Essay Four Part One: Formal Logic And Change

This essay should be read in conjunction with Essays Five and Six.

Readers should take note of the fact that this Essay does not represent my final view on any of the issues raised. It is merely 'work in progress'.

Word of warning: for some reason I cannot fathom, the codes that Microsoft have put into FrontPage (the web editor I have employed) appear to have made many of the font colours and some of the formatting in this Essay change somewhat erratically from week to week. I have tried to rectify this many times, but each time I seem to have failed!

In addition, if you are viewing this using Mozilla Firefox, you might not be able to read all the symbols I have used.

It's also worth pointing out that I have endeavoured to keep this Essay as simple as possible, minimising technicalities, since most dialecticians know little or no logic at all (this can be seen from the crass things they say about it (even academic Marxists slip up in this regard, too); on that, see here). In that case, the indulgence of those who know their logic is required; this Essay has not been written for them, unless, of course, they are dialecticians! Anyone who wants to read more substantial accounts of the approach to logic and language I have adopted here should consult the many works I have referenced in the End Notes and other Essays posted at this site.

This Essay is just under 62,500 words long; a summary of its main ideas can be found here.

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 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!]

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

(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: Conceptual Or Material?

(b) Conceptual Change -- Or Conceptual Distortion?

(c) Logic and Change

(d) Real Material Change

(5) Merely Academic?

(6) Is DL A Higher From Of Logic?

(7) Was There Any Logic After Aristotle?

(8) Explaining Change

(9) Thesis, Antithesis, Synthesis Debunked

(10) The Crass Things Dialecticians Say About FL

(11) And About Ordinary Language

(a) Mistaken Assumptions

(b) Descent Into Hegelian Confusion

(c) Ordinary Language Is Not A Theory

(d) Ordinary Language Does Not 'Assume' Things Are Static

(e) Ordinary Language Different From 'Commonsense'

(f) Ordinary Language Not Ideological

(12) Notes

(13) References

Abbreviations Used At This Site

Formal Logic Vs Dialectical Logic

"[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 to the conventions adopted here.]

FL And Change

Unfounded Allegations

In fact, as is well known, Rees's comments echo Hegel's criticisms of the FL of his day, which logic was itself a garbled and bowdlerized version of AFL.¹

The reasoning behind this attitude is outlined in TAR:

"Formal categories, putting things in labelled boxes, will always be an inadequate way of looking at change and development…because a static definition cannot cope with the way in which a new content emerges from old conditions." [Ibid., 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 to the conventions adopted here.]

Admittedly, throughout its history Logic had been confused by many with an assortment of unrelated disciplines -- such as, Metaphysics, Epistemology, Ontology, Theology, Psychology (and the so-called "Laws Of Thought"), Mathematics, and Science. Under such circumstances, it's understandable that the only legitimate role that FL can play -- the study of inference -- was all too easily forgotten. This is, alas, one more tradition DM-fans have been only too happy to maintain.³

Validity And Truth

As the histories of Philosophy, Theology and Mysticism have shown, from such esoteric assumptions it is but a short step to the derivation of truths from thought alone. A priori thesis-mongering and Idealism thus go hand-in-hand; if nature is Ideal, then truths can legitimately follow from thought/language alone. In other Essays posted at this site (for example, here and here) we will see that this is a step DM-theorists (and metaphysicians of every stripe) have been only too happy to take -- and many times over, too.

Nevertheless, there is precious little evidence to suggest that DM-theorists have ever given much thought to this particular implication of the idea that DL reflects the underlying structure of reality -- i.e., that their brand of logic implies reality is Ideal. If logic does indeed reflect the structure of 'Being', then 'Being' must be Mind. [On this, see Essay Twelve Part Four, to be published at a later stage.]

This conclusion only strengthens further the suspicion that the much-vaunted materialist "inversion", supposedly carried out on Hegel's system/method by early dialecticians , was merely formal --, which can only mean that DM is just an inverted form of Idealism. If this is so, then questions about the nature of Logic cannot but be related to the serious doubts raised here about the scientific status of DM. In that case, if Logic is capable of revealing scientific truths about nature -- as opposed to its being a systematic study of inference, and only that -- then it becomes harder to resist the conclusion that DM is indeed just a rotated form of Idealism.

Anyway, since the aim of this section is to examine the specific allegations DM-theorists level against FL, that particular topic will be addressed in other Essays posted at this site (in this case, Essay Three Part One, and  Essay Twelve Parts One and Four).

FL And "Static" Definitions

As it turns out, there is good reason to question the usual claim advanced by dialecticians that FL deals only with "static" definitions (etc.).

Variables And Change

Far from it being the case that FL is wedded to changeless forms, even traditional AFL employed variables to stand for propositions and predicates (general terms) long before they appeared in mathematics. This fact alone shows that traditional AFL was no more incapable of handling change than is modern Mathematics.⁷

As Engels himself pointed out, the introduction of variables into Algebra allowed mathematicians to cope with change. If that is so, it's not easy to understand why DM-theorists believe that traditional FL can't cope with change, too. If mathematicians are currently able to depict change by their use of variables (over the last few centuries), why deny this of traditional formal logicians who used the very same device 2400 years ago?

Of course, it could always be argued that variables that relate to quantities (as they feature in mathematics) are not at all the same as the variables that relate to concepts, properties or qualities (as they are employed in FL). This is undeniable, but not relevant. The point is that either sort of variable allows for change, even if this is so in different ways.

Static Terms Or Slippery Arguments?

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

L1: Premiss 1: No As are B.

L2: Premiss 2: All Cs are B.

L3: Ergo: No As are C.⁸

In this rather uninspiring valid argument schema the conclusion follows from the premisses no matter what legitimate substitution instances replace the variable letters. [Examples are given in Note 8.]

So, L3 follows 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. Some might regard this as a serious drawback, but this is no more a failing here than it would be, say, for Electronics to take no stance on the evolution of Angiosperms (even though it can be used to help study them). Otherwise, one might just as well complain that FL cannot predict the weather or eradicate MRSA.

Moreover, the truth-values (true or false) of each of the above premisses do depend on the interpretation assigned to the schematic letters. These premisses of L1 are not actually about anything until they have been interpreted; before that they are neither true nor false. Not only that, but the indefinite number of ways there are of interpreting schematic letters like those in L1 means that it's possible for changeless and changeable items to feature in any of its concrete instances.

[This 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 nor false, for obvious reasons.]

To illustrate the absurdity of the idea that just because FL uses certain words or letters it cannot handle change (and 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 numbers.

No one would be foolish enough to argue this way in mathematics, for that would be to confuse variables with constants. But, if this is so in mathematics, then DM-inspired claims about the alleged limitations of FL seem all the more bizarre -- to say the least.

Of course, it would be naïve to suppose that the above considerations address issues of concern to DM-theorists. As TAR itself points out:

"Formal categories, putting things in labelled boxes, will always be an inadequate way of looking at change and development…because a static definition cannot 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 does not put anything into boxes, and its practitioners do not deny change as a result.

[Sure, some of them might have had metaphysical reasons for denying change, but that cannot be blamed on logic.]

Indeed, without an ability to reason discursively (along lines that have been formalised in FL), dialecticians would themselves find it impossible to argue rationally.

For example, the argument above (from TAR) appears to draw certain conclusions from apparently 'fixed definitions' (or fixed/relatively fixed uses) of words, like "change" and "static", in order to make certain points about change itself. If, however, Rees's argument is now deliberately interpreted uncharitably (copying the tactic used by dialecticians when they (deliberately) misconstrue FL) it would soon turn into a self-refutation. Hence, in order to point out the supposed limitations of FL, Rees found he had to use the sorts of things he accused FL of employing: i.e., "static" terms.

Of course, if this unsympathetic way of reading Rees's book were correct -- or fair -- then 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 rapidly self-destruct.

If, on the other hand, dialecticians were to employ non-static categories consistent with their own precepts, then that would equally undermine any conclusions they 'derived'. This is because such categories (having no fixed meanings) would sanction no inferences, for it is not possible to decide what follows from what if the meaning of the terms employed is indeterminate. So, while it is unwise of DM-theorists to criticize FL for employing allegedly changeless categories, it would be even more inept of them to do this while using terms whose meanings are apt to change unpredictably. Hence, in practice, DM-theorists must either ignore their own principles and argue from 'fixed categories' about the limitations of FL, or they must construct a case against FL using 'slippery' terms, which could establish nothing whatsoever.

Like it or not, rational criticism of FL cannot succeed if either tactic is adopted.⁹

Change Of Denotation

The schematic letters employed above do not in fact possess "definitions" (only interpretations), hence questions as to their 'fixity' 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 varying the substitution instances of each and every schema. Such moves will have the effect of re-distributing truth-values among the constituent sentences without affecting the associated inferences.

Unfortunately, even this might still not appear to address the worry exercising DM-theorists, which seems to revolve around the alleged superiority of DL over FL, especially in its ability to depict complex change through 'internal contradiction'.

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

An Annoying Counterexample

Nevertheless, a more effective way of rebutting the claim that FL cannot handle change would be to provide a counterexample to it. The one given 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):

The following is an apt interpretation of MPP:

This simple interpretation of MPP (and one involving reasonably rapid change) is perhaps as good a counterexample as one could wish to find that refutes the claim that FL cannot handle transformations in nature (and society). 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 DM-theorists' accusations aimed at MFL are even less accurate than those they direct at AFL. Of course, the example above will hardly satisfy dialecticians, since no "new content" has been added in the conclusion. Fortunately, this is relatively easy to fix. Consider this one premiss argument:

Premiss 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 premiss, so new content has 'emerged', with no dialectics anywhere in sight. [And, as an additional bonus, it depicts change to our dialectical friends into the bargain.] This argument form is used in Mathematics and in Science all the time to derive results not available to those who are still super-glued to the old logic -- and, of course, who are unaware of this fact.

However, dialecticians will still wonder if the changes above are at all relevant to their concerns. DL is said by them to be superior in that it can account for social change, that is, it handles changes of far greater complexity than the above examples illustrate.

Nevertheless, these examples were aimed at countering the specific claim that FL cannot handle change. In later Essays we will see that DL itself cannot account for change of any sort -- whether these are simple or complex, and whether they occur in nature or society. In that case, no matter how poorly FL copes with change (if that is the case), DL fares incomparably worse.

Other Systems Of FL

Of even greater significance is the fact that over the last hundred years or so theorists have developed several post-classical systems of logic, which include (among others), modal, temporal, deontic, imperative, epistemic and multiple-conclusion logics. Several of these sanction even more sophisticated depictions of change than are allowed for in AFL or even MFL (i.e., so-called 'Classical Logic').¹²

Conceptual Change

Notwithstanding all of this, the feeling may perhaps persist that the above examples 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 what they imagine formal logicians take these to be, should the latter even accept/recognise this descriptor -- it's not easy to make much sense of their complaints.^12a

However, there are several confusions that might lie behind, or which might be motivating this odd belief in 'changeable'/'changeless' concepts.

Change In DM -- Conceptual Or Material?

The first confusion involves DM-theorists' own analysis of material change; they frequently depict it in terms that are highly reminiscent of the Hegelian doctrine which holds that change is fundamentally conceptual. How else are we to interpret the following words from TAR that any account of change must explicate how: "…new content emerges from old conditions"? [p.59.] How else are we to interpret Lenin's words?

"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. Emphasis 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.]

Or Trotsky's:

"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.]

Admittedly, Rees appealed to the usual materialist twist that has allegedly been imposed on Hegel's system (to turn it into "materialist dialectics"), as, indeed, did Lenin and Trotsky; but all three pointedly failed to explain how conceptual change is related to material change. 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' do, since that would be to confuse a concept with an object. [We saw that was a dead end in Essay Three Part One; we will meet it again in more detail soon.] Nor will it do to argue than concepts change because we reflect on them (that is, we employ the 'sophisticated' version of the RTK), since that still treats them as objects -- perhaps 'in the head', but certainly objects of "cognition". The problem now facing DM-theorists is how to explain such 'mental objects' while avoiding reductionism and 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 doesn't, and which merely stresses a passive 'subject'. Both theories will be criticised in Essay Three Part Six.]

[It's worth pointing out here that I am not denying conceptual change, merely questioning what dialecticians mean by "fixed concepts".]

Furthermore, how can change to material objects be recorded by our use of concepts? In DM-writings, as already noted, the impression is given that these two sorts of change are simply the same, or that one is a reflection of the other. Or, 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 and 'sanitation' of the mystical ideas dialecticians lifted from Hegel, which they have supposedly put back 'on their feet').

It could be objected that the above ignores the dialectic that operates between the "knower and the known", just as it fails to take note of the fact that our concepts change in accord with developments in material and social reality. Admittedly, DM-theorists have made attempts to account for the relationship between these two sorts of change (material and conceptual) along such lines, but, as noted earlier, they have done so by means of a detour into the RTK, buttressed by an appeal to practical activity linked to a materialist analysis of the dialectical relationship between the abstract and the concrete. Since these topics are addressed in other Essays posted at this site, no more will be said about them here.

Conceptual Change -- Or Conceptual Distortion?

A second source of confusion could lie in the fact that conceptual change is not at all easy to depict. Indeed, if it should turn out that conceptual change cannot be described using traditional (or even DM) terminology then the accusation that DL is superior to FL would become even less easy to sustain. In order to motivate this line of attack, a brief discussion of some of the problems involved in expressing conceptual change would be in order. Consider, therefore, the following sentence:

C1: Green has changed.

The word "green" in such circumstances would normally be understood as name of a person (as opposed to a term denoting a concept). However, if it were to be made clear that C1 related to the colour green, and not to an individual called "Green", it would probably be re-interpreted in the following way:

C2: This patch of green has changed.

This is because little sense can be made of the idea that the concept green could have changed (for reasons that will be explored below). In which case, C1 (interpreted now as C2) would be understood as referring 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 is 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's a singular term! This transforms the supposed concept into an object of some sort.

In that case, it's now difficult to say what "the concept green" designates -- at least not without completely misconstruing what C3 was apparently trying to say about the concept green itself. As noted above, "the concept green" could not in fact pick out the concept it appears to designate since that would transform its supposed target ('the concept green') into an object -- now denoted by the definite description "the concept green". Naturally, that would fatally compromise the distinction between concepts and objects, all the while failing to pick out the original concept intended.¹³

The paradoxical nature of sentences like C3 can be illustrated by a consideration of the following example:

C4: The concept green is a concept.

If it is first of all assumed that C4 is well-formed, then it looks like it is analytically true. In fact, and on the contrary, C4 is analytically false! This is because "the concept green" is a singular expression, and as such it relates to an object, and not a concept.¹⁴

Alas, absurd sentences like C4 are to metaphysicians what carrots are to donkeys; based on linguistic monstrosities like this, some thinkers hastily conclude that language -- or 'thought' (or 'reality', or 'everything') -- must be defective, or must be contradictory, or must be paradoxical. With reasoning like that one might as well argue that if a metre rule, say, has been made incorrectly the same must be true of all it is used to measure!

From linguistic sins such as these, committed by our philosophical ancestors, most of Metaphysics has descended without modification by unnatural selection; unfortunately, DM is not the only progeny of mutant syntax like this.¹⁵

In that case, it is not possible to specify how concepts change by means of sentences like C3; in such contexts the logical role of terms that supposedly designate concepts alters them in such a way that they no longer work as concept expressions.¹⁶

[It is important to note that I am not denying here that concept expressions can be nominalised, only that nothing 'ontological' follows from that superficial linguistic manoeuvre.]

Of course, it could be objected that the mere fact that we can't express conceptual change in the manner specified does not mean that it does not happen; after all, reality is not constrained by the limitations of language. Maybe not, but if an option of this sort cannot be put into language (or, if when it is, what it appears to say undoes what it attempts to say) then no option has been presented for anyone even to begin to consider.

Not only that, the above response clearly trades on the supposition that there are indeed concepts in reality that can change; but that would be true only if reality were mind-like. No one supposes -- it is to be hoped(!) -- that concepts pre-dated the evolution of sentient life, and they reside a sort of limbo world waiting to be thought about, and only then do they begin to change.

On the other hand, if reality is not mind-like, there can be no concepts in nature for our minds to reflect.

Alternatively, if it's claimed that the mind does indeed reflect reality, and it uses concepts to do this, it must distort reality by so doing (that is, it must do this in so far as there are no concepts 'out there' for it to 'reflect').

Now, we saw in Essay Three Part One that the defective logic dialecticians inherited from Hegel (where the misconstrual of the "is" of predication as an "is" of identity was based on an earlier confusion over the nature of predicate expressions, re-interpreting them as the names of abstract particulars) has already predisposed them toward making this mistake: i.e., the confusion between objectual with conceptual change. Only if concepts are viewed as abstract objects of some sort does it become natural 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 of its allegedly fixed concepts.

We can now see where the real problem lies; it's not with the 'fixed' concepts of FL, but with the slippery terminology of DL, which jargon is in turn based on a crass syntactical error committed by ancient Greek ruling-class theorists! And they did this because it was conducive to their world-view to re-configure reality conceptually. [Until Essay Twelve is published in full, there are brief explanations why I allege this here and here.]

In that case, it's still unclear what exactly is being proposed by those who speak of 'changing' or 'developing' concepts. Once more, this is not to suggest that we cannot make sense of conceptual change. Far from it; it's a constant feature of our social life. But we cannot do so by means of a philosophical theory that relies on an egregious distortion of language, and on doctrines heavily infected with AIDS.

[AIDS = Absolute Idealism.]

Logic And Change

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

Now, this latest twist does not contradict the observation made above (i.e., that what seem to be empirical truths about concepts cannot be expressed in language -- it was in fact maintained that they cannot 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, expressions for concepts become variables ranged over by Third Order quantifiers, and so on.¹⁷

Even so, such systems only indirectly relate to our ordinary use of words for change. Indeed, despite what certain Philosophers (and DM-theorists) claim, the vernacular is perfectly capable of expressing change; that is partly because the word "change" is an ordinary term itself, and partly because ordinary language was invented by those who daily interface with material reality in collective labour (etc.) -- 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 found in Hegel, or in DM. The vernacular contains literally thousands of different words that are capable of depicting change and development in almost limitless detail.^17a

Real Material Change

Again, it could be objected that the above considerations all revolve around the linguistic expression of change; whether or not the latter is possible is not relevant to the concerns expressed by DM-theorists. Their interest lies in studying real material change in nature and society, verified in practice, and by intervention and experiment -- in order to change the world. If this is so, then most of the above comments appear to be either academic at best, or misguided at worst.

Or so it could be claimed.

Nevertheless, it's worth noting once more that the points raised earlier were specifically aimed at the DM-thesis that FL cannot handle change, not at whether material change is or is not different from any of our attempts to depict it. Hence, the above complaint is itself misplaced. Since FL expresses only some aspects of some of the inferences we make in ordinary life -- formalising a fraction of the discursive principles implicit is our capacity to reason, and to picture the world, truly or falsely -- a defence of FL cannot suddenly pretend that our powers of depiction are not relevant. [Nor indeed can any attempt to show the opposite.] Of course, Informal Logic captures even more.

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

A Purely Academic Issue?

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

Oddly enough, the exact opposite 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, DL has made no contribution to technological innovation.¹⁸

In stark contrast to this, FL has played an invaluable role on the development of science and mathematics, and has featured in countless applications in technology and the applied sciences.

Indeed, one excellent example (among the many) of the impact FL on technology is the development of computers. Their origin goes back many centuries, but advances in mathematical logic (post 1850) proved to be decisive. The invention of Boolean and Fregean Logic, the mathematical logic of Russell, Whitehead, Hilbert, Peano, von Neumann and Church (etc.) -- along with the logico-mathematical work of Alan Turing -- all helped to make the development of computers possible. FL has not only contributed to the evolution of software and of computer languages, the principles of Propositional Calculus govern the operation of all standard processors (etc.).¹⁹

In addition, there are numerous other examples of the practical applications of FL, ranging from Cybernetics to Code Theory and 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 in 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 dialecticians repeatedly claim 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 cannot be solved by the simple expedient of "grasping" it.²⁰

DL -- A Higher Form Of Logic?

What then of the general boast that DL is a superior form of logic? Is there any way of confirming this? Perhaps there is; TAR's author claims that DL does not 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.]

If it can be shown that DL does all that Rees claims for it, then perhaps the academic quibbles noted above can be set aside. The rest of the Essays posted at this site are aimed at examining these claims, and more. However, a few awkward initial problems need to be addressed before the main picture can begin.

First of all, while it's clear that Relativity has largely superseded Newtonian Physics it's not at all obvious that this was related to the latter's inability to deal with "drawn out processes". Still less clear is what exactly FL and DL have in common that makes Trotsky's analogy with higher and lower mathematics at all apt. If anything, the opposite appears to be the case: DM-theorists are only too happy to begin their discussions of FL by pointing out that many 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). [This allegation is documented below, and in Note 23.]

Although lower mathematics is clearly limited in scope, none of its precepts are defective and professional mathematicians do not criticise it in any way --, quite unlike the attitude adopted toward FL by DM-theorists, who continually excoriate it.

[LOI = Law of Identity; LOC = Law of Non-Contradiction; LEM = Law of Excluded Middle.]

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

Furthermore, higher and lower mathematics are not inconsistent with each other. Hence, we do not find mathematicians correcting ordinary addition or multiplication, nor do we find them expanding on the limitations of, say, the equal sign, the cube root function or quadratic equations. Admittedly, higher mathematics contains concepts and rules not found in lower mathematics, but there is no suggestion that the latter's procedures and symbols are defective, or that they are the very opposite of what they are normally taken to be. Compare this with the sort of comments made by DL-enthusiasts about 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.]

Again, it is worth pointing out that fundamental criticisms of FL (like these) advanced by DL-fans are seldom if ever substantiated with examples drawn from the work of a single logician.²¹ Add to this 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 to the conventions adopted here.]

It would be difficult to find a single mathematician who is as dismissive of lower mathematics as Lenin is of FL, or any modern scientist, for that matter, who would be prepared to call Aristotle or Newton's work "inane" and fit only for "contempt" and "derision".²²

Was There Logic After Aristotle?

As already noted, DM-theorists (but particularly those who are active revolutionaries) almost invariably identify FL with AFL -- and, worse, with that bowdlerized version caricatured in Hegel's two badly misnamed books on logic. DM-theorists of earlier generations (such as Engels, and possibly Dietzgen) may perhaps be excused in this regard, since they largely wrote before the revolution that took place in logic in the decades after the 1870s; later Marxists are not so easy to excused.

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

For example, we find Trotsky (who was otherwise reasonably up-to-date in his knowledge of the sciences) writing the following in his "Open Letter to Burnham" -- approximately 60 years after MFL was initiated by Frege, and approximately 30 years after Russell and Whitehead's Principia Mathematica was first published:

"I know of two systems of logic worthy of attention: the logic of Aristotle (formal logic) and the logic of Hegel (the dialectic). Aristotelian logic takes as its starting point immutable objects and phenomena…. [P]lease take the trouble to inform us just who following Aristotle analysed and systematized the subsequent progress of logic." [Trotsky (1971), pp.91-92.]^22a

To which Burnham not unreasonably replied:

"[A]part from Aristotle, the only 'logic worthy of attention' is that of -- Hegel…. Comrade Trotsky, as we Americans ask: where have you been all these years? During the 125 years since Hegel wrote…[,] after 2300 years of stability, logic has undergone a revolutionary 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 systematized the subsequent progress of logic'…as if this demand were so obviously impossible of fulfilment that I must collapse like a pricked balloon before it…. 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…the monumental 'Principia Mathematica' of Russell and Whitehead…." [Burnham (1971), pp.236-37.]

Unfortunately, wilful ignorance like this among dialecticians has not noticeably changed much since Trotsky's day (with the notable exception of the work of logicians like Graham Priest, of course). Hence, we still find socialists of otherwise impeccable dialectical credentials repeating Trotsky's ill-informed opinions time and again, still confusing FL with AFL, still clinging to the dogma that Aristotle is and always will be the last (and only) word on the subject.

Worse still, Dialectical Marxists compound this inexcusable ignorance with an open failure to grasp what few degenerate ideas they mistakenly attribute to Aristotle.²³

Explaining Change

Turning to specifics: according to its supporters, the superiority of DL over FL arises partly from its ability to explain change and partly from the understanding it gives of the contradictory behaviour of nature and society, thus assisting in the revolutionary transformation of the latter. This, it is claimed, FL cannot adequately do.

However, not even mathematics can provide a scientific account of change -- even if it does play a major role in science. Mathematical objects have no causal impact on reality; they nowhere appear in nature.²⁴ And yet, this does not mean that mathematics is inferior to a 'higher' brand of 'Dialectical Mathematics'. Why DM-theorists use an analogous argument to depreciate FL is therefore puzzling.

Of course, some DM-theorists have attempted to offer their own account of the superiority of 'higher' over 'lower' mathematics, based, for example, on Engels's interpretation of Descartes's introduction of variables into Algebra, and on some rather obscure notes left by Marx concerning the nature of Differential Calculus.²⁵

Nevertheless, DM-apologists claim that when linked to a detailed analysis of material causes, their theory can provide a scientific account of change. This idea is discussed in detail in Essays Five, Seven Part One, Eight Parts One, Two and Three, and then systematically dismantled.

Notes

1. Key (relevant) aspects of Hegel's 'logic' are taken apart here -- more will be added when the rest of Essay Twelve is published (summaries here and here).

2. These allegations will be substantiated presently.

3. Again, these assertions will be substantiated in Note 4.

4. Validity is a formal property of argument schemas, whereas truth is a 'property' of propositions. [The word "property" is in 'scare' quotes since this term is being used technically, if not figuratively, here.] If the only legitimate role FL occupies is the study of inference, then, as such, it is only indirectly related to the 'search for truth'. Logic is therefore a science only in the wider (German) sense of the term -- that is, it's a systematic study of an area of enquiry (which is, in this case of course, inference).

The definition here is incorrect, as I have pointed out in the discussion pages.

[The confusion of FL with science proper is discussed below, in Note 5.]

For a clear definition of validity, see, for example, Tomassi (1999), pp.2-19, or Priest (2000), pp.1-6.

5. In line with many others (mostly those who know little logic), DM-theorists in general labour under the widespread illusion that FL is the study of the "Laws of Thought", or it's the "Science of Cognition" -- that is, that it's one of the sciences proper. For example, consider Lenin's description:

"Logic is the science of cognition. It is the theory of knowledge…. The laws of logic are the reflections of the objective in the subjective consciousness of man.... [These] embrace conditionally, approximately, the universal, law-governed character of eternally moving and developing nature." [Lenin (1961), p.182. Italics in the original.]

Here is Trotsky:

"Hegel himself viewed dialectics precisely as logic, as the science of the forms of human cognition....

"What does logic express? The law of the external world or the law of consciousness? The question is posed dualistically [and] therefore not correctly [for] the laws of logic express the laws (rules, methods) of consciousness in its active relationship to the external world....

"Thought operates by its own laws, which we can call the laws of logic...." [Trotsky (1986), pp.75, 87, 106. Trotsky is apparently referring to Hegel's Introduction to The Science of Logic (i.e., Hegel (1999), pp.43-64.]

We also find Novack, for instance, defining logic as:

"…the science of the thought process. Logicians investigate the activities of the thought process which goes on in human heads and formulate the laws, forms and interrelations of those mental processes." [Novack (1971), p.17.]

Lenin, Trotsky and Novack have clearly confused logic with psychology. If logic were the science of what went on in people's heads, then logicians would busy themselves with brain scans, surveys, psychometric tests, and the like. They certainly would not waste their with all those useless definitions, theorems and proofs.

And do dialecticians seriously think that people actually cogitate in syllogisms? [As we will see, Trotsky certainly did!] Or, that they use the formal calculi found in Principia Mathematica when they reason? They must if they believe that logicians study how people actually think.

Well, not only does Trotsky reckon human beings think in syllogisms, he believes chickens do too!

"The chicken knows that grain is in general useful, necessary and tasty. It recognises a given piece of grain as that grain -- of the wheat -- with which it is acquainted and hence draws a logical conclusion by means of its beak. The syllogism of Aristotle is only an articulated expression of those elementary mental conclusions which we observe at every step among animals." [Trotsky quoted in Woods and Grant (1995), p.89. A copy is available here (near the bottom of the page). In fact this appears in Trotsky (1973), p.400.]

Unfortunately, Trotsky failed to say how he knew so much about the logical skills of these Aristotles of the bird world -- or why, if animals have known about these things for so long, it took a genius like Aristotle to 're-discover' them about 1 million years after we left the 'animal kingdom', and countless million since 'we' branched off from our common ancestor with the birds!

Moreover, if chickens are such 'natural logicians', then perhaps among them there is a Feathered Frege, a Rooster Russell or even a Peano of the Poultry World?

Figure One: Aristotle, Frege, And Russell?

6. In Essays Twelve and Fourteen the connection between this way of thinking and ancient religious and mystical views of reality will be examined. The ideological impact on revolutionaries of the latter will also be detailed in Essay Twelve (summary here) and in Essay Nine Parts One and Two.

6a. It could be replied that if language is part of the world, it must have coded into it all sorts of things that are part of reality, too. This response will be defused in Essay Twelve, where it will be shown to depend on subtle forms of LIE. [A shorter version of that Essay can be found here.]

[LIE = Linguistic Idealism.]

7. One has only to leaf through, say, Aristotle's Prior Analytics to see that this is no invention.

This is what the late Professor Nidditch had to say:

"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.]

A comprehensive history of Logic can be found in Kneale and Kneale (1962); the rapid degeneration that Logic underwent after Aristotle's death is outlined in Peter Geach's article: 'History of the Corruptions of Logic' (i.e., Geach (1972b)).

8. With respect to this argument schema, the only condition validity requires is the following: if, for a given interpretation, the premisses are true then the conclusion is true. That claim is not affected by the fact that schematic premisses themselves cannot be true or false, since such schema express rules, and are hypothetical. [A clear explanation can be found here.] To be sure, Aristotle did not see things this way, but I do. [Even so, I have assumed here that these schemas are categorical, that is, that they aren't hypothetical.]

One interpretation of L1 (given in the text) that might illustrate this is the following:

Premiss 1: No moving object is stationary.

Premiss 2: All objects with zero velocity are stationary.

Ergo: No moving object is one with zero velocity.

[Certain stylistic changes were required here to prevent this ordinary language interpretation becoming somewhat stilted.]

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 do not have to employ what seem to be 'necessarily true' premisses (or, indeed, this particular argument form) to make the point:

Premiss 1: All human beings are aging.

Premiss 2: All Londoners are human beings.

Ergo: All Londoners are aging.

Admittedly, the term "aging" is not of the type Aristotle would have countenanced in a syllogism, so far as I can determine. However, if we free Aristotle's logic from his metaphysics, the inference is clearly valid, and 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 this stilted but genuine syllogism:

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

Premiss 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".]

To be sure, the above changes are not of the sort of that interest dialecticians, but, as I note in the main body of this Essay, examples like this have only been quoted to refute the claim that FL cannot cope with change. Combine that idea with the additional thought that dialectics can't cope with change itself (on that, see here), and the alleged 'superiority of DL over FL turns into its own opposite. Which is yet another fitting dialectical inversion.

There is an excellent account of Aristotelian Logic in Smith (2011).

And there is an equally useful account of MFL (i.e., now confusingly called "Classical Logic") in Shapiro (2009).

Readers should also consult Hirsch (2004), which, while deeply flawed, represents a major step in the right direction. [However, the editors of the on-line journal in which Hirsch (2004) appears did not see fit to publish my reply; it will be published at this site, sometime in the future.]

9. Naturally, this raises issues that lie at the heart of this dispute: whether or not concepts change over time as a result of inherent logical/rational processes. This aspect of DL (uncongenial as it is to the sort of historical materialism that refuses to make concessions to mysticism) will be examined in Essay Fourteen Part Two.

This also raises questions about the relative stability of meaning in language. That topic is dealt with in more detail in Essay Six -- here and here. See also here.

[LOI = Law of Identity.]

10. The reader should consult Essays Five, Six, Seven and Eight Parts One Two and Three on this.

11. In fact, MPP was known to the Stoics, circa 200 BCE. This item of breaking news has yet to reach the ears of majority of 'dialectical logicians', it seems. It looks like 2200 years is not quite long enough...

On Stoic Logic, see Kneale and Kneale (1962), pp.158-76, and Mates (1953).

In the argument in the main body of the Essay, "A" stands for "Assumption". The un-bracketed numbers relate to the premises used on each line to derive the conclusion, and the bracketed numerals refer to the line numbers. [In this, I have partially followed Lemmon's method of presentation. Cf., Lemmon (1993).]

An introduction to Natural Deduction (a system devised by Gerhard Gentzen) can be found in Lemmon (1993); an axiomatic approach to logic is set out in Hunter (1996), and more advanced logic can be found in Bostock (1997) and Mendelson (1979). A more recent and comprehensive survey of modern mathematical logic can be found in Hinman (2005).

Unfortunately(!!), Gentzen was either a Nazi or entertained Nazi sympathies. On this, see here, but this should no more affect our opinion of his work in logic than Hegel's political and social views affect how dialecticians regard his 'logic'.

11a. Care must be taken not to confuse interpretation in logic with interpretation in other disciplines or in ordinary discourse. "Interpretation" in logic relates to the substitution instances that result when variables are replaced with the relevant terms drawn from ordinary or technical languages, etc.

It might be objected that the antecedent and consequent here are not propositions -- that is, "Atoms of ⁶⁴Cu undergo beta decay" and "⁶⁴Ni atoms, positrons and neutrinos are formed" are not capable of being true or false. That is correct, but the argument is not beyond repair. However that repair would make the clauses involved highly stilted, if not unwieldy. The repaired version of the opening assumption would read something like this:

A1: If an atom of ⁶⁴Cu undergoes beta decay at T(1), then an atom of ⁶⁴Ni, k positrons and m neutrinos are formed at T(2).

Where the temporal and numerical variables are well defined. However, I rather think that A1 is scientifically uninteresting and possibly unverifiable, but that is no fault of logic.

12. The details of these other systems of Logic can be found in Goble (2001), Hughes and Cresswell (1996), Haack (1978, 1996), Hintikka (1962), Jacquette (2006), Prior (1957, 1967, 1968) and Von Wright (1957, 1963). A general survey of some of the background issues raised by Classical and Non-Classical Logic can be found in Read (1994). In fact, Graham Priest (who is both a defender of certain aspects of dialectics, and an expert logician) has written his own admirable introductions; cf., Priest (2000, 2008). Also worth consulting are the following:

http://plato.stanford.edu/entries/logic-temporal

http://plato.stanford.edu/entries/logic-modal/

http://plato.stanford.edu/entries/logic-epistemic/

http://plato.stanford.edu/entries/logic-manyvalued/

http://plato.stanford.edu/entries/logic-deontic/

http://earlham.edu/~peters/courses/logsys/nonstbib.htm

Despite this embarrassment of riches, freely available on the internet, DM-fans stoutly cling on to their studied ignorance, maintaining their self-inflicted nescience all the while pontificating about FL as if each one were a latter-day Aristotle. [Anyone who doubts this need only examine, say, Trotsky's lamentably poor 'answer' to James Burnham, in Trotsky (1972), pp.91-119; 196-97, 232-56. See also, here and here.]

12a. This is not strictly true; several examples of the rather weak attempts made by DM-theorists to argue that logic uses 'fixed concepts' will be examined below.

12b. Of course, as we will see, the former (reductionism) is avoided by means of a flat denial, but with no attempt at explanation other than a reference to the Part/Whole dialectic (criticised in Essay Eleven Part Two); the latter consequence (bourgeois individualism) is just ignored. In fact, in my 30-year hike across the desolated dialectical desert, I have only ever encountered one author (Bertell Ollman) who even so much as recognises this implication of the 'dialectical theory of knowledge', and even then he merely bats it off into the long grass for future consideration. [On that, see here.] 

13. The distinction between concepts and objects (or rather, the distinction between concept expressions and singular terms) is needed, otherwise propositions would turn into mere lists, and thus fail to say anything.

[This topic is discussed in more detail in Essay Three Part One (and briefly below, in Note 14). Many of the issues raised here are outlined with admirable clarity in Gibson (2004), and in extensive detail In Gaskin (2008). However, Gaskin's 'solution' is no solution at all; I will say more about this in a later Essay.]

Anyway, dialecticians themselves appear to need this distinction, otherwise their theory would be little different from "crude materialism"; they need concepts to remain concepts and not turn into objects or they will lose the capacity to express generality. [All this was explained in detail in Essay Three Part One.]

Indeed, if concepts and objects were one and the same, there would seem to be no advantage in seeking a conceptual account of change in, or to, material objects, for that would turn it into an abstract objectual account of material objects, only now it would be entirely unclear what the former 'objects' were (i.e., what these 'objects-cum-concepts' are), and how they could account for anything.

However, as far as the alleged change to concepts is concerned, and with respect to C2 and C3 in the main body of this Essay, there seem to be only two possibilities. Neither looks viable:

C2: This patch of green has changed.

C3: The concept green has changed.

(1) "The concept green" could designate all green objects. On reflection, this seems unlikely since C3 was specific in its reference to the "concept green", not to those objects that happen to instantiate it. Even though all or most of the latter could change, it would still leave the concept itself unaffected. Indeed, all green things seem to change at some point, but if the 'concept' also changed, we would not be able to express this fact in any obvious way.

So much was at least clear to Plato, but he (or at least later Platonists) 'solved' this problem by turning general words either into the names of abstract particulars (i.e., the "Forms"), or other singular terms that designated them, thereby destroying generality. [On this, see Essay Six, here.] Hence, this alternative would also leave the phrase "the concept green" no longer behaving as a general, but as a singular term, which would, plainly, no longer be operating as a concept expression. Concept expressions are general; singular terms manifestly aren't.

(2) "The concept green" could refer to an 'abstraction' residing perhaps in some 'mind' or brain -- or, which somehow 'inhered' in all objects that shared this 'property', or which constituted their 'form'). But, again, on reflection, this expression can't designate a 'collective idea of green', for there is no such thing. [Why this is so, if abstractionism were true, is explained at length in Essay Three Parts One and Two.] And, even if there were such an idea, calling 'it' a concept would be inept since, ex hypothesi, 'it' would then be an 'object', or collection of 'objects', not a concept. Moreover, if all green objects shared this common property, designating it this way would deny them that very role, since 'The concept green' itself would be an object, not a general property!

Of course, either option would simply confirm the view that it's not concepts that change, but objects that instantiate them which do.

The problem here is that we can't express in indicative sentences the logical role that concept expressions play without distorting that role; any attempt to do so simply destroys their capacity to function in the way we might imagine. [This is connected with the main theme of Essay Twelve Part One -- that is, that any attempt to formulate theories about how language 'latches onto the world', how it allegedly reflects nature, will always collapse into non-sensicality.] While Frege was aware of this 'difficulty', he could not account for it; Wittgenstein, I think, 'solved' this 'problem' by dissolving it. On this see the references given below.

The illusion that we can refer to conceptual change (perhaps in the crude manner envisaged in TAR and other DM-texts) is created by the transformation that concept expressions undergo when they are situated in new, but non-standard sentential contexts -- for example, if direct reference to them is attempted, or they are designated by singular expressions, and those terms are situated in indicative sentences (for example, in C3).

As C1 and C3 show, the claim that concepts can change rests on the nominalisation or particularisation of concept expressions -- by means of a Proper Noun (e.g., "Greenness"), or a definite description (e.g., "The concept green"), which, once more, turns what should be general expressions into singular terms. This then motivates the idea that because singular terms denote objects -- which can and do change -- these newly nominalised/particularised 'entities' must similarly be subject to change, and in like manner.

[Particularisation is the process by means of which general words are turned into singular expressions (Proper Names, Definite Descriptions, etc.), which then supposedly designate Abstract Particulars. (However, it's important not to confuse particularisation with Hegel's use of "particular".) This is not to suggest that the 'subject' term of such sentences can only be singular terms.]

C1: Green has changed.

C3: The concept green has changed.

Change in or to objects thus becomes a model for conceptual change, but only because in an endeavour to refer to, or denote, concepts we are forced to nominalise/particularise concept expressions. Naturally, this linguistic move is the first false step in the running together of these two distinct sorts of change.

In Essay Three Part One we saw how this simple error spawned a 2500 philosophical pseudo-problem about the nature of 'Abstractions', 'Universals', 'Categories', 'Ideas', 'Forms' and 'Concepts'.

However, it's worth adding that these 'abstract objects' were only conjured into 'existence' because the distinction between concepts and objects had been obliterated -- again by means of yet another grotesque distortion of language, as Marx suggested:

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

[Although, I'm not suggesting that Marx saw things this way, but there are hints in his early work that he was moving in this direction in the 1840s. On that, see here.]

Metaphysicians have repeatedly made mistakes like this, constantly falling prey to what might be called the "Nominalisation/Particularisation Fallacy". Those who have been misled along such lines seem to think that if a clause (or phrase) can be nominalised/particularised then there must be something (visible or invisible, in the 'mind' or in 'Platonic Heaven') that answers to it. [This misconception is related to the 'Fido-Fido' fallacy Gilbert Ryle described.]

So, on that basis, it's concluded that "the concept green" must exist (somewhere!) because the expression has just been particularised. Again, such inferences have only ever been justified by nominalisations/particularisations of this sort -- which conjure into existence 'abstract objects' at the drop of a noun.

This error also motivates the idea that since the ordinary use of words prevents such linguistic tomfoolery, technical devices must be invented that permit it -- and words like "Form", "Concept", "Being", "Property", "Category", "Nothing" and "Becoming" are then pressed into service. The supposed meaning of such empty phrases now appears to allow profound 'philosophical' truths, valid for all of space and time, to be derived from thought alone. In this way, the 'thoughts' (of lone thinkers, divorced from the constraints social life puts on the use of language) seem able to penetrate to the heart of reality, uncovering 'hidden truths' in the comfort of their own heads. But, the only rationale for this manoeuvre is a terminological trick motivated by an inept (and ancient) transformation of concept expressions into the names of abstract particulars.

In DM, this (distorted) approach to the vernacular resurfaces as part of the claim that the logic of ordinary discourse must be "surpassed" by the use of highly obscure jargon -- found, for example, in Hegel's Logic, which not only permits such 'word magic', it insists on it.

However, since singular terms are not concept expressions (nor vice versa), moves like this must always fail. That's because, in order to pick out the alleged reference of a general term, a singular term supposedly denoting it has been introduced. But, this term now designates an abstract object -- it has to be abstract, for if it were material there would be no need for this charade. So, this newly introduced expression no longer operates as a general term, but as singular expression. Hence, because of this Ancient Greek segue, concepts now appear to be strange sorts of objects -- or, alternatively, objects now look like peculiar sorts of concepts -- that can stand in relation to other objects. [This observation will be expanded upon in Essay Twelve (in order to reveal where, for example, Hegel's account of truth goes badly astray). This move also underlies all the (Idealist) talk about "internal relations" one finds in DM. More on that in Part Two of this Essay.]

Now, instead of finding fault with the linguistic distortion that created such abstractions to begin with (but which cannot work anyway since this move destroys the unity of the proposition -- this was explained in Essay Three Part One), dialecticians assume that reality itself must be 'contradictory' That in turn is because it's now 'clear' to them that a singular expression cannot be identical with a Universal, so the Universal must be transmogrified into an Abstract Particular.

[Again, the background to this can be found here, in connection with the traditional confusion of general words (concept expressions) with the names of Abstract Particulars.]

These bogus moves suggest that further adjustments now have to be made to the original 'concepts', indicating -- to those taken in by this linguistic conjuring trick -- that there is "movement" in 'concepts', by means of which they are now said to possess "identity-in-difference", which doctrine forms the basis for, or the motor of, universal development. That's because these artificial 'concepts'/'objects' now seem capable of change, since they have been altered so that they resemble material objects.

We can see this, too, in Hegel's confusion of the LOI with the LOC, in the course of which he ran together concepts, objects, propositions, and judgements -- along with a whole host of other things. [This is something that dialecticians in general also do (and that includes HCDs), since their thinking has been heavily skewed by their uncritical acceptance of that Hermetic bungler's logical howlers. Anyone who objects is accused of 'pedantry'.]

In this way, a bogus (local) change, imposed on a handful of ordinary words, is taken to reflect an 'essential' feature of the development of everything in nature, and for all of time --, which is then promptly imposed on reality.

[In Essay Twelve, an epistemological version of this dodge is called the RRT. The implication of this theory is that, despite what its supporters tell us, language is no longer said to reflect the world, the world is made to reflect (distorted) language. This represents an essential move in the setting up of a pernicious strain of LIE. (We saw here and here how the entire dialectic is based on a series of logical blunders of this sort.)]

[LOI = Law of Identity; LOC = Law of Non-Contradiction; LEM = Law of Excluded Middle; RRT = Reverse Reflection Theory; LIE = Linguistic Idealism; HCD = High Church Dialectician (explained here).]

We can see this, too, in Hegel's ambitious 'derivation' of 'Nothing' from 'Being', which is a verbal trick that only works if these 'concepts' are treated as objects of some sort ('named' by the words "Being" and "Nothing").

[This 'argument' (unwisely praised by Lenin and Trotsky!) is destructively analysed in Essay Twelve Part Three (summary here). The tangled rat's nest -- otherwise known as Hegel's Logic -- is in fact a sub-Aristotelian Grimoire replete with syntactic screw-ups like this, which have been unwisely accepted by Hegel-groupies ever since.]

We can see this happening, too, in these words of Engels's:

"The identity of thinking and being, to use Hegelian language, everywhere coincides with your example of the circle and the polygon. Or the two of them, the concept of a thing and its reality, run side by side like two asymptotes, always approaching each other but never meeting. This difference between the two is the very difference which prevents the concept from being directly and immediately reality and reality from being immediately its own concept. Because a concept has the essential nature of the concept and does not therefore prima facie directly coincide with reality, from which it had to be abstracted in the first place, it is nevertheless more than a fiction, unless you declare that all the results of thought are fictions because reality corresponds to them only very circuitously, and even then approaching it only asymptotically." [Engels to Schmidt (12/3/1895), in Marx and Engels (1975), p.457, and Marx and Engels (2004), pp.463-64. Bold emphasis added.]

"The fact that identity contains difference within itself is expressed in every sentence, where the predicate is necessarily different from the subject; the lily is a plant, the rose is red, where, either in the subject or in the predicate there is something that is not covered by the predicate or the subject…. That from the outset identity with itself requires difference from everything else as its complement, is self-evident." [Ibid., pp.214-15. Bold emphasis alone added.]

Engels thus clearly saw concepts as object-like. [More on this, here.]

Plainly, these artefacts of the imagination can't undergo change in the material world (at least not in the way that objects do), and that is why these tendentious manoeuvres have to take place in the 'hidden' world of the 'mind', even though we only have a set of distorted words on hand as 'proof' that any of this has actually occurred.

Indeed, this 'linguistic miracle' is so profound that it can, on its own, create a whole world of changing 'concepts', hidden from human gaze, which 'exist' in, and constitute, a world that is more real than the material world from which they had allegedly been 'abstracted'. In fact, this 'occult world' encapsulates the essence of the material world, its a priori structure and motive force.

As noted earlier, Hegel performed this conjuring trick on 'Being' to produce 'Nothing', and hence 'Becoming':

"Being is the indeterminate immediate; it is free from determinateness in relation to essence and also from any which it can possess within itself. This reflectionless being is being as it is immediately in its own self alone.

"Because it is indeterminate being, it lacks all quality; but in itself, the character of indeterminateness attaches to it only in contrast to what is determinate or qualitative. But determinate being stands in contrast to being in general, so that the very indeterminateness of the latter constitutes its quality. It will therefore be shown that the first being is in itself determinate, and therefore, secondly, that it passes over into determinate being -- is determinate being -- but that this latter as finite being sublates itself and passes over into the infinite relation of being to its own self, that is, thirdly, into being-for-self.

"Being, pure being, without any further determination. In its indeterminate immediacy it is equal only to itself. It is also not unequal relatively to an other; it has no diversity within itself nor any with a reference outwards. It would not be held fast in its purity if it contained any determination or content which could be distinguished in it or by which it could be distinguished from an other. It is pure indeterminateness and emptiness. There is nothing to be intuited in it, if one can speak here of intuiting; or, it is only this pure intuiting itself. Just as little is anything to be thought in it, or it is equally only this empty thinking. Being, the indeterminate immediate, is in fact nothing, and neither more nor less than nothing.

"Nothing, pure nothing: it is simply equality with itself, complete emptiness, absence of all determination and content -- undifferentiatedness in itself. In so far as intuiting or thinking can be mentioned here, it counts as a distinction whether something or nothing is intuited or thought. To intuit or think nothing has, therefore, a meaning; both are distinguished and thus nothing is (exists) in our intuiting or thinking; or rather it is empty intuition and thought itself, and the same empty intuition or thought as pure being. Nothing is, therefore, the same determination, or rather absence of determination, and thus altogether the same as, pure being.

"Pure Being and pure nothing are, therefore, the same. What is the truth is neither being nor nothing, but that being -- does not pass over but has passed over -- into nothing, and nothing into being. But it is equally true that they are not undistinguished from each other, that, on the contrary, they are not the same, that they are absolutely distinct, and yet that they are unseparated and inseparable and that each immediately vanishes in its opposite. Their truth is therefore, this movement of the immediate vanishing of the one into the other: becoming, a movement in which both are distinguished, but by a difference which has equally immediately resolved itself." [Hegel (1999), pp.82-83, §130-34. Italic emphases in the original.]

Attentive readers will no doubt have noticed that Hegel refers to each these 'concepts' with an "it", and asserts that 'they' can or can't have properties/'determinations' (just like any other object), failing to spot that by doing this he destroyed their generality, nullifying the whole exercise. [This argument will be returned to the Idealist swamp from which it slithered in Essay Twelve Parts Five and Six.]

It could be argued that Hegel is talking about conceptual subordination here not object-concept subsumption. The former involves concept-to-concept predication, whereas the latter involves concept-to-object predication. [On this, see Redding (2007), pp.85-114.] The problem with this response is that Hegel strangled it before birth when he nominalised the 'concepts' he employed (as "Being", "Nothing" and "Becoming").

These days, the bedraggled occupants of Hegel's Hermetic House of Horrors -- DL-fans -- also have a method that supposedly gives 'life' to 'concepts' (by nominalising them as abstract particulars), when in fact it kills them by destroying their capacity to express generality -- vitiating the whole exercise.

Hence, and once more: a move in language is held to mirror, or to reveal, movement in thought/reality --, but, as noted above, the former is held (by Idealists and naive DM-fans alike) to reflect changes which are far more profound than plain and simple material development. Indeed, 'conceptual change' of this sort is said to drive material development. In this way it turns out that nature is 'dialectical' only because of a series of logical/syntactical blunders, which 'allowed' Dialectical Magicians to conjure the underlying logic of 'Being' and 'Becoming' into existence -- literally from 'Nothing' --, as these merge into, and re-emerge from, 'Nothing'.

The Big Bang from the Big Distortion.

It's worth re-emphasising here that the only 'evidence' for these 'impressive' moves is this inept analysis of a relatively minor, indicative sentential form found almost exclusively in Indo-European languages!

However, what finally emerges at the end of this Ancient Linguistic Conjuring Trick is not in fact an account of how concepts change, but how a bogus linguistic ceremony can be substituted for a genuine account of change in the material world!

This inept syntactical 'research programme' (now over 2400 years old) deliberately runs together the logical role played by singular and general terms, names and concept expressions. [Why this was deliberate is explained in Essay Twelve (summary here).]

Be this as it may, for present purposes it's worth asking the following question: If these logical 'categories' (the singular and the general -- concepts and objects) are 'identical', how is it possible to depict the functioning of either or both of them? Surely, a name only functions as a name alongside other expressions that aren't names. Similarly with predicates/concept expressions. If every word named something (concrete or abstract), how could we say anything about anything?

As was argued in Essay Three Part One, if sentences were composed solely of names (or singular terms), they would be no different from lists. Lists fail to say anything -- unless they are articulated by the use of concept expressions/predicates -- and only if these aren't viewed as designating abstract particulars.

Propositions, on the other hand, can be used to assert or deny things. That being so, propositions can't contain only names and/or singular terms. Otherwise we would not be able to assert or deny anything by means of them.

Of course, this is part the reason why DM-'propositions' collapse into non-sense: the inept syntactical theory dialecticians have inherited from Hegel and traditional thought has emptied them of sense by turning the sentences used to express them into mere lists, preventing them from saying anything at all.

14. Compare the following with C3:

C3: The concept green has changed.

C5: This leaf is green; next month it will be brown.

C5a: These leaves are green; next moth they will be brown.

C5 succeeds in depicting change -– but, plainly, that's because it describes change to an object (or in C5a, to a set of objects), not a concept.

In the first half of C5, the concept green is expressed by the use of the one-place predicable "ξ is green", which, when applied as a rule to the singular term, "This leaf", forms the first clause of C5.

[It could be objected that if the comments reported in this Essay are correct, the above sentence -- i.e., "the concept green is expressed by the use of the one-place predicable "ξ is green" -- is itself ill-formed. Well, it certainly lacks a sense -- it cannot be true or false -- but that's not a problem for the case being presented here because the 'offending' sentence is itself a rather badly-worded rule, hence it does not need to be true or false to be understood. More on this in Essay Twelve Part One. (And it's badly-worded only because of the constraints under which I am working here -- defending ordinary language in the face of those who distort it, but who should know better: DM-fans!).

The use of these rather odd looking stencils (i.e., "ξ is green") is explained here. It is further justified, here, and below.]

[Incidentally, a predicable is an expression that is capable of being predicated; it's a predicate when it is so predicated.]

By way of contrast, in C3, the phrase "The concept green" operates as a singular term, which cannot express a rule, whereas "ξ is green" can. [Why that is so is explained in Essay Three Part One.]

Nevertheless, "The concept green", acting now as a singular term (when coupled with the one-place predicable "ξ has changed"), enables the formation of sentences like C3 -- plainly when the phrase "The concept green" is used to complete it.

But, because of this C3 is no longer an ordinary sentence. Despite what it seems to say, it cannot now be about the concept green. This is because although "The concept green" purports to pick out a concept, as a singular term it can only designate an object. This means that C3 is now thoroughly misleading. While C5 itself succeeds quite uncontroversially in expressing material change, C3 fails to depict anything at all because of its distorted linguistic form.

Even if (per impossible) the phrase "The concept green" could designate anything non-misleadingly, it couldn't serve as an archetype for the role that legitimate concept expressions play in sentences like C5. Once more, that's because a singular term (i.e., "The concept green") cannot express a rule, which is what the ordinary use of "ξ is green" actually achieves.

That is, anyone who understands the convention expressed by "ξ is green" -- i.e., that sentences can be formed by replacing "ξ" with singular expressions (or other legitimate 'subject' terms) -- will have mastered a rule for the sue or "green" (in such contexts). [Again, why that is so is explained in Essay Three Part One.]

So, "ξ is green", as it appears in sentences like C5, is the expression of a rule. Of course, ordinary speakers plainly aren't aware of stencils like "ξ is green", nor need they be. These stencils merely assist us in understanding the patterns that are illustrated in our formation and use of such simple sentences. Nor does it mean that this is the only way that C5 can be analysed, or that we have to view things this like this, but this way of depicting things is brings out the rule-governed way we all form sentences like C5. Moreover, one advantage of picturing things in this manner is that it underlines the fact that a singular term like "The concept green" cannot express a rule, whereas "ξ is green" can.

This is, of course, just a formal way of making the point that description is different from naming, or designating -- which distinction  remains valid no matter how we try to depict or formalise it.

However, the actual marks on the page/screen (i.e., "ξ is green") are nowhere to be found in C5. This incomplete expression is in fact the common pattern that underlies all the legitimate sentences that can be formed from it by the substitution of singular terms for the gap marker "ξ" -- as in, "This apple is green", "That lawn is green", "Your shirt is green", etc. The rule-governed use of the template "ξ is green" allows for the formation of an indefinite number of propositions in the same way -- again, even though it nowhere appears in any of its instances.

[As already noted, there are other ways of looking at such sentences, but none, I think, brings out the nature of the patterns underlying the rule-governed way we produce and understand indicative sentences -- or, at least, none that do so without falling onto the nominalisation/particularisation trap mentioned earlier.]

Moreover, the singular term used in C3 (viz.: "The concept green") cannot actually do what was intended of it -- that is, it cannot depict a grammatical 'truth' about the role of the stencil "ξ is green" as it is used in C5 (or, the role that "is green" plays in C5).

C3: The concept green has changed.

C5: This leaf is green; next month it will be brown.

[This underlies a theme that runs through Wittgenstein's work, that we cannot express by means of indicative propositions how key logical/grammatical features of language work -- this the point of the so-called "saying/showing" distinction found in the Tractatus.]

However, this will certainly not be the aim of anyone who wants to use a sentence like C3. In fact, the use of C3-type sentences (or even the more obscure versions found in DL -- their use in modern philosophical logic is another matter entirely) was originally aimed at unmasking nature's hidden 'essences', which supposedly underpin all of reality. So, if dialecticians wants to say something like the following they will only end up saying nothing comprehensible (as we saw here):

"Thus, for instance, if I affirm: 'John is a Man' I affirm that 'John' is a particular specimen of the general (or 'universal') category 'Man'. I understand what 'John' is by subsuming him under (or 'identifying him with') the wider category 'Man'.

"Metaphysical reasoning proceeds on the tacit or explicit assumption that the general category 'Man' and the particular category 'John' exist independently of each other: that over and above all the Particular 'Johns' in creation…over and above all particular men, there exists somewhere -– and would exist if all particular men ceased to be, or had never been -– the general category 'Man.'

"…The dialectical method traverses this rigid metaphysic completely. The category 'Man' includes, certainly, all possible 'men.' But 'Man' and 'men', though distinct, separate, and separable logical categories, are only so as logical discriminations, as ways of looking at one and the same set of facts. 'Man' -- is -- all men, conceived from the standpoint of their generality -- that in which all men are alike. 'Men' is a conception of the same fact -- 'all men' -- but in respect of their multiplicity, the fact that no two of them are exactly alike. For dialectics, the particular and the general, the unique and the universal -- for all their logical opposition -- exist, in fact, in and by means of each other. The 'Johniness' of John does not exist, cannot possibly be conceived as existing, apart from his 'manniness'. We know 'Man' only as the common characteristic of all particular men; and each particular man is identifiable, as a particular, by means of his variation from all other men -- from that generality 'Man' by means of which we classify 'all men' in one group.

"It is the recognition of this 'identity of all (logical pairs of) opposites,' and in the further recognition that all categories form, logically, a series from the Absolutely Universal to the Absolutely Unique -- (in each of which opposites its other is implicit) -– that the virtue of Hegel's logic consists….

"Let us now translate this into concrete terms. John is -- a man. Man is a category in which all men (John, and all the not-Johns) are conjoined. I begin to distinguish John from the not-Johns by observing those things in which he is not -- what the other men are. At the same time the fact that I have to begin upon the process of distinguishing implies…that, apart from his special distinguishing characteristics, John is identical with all the not-Johns who comprise the rest of the human race. Thus logically expressed, John is understood when he is most fully conceived as the 'identity' of John-in-special and not-John (i.e. all man) in general.

"…When I affirm that 'John is a man' I postulate the oppositional contrast between John and not-John and their coexistence (the negation of their mutual negation) all at once. Certainly as the logical process is worked in my mind I distinguish first one pole, then the other of the separation and then their conjunction. But all three relations -- or better still, the whole three-fold relation -- exists from the beginning and its existence is presupposed in the logical act…." [Jackson (1936), pp.103-06. Quotation marks altered to conform to the conventions adopted at this site.]

That's because they will have seriously distorted language in an attempt to say what they thought they wanted to say. Here, "The category 'Man'" cannot tell us anything about the logical role of "...is a man" (or if you like "ξ is a man") in "John is a man". But, the bogus form of words used by comrade Jackson is typical of the way that DL-fans express themselves, and typical of the way that traditional theorists have expressed themselves for the last 2400 years.

Hence, C3-type sentences attempt to say something about what it is that predicates (or concepts) allegedly refer to (or "reflect"). In this particular case, C3 is trying to say that whatever it is that "...is green" supposedly denotes, or refers to, has itself changed.

However, as we have seen, "...is green" is not a referring expression!

In that case, there is no "underlying reality" here for it to point to or 'reflect'.

[Naturally, that observation alone completely undermines the DM-theory of knowledge. More details here, and in the rest of Essay Three, when it is published.]

The above observations do not imply that I think there is no such thing as 'reality', only that if we want to state truths about the world it would be a good idea not to use distorted language trying to do so -- indeed, as Marx indicated.

To put this another way: if there were "essences" of this sort 'out there', somewhere in reality (howsoever this is conceived), then they can't be the referents of predicate expressions, since the latter are not singular terms. They are not referring expressions; they are descriptive and/or attributive.

But -- just to continue this ancient metaphysical fantasy a little longer --, if "essences" constituted the general features of reality, then none of our general terms could be used to denote them. Any attempt to do this would transform the general terms used in such an endeavour into singular expressions, and that would imply that the "general features of reality" were in fact abstract particulars (as we saw happen in Essay Three) --, at the same time as robbing language of its capacity to express generality (once more, by turning predicates into singular terms).

So, instead of reporting a change to a concept (as had been intended), C3-type sentences indirectly record a bogus logico-grammatical transformation that has been imposed on a concept expression -- such as "ξ is green" --, changing it into a singular term which allegedly names/designates an 'abstract particular', such as "The Concept Green".

C3: The concept green has changed.

C5: This leaf is green; next month it will be brown.

Change in the real world (properly expressed in sentences like C5) would in this way be conflated with the spurious changes that have been imposed on concept expressions (in 'propositions' like C3). As we have seen, movement in material reality can't be depicted this way, and that is what prevents dialecticians from expressing the very thing they had claimed they had all along wanted to do.

So, by tinkering around with the capacity ordinary language already has for expressing change, dialecticians merely produce empty strings of words.

This is the linguistic dagger that Idealist thinkers (and their latter-day clones -- dialecticians) have repeatedly driven through the heart any theory that emulates these bogus linguistic moves.

'Philosophical' sentences like C3 try to express the logical role of concept expressions by constructing what seem to be empirical propositions about language itself, or about concepts themselves; but in order to do that they have to change concept expressions into singular terms, which now allegedly refer to or designate something suitably "abstract", and non-material. But, if predicate/concept expressions do not refer, and never have, and can only be made to do so by altering them in this way, then it's no wonder sentences like C3 create confusion or generate 'paradox' -- and thus provide endless/useless employment for generations of traditional Philosophers, who then to try to solve the pseudo-problem this wrong turn generated. It's no surprise then that this 'problem' has resisted all attempts to solve it for over two thousand years!

Unfortunately, there is no way out of this logical cul-de-sac. As soon as concept expressions are transformed into singular terms they cease to express concepts; they now denote objects, or supposed objects (albeit, 'abstract objects'). Worse still, in so doing they misrepresent the role that ordinary, materially-grounded concept expressions (like "ξ is green") play in sentences like C5.

Naturally, this means that no philosophical theory of conceptual change is possible -- and that includes that found in the runt of the litter, DM.

[Of course, this does not mean that we cannot make sense of conceptual change by other means. How this is to be achieved will be entered into in a later Essay (but Marxists (and others) have been doing this for years).]

For example, consider these attempts to state putative truths about a specific concept:

C6: The concept green is a concept.

C7: The concept green is a concept expression.

C8: "The concept green" is a concept expression.

C9: F is a concept expression.

C10: F is a concept.

C11: "F" is a concept expression.

C12: "F" is a concept.

[To be sure, several of the above blur the use/mention distinction, but this does not, I think, materially affect the point I wish to make.]

The apparently analytic 'truth' in C6 is, if anything, analytically false, since "The concept green" is plainly not a concept but an object (or rather it designates one)! Hence, and paradoxically, C6 is 'true' just in case it is 'false'!

C7 is even worse, for it suggests that a denoted object is in fact a linguistic expression. C8 is worse still: "The concept green" cannot be a concept expression since it's a singular term. C9 and C10 are fake concept expressions; the letter "F" (as opposed to what it stands for) cannot be a concept expression -- its just a letter! If, instead, "F" is used, as in C11 and C12, it becomes a singular term again, denoting whatever the key to this particular schema says it denotes.

[Some might wonder how we can ever set-up an adequate syntax; but whatever we set-up, when we do this, we are not listing truths, merely expressing rules for the use of certain symbols (formal rules we do not need in ordinary language, since the overwhelming majority of us use sentences like C5 every day of our lives, without any fuss.]

The locus classicus for modern discussion of this topic is Frege (1892), upon which much of my own thinking has been based. Further background to this topic can be found in Davidson (2005), Dummett (1955, 1981a, 1981b), Geach (1976), Fisk (1968), Gaskin (2008), Gibson (2004), Potter and Ricketts (2010), Slater (2000) -- now reprinted in Slater (2002, 2007a) -- and Textor (2010). [For an alternative view, see Kenny (1995), criticised in Slater (2000).]

15. Distorted language like this motivates metaphysical systems in general; indeed, much of traditional Philosophy is based on muddles such as these. [On that, see Essay Twelve Part One.]

[Indeed, examples of this sort of confusion are given throughout this site; this particular one was analysed in detail in Essay Three Part One. See also Note 13 and Note 14.]

This partly explains why ontological and epistemological fairy-tales have had to be invented to provide 'objects' to which the artificial terms introduced as a result refer/relate (such as Forms, Universals, Ideas, Concepts, Categories, and the like). Naturally, this means that 'Ontology' (as an entire discipline) is completely bogus.

16. On this, see Note 13 and Note 14 above.

17. Higher-order Logic is outlined in Boolos and Jeffrey (1980), pp.197-207, and Enderton (1972), pp.268-89. See also here.

17a. Nevertheless, one bemused commentator has attempted to respond to this point (but without checking the detailed argument presented in Essay Twelve (partially reproduced below), in the following manner:

"Now this is very odd. Ordinary people are just as metaphysical and superstitious as the educated, though there is evidence to indicate that special types of superstitious thinking may be endemic to certain classes. But clearly ordinary language, its richness notwithstanding, is inadequate as is, due to imprecision as well as its ideological content, including inappropriate metaphorical content. At the very least, why else would we need the apparatus of formal logic, mathematics, notational systems, technical terminology, ideology critique?" [More on this here and here. Bold added.]

The reader will no doubt have noticed this commentator's use of metaphor (highlighted in bold) in his bid to criticise ordinary language for doing likewise. This can only mean that this criticism itself (unwisely written in ordinary language, too, it seems) suffers from the same unspecified 'limitations' this critic claims to have found in the vernacular. Hence, no safe conclusions may be drawn from what he says -- indeed, and as we will see (in the next section), this lame attack on the vernacular readily self-destructs.

Moreover, the above comments reproduce the usual confusion of 'commonsense', or everyday beliefs (disguised as "ideological content" and "superstitious beliefs"), with ordinary language. In that case, they are worthless. As will be argued in detail below, the fact that we can in ordinary language negate every indicative sentence expressing a 'commonsense'/'superstitious'/ideological belief shows that ordinary language cannot be identical with 'commonsense'/'superstition'/ideology.

And since this critic unfortunately gave no examples of the "ideological" contamination of ordinary language with allegedly suspect 'beliefs', not much can be made of that unsupported allegation, either.

Ordinary Language

Dialecticians' Mistaken Assumptions

[This section forms part of Note 17a.]

This is how the contrary argument will be put in Essay Twelve (some of it has already been posted in Essay Six, but it is re-presented here in a highly edited form):

John Rees put things this way:

"Ordinary language assumes that things and ideas are stable, that they are either 'this' or 'that'. And, within strict limits, these are perfectly reasonable assumptions. Yet the fundamental discovery of Hegel's dialectic was that things and ideas do change…. And they change because they embody conflicts which make them unstable…. It is to this end that Hegel deliberately chooses words that can embody dynamic processes." [Rees (1998), p.45.]