advanced by DM-theorists) has been neutralised here and here.]

Finally, if an individual's memory of the concept green hadn't changed, there would be 'fixed and changeless concepts', after all -- namely one such for each colour, taste, smell...

[There are other, perhaps more fundamental reasons, explored in Essay Three Parts One and Two, that fatally undermine any theory that implies we 'cognise' concepts individually, or even as individuals. They will be briefly covered again in what follows and in the End Notes associated with those comments.]  

Be this as it may, it now becomes difficult to decide precisely what "the concept green" actually designates -- at least not without completely misconstruing what C3 is apparently trying to say about 'the concept green' itself (but, again, only if we insist on interpreting concepts traditionally). As noted above, "the concept green" can't in fact pick out the concept it appears to designate since that would transform its supposed target (i.e., what the "the concept green" is said to signify -- that is, 'the concept green' itself) into an object -- now denoted by the definite description, "the concept green". Naturally, that would fatally compromise the distinction drawn between concepts and objects, all the while still failing to pick out the intended concept! As noted above, concepts are actually expressed by a specific use of general terms, but only when we aren't trying to refer to them!¹³

C3: The concept green has changed.

The paradoxical nature of sentences like C3 may perhaps be illustrated by a consideration of the following (where "ξ is a concept" is seemingly predicated of "The concept green"; the use of Greek letters  -- like "ξ" in "ξ is a concept" -- is explained here):

C4: The concept green is a concept.

If it is first of all stipulated that C4 is well-formed (even though it isn't!), then it looks like it is analytically true. In fact, and on the contrary, C4 is analytically false (i.e., if we also allow for the use of those two philosophical terms-of-art here for the purposes of argument -- i.e., "analytically true" and "analytically false")! That is because (once more) "the concept green" is a singular term, and as such it designates an object, not a concept!¹⁴

[The words "false" and "true" in the above paragraph should both be in 'scare quotes', but they aren't because of the assumption made that C4 is well-formed.]

Alas, absurd sentences like C4 are to metaphysicians what carrots are to donkeys. So, beginning with linguistic monstrosities like C4, some theorists hastily conclude that language -- or 'thought' (or 'reality', or 'Being', or 'everything', or whatever) -- must be defective in some way, or must be 'contradictory', or must be paradoxical, or must be this, or must be that. That is because Traditional Philosophers imagine they can dictate to 'reality' what it must be like based solely on their idiosyncratic use, or distortion, of language (exemplified by C4). But, this is just the RRT again.

With reasoning like this one might just as well argue that if a metre rule, say, had been manufactured incorrectly, then everything it has been used to measure must be defective, too! To be sure any subsequently recorded lengths will be incorrect, but the objects that had been measured will remain sublimely unaffected.

From linguistic sins such as these -- committed by our philosophical forebears -- much of subsequent Metaphysics has descended without modification by unnatural selection. Unfortunately, DM isn't the only deformed progeny of mutant syntax such as this.¹⁵

In that case, it isn't possible to specify how concepts change by means of sentences like C3. In such sentential contexts, the (actual) logical role of terms that supposedly signify concepts means they no longer function as concept expressions, or even as expressions signifying concepts.¹⁶

C3: The concept green has changed.

[It is important to add that I am not denying that concept expressions can be nominalised or particularised, or that we can't legitimately use expression like "The concept green", only that nothing metaphysically deep, paradoxical, or 'ontological' follows from this superficial linguistic transformation. Nor am I denying conceptual change!]

Of course, it could be objected that the mere fact that we can't express conceptual change in the manner suggested above doesn't mean that it doesn't happen or doesn't exist; after all, reality isn't constrained by the real or imagined limitations of language.

Maybe not, but if a 'development' like this can't be put into words without the sort of distortion outlined above following from it -- or, when it is put into words, what it appears to say undermines what some individuals might imagine such expressions can be used to say about a concept -- then no coherent option has been presented for readers to consider.

Not only that, but the above objection clearly trades on the supposition that there are indeed concepts in reality that can change; but that itself would be true only if reality were mind-like. No one supposes -- it is to be hoped(!) -- that actual concepts pre-dated the evolution of sentient life, or that they reside in a sort of 'limbo world', waiting to be thought about, and only then do they begin to change (which seems to be Hegel's position -- that is, if it were even possible to determine what he says about anything beyond the price of bread!).

On the other hand, if reality isn't mind-like (and which Dialectical Marxist wants to claim the opposite?), then there are no concepts in nature for our minds to reflect. Or, rather, it makes no sense to suppose there are -- at least, not without turning them into objects once more.

Alternatively, if it is now claimed that 'the mind' can and does reflect reality (howsoever that metaphor is fleshed out), and it employs concepts to that end, then it will end up distorting 'reality' by so doing. That is, it must actively distort 'reality' in this way because there no concepts 'out there' for it to 'reflect'. Any attempt to say what they are (if there are any!) transforms them into objects, not concepts (in the above manner)!

Others might refer to George Novack's argument (which unfortunately conflated Logical Positivism with Analytic Philosophy in general):

"Locke analysed, among other things, the function of precise terms in the process of knowledge. But, like Hobbes, he held that 'words are wise men's counters; they do not reckon by them; but they are the money of fools.' The logical positivists are 'foolish' in this sense. They think that words are more important for reasoning than the realities they represent. Instead of focusing on real things and relations and their conceptual reflections in the human mind, they limit themselves to dissecting the structure of sentences and focusing endlessly and fruitlessly over the multiple meanings of logical formulations and grammatical terms.... It is useful and often necessary to eliminate unclarities and ambiguities from language to improve the functioning of that indispensable instrument of thought. But it is a paltry enterprise to convert this task into the paramount aim of philosophy. On the intellectual plane this is equivalent to reducing the process and purpose of material production to the sharpening and cleaning of a tool...." [Novack (1971b), pp.107-08. Links added; paragraphs merged.]

After a sideswipe at Wittgenstein (which wasn't itself based on anything the latter actually argued!), Novack continues:

"The logical positivists have created a modern scholasticism which threshes the empty husks of once valuable ideas and squabbles over the meanings and relations of terms apart from their connections with things in their development." [Ibid., p.108.]

Ignoring Novack's idiosyncratic understanding of Locke and Hobbes for the moment, when he originally wrote all this (in the late 1960s) Logical Positivism [LP] had been a dead duck for nigh on twenty years. Notwithstanding that, attentive readers will note that, true-to-form, Novack nowhere quotes or cites a single LP-er in support. Of course, it could be objected that Novack devoted an entire section to A J Ayer, a leading advocate of Logical Empiricism [LE] after Ayer abandoned LP sometime in the 1950s. [Ibid., pp.109-12 -- a whole three pages, wow!] He also mentions Bertrand Russell and Rudolph Carnap, two more leading LP-ers of the first half of the twentieth century (except Russell was never an LP-er!). Novack (a leading Trotskyist) then refers his readers to a book by that (Stalinist!) Philosopher, Maurice Cornforth -- i.e., Cornforth (1965) -- for more details. But, he fails to quote Ayer, let alone Russell or Carnap, in support of his wild allegations! And he also manages to conflate LP with LE!

Be that as it may, what about Novack's allegations themselves?

First of all, the LP-ers (many of whom were Marxists and socialists, an inconvenient fact also ignored by Novack) were concerned to rescue science from the clutches of the metaphysicians, as they saw things. So it is farcical to argue that:

"The logical positivists have created a modern scholasticism which threshes the empty husks of once valuable ideas and squabbles over the meanings and relations of terms apart from their connections with things in their development." [Novack (1965), p.108.]

The LP-ers weren't interested in analysing sentences or words for its own sake, but in a better understanding of the logic of both technical and ordinary language in order to more clearly comprehend the nature of science. We now know the foundation of their entire approach was seriously misguided, but that doesn't excuse Novack's egregious misrepresentation of their otherwise laudable intentions.

Second, it is rather odd that Novack believes that being clear about our use of important words -- the meaning of which DM-fans take for granted and on which they impose their own idiosyncratic understanding (such as "consciousness", "mind", "matter", "image", "contradiction", "negation", "opposite", "knowledge", "facts", "motion", "place", and even the verb "to be"!) -- is in any way different from what those words express about the world and with which we interact. For example, clarity about how we use colour terms tells us about the nature of colour as we conceptualise it -- and hence what colour is --, which in turn sets conceptual boundaries not only to how much science can also tell us about it, but whether or not what we are told is or isn't itself misguided. As I have argued in Essay Thirteen Part One (edited):

[It] could be argued that colours are certainly material. However, such a response would be a mistake. Colour perception may have causal and/or material concomitants, but colours can't be material. If they were, it would make sense to ask of what they are composed. Of course, colour isn't made out of anything not already coloured and it has no constituent parts (which aren't already coloured, too). So such a question would have no answer that wasn't viciously circular (i.e., it would be rather like saying matter is made of matter). Nor does colour possess many of the other characteristics and classic qualities of matter: it isn't impenetrable and has no inertial properties, for example. It could be argued that light has momentum (or, rather, "carries momentum"); that is undeniable, but colour isn't the same as light. We might ask "What momentum does red light carry?" but not "What momentum does red carry?"

In that case, it is little use being told that a certain colour is F, or is G (where "F" and "G" go proxy for suitable reductive phrases or (compound) clauses, such as "energy of a certain wavelength", or "a disposition to excite in us certain perceptions"), for unless F and G contain or use terms drawn from the vocabulary of colour, we would be no further forward. Manifestly, "energy of a certain wavelength" has itself only been identified as causing the perception of colour because of the fact that we already perceive colour and have a specific vocabulary to match.

On the other hand, if F and G do contain or use words drawn from the vocabulary of colour, all such reductive definitions would be circular.

[Which is just another way of saying that we can't get behind the vocabulary of colour without already presupposing a mastery of it, rendering pointless the entire exercise.]

For example:

C1: The colour red is a neural event E whereby a subject sees red.

C2: The colour red is a neural event E whereby a subject reports seeing red.

C3: The colour violet is caused by light of wavelength of approximately 400nm hitting the retina creating a perception of violet.

Here, as seems clear, a prior understanding of the use of "red" or "violet" would inform the imputed scientific facts (and this would be the case for both subject and researcher), not the other way round. [The significance of that particular observation is explored in Essay Thirteen Part Three.]

On this, see Stroud (2000).

Again, it could be objected that colour is actually made out of photons of different energies, or of light of different wavelengths. However, that response simply confuses the causal agent responsible for our colour perception with colour itself.

Once more, it might be objected that colour is caused by the interplay between light rays and the microstructure of atoms, or that colour is a dispositional property of material objects -- or perhaps even a dispositional property of perceivers themselves. Whether these claims are true (or not) won't be entered into here; but, once again, these responses confuse the causal agents and/or concomitants responsible for colour perception with colour itself. [These and other related topics are discussed at length in Wittgenstein (1980). Cf., Glock (1996), pp.81-84, Hacker (1987), Hanfling (2000), Harrison (1972, 1973), and McGinn (1991).]

As Professor Laurence Goldstein notes:

"Take blueness, for example. What enters our eyes -- the blue light -- is simply (objectively) electromagnetic radiation. Yet the electromagnetic radiation is not blue. Colour has at least three dimensions -- hue, brightness, and saturation -- and four of the hues -- red, green, yellow, and blue -- are primary, that is, visibly non-composite. There can be reddish blues, but no yellowish blues or reddish greens. Yet such characteristics of colour are not characteristic of electromagnetic radiation. For example, no unique wavelength can be identified with a unique hue, since identical colour experiences may be produced by different combinations of wavelength. So light of any particular wavelength cannot be identified with a colour, that is, light is not coloured.

"Blueness, then, is not a property of electromagnetic radiation. Perhaps it is a property possessed by blue objects, that is, a property that they possess whether or not anyone is looking at them. But are objects intrinsically coloured? There is a strong temptation to suppose that all the objects that we perceive as blue have something, for example a certain molecular surface structure, that makes them so. Yet, when we actually conduct a detailed analysis of the different kinds of blue things that we see, it soon becomes clear that this supposition is incorrect. The blueness of the sky is due to the scattering of white light by particles of a certain size, and the same cause is responsible for the blueness of the eyes of some Caucasians and of the facial skin of many monkeys. But the blue of a rainbow has quite a different cause from that of the blueness of certain stars. And what makes sapphire blue is quite different from what makes some birds blue, and both are different from what causes the blue of certain beetles." [Goldstein (1990), pp.185-86. Spelling altered to conform with UK English. Italic emphases in the original. Links added.]

Although, Professor Goldstein concludes that colour isn't an "objective property of things" (p.186), that observation isn't so much false as non-sensical. [On the status of such hyper-bold claims about 'things-in-themselves', see Essay Twelve Part One. Again, see Stroud (2000).]

Be this as it may, the point is that Professor Goldstein is right when he points out that electromagnetic radiation itself isn't coloured.

Some, like the above Professor, might claim that colours are 'mental' phenomena and exist only in conscious minds, not in the external world. But, that, too, is an age-old mistake. Colours don't exist merely in the mind since (plainly!) they exist in the outside world; any theory that located colours exclusively in the minds of perceivers would clearly have misidentified them. So, when, for instance, a scientist describes Copper Sulphate crystals as blue, she is referring neither to the contents, nor to the state, of her mind or central nervous system. Anyone who thought otherwise would simply have drawn attention to their own misuse of language....

Nevertheless, we all already know what colour is (or, at least, competent speakers of the language already know) -- we learnt what it is when we were taught how to speak about it and how to interact with coloured objects. In fact, we must already understand what colour terms mean if we are to be informed by scientists what its physical concomitants and properties are supposed to be. We certainly couldn't be educated (or re-educated) by them concerning the physical nature of colour if no one understood what the word "colour" already meant.

That non-negotiable logico-linguistic constraint applies with equal force to scientists themselves; they too must grasp what ordinary colour terms mean (and they must do so in the same way that the rest of us do, or they won't be speaking about colour, but about 'colour') if they are to study successfully the physical properties of the correct natural phenomenon. So, scientists (and/or sceptics) can only undermine the ordinary use of the word "colour" (if that is what they do) at the cost of making all they say about 'it' entirely vacuous. If colour isn't what we suppose it to be when we use the ordinary language of colour, then we must surely lose the solid ground upon which scientists sought to build a properly scientific explanation of 'it'.

This means that the claim that colour is a (dispositional) property of material objects can't be the whole truth about it, in that it isn't all that colour is. And this "all" can't be accommodated to any theory without a prior recourse to the ordinary language of colour....

Of course, it could be objected that the nature of colour is a scientific not a linguistic issue --, but that rejoinder would be equally misguided. As we saw earlier (in relation to the word "change"), it isn't up to scientists, philosophers or dialecticians to tell us what our colour words mean (and that constraint applies to the rest of our everyday vocabulary, too). Any attempt to do so would plainly undermine the language used in any endeavour to do just that.

Again, it could be objected that this isn't something that can be settled by (or, indeed, brushed aside with) an appeal to the ordinary meaning of words. This is a scientific and/or a philosophical issue.

However, scientists, philosophers and/or dialecticians will have to use language in order to tell us what they take colour to be (i.e., if they are to address the right subject of their enquiries), and, plainly, in order to make a correct start they themselves will have to begin with terms drawn from the vernacular -- otherwise they would be aiming their comments at some other target, not colour.

Now, it is precisely here that any attempt to revise (or even tinker with) the vocabulary of colour that we already have will back-fire. Since the details underlying that observation have been worked-out in detail elsewhere, and because further discussion will take us too far from the main theme of this Essay, I will leave the reader to re-familiarise herself with that discussion (in the course of which, she will need to replace the word "change" with the colour terms of her choice).

Finally, Novack asserts, without proof, that Wittgenstein was an empiricist (Novack (1971b), p.109); he compounds this error a few pages later by adding the following:

"Since Bishop Berkeley set forth his subjective idealism and Hume his doubts about any rational proofs for the objective existence of causation and natural law, subjectivism and skepticism have tainted empiricism and its adherents. These features are exhibited in exaggerated form by contemporary logicians like Wittgenstein who do not believe that the world exists apart from their sensations and ideas about it. As Wittgenstein says 'The world is my world,' that is, reality is as I alone sense and interpret it." [Novack (1971b), pp.113-14. Links added.]

Leaving aside for the moment Novack's serious misrepresentation of Hume, his characterisation of Wittgenstein is about a wrong as anything could be. Novack's only 'evidence' for his claim that Wittgenstein was a subjective idealist is a brief comment that appeared near the end of his first book, the Tractatus (i.e., Wittgenstein (1972), 5.62, p.115). That short sentence is situated in a series of remarks about solipsism, which fact Novack ignores since it would have torpedoed his argument:

"This remark [i.e., from the previous paragraph: 'We cannot think what we cannot think; so what we cannot think we cannot say either...' -- RL] provides the key to the problem, how much truth there is in solipsism. For what the solipsist means is quite correct; only it cannot be said, but makes itself manifest. The world is my world: this is manifest in the fact that the limits of language (of that language which alone I understand) mean the limits of my world.... Here it can be seen that solipsism, when its implications are followed out strictly, coincides with pure realism. The self of solipsism shrinks to a point without extension, and there remain the reality co-ordinated with it." [Wittgenstein (1972), 5.62, 5.64, pp.115-17. (This links to a PDF of two parallel translations; I have used the one on the right, the Pears and McGuinness version.) Bold emphasis alone added; paragraphs merged.]

In the Tractatus, what Wittgenstein meant by "said" was our use of indicative sentences that have a sense -- that is, propositions that are capable of being true or are capable of being false. In which case, when the implications of solipsism are worked out (but it is unclear how that could even happen if what a solipsist wants to say -- or "mean" -- isn't expressed in propositions like this) it coincides (i.e., it collapses into) "pure realism", and all that is left is "reality", which is what Novack would call "the objective world". The reason for Wittgenstein asserting this is connected with the entire logic of the Tractatus, which involves an attempt to show that our employment of fact-stating language isn't based on sensation, but on the logical possibilities such a use of language expresses, so that when we try to say anything, plainly, we have to use language, and that is what commits us all to the same (possible) facts language is capable of expressing, the same logic, and hence to same "reality". The solipsism tries to say "the world is my world" (and Wittgenstein indicates he agrees with that intention, the solipsist is correct to say "the world is my world" since that is what the solipsist, not Wittgenstein, believes), but in so doing solipsism drops out of the picture. In the end what solipsists think they want to say can't actually be said without lapsing into "pure realism", the exact opposite of what they intended. The only way that the solipsist can avoid this is by saying nothing.

So, Novack couldn't be more wrong about Wittgenstein. [On this, see White (2006), easily the best (current) introduction to Wittgenstein's Tractatus.]

As we saw in Essay Three Part One, the defective logic dialecticians inherited from Hegel (whereby they misconstrue of the "is" of predication as if it were an "is" of identity) was founded on an even more archaic confusion over the nature of predicate expressions, re-interpreted as the Proper Names of Abstract Particulars, which is what motivated this error -- i.e., the confusion of objectual-, with conceptual-, change.

When concepts are viewed as abstract objects of some sort (that exist in the 'mind', or 'somewhere in reality') it become almost impossible not to conflate these two sorts of change.

So, no wonder then that dialecticians who take logical advice from Hegel end up talking about concepts developing, and berate the rest of us with tall tales about the 'limitations' of FL because it supposedly uses 'fixed concepts'!

We can now see where the real problem lies; it isn't with the 'fixed concepts of FL', but with the slippery jargon found in DL, which is in turn based on an egregious syntactical error committed by a set of ruling-class hacks in Ancient Greece! And they did that because it was conducive to their world-view to re-configure reality conceptually, and hence represent it as 'Mind'-like, or the product of 'Mind'.

[FL = Formal Logic; DL = Dialectical Logic.]

[Until Essay Twelve is published in full, there are several much briefer explanations why I have alleged this, accessible here, here, and here. It is also worth pointing out that the above remarks won't be fully understood by anyone who hasn't read Essay Three Part One!]

In that case, it is still unclear what exactly is being proposed by those who speak about 'changing', or 'developing', concepts. Once more, this isn't to suggest that we can't make sense of conceptual change, or of general terms that express change in the vernacular (such as "river", "walk", "run", etc.). Far from it; it is an integral feature of our social life and our use of language. But, we certainly can't do so by using a philosophical theory that relies on:

(i) An egregious distortion of the medium by means of which it is, or can be, expressed; and on,

(ii) A set of doctrines based on Ancient Greek and Hegelian Mysticism (upside down or 'the right way up').

Logic And Change

Despite the above, it is also possible to express conceptual change in FL by means of an ascent into Second Order Logic.

Now, this latest twist doesn't contradict the observation made in the previous sub-section (i.e., that what seem to be empirical truths about concepts can't be expressed in language -- it was in fact maintained that they can't be directly expressed by means of distorted sentences), since higher order logic is, among other things, a calculus that expresses rules of inference, not logical (or any other) truths.

In Second Order Logic, concept expressions become variables ranged over by Third Order Quantifiers, and so on.¹⁷

Even so, such systems only indirectly relate to the ordinary use of the words we have for change. Despite what some Philosophers and practically every DM-theorist claim, the vernacular is perfectly capable of expressing change -- and changes of almost unimaginable complexity, too. That is partly because (a) The word "change" is an ordinary language term itself, and (b) The vernacular was invented by those who interface with material reality in collective labour (etc.) on a daily basis -- i.e., workers. In fact, as will be demonstrated below, and in Essay Six, ordinary language is capable of expressing change far better than the obscure 'language' Hegel inflicted on his readers -- or, indeed, the vague and obscure terminology one finds in DM. The vernacular contains literally thousands of words that are capable of depicting change and development in almost limitless detail and complexity.^17a

Real Material Change

Again, it could be objected that the above considerations concentrate on the linguistic expression of change. Whether or not it is possible to represent change in the vernacular isn't really relevant to the issues that exercise DM-theorists. Their focus is on real material change in nature and society, utilising ideas developed both out of, and tested in, practice, in order to help end class society. That being the case, the above comments are academic, at best, misguided, at worst.

Or, so it might be maintained...

Nevertheless, it is worth noting yet again that the points raised earlier were specifically aimed at the claim advanced by Dialectical Marxists that FL can't handle change, not at whether material change is or isn't different from any of our attempts to depict it. Hence, the above complaint is itself misplaced. Since FL systematises certain aspects of some of the inferences we make, or are able to make, in ordinary life -- formalising but a fraction of the discursive principles implicit in our capacity to reason, communicate and picture the world, truly or falsely -- a defence of FL (even if that were what is being done here, which it isn't; FL needs no defence) can't suddenly pretend that our expressive powers and the discursive tools by means of which we manage to communicate aren't relevant.

[FL = Formal Logic; IF = Informal Logic; DL = Dialectical Logic.]

[Of course, IF is capable of expressing even more of the above inferences.]

Anyway, the DM-account of material change is analysed in detail in other Essays posted at this site (for example, Essays Five, Seven Part Three, Eight Parts One, Two and Three). There, it will be shown that dialecticians themselves are incapable of doing the very thing they find fault with in FL -- that is, accounting for, or even depicting, change!

A Purely Academic Issue?

At first sight, it might seem pretty obvious that a logical system based on a static view of the world -- as is alleged of FL -- would have few if any practical consequences or applications. On the other hand, it would appear equally clear that a different logical system based on the opposite view of reality -- as is claimed of DL -- should have countless practical applications, at least in in science and technology.

Ironically, the exact opposite of this is the case: DL has no discernible practical or scientific applications and has featured in none of the advances in the natural or physical sciences (and arguably none even in the social sciences) -- ever. Worse still, DL has made no contribution to technological innovation or development.

[Some might object and point to the successful application of DL in Biology, for example. I shall bat that idea out the park later on in this Essay, alongside other alleged applications of DL -- in the next main section, for instance.]

In stark contrast, FL has played a key role in the development both of science and mathematics, and has featured in countless applications in technology and the applied sciences.¹⁸

Indeed, the development of computers is a particularly good example (among the many) of the impact of FL on science and technology. The origin of computers goes back many centuries, but advances in control systems (in the textile industry in the 18^th century) -- including the path-breaking work of Ada Lovelace, Lord Byron's daughter -- alongside the development of Mathematical Logic (post 1850), proved decisive (this links to a PDF). The invention of Boolean and Fregean Logic, the mathematical logic of Russell, Whitehead, Hilbert, Peano, von Neumann and Church, among many others -- along with the logico-mathematical work of Alan Turing -- all helped make possible the development of computer technology. FL not only contributed to the evolution of software and computer languages, the principles of Propositional Calculus govern the operation of all standard processors.¹⁹

In addition, there are many other examples of the practical applications of FL, ranging from Cybernetics to Coding Theory, from Linguistics to Game Theory and Discrete Mathematics. The question is: Can DM-theorists point to a single successful application of DL in technology or the natural and physical sciences? The answer is reasonably plain: they can't. But this glaring failure becomes all the more revealing when it is remembered that Dialectical Marxists never tire of bragging that their 'logic' is superior to FL when it is applied to the material world.

This is perhaps one paradoxical mismatch between DM and recalcitrant reality that can't be solved by the simple expedient of "grasping" it.²⁰

"Every individual is a dialectician to some extent or other, in most cases, unconsciously. A housewife knows that a certain amount of salt flavours soup agreeably, but that added salt makes the soup unpalatable. Consequently, an illiterate peasant woman guides herself in cooking soup by the Hegelian law of the transformation of quantity into quality…. Even animals arrive at their practical conclusions…on the basis of the Hegelian dialectic." [Trotsky (1971), pp.106-07. Italic emphasis in the original.]

"The Communist Party's official interpretation of Marxism, dialectical materialism, fit Oparin's speculation on the origins of life as 'a flow, an exchange, a dialectical unity'. This notion was re-enforced by Oparin's association with Lysenko." [Quoted from here. Accessed 08/07/2018. Bold added. Original changed; other links omitted.]

"3. In Oparin's formulation, there were first only simple solutions of organic matter, the behaviour of which was governed by the properties of their component atoms and the arrangement of these atoms into a molecular structure. Gradually though, he said, the resulting growth and increased complexity of molecules brought new properties into being and a new colloidal-chemical order developed as a successor to more simple relationships between and among organic chemicals. These newer properties were determined by the interactions of these more complex molecules.

Of course, if and when things go wrong in non-Soviet, non-DM science, Dialectical Marxists inconsistently fail to attribute that to "unconscious dialectics". Instead, they put it down to "bourgeois logic/ideology", "formal thinking", or an unwise adherence to "commonsense", etc., etc. Which is odd given the fact that all the evidence suggests that logic (both Formal and Informal) has actually helped scientists refine and test their theories for centuries, while there is none whatsoever that DL has featured anywhere at all -- except, of course, negatively (in the case of Lysenko and Olga Lepeshinskaya -- who was a personal friend of Lenin's -- for example). [On the latter scientific fraud, see below.]

Small wonder then that DM-supporters also believe that appearances 'contradict underlying reality'. In view of the above, they would, wouldn't they? That particular Hegelian theory has 'allowed' Dialectical Marxists to rationalise countless mismatches between DM and the facts. [On that, see Essay Nine Part Two. and Essay Three Part Two.] But this is surely an odd sort of thing for materialists to find themselves arguing: if the material world contradicts a certain (favoured) idea, ignore reality and cling to that idea! DM-fans consciously do that! Here is one of them actually doing it -- this is Herbert Marcuse, commenting on Hegel:

Admittedly, different forms of atomism were prominent in early modern science, but Atomic Theory and the belief in the existence of molecules wasn't universally accepted among scientists until after (i) The publication in 1905 of Einstein's work on Brownian motion and (ii) The work of Jean Baptiste Perrin, a decade later. [Cf., the remarks on this topic in Miller (1987), pp.470-82; a detailed history can be found in Nye (1972).] Also, worthy of note is the fact that classical Atomic Theory (propounded by John Dalton) had to be rejected before these novel innovations became generally accepted.

Finally, L&L offer their readers only sketchy details concerning exactly how DM has featured in their research; indeed, the latter are pitched at such a low intellectual level that it would make both of them fail any of their undergraduates who turned in such fourth rate, superficial material. [I have said more about L&L in Essay Eleven Part Two.]

DL -- A 'Higher Form' Of Logic?

Judge For Yourself

[LOI = Law of Identity; LOC = Law of Non-Contradiction; LEM = Law of Excluded Middle; FL = Formal Logic; DL = Dialectical Logic.]

What then of the general boast that DL is a superior form of logic? Is there any way of confirming such a claim? Perhaps there is; John Rees argued that DL doesn't reject FL, and neither is it:

"[A]n alternative to 'normal' scientific methods or formal logic…. Formal Logic, like Newtonian physics, has proved inadequate to deal with 'more complicated and drawn out processes.' So the dialectic stands in the same relation to formal logic as Newtonian physics stands to relativity theory or, as Trotsky puts it, as 'that between higher and lower mathematics'." [Rees (1998), p.271, quoting Trotsky (1971), p.63. Quotation marks altered to conform with the conventions adopted at this site.]

If it can be shown that DL does all that Rees claims for it, then perhaps the 'academic' quibbles aired in this Essay can be set aside. Independent of that, other Essays posted at this site have examined these and similar claims, and much more besides (for example Essay Five, Essay Six and Essay Eight Part Three), the result of which is that DL stands to FL what Dowsing does to Hydrodynamics.

Despite this, several rather awkward, initial 'problems' need to be resolved  before this Essay can resume its role as an anti-DM wrecking ball.

First of all, while it is clear that Relativity has largely superseded Newtonian Physics, it isn't at all obvious that that was related to the latter's inability to deal with "drawn out processes". Still less clear is exactly what FL and DL have in common that makes Trotsky's analogy with higher and lower mathematics at all apposite. If anything, the opposite appears to be the case. In fact, Dialectical Marxists are only too happy to begin their discussions of FL by pointing out that most of what they (but no one else) take to be its central tenets are in fact fundamentally defective. This includes the LOI, the LOC and the LEM (among others). [These seemingly baseless allegations will be fully substantiated in the next sub-section.]

Furthermore, although lower mathematics is clearly limited in its scope, none of its precepts are defective, nor do we find professional mathematicians (or even amateur dabblers) criticising it in any way from the outset because of that, quite unlike the attitude adopted toward FL by DM-theorists, who constantly excoriate it for limitations we are in the middle of showing are entirely baseless.

Secondly, and as will be demonstrated in Essays Five and Six (links above) both Trotsky's attempt to criticise the LOI and Engels's 'analysis' of motion collapse into incoherence with remarkable ease. In stark contrast, higher mathematics doesn't disintegrate when we pass beyond its 'lower' forms. In fact, far from being able to handle "more complicated and drawn out processes", as those two Essays will demonstrate, DL has great difficulty coping with an ordinary bag of sugar and the movement of the average cat on or off a mat!

Furthermore, higher and lower mathematics aren't inconsistent with each other. Hence, we don't find mathematicians correcting elementary addition, subtraction, multiplication or division, for example; nor do we find them expanding on the limitations of, say, the equal sign, the cube root function, or, indeed, any of the methods used to solve simple linear equations. Admittedly, higher mathematics contains concepts and rules not found in lower mathematics, but there is no suggestion that the latter uses defective procedures, methods or symbols, or even that they are the exact opposite of what they are normally taken to be. Compare that with the sort of comments made by DL-enthusiasts concerning FL:

"Trotsky saw that it was the inadequacies and contradictions of formal logic that drove theorists toward dialectical formulations. Even those who pride themselves on a 'deductive method', which proceeds 'through a number of premises to the necessary conclusion,' frequently 'break the chain of syllogisms and, under the influence of purely empirical considerations, arrive at conclusions which have no connection with the previous logical chain.' Such ad hoc empirical adjustments to the conclusions of formal logic betray a 'primitive form of dialectical thinking.'" [Ibid., p.272. Quotation marks altered to conform with the conventions adopted at this site.]

Add to that Lenin's remarks:

"The inaneness of these forms of formal logic makes them deserving of 'contempt' and 'derision'…. Hegel shrewdly adds [concerning the Syllogism]: 'Boredom immediately descends when such a syllogism is heard approaching.'" [Lenin (1961), pp.93, 177. Quotation marks altered to conform with the conventions adopted at this site.]

Again, it is worth pointing out once more that fundamental criticisms of FL (like those above) advanced by DL-fans are never substantiated with examples taken from the work of a single logician.²¹ It would be difficult to find a single mathematician who was as dismissive of lower mathematics as Lenin was of FL -- or, indeed, any contemporary scientist who would be prepared to call Aristotle or Newton's work "inane" and fit only for "contempt" and "derision".²²

Returning now to the DM-fairytale that there are exactly three principles underlying FL: In fact, there are countless principles employed in MFL --, indeed, as many as there are authors prepared to invent and/or define them. But, as we are about see, this hoary old DM-fable isn't even true of AFL!

As we are about to see, that is precisely what he and other Dialectical Marxists regularly do when they attempt to summarise, discuss or criticise FL!

[1] George Novack

True to form, however, we are never told what the As he speaks about are, or what they stand for (why that is important with be discussed later), but Novack (and all the rest considered below) nowhere even considers the possibility that A might be identical with itself at t₁ and then change while it is still identical with itself at t₂ (t₂ > t₁) -- that is, A, whatever it is, is self-identical as it changes from moment-to-moment, even if it isn't identical with what it used to be! Humanity invented tensed verbs (alongside a complex vocabulary of adverbs and adjectives) to handle such possibilities, and they did so long before Aristotle existed.

[Recall ">" here means "later than".]  

[On this, see Parsons and Cola (2025), as well as here.]

[On that, see my comments over at Wikipedia, here, where I have shown that the passages taken from Aristotle's work, to which some appeal in their attempt to show he did in fact use, or at least acknowledge, the LOI, don't in fact show this. Readers are referred there for more details. But, it is important to add that I have posted about half a dozen comments about this on the same page. So readers should scroll down to find them.]^22a1

Logic has moved on considerably since Aristotle's day, as have mathematics and the sciences in general. No one today -- other than traditionalists -- would be happy with Aristotle's characterisation of contradictions, etc. However, it is nevertheless apparent from what Novack and the other DL-fans quoted below have to say that they are significantly less logically advanced than Aristotle was 2400 years ago! It is equally clear that Novack didn't consult Aristotle's writings before he simply made up the above comments, just as it is equally clear that the same can be said of the other DM-fans quoted in what follows. For example, Novack pointedly confused the LOI 'stated negatively' with the LOC:

"[L]ogicians as distinguished as Aristotle and Russell have fallen into almost inextricable confusions, so that you just cannot tell whether a predicate is something within language [talk about talk -- RL] or something represented by means of language [talk about things -- RL]." [Geach (1968), pp.22-23 (this links in fact to the 3^rd (1980) edition and so has different page numbers: pp.49-50.]

(d*) not both p not-p (sic)