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

 

Preface

 

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

 

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

 

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

 

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

 

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

 

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

 

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

 

(6) This Essay was written before Redding (2007) was published, and before I had been made aware of the following two books: McGill and Parry (1971), and Burger et al (1980) -- but, more specifically, Cohen (1980). I will add some thoughts about these three works in a later re-write, too.

 

(7) Update June 2012: I have now written a detailed examination of Michael Kosok's ill-advised and egregiously unsuccessful attempt to 'formalise' Hegel's 'logic'.

 

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

 

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

 

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

 

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

 

As of January 2016, this Essay is just under 71,000 words long; a summary of some of its main ideas will be published at a later date.

 

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

 

 

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

 

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

 

(b) 'Science Of Thought'?

 

(c) Yet Another Semantic Muddle

 

(d) Rosa's 'Pedantry'?

 

(2) Hegel Screws Up Big Time

 

(a) Identifying The Problem

 

(b) 'Law Of Identity' Mis-Identified

 

(c) More Dark Decrees From Hegel's Dialectical Dungeon

 

(d) 'Difference' -- Unrecognisable

 

(e) The Fog Thickens

 

(f) Zeno -- No Help At All

 

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

 

(3) The Main Feature

 

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

 

(b) A 'Unity Of Opposites'?

 

(c) The Magical Use Of 'Negation'

 

(o) Hegel's Hermetic House Of Horrors

 

(d) Acid Corrodes Hegel's 'Logic'

 

(e) Two Senses Of "Independent" Conflated

 

(f) Threadbare

 

(g) What A Dialectical Dog's Dinner!

 

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

 

(5) Kosok's Kooky 'Logic'

 

(a) Preliminary Points

 

(b) An Elaborate Hegelian Hoax?

 

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

 

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

 

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

 

(f) Psychotic 'Semantics'

 

(g) Sesame Street 'Logic'

 

(h) Sinking Deeper Into Semantic Quicksand

 

(i) Old MacDonald's Farm

 

(j) Matrix Re-Loaded

 

(k) Ordinary Versus 'Dialectical' Logic

 

(l) Kosok Elevated To A Higher Plane?

 

(m) Welcome To The Twilight Zone

 

(n) Matrix Revolutions

 

(6) References

 

(7) Notes

 

Why I Oppose Dialectical Materialism

 

Abbreviations Used At This Site

 

Return To The Main Index Page

 

Contact Me

 

 

Well, What Are 'Dialectical Contradictions'?

 

The Best Marxist Article I have Ever Read On This Topic

 

Easily the best (Marxist) account of 'dialectical contradictions' I have come across in my trawl through the wastelands of 'Dialectical Logic' is to be found in Lawler (1982). Having said that, I should immediately qualify it by adding that Lawler's essay is the best of the worst, for his analysis of this terminally obscure example of Hegelian gobbledygook is no better than his analysis of Bertrand Russell's criticism of Hegel for confusing the "is" of identity with the "is" of predication, discussed in Essay Three Part One.

 

In fact, there are so many logical and philosophical errors in Lawler's article that any conclusions he draws are not worth the paper that even WMD dossiers were printed on.

 

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

 

 

'Science Of Thought'?

 

First of all, running through the entire article is the traditional confusion of logic with the 'science of thought', which Lawler nowhere tries to defend, and about which he does not even comment. Indeed, he quotes Engels in support:

 

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

 

Lawler then adds:

 

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

 

However (and as noted in Essay Two), when it comes to Philosophy, dialecticians are in general as consistently traditional as they are thoroughly confused. Indeed, they are quite happy to copy, and then compound, the errors of Ancient Greek and early modern Hermetic thinkers, spinning their own webs of a priori Jabberwocky-lore, employing obscure jargon they struggle to explain even to their bemused readers, or, indeed, one another.

 

[How DM-theorists manage to descend into confusion is the subject of Essays Three Parts One and Two, and Twelve Part One. Why they do it is explained in Essays Nine Part Two and Fourteen Part One (summary here).]

 

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

 

Moreover, as we have already seen (in Essay Four), Logic can't be described as the science of thought, for if it were, logicians would perform brain scans and psychometric tests, or they'd conduct surveys (etc.). They certainly wouldn't waste their time on all those useless definitions, axioms, and proofs.

 

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

 

Nevertheless, we shouldn't let these relatively minor dialectical defects distract us from the more serious errors Lawler's article contains.

 

 

Another Semantic Muddle

 

Lawler now tackles this topic with a consideration of Hegel's criticism of the LOI, which he regards as central to understanding the nature of 'dialectical contradictions'. But, as we have seen (and will see below), Hegel's criticism of the LOI is worthless, since he confused predication with the (supposed) relation of identity, which then 'allowed' him to conjure an Ideal universe out of a reconfiguration of the diminutive verb "to be", a stunning trick even David Blaine couldn't match.

 

[LOI = Law of Identity, which Lawler calls "The principle of Identity"; DM = Dialectical Materialism.]

 

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

 

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

 

[However, since Hegel got us into this mess, I reckon he's Stan.]

 

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

 

First of all, Lawler is decidedly unclear about the denotation of the letter "A"s he employs.

 

[Why this isn't a minor, 'pedantic' (or 'semantic') detail will become clearer as this Essay unfolds. Anyway, Lawler's article is full of 'semantics' and fine distinctions -- as, indeed, is Hegel's 'logic'.]

 

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

 

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

 

We have already seen that this is a thoroughly inadequate way to characterise identity (either in logic or in ordinary language), but the point at issue here is the fact that Lawler views these "A"s as the names of objects and concepts -- or perhaps even as those entities themselves --, i.e., three different kinds of 'things'.

 

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

 

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

 

[LEM = Law of Excluded Middle.]

 

As we will soon see, the principle of identity doesn't imply what Hegel, or even what Lawler himself (since he nowhere corrects Hegel), says it does, but that isn't of immediate concern. However, when Lawler qualifies what he takes Hegel to mean, he clearly now views these "A"s as propositions:

 

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

 

Propositions (indicative sentences, or predicables) are what one asserts, not names: "I asset Socrates" is unvarnished nonsense. So, these "A"s are no longer the names of objects or concepts, but the names of, or proxy letters for, propositions. That is now four different 'kinds' of things.

 

Of course, it could be argued that Lawler is merely saying that such things cannot be asserted (etc.) of A, making A an object, or perhaps the name of an object, but that is hardly likely; Lawler and/or Hegel were surely not keen to uncover truths about mere names. But, even if they were, in the above passage, "A" itself would both be an object and what can be asserted of an object (i.e., it might be a predicate expression, for example).

 

[In general, where feasible, I will highlight in bold any "A"s that appear in the rest of this Essay to indicate when I am using, rather than when I am merely mentioning them. This will, among other things, prevent confusion between this letter and the indefinite article. The word "predicable" is explained here.]

 

Despite this, Lawler's wording doesn't support this contention; he pointedly says:

 

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

 

As opposed to:

 

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

 

If Lawler had meant these "A"s to be names, or the names of objects (or, indeed, objects themselves), then he would have used the latter phrasing.

 

[Anyway, as we shall see below, these endlessly accommodating letters are unambiguously propositional variables.]

 

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

 

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

 

Of course, it is always possible that Lawler is merely aping a tradition that runs right through ancient/early modern logic, which treats all logical expressions equally sloppily (and which, as it turns out, is the tradition that presided over the creation of the bowdlerised version of AFL that was inflicted on Hegel (and anyone else who was taught philosophy) in the 18th century -- the kind of sloppy 'formalism' one finds in Kant's Logic, for example), which seems to be the most likely explanation for Lawler's confusion here, given the other things we are about to discover. [However, having said that, please note the caveats I have added here.]

 

[AFL = Aristotelian Formal Logic.]

 

Nevertheless, it is this careless approach to logic and logical symbolism that 'allowed' Hegel (and now Lawler) to construct some rather 'innovative' metaphysics. Indeed, as Bertrand Russell noted:

 

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

 

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

 

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

 

But, after another flip, on page 21, Lawler now says:

 

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

 

Although Lawler doesn't mention those "A"s directly here, given the context of his argument, they have now clearly become "things", once again. However, on page 22, they transmogrify into "entities":

 

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

 

And, in the same paragraph, they morph into "beings" (or, at least, into what is true of "beings"):

 

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

 

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

 

At any rate, so far this makes these letters eight different kinds of 'things'.

 

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

 

On page 24, these chameleonic "A"s now change into "terms", or perhaps even propositions again:

 

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

 

As noted above, anything capable of being asserted must be an indicative sentence, or a clause, at the very least (and thus perhaps a proposition). To be sure, predicates can be asserted of named individuals (etc.) -- or, perhaps better: true or false sentences can be formed when predicables are used to map names, or other singular terms, onto sentences. As should seem obvious to any language-user, it isn't possible just to assert a bald "term", predicate or concept expression of nothing whatsoever. Uttering "ξ is a warmonger" (or "...is a warmonger", or even "is a warmonger") is to assert nothing (i.e., it is to make no assertion) -- and the same is true of merely uttering the word "warmonger".

 

[The use of Greek letters like "ξ" is explained here, and in Note 1. A predicable is a predicative expression that can be predicated of an individual (or which can sensibly be attached to a subject term), whether or not it is so predicated. Compare this with our use of "sinkable"; if a ship is sinkable that doesn't imply it has actually sunk. Or, indeed, with "edible". So "ξ is a warmonger" is a predicable; it becomes a predicate in sentences like this: "Tony Blair is a warmonger", and in that way "ξ is a warmonger" can be transformed into an assertion.]

 

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

 

Furthermore, one can point at an animal, say, and utter the word "cat", but that is the equivalent of saying "That is a cat". Without the pointing gesture, nothing would have been asserted. And one can utter the phrase "A cat" in answer to a question, such as, say, "What animal seems to know more logic than Hegel?" In such a reply, the utterance of "A cat" is just a paraphrase of the proposition "A cat seems to know more logic than Hegel". The phrase "A cat" on its own would not be an assertion without that question providing the given background.

 

To be sure, Hegel appears to think that objects/'concepts' can be true:

 

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

 

Unfortunately, detailed consideration of the above will take us into areas that will be discussed in Essay Twelve (when it is published in full); suffice it to say here that Hegel's confusions (in this instance) have clearly arisen out of his conflation of predicate expressions with singular terms, compounded by the adoption of the Medieval Identity Theory of Predication. [More on that here.]

 

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

 

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

 

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

 

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

 

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

 

On page 26, these impressively Heraclitean (if not worryingly Cratylean) letter "A"s now morph into relations (as far as can be ascertained, that is!), or perhaps the 'names' of relational expressions(!) in Lawler's hands:

 

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

 

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

 

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

 

That is now ten, or possibly eleven, different denotations for these semantically-dithering letters.

 

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

 

At the very least these morphoholic letter "A"s now stand for propositions again, since Lawler says they can be asserted. This interpretation is confirmed in the next-but-one paragraph:

 

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

 

Well, if Hegel was indeed faced with such simple-minded opponents, then it is little wonder he got away with so many logical howlers. But, and to ask the obvious, what is so contradictory about someone changing his/her mind (if that is what one of these 'simpletons' did)?

 

In fact, this is the only way to read this manufactured example (i.e., as a change of mind) that doesn't picture Hegel's opponents as sub-literate morons.

 

Nevertheless, in the above passages, Lawler's "A"s have transmuted once more into propositions and/or predicates -- or perhaps even into properties, or property tokens (that is, words that stand for singular instances of a property).

 

On the very next page (but in the same paragraph), it becomes clear that these eternally plastic "A"s are indeed relations, or nominalised relational expressions (or maybe even nominalised relational phrases(?)); in fact it is quite plain that this is exactly what they are:

 

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

 

Since phrases can neither be true or false, Lawler's reasoning is, shall we say, 'innovative'. Nevertheless, these busy "A"s have plainly undergone yet another denotational make-over, and now stand for "identity held aloof from difference"!

 

[The phrase "identity held aloof from difference" might appear to some to make sense, but that would only be because they have become inured to this odd way of talking -- perhaps as a result of reading far more Hegel and Traditional Philosophy than is good for any human being to have to endure. Even so, such individuals might not have noticed that relational expressions which have been nominalised can no longer serve as relational expressions.  "A identity A" says nothing, nor does "A difference B". (This Ancient Greek grammatical/logical ploy (that is, nominalising everything in sight, unwisely appropriated by Hegel) was exposed for what it is in Essay Three Part One.)]

 

The mercurial career of these infamous "A"s continues apace; on page 28 they now metamorphose into indexicals:

 

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

 

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

 

In this passage, Lawler's "A" and "not-A" plainly stand for "here" and "not-here", respectively. A change of identity, maybe, but this is still no less an example of lamentably sloppy logic, for all that.

 

That is now at least thirteen different identities for these impressively changeable letters!

 

However, as we saw in Essay Five, the above 'analysis' of motion has more holes in it than a lorry load of Polo Mints. There is no 'commonsense' definition of the things Lawler mentions; ordinary language -- let alone 'commonsense' -- allows for complex and highly varied depictions of location and movement, which Idealists like Hegel simply ignore.

 

On page 32, these change-oholic "A"s remain in morphological hyper-drive as they become parts (or, perhaps, 'reflected' parts) of one another:

 

"One might readily grant that the definition of A includes A's relating to something that is not A (some non-A which is not-A). This does not mean that non-A or what is not-A is a part of A or part of A's identity….

 

"It is necessary to ask, first of all, whether and in what sense the fact that A necessarily relates to what is not-A permits us to insert not-A in A….

 

"…it seems reasonable to look for some 'imprint' of this 'other' in A, so that in some sense not-A is internally constitutive of A." [Ibid., p.32. Italic emphases in the original.]

 

These denotationally-promiscuous letter "A"s, it seems, can take on any form whatsoever in order to make this Hermetic Hodgepodge even seem to work. I have now been able to identify at least fourteen different denotations for them in this article. This means that Lawler is a verbal-trickmeister to rank with the best. He could have word-juggled for his country.

 

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

 

For over two thousand years traditional Philosophers have been playing on themselves and their audience what can only be described as a series of complex verbal tricks. Since Greek times, metaphysicians have occupied themselves with deriving a priori theses solely from the meaning of a few specially chosen (and suitably doctored) words. These philosophical gems were then peddled to the rest of humanity, dressed-up as profound truths about fundamental aspects of reality -- peremptorily imposed on nature, almost invariably without the benefit of a single supporting experiment.…

 

Even before the first Marxist dialecticians put pen to misuse, they found themselves surrounded on all sides by ideas drawn from this ancient tradition. Clearly, they faced a serious problem: if they imposed their ideas on nature in like manner, they could easily be accused of constructing a comparable form of Idealism. On the other hand, if they didn't do this, they wouldn't have a 'philosophical' theory of their own to lend weight to, and provide a bedrock for, their claim to lead the revolution. Confronted by traditional patterns-of-thought (which they had no hand in creating, but in which tradition they had been socialised and educated), which they were only too happy to appropriate, DM-theorists found there was no easy way out of this minefield -- or at least none that managed to keep their theory the right side of Idealism.

 

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

 

This is not to claim that dialecticians were/are unaware of the Idealism implicit in traditional thought; on the contrary, their excuse for ignoring the pernicious influence of Idealism on their own theory is that the materialist flip they say they inflicted on Hegel's core system was also capable of transforming theoretical dirt into philosophical gold.

 

However, flip or no flip, their thought is still thoroughly traditional: it is dogmatic, a priori, and framed in jargon lifted straight from the Philosophers' Phrase Book. Even though few DM-theorists deny that Traditional Philosophy itself is predominantly Idealist, not a single one has avoided appropriating its conservative approach to such easily won, a priori 'knowledge'.

 

So, despite the fact that dialecticians constantly claim that DM has not been imposed on nature -- for that would surely brand their theory "Idealist" -- they all invariably end up doing exactly that, imposing their theory on the world. In so doing, they merely underline the fact that traditional thought has found a new batch of converts among erstwhile radicals.

 

We are now in a position to see why this was asserted quite so forcefully back then. Lawler's defence of Hegel depends solely on a sloppy use of language and logic, wherein predicate expressions are turned into names, and objects, 'terms', indexicals and relations/relational expressions are all jumbled together. Now that they are 'object-like', these items can be put in some sort of spurious relation to one another.

 

[Indeed, this is the only way those spooky Hegelian "internal relations" can be generated (as Bertrand Russell correctly observed) -- which "relations" still, to this day, defy scientific detection. Not that anyone in the dialectical fraternity (or beyond) is searching for them all that hard, or with any urgency.]

 

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

 

Now, it could be objected that these minor semantic niggles aren't really all that important; after all, it is quite clear what Hegel and Lawler meant. Anyway, it might be possible to repair both accounts so that they pass such 'pedantic' hurdles with ease.

 

That, naturally, remains to be seen. But, since (1) Lawler's article is by far and away the best Marxist defence of this terminally obscure Hegelian notion (i.e., 'dialectical contradiction') I have so far seen, the omens don't look too promising. This should, of course, indicate to the reader just how bad things are in this back-water of traditional/dialectical myth-making. In that case, (2) a 'dialectical rescue' is highly unlikely from this 'Marxist' wing of Idealism. Even academic dialecticians regularly commit serious errors like this -- and worse. Moreover, they all fail to notice these blunders, let alone acknowledge them, even after they have been exposed. This shows just how logically purblind this ruling-class gobbledygook has rendered them. [The latest examples of this can be found here (unfortunately, this link now appears to be dead!), here, here, here, here, here, here, and especially here.]

 

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

 

Naturally, I exclude Graham Priest's work from these impertinent accusations, not least because (a) it is far from clear whether the 'contradictions' he considers are 'dialectical' to begin with (that is, if it were possible to decide on this issue!), or are even contradictions to begin with -- and (b) he is generally very careful with both his syntax and his semantics. Nevertheless, as far as I am aware, he has not yet noticed the logical blunders I have exposed in these Essays.

 

 

Rosa's Pedantry?

 

However, to any who think that this sort "pedantry" (aka "semantics") -- or attention to detail -- can be ignored, it is worth pointing out that this is the only way they can excuse their own sloppy approach to philosophy, and the only way they can make their ideas even seem to work.

 

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

 

This is quite apart from the fact that, as we will soon see, Hegel actually attempted to substantiate his core ideas using a series of 'semantic'/'pedantic' arguments -- as did Lenin and Engels, and as have subsequent DM-theorists. In which case, if this 'pedantic' approach to philosophy and logic is Ok for the goose, it's OK for the gander, too.

 

Indeed, it was Hegel's (and latterly Lawler's) 'pedantry' and 'innovative semantics' that created the problem in the first place!

 

[We saw this in the opening sections of this Essay, and will meet it again, below.]

 

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

 

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

 

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

 

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

 

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

 

Do the above 'pedantry-sleuths' take Lenin to task for writing passages like the following?

 

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

 

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

 

"One asks, how can sane people in sound mind and judgment assert that 'sense-perception [within what limits is not important] is the reality existing outside us'? The earth is a reality existing outside us. It cannot 'coincide' (in the sense of being identical) with our sense-perception, or be in indissoluble co-ordination with it, or be a 'complex of elements' in another connection identical with sensation; for the earth existed at a time when there were no men, no sense-organs, no matter organised in that superior form in which its property of sensation is in any way clearly perceptible.

 

"That is just the point, that the tortuous theories of 'co-ordination,' 'introjection,' and the newly-discovered world elements which we analysed in Chapter I serve to cover up this idealist absurdity. Bazarov's formulation, so inadvertently and incautiously thrown off by him, is excellent in that it patently reveals that crying absurdity, which otherwise it would have been necessary to excavate from the piles of erudite, pseudo-scientific, professorial rigmarole." [Lenin (1972), pp.124-26. Quotation marks altered to conform to the conventions adopted at this site. Italic emphases in the original; bold emphases and links added.]

 

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

 

If they have taken Lenin to task for his 'semantics', or his 'pedantry', they kept that pretty quiet!

 

Unsurprisingly, Trotsky concurs:

 

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

 

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

 

 

Hegel Screws Up Big Time

 

Identifying The Problem

 

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

 

Nevertheless, in order to consider every option open to Dialectical Mystics to say what they mean by 'dialectical contradiction', Lawler's (and by implication, Hegel's) argument will be considered on its (/their) own merits, and in extensive detail.

 

This is where we will see how and why Lawler's semantic sins (detailed above) have led both of them astray.

 

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

 

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

 

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

 

[LOI = Law of Identity.]

 

To be sure, Hegel was writing at a time when little work had been done on this 'law', but Lawler wasn't. And yet he refers his readers to no modern work in this area; had he done so Hegel's 'definition' would have been seen for the logical joke it is. [On this, see here, and here.]

 

Putting this serious omission to one side for now, Lawler continues:

 

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

 

This is so full of errors it is difficult to know where to begin. Lawler (following Hegel) tells us that the other principles of FL follow from the LOI, or rather from the latter being stated "negatively". These other principles are the LOC and the LEM –- but notice, once again, the common error that all dialecticians make (which was exposed in Essay Four) -- that is, of thinking that FL has just three fundamental principles.01

 

Notice, too, how every single DM-fan fails to substantiate this constantly repeated allegation. And no wonder, it is completely false. Not even AFL was based on these three so-called 'laws'. It seems in this regard, therefore, that academic Marxists (HCDs) are just as benighted as their more lowly LCD brethren were shown to be (here). Naturally this sorry state of affairs isn't unconnected with the fact that both wings of Dialectical Darkness think that, to a greater or lesser extent, humanity can learn something useful from Hegel.

 

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

 

Hegel (and now Lawler) offers no proof of this supposed 'inference', nor could he (they). The LOI concerns the relation that is supposed to hold between an object and itself (or perhaps between its names, depending on how one reads this 'law'); it doesn't concern the truth-functional link between propositions, which is the proper domain or those other two 'laws'.

 

Hence, Lawler follows up with the following remark:

 

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

 

But, this 'derivation' only works because of the aforementioned confusion over the denotation of those letter "A"s (which explains why I went into all that 'pedantic' detail over this very point at the beginning of this Essay!). He first of all tells us that these "A"s relate to "a thing or concept", but then they are immediately transformed into what can or can't be "asserted". [Readers might now like to try and assert "Paris" or "DNA", or even "cat". (That is, try to assert these things (as in "I assert cat") , not assert something about them.) E-mail me with the results!]

 

Now, in relation to the LOC, if these letters designate propositions (i.e., if they are propositional variables), no problem. In which case: "One cannot assert something to be true and at the same time, and in the same respect, assert it to be false" would at least be a passable first stab at a definition of the LOC (in urgent need of improvement, however -- on that, see here and here); but by no stretch of the imagination can these letters designate propositions when they appear in the LOI. That 'law' doesn't concern the alleged identity of a proposition with itself (which means that, contrary to what Hegel says, the LOI isn't even a tautology -- on that, see below). But, even if this were the case with the LOI, that fact would have no implication for the LOC. The LOC neither rules in, nor rules out, relations of identity between propositions (but see below), since it isn't concerned with the identity of propositions to begin with. Indeed, if a proposition lacked identity it wouldn't be a proposition. On the other hand, if, per impossible, it possessed identity, it would be an object, not a proposition.

 

[On why propositions aren't objects, nor the names thereof, see Note Two.]

 

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

 

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

 

They aren't tautologies in any straight-forward sense partly because identity statements aren't molecular --, that is, identity statements purport to express a relation between an object and itself (or between its names). They aren't comprised of sub-clauses, or simpler propositions. [On this, see Glock (1996), pp.164-69.] Identity statements can't be expressed as tautologies in the truth tables, either. Of course, the identity sign is always given, or is defined as having the value "true" in the truth tables (if the flanking names or variables warrant it), but that truth-value isn't derived from the truth-values of its constituent propositions/clauses, since there are no constituent propositions/clauses in identity statements -- unlike genuine tautologies (in logic).

 

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

 

T1: A vixen is a female fox.

 

T2: A regicide is a king-killer.

 

Propositions expressing identity contain what appears to be a relational expression (which is symmetrical, reflexive, and transitive), but they can't be tautological in the sense of "saying the same thing". That is because both halves do not "say the same thing" -- since they do not say anything at all. The first "A", in "A = A", if it is a name or other singular term, doesn't say the same thing as the second "A" since neither of these "A"s says anything. Only clauses, propositions or sentences do this, or can be used to do it. On the other hand, if "A" is a propositional variable it can't be put into a relation with itself, since it isn't an object, nor is it the name of an object.

 

Discursively,  T2, for instance, expresses an explanatory rule of language (or, in logic, a substitutional rule), and so it can't be true or false (this was argued at length in Essay Twelve Part One). Rules themselves can't be true or false, only practical or impractical, useful or useless.

 

By way of contrast, "A vixen is a vixen" and "A regicide is a regicide" aren't rules of language (except in highly specialised circumstances). However, if "A vixen is a vixen" is interpreted predicatively -- that is, as "ξ is a vixen" -- it can't be saying the same thing as "A vixen", since "A vixen" is plainly not of the form "ξ is a vixen". Hence, in "A vixen is a vixen", the two halves can't be "saying the same thing" because "A vixen" isn't saying anything, let alone "the same thing", since it isn't saying anything at all. If it were saying something, "ξ is a vixen is a vixen" would make sense, since, "ξ is a vixen" would "say the same thing" as "A vixen" (and could be substituted for it in "A vixen is a vixen" to give "ξ is a vixen is a vixen"). So, "A vixen is a vixen" can't be a tautology. What is more, "...is identical with ξ" doesn't "say the same thing" as "ζ is identical with...", either!1

 

Of course, it could be objected that the above would mean that "A vixen is a female fox" isn't a tautology since "A vixen" and "ξ is a female fox" aren't "saying the same thing" (in the strict sense meant in the previous paragraph), which is absurd.

 

Indeed, and that is why that sentence was called a rule (as opposed to a tautology), since it expresses a rule for substituting synonymous terms in English (or in other languages with the same facility), so that anyone who used the phrase "a vixen" in a sentence would be saying the same as anyone using "a female fox" in the same sentence (in non-opaque contexts). For example, these two "say the same thing", or can be used to say it:

 

F1: A Vixen turned the bins over last night.

 

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

 

[Always assuming, of course, that the phrase "last night" referred to the same night in question!]

 

It could be objected that the identity "Cicero is Tully" works in the same way, so that anyone who used "Cicero" in a sentence would be saying the same as anyone using "Tully" in the same sentence (in non-opaque contexts). Of course, in this case we would have co-referential terms that could be substituted for one another salva veritate (in non-opaque contexts) -- that is, such a substitution wouldn't affect the truth value of the sentences involved. Now, if that is what is meant by "tautology", all well and good, but it is certainly not what Hegel or Lawler meant.

 

[MFL = Modern Formal Logic.]

 

It could also be argued that F3 and F4 are identity statements. Maybe so, but that doesn't automatically make them tautologies -- unless we modify or re-interpret this term along lines mentioned above.

 

F3: A vixen is a female fox.

 

F4: A regicide is a king-killer.

 

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

 

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

 

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

 

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

 

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

 

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

 

 

The Law Of Identity Mis-Identified

 

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

 

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

 

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

 

L1a: p = p.

 

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

 

Or, perhaps even:

 

L1b: (x) [Fx = Fx].

 

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

 

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

 

L1c: (x) [Fx º Fx],

 

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

 

Even then, neither of these would have any bearing on the relation they are supposed to have with their alleged negative/'opposite' -- as Lawler alleged --, but which might be the case with the following:

 

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

 

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

 

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

 

That is because there are no rules for deriving either L2 or L3 from L1a or L1b (or from less formal versions of either), or indeed from anything analogous. And it isn't hard to see why. [More about this presently.]

 

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

 

However, as noted above, the real problem here is that if the negative particle attaches to singular terms, so that it is interpreted as an operator mapping singular terms onto 'negative' singular terms (whatever that means!), then it can't also be a sentential operator mapping a sentence or proposition onto its negation, which is what it has to be in the LEM and the LOC.

 

That is:

 

P1: N*(A) º ¬*A.

 

Or even:

 

P2: N*(A) = ¬*A.

 

[Where "N*" is just such a general 'negative operator', "A" is a name variable, and "¬*" is a 'negative' particle in this modified logic. (I have used asterisks to highlight the non-standard nature of the symbols I have had to use here.)]

 

Of course, given the above syntax, P1 is ill-formed, too. That is because neither "N*(A)" nor "¬*A" are propositions/sentences. If we supplied names, so that P1 yielded, say, "Neg(Socrates) if and only if Not(Socrates)", we would soon see P1 for the unvarnished nonsense it is.

 

On the other hand, if the negative particle above is a sentential operator mapping a sentence or proposition onto its negation, then it can't also be an operator mapping names in the above manner.

 

P3: N(A) º ¬A.

 

P4: N(A) = ¬A.

 

[Where "N" is a negative operator, "A" is now a propositional variable, and "¬" is the negative particle in logic.]

 

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

 

P3, on the other hand, seems to be alright as it is: "Neg(Paris is in France) if and only if it is not the case that Paris is in France" is certainly odd, but not nonsense.

 

Once again, that is why it is so important to keep track of the denotation of the "A"s Hegel and Lawler used/mis-used.

 

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

 

[Of course, there are other ways of expressing the 'negative form' of the LOI; for example, it could be "¬[(A = A) & (A = ¬A)]". However, the latter form has problems of its own; these are explored below, and in Note 2.]

But, as far as the LOC and the LEM are concerned, "A" clearly stands for a proposition, a declarative and/or indicative sentence, or a statement (again, depending on one's philosophical logic) -- i.e., it goes proxy for expressions that are capable of being true or false.

 

By way of contrast, in the LOI, "A" goes proxy for a singular term. Here, this letter isn't a propositional or sentential variable. So, for example, "Caesar" -- a singular term -- on its own isn't capable of being true or false. Hence, if "¬" is taken to be a propositional or sentential operator, again, "¬A" would make no sense -- "It is not the case that Caesar" is nonsensical, once more.

 

Alternatively, if "A" is a sentential or propositional variable, "¬(A & ¬A)" would become "It is not the case that Caesar is identical with Caesar and Caesar is not identical with Caesar" (where, for instance, "A" stands for "Caesar is identical with Caesar", and not just "Caesar" on its own, as would be the case in the LOI), which seems to make sense, but only if one is questioning the LOI.

 

The other form mentioned above (i.e., "¬[(A = A) & (A = ¬A)]") fares little better (even if it isn't patent nonsense), becoming, for example: "It is not the case that ((Caesar is identical with Caesar) and (Caesar is not identical with Caesar))" -- i.e., if "¬" is still a sentential or propositional operator.

On the other hand, if "¬" operates on names, or singular terms, then "¬(A & ¬A)" would make no sense at all. In that case, "¬(A & ¬A)" would become "Not (Caesar and not Caesar)".

 

But, once again, "Not Caesar" isn't an expression that is capable of being true or false. In which case, given this use of "¬", "¬(A & ¬A)" can't be the LOC. "Not (Caesar and not Caesar)" isn't the LOC; it is just plain gibberish.

 

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

 

[This isn't to suggest that the negative particle can't attach to names (in fact, see here), only that when it does, it must assume a different role (and thus a different meaning) from the role it occupies when it operates on sentences/propositions. Indeed, as we have seen here, when the negative particle attaches to a name (in what appear to be relational expressions (e.g., "Paris is no Vienna", or "Brutus is not Caesar")), its role changes dramatically.]

 

The dilemma is now quite stark:

 

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

 

(2) On the other hand, if "¬" operates on sentences or propositions, mapping them onto their negations, and if "A" is a sentential or propositional variable, then the LOI ("A = A") would become, for example: "Caesar is identical with Caesar is identical with Caesar is identical with Caesar" (interpreting "A" here as the proposition "Caesar is identical with Caesar", again), which isn't the LOI!

 

Recall that in option (2), "A" has to go proxy for a proposition or sentence (in this case "Caesar is identical with Caesar"), not a name.

 

Exception might be taken to the use of "A" to stand for the proposition "Caesar is identical with Caesar". [DM-fans can't in fact lodge this objection since, as we have seen, according to them and their sloppy syntax/semantics, these "A"s can be anything we please!)]

 

In that case, let us take any randomly chosen proposition to replace each "A" in the LOI. That being done not much changes: "Paris is in France is identical to Paris is in France". (Interpreting the "A" here as "Paris is in France").

 

[Remember this doesn't yield "'Paris is in France' is identical to 'Paris is in France'", but "Paris is in France is identical to Paris is in France".]

 

Is anyone prepared to accept that as an example of the LOI? (In case someone is so prepared, I will consider that desperate (and unwise) move presently.)

So, Hegel was only able to 'derive' the LOC from the LOI by allowing these "A"s to slide effortlessly between two radically different semantic roles: between denoting singular terms and denoting propositions/'judgements'/sentences (and, in fact, denoting a whole host of other things besides -- such as processes, concepts, relations, relational expressions, etc. -- on that, see an earlier section of this Essay). But, as soon this is done, the negative particle changes its meaning in the above manner -- that is, it changes from a sentential operator to a name modifier, and we end up with nonsense.

 

If we now choose to ignore the above fatal defects in Hegel's argument, and if L2 had have been:

 

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

 

things might work out differently (no pun intended).

 

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

 

Alas, even then, the problems associated with Hegel's 'derivation' won't go away. Quantifying across propositions (if that were possible, and if we could make sense of the use of an "=" sign between propositional variables/tokens), we might be able to obtain the following:

 

L4: (p) [(p = p) ® ¬(p ≠ p)].

 

[This says: "If a proposition is identical with itself then it is not the case that it is not identical with itself." (On a side issue, some logicians are quite happy to quantify across propositions -- or sentences/statements -- but, while this might be a handy formal device, it can't relate to anything in a natural language. On that see Glock (2003), pp.102-36, and Hacker (1996), p.288, n.65).]

 

Or, perhaps more simply:

 

L4a: [(p = p) ® ¬(p ≠ p)].

 

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

 

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

 

L5: ¬(p = p) v ¬(p ≠ p),

 

and thus (by De Morgan's rules) we can derive:

 

L6: ¬[(p = p) & (p ≠ p)].

 

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

 

L7: ¬(Γ & ¬Γ).

 

[Again, these and other symbols were explained here.]

 

Which, of course, looks like the LOC.

 

Unfortunately, we have as yet no rules for parsing the identity sign in the required manner, i.e., so that (p ≠ p) º ¬(p = p). Until we do, this derivation cannot work. [There are, however, other serious problems with this 'derivation'; on that see Note 2.]

 

[On the rules we do have, see Bostock (1997), pp.323-33 (this links to a PDF), Lemmon (1993), pp.159-67, and Quine (1974), pp.221-26.]

 

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

 

L7: ¬(Γ & ¬Γ).

 

Even so, it is worth pointing out again that if a proposition isn't identical with itself, it can't be a proposition (but must be an object). In that case, nothing could follow from it. On the other hand, if it is identical with itself, it would once more be an object, not a proposition -- and, again, nothing follows from an object.2

 

Either way, we hit a brick wall.

 

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

 

L9: (x) [Fx = Fx],

 

and:

 

L10: (x)(y)(F) [(Fx º Fy) ® (x = y)],

 

there is an unambiguous identity sign between propositions (or between two tokens of the propositional inscription, "Fx"), and an equivalence sign between "Fx" and "Fy" (in L10). So the counter-claims made earlier (against Hegel) can't be correct.

 

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

 

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

 

So, these signs in effect express rules that are applicable to signs/symbols; they do not express an identity (or an equivalence) between lifeless marks on the page, or even between propositions that exist in an ethereal realm somewhere.

 

[To be sure, there are, and have been, philosophers and logicians who hold/have held such views, but they, too, have confused propositions with propositional signs, or even with objects of some sort. On this, see Glock (2003), pp.102-36, and Hacker (1996), p.288, n.65, once more.]

 

Indeed, the second of the above (L10 -- reproduced below) shows that this is so by implicitly interpreting the equivalence sign as a symbol expressing an identity between objects (or variables that take the names of objects) of some sort. In that case, schemas like L9 and L10 do not contradict what was maintained earlier, which was that where the sign for identity is used, it supposedly expresses a relation between objects (or between an object and itself -- or, between its/their names), not between concepts, predicates or propositions.

 

L9: (x) [Fx = Fx].

 

L10: (x)(y)(F) [(Fx º Fy) ® (x = y)].

 

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

 

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

 

L9: (x) [Fx = Fx].

 

L10: (x)(y)(F) [(Fx º Fy) ® (x = y)].

 

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

 

Of course, in schematic sentences like L1b/L9, "="  would be replaced by "º", that is, by a biconditional or equivalence symbol (indeed, as we saw earlier). That is because "=" features in two-place linguistic functional expressions (i.e., "ξ = ζ"), which can only take names or singular terms as arguments. So, as noted above, L1b/L9 are ill-formed as they stand. Once more, there are/have been philosophers and logicians who hold that the identity sign can be used between non-singular terms, but they have yet to explain why this doesn't imply that this sign and these variables/non-singular terms have a different meaning.

 

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

 

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

 

[Or, indeed, "Ω" and "Ψ" can stand for anything we like, aping the sloppy attitude to syntax adopted by Hegel and Lawler.]

 

Even then, we would need some sort of argument to show that "=" is identical with ""; but how might that be done, for goodness sake? This would, of course, leave it quite mysterious whether or not the word "identical" in "'=' is identical with "''" is itself identical with the first or the second use of these two signs, prompting the very same question (no irony intended) about the word "identical" used to ask that very question -- and so on, ad infinitem.

 

Nevertheless, one thing is clear: MFL and ordinary language succeed in capturing the full range of words we have for identity (etc.) far better than the syntactic and semantic goulash we find both in Hegel's 'Logic' and in DL. In fact, as Essays Three through Seven show, DL can't handle the simplest of ideas/objects (such as a bag of sugar!), let alone anything more complex.

 

[DL = Dialectical Logic; LEM = Law of Excluded Middle.]

 

Hence, and once again, the suggested Hegelian 'derivation' of the LOC (i.e., the one expounded by Lawler) can't work if these "A"s are read as objects or the names of objects (since objects/names can't be true or false) -- nor, indeed, can it work if propositions are viewed as objects.

 

Once more, that is why it is so important to be clear about the denotation of these letters, and why such a fuss was made about it earlier.

 

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

 

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

 

Here, the letter "A" oscillates once again between a predicative and a naming role. If so, the LEM, as stated above, is no less mis-described than Lawler's attempt to connect the LOI with the LOC. The LEM concerns the truth possibilities of propositions, or the truth of predicates applied to individuals (or objects). But, "Something must be either Caesar or not be Caesar" makes no sense (if, that is, the "A" is taken to be a name variable), as we saw earlier.

 

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

 

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

 

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

 

These have been adapted from Geach (1956); Geach calls the first the "logical definition", and the second the "semantic definition". As he goes on to note, "F" goes proxy for any predicate arbitrarily chosen (for example, "ξ is green"), while "G" goes proxy for any predicate "used as such". So, any instance of E2 (such as E4) would have to use a quoted predicable:

 

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

 

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

 

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

 

E5: Either p or not p.

 

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

 

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

 

Similarly, the LOC isn't about the predication of a 'negative name' to the same named individual or object(!), as Lawler would have us believe:

 

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

 

However, I suspect the above should really be read as follows:

 

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

 

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

 

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

 

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

 

Nevertheless, as with most topics in logic, things are never quite so simple. As we saw briefly above, we need to distinguish between sentential negation (i.e., "not p"), predicate negation (i.e., "not F"), predicate-term negation (i.e., "not-F" or "non-F"), and, for want of a better term, 'name modification' (i.e., "not A", as in "not Caesar"). It is unclear, though, which of these Lawler intended in the above passage. But, his indiscriminate employment of "A", "not A", "not-A" and "non-A" suggests he is either unaware of this distinction, or he considers it unimportant. [The same unfortunately seems to be true of many of Hegel's epigones (even though, for example, Redding (2007) tells us Hegel himself was aware of some of these distinctions).]

 

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

 

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

 

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

 

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

 

if we view it traditionally with gaps instead of functional place-holders --, or, as:

 

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

 

otherwise.

 

But, these aren't even sentences, so it isn't possible to make sense of them!

 

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

 

As we saw earlier, this would only be 'true' if these expressions were interpreted as names (or objects?), and not as predicate expressions or properties -- or, perhaps, as the names of whatever it is that predicates (or property tokens) supposedly designate.

 

But, in that case, Lawler's:

 

B3: "A cannot be non-A"

 

would in fact yield:

 

B4: "C cannot be D".

 

That is because Lawler clearly sees these "A"s as the names of properties (or, if they are represented by predicate expressions, the latter will also be names). So using "C" for the name of whatever "...is red" is supposed to stand for, and "D" for whatever "...is non-red" is supposed to designate, we would obtain "C cannot be D".

 

And that is because, "...is red" must 'name' something different from "...is non-red".

 

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

 

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

 

That is plainly because Lawler's 'definition' tries to relate a term to its negated 'other', but his own (sloppy) semantics prevents him from doing precisely that!

 

The reader will note that at the beginning of the above passage (reproduced below), "A" is a predicate letter, but by the end it has morphed into a name! This is clear from Lawler's own paraphrase, "where 'non-A' is something that is not A, or some part or property of A." [Bold added.] But, this is just another example of the tangled web of confusions that were highlighted earlier.

 

Now, there might be a way of reading these predicate expressions that allows them to be grafted into the LEM in the way Lawler imagines; I can't say since he doesn't say. [And, what is more, no one else has, either! DM-fans don't "do detail". They simply label any attempt in that direction "pedantry" and then take their bat and ball home.]

 

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

 

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

 

P1: Non-A is not A.

 

Or, it could be:

 

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

 

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

 

But, Lawler immediately qualified this by saying that "non-A" is "something that is not A, or some part or property of A". In which case, as noted above, he appears to mean:

 

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

 

Or, perhaps even:

 

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

 

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

 

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

 

 

More Dark Declamations From Hegel's Dialectical Dungeon

 

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

 

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

 

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

 

However, Lawler continues:

 

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

 

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

 

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

 

The problem is that these moves have the effect of changing propositions into lists, which destroys their capacity to say anything at all. [Why that is so is explained in detail here.] Any conclusions that 'follow' from this linguistic sleight-of-hand are, as a result, entirely bogus, since nothing can legitimately follow from the names of abstract objects (like "Identity", "Essence", "Difference", or "Being"), nor from a list of the same. Conclusions, of course, can only follow from propositions, or clauses.2a

 

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

 

If so, this still won't work since there is no such thing as Identity (i.e., it is isn't an object, but a (supposed) relation between an object and itself -- or, in language it supposedly functions as a relational expression).

 

[I have used "supposed" here, since, as we saw in Essay Six, the identity 'relation', or, at least, its linguistic form, is best seen as the expression of a rule for the use of singular terms; I have tended to ignore this distinction in this Essay to avoid needless pedantry.]

 

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

 

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

 

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

 

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

 

Here, plainly, "A" stands for "identity" and "not-A" for "difference". But, once again, the only thing that motivates talk like is the sloppy syntax and semantics analysed earlier. Without it, no contradiction can follow, as we have seen.

 

The problems this now creates for Lawler's interpretation of Hegel become clearer if we consider the latter half of a passage quoted above, along with what follows:

 

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

 

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

 

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

 

However, if this is correct, and if Hegel were the genius we have been led to believe, he should have pointed out what seems obvious to those who don't use language in such odd ways: 'abstract identity' can only be conjured into existence if relational expressions are transmogrified into singular terms that name 'abstract particulars'. This is indeed what happened in the 'theories' of those Hegel was criticising, but he didn't question such moves, he only succeeded in compounding the problem by adding some novel confusions of his own. But, if we refuse to follow those whom Hegel was targeting, and reject this way of talking, then the obverse conclusions should be rejected too: Hegel's 'dialectic' (which is itself based on similar moves, but in the opposite direction). So, Hegel doesn't question this way of talking, he merely uses it to his advantage.

 

It could be objected that Hegel was aware of this (i.e., that universals (and perhaps predicates) have been turned into abstract particulars (or the names thereof):

 

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

 

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

 

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

 

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

 

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

 

"The copula 'is' springs from the nature of the notion, to be self-identical even in parting with its own. The individual and universal are its constituents, and therefore characters which cannot be isolated. The earlier categories (of reflection) in their correlations also refer to one another: but their interconnection is only 'having' and not 'being', i.e. it is not the identity which is realised as identity or universality. In the judgment, therefore, for the first time there is seen the genuine particularity of the notion: for it is the speciality or distinguishing of the latter, without thereby losing universality....

 

"The Judgment is usually taken in a subjective sense as an operation and a form, occurring merely in self-conscious thought. This distinction, however, has no existence on purely logical principles, by which the judgment is taken in the quite universal signification that all things are a judgment. That is to say, they are individuals which are a universality or inner nature in themselves -- a universal which is individualised. Their universality and individuality are distinguished, but the one is at the same time identical with the other.

 

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

 

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

 

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

 

This 'allowed' Hegel (just as it later 'allowed' Lenin) to generate 'contradictions' to order, and then impose these 'contradictions' on reality, for all of space and time (as we saw in Essay Three Part One).

 

This can be seen from the fact that Hegel makes this very point in the following paragraphs:

 

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

 

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

 

As noted above, Hegel is here appealing to the Identity Theory Of Predication to motivate his argument.

 

But, even if the objector were right, and Hegel had anticipated this point, the fact is that he nowhere repudiates it, but uses it to 'derive' several quirky results of his own -- based solely on seriously defective logic like this.

 

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

 

Not much, it seems, since the whole topic (indeed, the whole of Hegel's work) amounts to little other than a systematic capitulation to the misuse, and distortion, of language on a grand scale.

 

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

 

(1) (x)(y)((x = y) º (Fx ® Fy)).

 

(2) (x)(y)((F)(Fx º Fy) ® (x = y)).

 

(3) j(y) º [(x)((x = y) & j(x))].

 

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

 

["" is the universal quantifier, equivalent to "All" or "Every"; "" is the existential quantifier, equivalent to "Some" or "At least one"; "º" is the sign for logical equivalence, i.e., "If and only if"; "j" and "F" are predicate letters; "®" is the implication arrow, equivalent to "if...then"; "x" and "y" are bound variables (often equivalent to "it", but that depends on context); "¬" is the sign for negation; "Γ" is a general symbol standing for any wff (i.e., "well formed formula", pronounced "woof"); "p" and "q" are propositional variables; "&" is, obviously, "and"; "v" is the inclusive "or" (i.e., "and/or"). How these are used is explained here.]

 

To be sure, different signs are employed here, but many are equated.

 

Of course, someone could argue that all four of the above nonetheless involve "difference", but that would be to misread what they actually say.

 

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

 

Moreover, it is worth adding that this 'problem' has been compounded by the fact that Hegel and Lawler slide between two, dare I say it, different uses of the word "identity/identify" -- that is, between "identity" when it is used (1) To provide an empty (or perhaps significant) identity statement for any given object, and "identify" when it is used (2) To highlight the capacity most of us have of being able to discriminate, pick out, or to recognise a person, property, location, smell, taste, sound, process or object from moment to moment.

 

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

 

Naturally, identification (i.e., use (2), above) could in some circumstances involve a capacity to differentiate among objects, but this isn't necessarily so in all cases (as was argued here).

 

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

 

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

 

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

 

Of course, to do the former (i.e., (1) above) we don't need to refer, or allude to --, or even so much as vaguely hint at --, 'difference'. However, in order to do the latter (i.e., (2) above), an ability to tell one object/human being from another clearly helps. But, the two skills (if such they may be called) are not at all the same (irony intended).

 

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

 

Surely this is philosophy for Idiots and not just Idealists!

 

[For several examples of significant identity statements, see here. I have also given examples where 'difference' cannot be a factor.]

 

Lawler now inflicts yet more of the same on his readers:

 

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

 

We have already seen that 'subjects' (I assume Lawler means names here, or some other singular designating expression) assert nothing (nor can we assert anything by the mere use of names, or other singular terms -- try asserting "Plekhanov", or "The 42nd president of the United States of America"). Hence, by the use of names (or other singular terms) nothing different can be asserted from anything that can be asserted by the use of predicates. So, if names (and other singular terms) do not assert anything to begin with, they can hardly assert anything different from predicates. [All this was argued in detail in Essay Three Part One.]

 

The idea that names on their own can assert something is based on the ancient, mystical notion that every particular has associated with it a "complete description", or concept, that 'God' alone knows, which identifies it uniquely. This doctrine reached its most sophisticated form it seems in Leibniz's work, and it clearly influenced Hegel (as it has his DM-clones). In which case, an 'essential' proposition about an individual will involve the predication of its internally-linked properties, which, because they are part of that individual's 'complete notion', are supposedly identical with their subject. They have to be identical with their subject since they express its 'essence' -- but, for Hegel they are also different, otherwise we couldn't discriminate among them --, and, indeed, they couldn't develop. So, they have "identity-in-difference'. It is out of this Mystical Mudhole that Hegel's odd-ball ideas slithered.

 

[On this, see here and here. At a future date, I will publish a up-dated version of one of my undergraduate essays on this topic, which shows how and why this ancient idea gained currency among Traditional (Rationalist) Philosophers. This is also connected with several of the things I have to say about ancient theological ideas concerning the nature of 'God' -- and how these were connected with the so-called "scientific revolution" of the 17th century -- in Essay Eleven Part Two.

 

Fortunately, this entire line-of-argument falls foul of a fatal objection I raised against all such 'essential' propositions (in Essay Twelve Part One -- summarised briefly here), namely that they don't have negations (this means, for example, that there is no such thing as the 'Power of Negativity'). Hence, 'Spinoza's Greedy Principle' (as I have called it -- i.e., 'Every determination is also a negation'), upon which the entire dialectic is based, turns out to be devoid of content. This throws a huge spanner into the dialectical machinery, halting the DM-juggernaut in its tracks. I will explain in detail how and why this is so in Essay Twelve Part Five.]

 

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

 

This is undeniable, but it isn't Hegel's argument. And even if it were, it would have nothing to do with the alleged identity between a predicate and a subject term. The latter is based on the identity and difference that supposedly exists between the two halves of a proposition ('subject' and 'predicate'), which are both said to assert the same thing and something different. But, since, only one is capable of asserting anything (or, rather, only one is capable of being so used -- the 'predicate part'), we can't even derive an 'identity' (in what is asserted) here, never mind a 'difference'. If they both do not asset anything, then they can hardly assert something different.

 

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

 

We also saw earlier that predicates needn't be physically different from 'subjects' (nor even divorced from them in time or in location); so Lawler's 'argument' is hopeless from beginning to end.

 

Once again, it is only by blurring the distinction between subject and predicate expressions that slip-shod logic like this is able to limp along.

 

 

'Difference' Rendered Unrecognisable

 

Unfortunately, there's more:

 

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

 

But, Lawler should have pointed out that this logically-benighted Hegelian riposte only works if the identity relation is nominalised and turned into the name of an abstract particular, and the alleged contrast (or comparison) with "difference" is modelled on that which might or might not exist between two objects.

 

Now, even though Lawler (and, as far as I can determine, Hegel) did not identify (no irony intended) the 'simpletons' criticised in the above passage, it is quite easy to see what 'they' should have said in return to prove 'they' were more than a match for both:

 

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

 

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

 

In fact, this manoeuvre doesn't just relate to, it helped create and then motivate the empty Idealist, two thousand year  flap over 'Subject/Object Identity', which became the main problematic of German Idealism. Hence, if names and predicates are both objects of some sort (or they designate objects), and 'Being' is the Subject/Object/Predicate par excellence, then the inter-identity (or lack of it) between these terms naturally becomes a 'problem'. But, if only names actually work as names --, whereas predicates merely describe the objects so named --, then the countless centuries devoted to 'solving' this pseudo-problem can be seen for what they are: a monumental waste of effort.

 

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

 

Indeed, as we will see later (in Essay Twelve Part Six, when it is finished, and Thirteen Part Three (here and here), this doctrine arose out of the Ancient Greek idea that there was something called "non-propositional thought" (which notion surfaced in Aristotle and Plotinus, for example), which concerns the supposed relation between the Mystical Knower and the Hermetic Unknown. This misbegotten doctrine not only supplies the 'rationale' (if such it might be called) that motivated the nominalisations we have encountered in this Essay, it also motivates the Identity Theory of Predication (the validity of which was also required in order to initiate and then enable Hegel's Idealist acrobatics).

 

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

 

So much philosophical hot air generated from a seemingly insignificant semantic blunder, and invented by supposedly intelligent theorists!

 

A deep puddle of Metaphysics condensed from a cloudy use of grammar, to paraphrase Wittgenstein.

 

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

 

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

 

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

 

Now, Hegel (or one of his groupies) can maintain the above doctrines until the cows next evolve for all the good it will do him (or them). Only those naive enough to fall for the systematic nominalisation of relational expressions will be embarrassed by the 'simpleton's' response, recorded earlier.

 

The sorry tale continues:

 

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

 

This is not much better; if anything, it is worse. Exactly who wanted to "banish" difference is somewhat unclear. How they might manage to pull this trick off is even less obvious. Organise a picket? Obtain an injunction? Utter a spell? Seek a Papal Interdiction? Issue a Fatwā? Cast it into Outer Darkness...?

 

Nevertheless, the conveniently fictional characters to whom Hegel and Lawler allude, and their impossible antics, need not bother us for now. What is more worrying is the uncritical way that Lawler accepts this lamentable 'argument'. Quite apart from the odd examples of identity Lawler quotes (for instance, his "white is white" can only work once more by nominalising the predicate "ξ is white", so that "white" is treated as the name of an abstract particular, and thus no longer serves as a predicate expression), the alleged diversity involved is no argument for the existence of the other nominalised entity in this mutant pair, (i.e., "difference"), which is a creature of Hegel's (and now Lawler's) fevered imagination.

 

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

 

More to the point, even if it could be shown that the most ardent supporters of 'abstract identity' (and I assume Leibniz would be near the top of the list here) were guilty of all the errors Hegel and/or Lawler lay at their door, only if these two could also show that those committed to a belief in 'abstract identity' were also committed to the odd idea that everything was identical with everything else (and thus that there is no such thing as 'difference') could they also show that 'abstract identity' automatically excluded 'difference', which conclusion they seem to take for granted. But has a single believer in 'abstract identity' held such a weird idea? Certainly not Leibniz. It is arguable that Parmenides, his disciples, and other Absolute Monists (such as the Indian supporters of Advaita Vedanta, such as Adi Shankara) did. But, few of those were around in Hegel's day, and their ideas weren't influential in the 19th century (nor now, for that matter). Even so, it is plain that even a rigid commitment to 'abstract identity' does not deny, or even so much as hint at a denial, of diversity. If it does, Hegel and Lawler unwisely omitted the proof.

 

But, let us assume that an 'abstract entity' -- named by the word "difference" --, does indeed exist. If so, it must be a particular of some sort, which means that "difference" can't be a general term, but a singular designating expression. In that case, it can tell us nothing about the many and diverse relations that exist in the material world. So, even if Hegel were right, we wouldn't need to appeal to this 'entity'/word (indeed, we would be wise to ignore it) in order to understand how to construct (or even reject) identity statements, let alone begin to study diversity.

 

In which case, we hit the same annoying, material/semantic brick wall every time. Once particularised (a là traditional logic/metaphysics), words like "Identity" and "Difference" lose all contact with their original meaning, and thus cease to have a meaning (since they no longer function as supposed relational expressions).

 

 

The Fog Thickens

 

From here on in, Lawler's attempt to clarify the meaning of the mist-engulfed phrase "dialectical contradiction" only succeeds in lobbing a few more smoke bombs at it:

 

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

 

In fact, and independently of the LOI, the normal use of the name "A" (if this is what this letter is meant to be in the above passage) wouldn't imply that the item in question wasn't other than A. So, our use of names in fact contains no hidden reference, or even a faint allusion to a negative particle attached to a name -- as in "not A", or even "not-A".

 

This is so for at least two reasons:

 

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

 

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

 

[Notice, it is our use of names that implies this, not the name itself. However, if Hegel and Lawler have a different understanding of names, then their odd ideas would apply to this idiosyncratic term, 'name', and not to what we ordinarily call names. (This comment of course, assumes that Hegel and Lawler are interpreting the "A" here as the name of an object or 'entity'. This might be an unsafe assumption, however, given the profligate and careless way they both throw this letter at their readers.)]

 

Be this as it may, as we have seen, the following can't be an implication:

 

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

 

That is because, if "A" is an object, or the name of an object, no implication is possible. Objects do not and cannot imply other objects, and neither can expressions that have been nominalised. Of course, as we saw above, our use of such names (typically in sentences) can imply all manner of things (by means of what has come to be known as "conversational implicature"), but Lawler Hegel have yet to show that we do in fact use names in this odd way -- or, how it is even possible to use names in this way.

 

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

 

Consider an example of Lawler's: while it is true that "a cow is a cow" -- "A is A" -- it is also true that "a cow is brown" -- "A is B" --, while it is also true that "brown is not a cow" -- "B is not-A".

 

Now, it is little use dialecticians objecting to the semantic 'looseness' of this counter-example (with the terms here sliding between nouns and adjectives), since the "A"s they use are subject to no little dialectical double-dealing themselves. Hence, DL-fans have no more right to complain about 'sloppy semantics' when it is used against them than George W Bush has a right to moan about "terrism". If this counter-example is to be ruled out-of-court on semantic grounds, then much of Lawler's (and hence Hegel's) argument would go with it.

 

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

 

Indeed, Lawler himself calls a colour term an 'entity':

 

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

 

Once more, someone could object that even if the above were correct, B is still not A, so there is still a negative relation here. But, as we have seen, the required relation can only be forged if the propositions/predicates involved are nominalised. And, as we also saw earlier, even if the "is" here is viewed as one of identity, and not of predication, this argument still hits a brick wall.

 

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

 

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

 

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

 

Again, these 'inferences' only work if they are expressed propositionally, whereas the relations they express only apply if they are not.

 

However, there is no "negative relation" of A to not-A (since predicates aren't objects), and that means that it isn't the case that "A is itself in not being not-A". The whole passage is thus about a genuine as one of Gordon Brown's smiles.

 

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

 

On the one hand, if the NON works, it can't apply to negation; on the other, if the NON applies to negation, it can't work.

 

[NON = Negation of the Negation.]

 

 

Zeno -- No Help At All

 

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

 

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

 

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

 

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

 

Perhaps this is too hasty?

 

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

 

Here, it seems, we can grasp this terminally obscure notion (i.e., "dialectical contradiction") by means of the hopelessly unclear (i.e., "unity of opposites").

 

As might be expected of a Christian mystic like Hegel, but not of an atheist like Lawler (if he is one), a 'solution' to this paradox is no more helpful that the 'solution' to the equally intractable 'problem' of the Nature of Christ, in the Christian doctrine of the Incarnation, which 'solution' also comes in the form of an even more paradoxical set of words (wherein Christ is a 'unity of opposites', too, God and Man:

 

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

 

Well, that clears things up nicely...

 

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

 

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

 

As we noted in Essay Three Part One, this remarkable a priori 'truth' is 'true' solely because Hegel's system depends on a methodology derived from an ancient ruling-class tradition, which systematically distorts ordinary language in order to concoct such 'interesting' results -- as Marx noted:

 

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

 

[On this in general, see here.]

 

Lawler then notes that Hegel's analysis of 'dialectical contradictions' begins from the 'common sense' view of motion and place, and proceeds from there. He adds that it isn't relevant to argue that modern, mathematical definitions of motion are more precise -- or rather, that this line-of-thought would constitute an effective response if it could be shown that:

 

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

 

But, (1) above does not apply, since ordinary language does not collapse into paradox -– that is, not unless it is twisted out of shape, a là Hegel, or a là Zeno -- again, as we saw in Essay Five. And (2) only applies if the terminology that mathematicians use is twisted in like manner, and functional expressions are transmogrified, for example, into the names of 'categories' (i.e., into 'abstract particulars', once more).

 

 

Every Magic Trick Requires A Diversion Of Some Sort

 

Lawler now diverts attention once more with a detour into 'diversity':

 

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

 

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

 

Once more, this argument only appears to work because the (supposed) identity relation and its alleged opposite, 'difference', have been nominalised and turned into 'abstract particulars', and then unceremoniously lumped together in the 'category' of 'diversity'. But, if these relations aren't 'abstract particulars' (and can only be made into them by yet more linguistic distortion), then they can't be lumped together. Conversely, if they are lumped together, then they cease to be relations. Either way, this entire way of looking at these two 'relations' falls apart.

 

It could be objected that if we think about the similarities between objects, then we must of necessity forget about their differences, and vice versa, which is all Lawler and/or Hegel need.

 

However, this is just hand-waving in advance of the genuinely magical moves soon to be performed (which serve to distract) -- and these aren't even convincing moves. While Empiricist philosophers (who, it seems, might be the real target of this impressive display of prestidigitation), like Hume -- as we shall soon see --, might be guilty of emphasising diversity (attributing 'identity' to a mere 'habit of the mind'), no sane scientist (not in the grip of a philosophical theory, that is!) would forget about the similarity between the diverse objects of his/her study. When, for example, classifying animals into the various genera in the Canidae family, no competent zoologist would forget the characteristics that unite them all in that family even while he/she is distinguishing between them -- deciding which species are to be collected in the genus Alopex, the genus Lycalopex, or the genus Vulpes, and so on. Hegel might forget this, and Lawler's memory might be insecure in this respect, which might be why they didn't choose science as a career, but one suspects Carl Linnaeus wasn't quite so anamnetically-challenged.

 

Hence, this isn't even remotely correct:

 

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

 

Be this as it may, as noted above, all this hand waving is merely part of the preparation for the main event: the rationale underlying Hegel's account of causation, and thus, his appeal to 'contradictions' as the motive force behind all change and movement -- which is the point of this remark:

 

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

 

This connection will become a little clearer when we review what I argued in Part Two of this Essay:

 

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

 

Hume had argued that there is no logical or conceptual connection between cause and effect. This struck right at the heart of Rationalism, and Hegel was keen to show that Hume was radically mistaken. Kant had attempted to provide a reply, but his solution banished causation into the Noumenon, about which we can know nothing. That was totally unacceptable to Hegel, so he looked for a logical connection between cause and effect. He found it in (1) Spinoza's claim that every determination is also a negation (which, by the way, neither theorist even attempted to justify), and (2) in his argument that the LOI stated negatively implied the LOC (which it doesn't).

 

Based on this, he was 'able' to argue that for any concept A, "determinate negation" implies it is also not-A, and then not-not-A.

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

 

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

 

Plainly, this paired unique opposite, not-A, is essential to Hegel's theory, otherwise, he could provide no explanation why A should be followed by a unique not-A and not just any old not-A -- say, B, or, indeed, something else, C, for example.

 

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

 

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

 

Hence, Hegel introduced this unique "other" with which each object and process was conceptually linked -- a unique "other" that was internally connected with A  --, something he claimed could be derived by 'determinate negation' from A. [How he in fact derived this "other" will be examined in Essay Twelve Part Five, but a DM-'explanation' -- and criticism of it -- can be found in Essay Eight Part Three. (This argument can be found below, in the next few sections of this Essay -- added comment.)]

 

This special not-A was now this unique "other" of A. Without it his reply to Hume falls flat.

 

Engels, Lenin, Mao, and Plekhanov (and a host of other Marxist dialecticians) bought into this spurious 'logic' (possibly unaware of the above 'rationale'), and attempted to give it a 'materialist make-over'. And that is why this Hegelian theory (albeit "put back on its feet") is integral to classical DM; it supplied Engels, Lenin and Mao (and all the rest) with a materialist answer to Hume.

 

[There is a far better way to neutralise Hume's criticisms, and those of more recent Humeans, that doesn't make change impossible. More details will be given in Essay Three Part Five. Until then, the reader is directed toward Hacker (2007), and Essay Thirteen Part Three.]

 

And here is Lenin's acknowledgement of this principle:

 

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

 

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

 

Lenin wrote in the margin:

 

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

 

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

 

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

 

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

 

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

 

The most relevant and important part of which is this:

 

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

 

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

 

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

 

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

 

So, Hegel's theory (coupled with the part-whole dialectic), was at least a theory of causation and of the course of history, and the above dialecticians were absolutely right (as they saw things) to incorporate it into DM. It allowed them to argue that, among other things, history isn't accidental -- i.e., it isn't just one thing after another -- it has a logic to it. Hence, Hegel's 'logical' theory enabled them to argue, for example, that capitalism must give way to the dictatorship of the proletariat, and to nothing else. Hume's criticisms -- or, rather, more recent versions of them (which, combined with contemporary versions of Adam Smith's economic theory (Smith was a friend collaborator of Hume's) in essence feature in much of modern economic theory and philosophy, and thus in criticisms of Marx's economics and politics) -- are a direct threat to this idea. If these critics are right, we can't predict what the class struggle will produce. Or rather, if Hume is right, the course of history is contingent, not necessary, not "rational".

 

As far as I can tell, very few dialecticians have discussed this aspect of their theory. The only ones that seem to do this (that I have come across in over 25 years of looking) are Ruben (1979), and Fisk (1973, 1979) -- although, as we will see in Note 70, Meikle (1979) also depends in large part on this notion. [I will examine Fisk's arguments, which are by far the most sophisticated I have seen, in a later re-write of this Essay, and in other Essays.]

 

Which explains why Lawler now proceeds to make the following point (which, it seems to me, is aimed directly at the empiricists (like Hume) mentioned above -- hence his comment about "correlational methodology" -- who seem to want to turn the supposedly 'objective' relations that exist in nature into subjective impressions):

 

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

 

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

 

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

 

Here, at last, we have the point of the whole exercise; all that has gone before is simply stage-setting.

 

Even so, it is worth pointing out that the antithesis Hegel drew between organic and inorganic matter/nature is surely defective. If he were right, then inorganic matter/nature didn't exist before organic molecules evolved! Moreover, in the postulated 'heat-death of the universe', inorganic and organic matter must, it seems, survive, since they have no unique 'other' to turn into! With or without this 'heat death', inorganic and organic matter/nature must be eternal beings, and for the same reason. [I return to make a similar point, here.]

 

 

The Main Feature

 

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

 

As we approach the denouement of this elaborately staged feat of magic -- i.e.,  the attempt to locate some (any?) sense in the phrase "dialectical contradiction" -- Lawler confronts those who think that Hegel:

 

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

 

Well, how does Lawler answer the query about this non-contradiction?

 

[Yes, that is correct; "A and not-A" is a non-contradiction -- unless, that is, Lawler abandons the idea that "A" is an "object", or name of an object, and interprets it as a proposition, or propositional variable. But, as soon as he does that, it can stand in no relation to anything, since propositions are not objects, nor yet the names of objects.]

 

He does so as follows:

 

"One might readily grant that the definition of A includes A's relating to something that is not A (some non-A which is not-A). This does not mean that non-A or what is not-A is a part of A or part of A's identity. Such a position would lead to regarding all interacting beings as constituting essentially one being. Only the relation to non-A (not-A) seems to be a property of A -- not non-A or not-A itself. Hegel clearly wants to claim more than this. To understand dialectical 'identity' it is necessary to recognize the insufficiency of the abstract concept of 'identity'. Despite Hegel's detailed critique of this category, critics commonly persist in interpreting dialectical contradiction as the assertion of the undialectical identity of A and not-A." [Ibid., p.32. Italic emphases in the original.]

 

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

 

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

 

 

Unity Of Opposites?

 

Now, as Lawler goes on to indicate, Hegel rejects the open insertion of "not-A" for "A" (which, if it were correct, would in fact be bad news for Diabolical Logicians -- as we saw in Essay Four), and he quotes in support an obscure passage from Hegel that seems to be devoid of earthling sense:

 

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

 

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

 

Lawler then proceeds as follows:

 

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

 

This represents Hegel's way of:

 

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

 

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

 

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

 

Now, as we saw in Essay Seven, and above, this example of homespun neo-Romantic pseudo-science won't wash (but note here Lawler's confusion between "internal" (meaning "logically internal") and "internal (meaning "spatially internal"), which was noted in Essay Eight Part One); there is no intrinsic difference between living and non-living matter, so the alleged contrast is bogus. In fact, the above is more an expression of the obscure ideas found in mystical vitalism (and which were current in Hegel's day) than it is an accurate reflection of living things themselves.

 

But, what should we say of lifeless matter as it was before life evolved? Then, there was nothing with which it could be 'contrasted'; it had no "other". Did that mean lifeless matter had no 'identity', no 'Being'? Did it gain an 'identity' only when the first living things evolved? In that case, was life (logically?) bound to evolve just to help provide an 'identity' for non-living things? Indeed, does this classic example of a priori superscience mean that life in the universe cannot (logically cannot) ever cease --, otherwise lifeless matter will once again lose its 'identity'?

 

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

 

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

 

Perhaps we need to understand 'dialectical negation' a little better, so that the above materialist impertinences can safely be ruled out? Lawler is ready to help:

 

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

 

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

 

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

 

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

 

Well, maybe not Hegel, but certainly Lawler should.

 

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

 

And even if they did (but on that, see here), that would have ontological implications only for Idealists.

 

 

The Magical Use Of 'Negation'

 

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

 

"In the first place, negation cannot be understood in the formal sense, according to which the existence of some entity implies the nonexistence, pure and simple, of another." [Ibid., p.35.]

 

The ripe old fun we had at the expense of assorted LCDs (in Essay Four) was perhaps too hard only on them, for here we find an HCD like Lawler make all the usual sophomoric mistakes we have come to associate with this backwater of sub-Aristotelian 'logic'. What the dialectics has "formal" negation got to do with any of 'nonexistence'? Precisely what non-existence of which entity does the following imply: "Blair owns a copy of Hegel's Logic" and "Blair does not own a copy of Hegel's Logic"?

 

Would that it were this easy to consign Hegel's confused book (or Blair) to Logical Limbo!

 

And while we are at it, the non-existence of precisely what is implied by the existence of the Eiffel Tower? Of course, it could be argued that had the Eiffel Tower never been built, something else would occupy its place, which, of course, 'it' now does not. But, this "something else" could still exist somewhere else. The very best this argument could show is that the presence of the Eiffel Tower (where it is), or whatever, prevents anything else occupying the same space, not that 'it' (this vague 'something') cannot exist

 

However, given the complexities involved in our use of the word "place" (on this see Essay Five), not even this is as secure an inference as it might first seem. For example, someone could itemise the Eiffel Tower first in their list of favourite structures, and then The Great Pyramid first in their list of places to visit next. Here, these two would then occupy the same place in both lists, namely, first, and at the same time. And this doesn't even involve the use of their names (i.e., their written names), since both lists could be committed to memory.

 

Someone could object that this example merely concerns the appearance of names in two lists (wherever those lists are situated), not the structures themselves. Maybe so, but this example was quoted merely to show that two objects (names, or whatever) can occupy the same place at the same time; hence the occupancy of one does not always imply the non-occupancy of the other. If so, Lawler's argument above is defective.

 

Someone could still object, arguing that no two items could occupy the same place in the same list at the same time (but, only those who accept the LOI are allowed to advance this objection, and thus use the phrase "same list"!). But, even if that were the case (and there is good reason to suppose it isn't, but I will let that pass for now -- the reader is left to ponder that for herself), it is worth recalling that this counter-example was only quoted to show that Lawler's inference is not safe, since there are examples where one object does not always imply the non-existence of others (using his way of expressing things). For his argument to work, it must always do this.

 

It could be argued that the material that constitutes the Eiffel Tower, in that is has been used to make this structure, could have been used to make something else, which, as a result does not exist. Indeed, but then that "something else" could have been made by other material. Now, we could go on like this for some time, arguing that the material constituting this "something else", in that it has been used to make this "something else", denies the existence of yet another "something else", and so on..., but this won't save Hegel, or Lawler. That is because, for any object that is allegedly denied existence in this way, we can always substitute another that might have existed in its place, ad infinitem. With such airy-fairy fancies, after all, anything goes -- not just in the construction of such fancies, but in their refutation, too.

 

[LOI = Law of Identity.]

 

And, even if two contradictory sentences could be found that did imply that something or other did not exist if something else did, what would that have to do with formal negation in general, as opposed merely to a particular instance of it?

 

Of course, ordinary negation is very complex -- on that, see Horn (1989) -- but, formal negation is the result of either (1) the use of sentence-forming or (2) clause-forming, operators. That's it! Anything else ain't formal negation, howsoever much this "anything else" allows this virulent strain of Hermetic Herpes to proliferate. [So-called "predicate term negation" will be ruled out of court in Essay Twelve Part Five -- but even if that ruling were mistaken in some way, it isn't too clear how this might assist Hegel/Lawler.]3a

 

However, Lawler doesn't appear to mean the exclusion of other objects in this way. He has in mind something a little more specific, and inter-active:

 

"And yet intuitively we recognize in real life some entities do destroy others, or less radically, they 'clash,' collide or struggle. It is common to regard such practical negativity as external or accidental to the nature of the entity or entities involved. The entities are regarded as in themselves self-subsistent 'positives' which may 'interact,' modify, and sometimes interfere with or destroy one another." [Ibid., pp.35-36.]

 

If so, the mere existence of one object does not automatically imply the non-existence of another; if it did, there'd be nothing to struggle against or interfere with, would there?

 

Lawler continues:

 

"To place negativity within the framework of necessarily related beings, however, it is necessary to conceptualise negativity differently and paradoxically. It is necessary to say that the negative or destructive tendency is not extrinsic to the connections that positively constitute the beings involved, but are (sic) (also) intrinsic to that constitution. The negativity is not an unfortunate by-product, which one might possibly eliminate, of the positive relations necessary for the thing's development. It is intrinsic to that positive connection." [Ibid., p.36.]

 

There are so many things here that Lawler just takes for granted he stands in danger of being indicted on a conceptual robbery charge.

 

What has a "clash" got to do with 'negativity', or even with negation? And what has 'intuition' got to do with recognising the destructive aspects of nature? And why do we have to agree with the claim that these features are internal (intrinsic), but reject the idea that they are external (extrinsic)? All we are given here (by Lawler) are a few manufactured terms-of-art that he (following Hegel) says mean that objects are related to their significant "others" in a quirky sort of way. On examination, all turn out to be based on a motley collection of transmogrified words with an ill-defined "not" attached to them, and nothing else. So, apart from an appeal to yet more sloppy logic, there is nothing to indicate that these 'internal relations' are any more real than gryphons and harpies.

 

Perhaps because he recognises the bogus nature of this alleged 'necessity', Lawler now retreats into the subjunctive mood:

 

"Hegel's procedure in advancing this position may be open to criticism to the extent that he attempts to deduce (idealistically) necessary 'inner negation' in reality from an analogous process in thought. However, such dialectical negation may nevertheless be real and the dialectical negativity characteristic of certain thought processes may also characterise extra-mental processes." [Ibid., p.36. Bold emphasis added.]

 

But, the "dialectical negativity" of "certain thought processes" is as genuine as a $13 bill. So, unless the universe is itself as logically-challenged as this passage clearly is, 'innovative' reasoning of this sort will find no correlate in nature. [Perhaps Lawler has access to the missing container-loads of data (that went 'walk-about' soon after Lenin made similar, but even more grandiose claims, several generations ago) that 'support' such hyper-bold claims?]

 

Well, here it is; here is the missing 'evidence' -- and, surprise, surprise, it is just as watery-thin and unimpressive as the 'data' produced in support of the sort of Mickey Mouse Dialectical Superscience we met in Essay Seven, much of it scraped-together by the aforementioned conceptually-'challenged' LCDs:

 

"Thus we intuit a negative side to the relation of living beings to the non-living environment. Gravitational, electromagnetic, geological, meteorological, solar, etc. forces constitute obstacles to the development of life as well as necessary conditions. The fact that certain optimal conditions of inorganic processes are required for life to evolve does not mean that the negative forces which otherwise would have prevented the appearance of life have simply ceased to exist. Rather, the optimal conditions permit them to be 'surmounted' or 'overcome,' but not eliminated. Moreover, this 'surmounting' of the negative life-destroying forces of the environment is intrinsic to the development of life. Life can only develop by 'repelling' the negative forces of its environment -- by 'negating its negation.'" [Ibid., p.36.]

 

We have already seen in Essay Eight Part Two that this way of depicting forces doesn't work, howsoever it (or they) are re-packaged. Even so, and flowery language to one side, the forces at work here are all manifestly external; there are no internal relations (except, of course, those conjured into existence by yet more Hegelian Hocus Pocus).

 

And, like it or not, life arose because of the operation of material/causal factors at work in nature, not logical principles inherent in Hegel's 'concepts'.

 

But what, we might ask, has become of all that earlier talk about those eternally-plastic letter "A"s, which were said to have one, and only one, "other"?

 

"A's identity involves its necessary relation to what is not-A, and that this not-A is 'its own other' -- a definite other being and not any being whatsoever -- and that this relation to some definite other is necessary for the existence of A or is essential to the constitution of A (A's identity)…." [Ibid. p.32. Italic emphases in the original.]

 

And yet, we have just been informed of "forces" (plural) that oppose life. So life, it seems, is exempt from this Hegelian caveat, in that it appears to have hundreds, if not thousands of "others". Of course, that depends on how we count forces. [Is, for example, each molecule of, say, Carbon Monoxide, or Ozone, an opposing force? Or do they work in gangs?]

 

[We mustn't expect answers to such questions; this is Mickey Mouse, a priori superscience, after all.]

 

Fortunately, Lawler has an answer:

 

"For the same reasons that we argued for the 'imprint' of the 'other' in an entity chosen for study, we should expect to find an imprint within the entity of this opposition that exists between entities. For example, the internal process of growth is opposed by excessive heat -- a physical or inorganic force. Growth must surmount this force which tends to inhibit or suppress growth. Extreme temperatures would prevent life altogether. At the same time, growth is dependent upon heat. Systems of temperature self-regulation develop whereby the negative effects of heat are, within limits, negated while the positive effects are absorbed. Normally we think of heat as having positive effects within certain ranges and negative effects outside of those ranges. But even within the 'positive' range, heat would still be destructive without the heat-regulating mechanism of the organism.... Thus, even within optimal ranges heat tends to negate life." [Ibid., pp.36-37. Italic emphasis in the original.]

 

What has happened to all those "imprints" we met earlier? Where is heat itself (not its regulation) "imprinted" in a cell? And, where are cells "imprinted" in heat? [Or, does "imprinting" only work one way?] And where is the cell's regulation force "imprinted" inside heat? And what has happened to heat's own "other", cold?

 

Of course, heat is not a force; the word is, in such contexts, merely shorthand for the energy we accredit to certain molecules. Hence, it is even more difficult to see how the vibrational energy of, say, a Carbon-Carbon bond could be the unique "other" of..., well what?

 

Cells have to regulate more than just heat; homeostasis is maintained inside cells by a variety of processes. In that case, we are forced to ask: Do cells have several (perhaps countless) significant (internal) "others"?

 

Despite this, the processes Lawler describes are all causal; there are, alas, no Hegelian concepts here for Biophysicists to study. Unsurprisingly, and as far as is known, no PhD thesis has ever been commissioned to study these Hegelian 'forces' -- not even by Haldane, Bernal, Levins, Lewontin or Rose. [If anyone knows of one, e-mail me!]

 

Nevertheless, this might be to miss the point:

 

"The expression 'tends to' has been used advisedly, since 'full' realisation of a dialectical negation would amount to the destruction of both external and internal conditions of existence, and hence total self-suppression. Dialectical negation is not abstract or formal negation of the 'other,' but is 'mediated' by the other itself. (This is not to deny 'relatively immediate' forms of negation, such as destructive 'clashes'; these can often be understood, however, in terms of the underlying necessary dialectical relations of which they constitute a 'form of expression.'[) -- RL] In a dialectical negation, what is negated is at the same time a necessary condition of existence. For example, life is maintained both through and in opposition to non-living conditions -- both externally and internally. The opposition must be relative, not absolute, however, because the 'full' realisation of the negation (corresponding to 'abstract negation' in thought) would mean self-destruction. Thus, dialectical negation falls short of the 'full' negativity of logical negation or logical contradiction." [Ibid., p.37. I have added a missing bracket.]

 

So, how precisely does heat 'mediate' here? Unfortunately, Lawler neglected to say, just as he neglected to say how organisms know when, where and how to dial-down the negations they encounter so that they do not experience the full fury of these nasty and destructive logical contradictions. Maybe they know more logic than Hegel?

 

[Incidentally, Lawler also forgot to include a vague demonstration, or even so much as a weak argument, showing that logical contradictions have anything to do with destruction (which they don't). (On this, see below.)]

 

To be sure, Hegel did argue as follows:

 

"If the contradiction in motion, instinctive urge, and the like, is masked for ordinary thinking, in the simplicity of these determinations, contradiction is, on the other hand, immediately represented in the determinations of relationship. The most trivial examples of above and below, right and left, father and son, and so on ad infinitum, all contain opposition in each term. That is above, which is not below; 'above' is specifically just this, not to be 'below', and only is, in so far as there is a 'below'; and conversely, each determination implies its opposite. Father is the other of son, and the son the other of father, and each only is as this other of the other; and at the same time, the one determination only is, in relation to the other; their being is a single subsistence. The father also has an existence of his own apart from the son-relationship; but then he is not father but simply man; just as above and below, right and left, are each also a reflection-into-self and are something apart from their relationship, but then only places in general. Opposites, therefore, contain contradiction in so far as they are, in the same respect, negatively related to one another or sublate each other and are indifferent to one another. Ordinary thinking when it passes over to the moment of the indifference of the determinations, forgets their negative unity and so retains them merely as 'differents' in general, in which determination right is no longer right, nor left left, etc. But since it has, in fact, right and left before it, these determinations are before it as self-negating, the one being in the other, and each in this unity being not self-negating but indifferently for itself." [Hegel (1999), p.441; §960. Italic emphases in the original.]

 

The above paragraph quite nicely highlights Hegel's warped and prejudicial thinking. This is neatly summed up by Rosenthal:

 

"...[D]espite Hegel's obvious preference for patrilineal forms of descent -- 'father is the other of son,' he writes, 'and son the other of father, and each only is as this other of the other'... -- reality...is burdened with two biological sexes. Clearly, a father can still be a father, even if his 'other' happens to be a daughter, and a son cannot be a son without another 'other' besides his father." [Rosenthal (1998), p.218.]

 

And if a man were to reproduce with his daughter (surely a common occurrence, at least among royalty), then her son will also be her brother (and the child's mother will be his sister), as well as being son and grandson, all at one go, to the father.

 

Of course, the situation is even worse than this, for Hegel seemed to be fixated only on alleged binary relations (but what is so 'contradictory' about right and left, or above and below?).

 

What about tripartite relations (like speed, distance and time, or mass, density and volume)? Or, the three "colour charges" belonging to Quarks in Quantum Chromodynamics?

 

Or, multivariate analysis in statistics, or relations like the points on a compass?

 

 

Figure One: Has Hegel Lost His Bearings?

 

If this particular example is regarded as a little too 'abstract' (but those who think so should check out the next 'abstract compass' they use on a walk in the mountains, say, or in a boat; it will then seem pretty material), think of the same figure, but now representing people sat around a circular table. Each individual will be sat next to at least two contingent 'others', while sat opposite many 'others'. And, worse still, none of these will 'pass over' into any of its 'others' (as Hegel imagined). If we now move into three dimensions, and consider objects placed around a globe, Hegel's 'logic' will begin to look even more ridiculous. [Of course, these can all be translated into Relational Algebra, so this is an apposite counter-example. Now, this particular argument might be criticised as unfair, since formal systems like this were invented after Hegel's demise -- but that just shows, once more, how hopelessly parochial Hegel's 'logic' really is.]

 

It could be objected that individuals sat around a table aren't dialectically linked, so the above counter-example is misguided. Maybe so, but the point of raising this example is still apposite. Many things in nature and society have plenty of 'others'. Hegel was fixated on binary relations and completely ignored multivariate examples.

 

Of course, it could be argued that "opposite" in such circumstances would mean "diametrically opposite"; so North, for example, would be the opposite of South in this sense. Even then, there would be a problem for anyone sat at the centre of the table (or group, if we remove the table but maintain the seating arrangement) mentioned above; that individual would have many 'opposites'. Moreover, each individual/direction will have two other individuals/directions next to them. These would still be multivariate relations Hegel ignored. [On this, see below.] Of course, if we move into three dimensions (again, see below) there would be many more such opposites.

 

And do not even begin to think about large finite relationships, such as "the millionth woman to give birth to a child in the USA since January 1st 1967", or "the ten thousandth individual to visit the USA in April 2011", who are such only because of the ordering relations among our numbers and the individuals to whom they are connected; each is only what he or she is because of the 999,999 or the 9999 individuals/'others' who preceded them. And we needn't concoct unlikely examples. We encounter such things all the time, as in "You're the fourth person who has asked that question today", "That's the tenth paper we've sold this morning", and so on. [If there are such things as 'internal relations', they surely apply here.]

 

Hegel's other examples are no less bogus. Sure, in two dimensions, something can be to the right only if some 'other' is to the left, but what about a third object between the two? It would only be between because it has at least two 'others'. And if we move into three dimensions once more, while something will be to the right and left of the very same 'other' (if it is located on a sphere, this 'other' will lie to the West and the East), it will rest between at most eight others (which reside at the vertices of an imaginary cube which surrounds it, and many more if we imagine other Polyhedra). Of course, the same observations apply to "above" and "below". On a globe, Scotland is both above and below England (if by that we mean North and South) -- travel far enough along a line of longitude (say, 3 Degrees West) in both directions ('up' or 'down'), and you will reach Scotland from England. But, if we are allowed to leave the surface of that sphere, one can travel from one point to any other point in countless different ways.

 

So, just as three-, or even n-, dimensional geometry has shown that Euclid's system was somewhat limited, it seems it has had the same effect on DM-Superscience.

 

Indeed, as Wittgenstein noted, metaphysics is a disease of the intellect brought on by an unbalanced diet of too few examples.

 

 

Hegel's Hermetic House Of Horrors

 

Before we reach the final part of this guided tour of Hegel's Hermetic House of Horrors, Lawler summarises the story so far:

 

"But perhaps it would be better to say that logical negation or the law of noncontradiction is an abstract representation of a certain limit of dialectical negations in reality. The ontological significance of the law of noncontradiction would be found in the nature of dialectical contradiction, with the impossibility of fully realising relative negations without the suppression of the entity that negates." [Lawler (1982), p.37.]

 

Earlier we met this comment:

 

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

 

But, while we are reasonably clear about the nature of contradictions (in ordinary language and FL, at least), we still remain in the dark about 'dialectical contradictions' --, other than their merely being the products of Hegel's insecure grasp even of the primitive logic of his day, and (at least, in his theoretical deliberations) of ordinary language, too -- balanced, of course, by its own "other": an all too secure grasp of mysticism.

 

Unfortunately for Lawler, and for Hegel, the LOC has no ontological implications (it isn't about "non-being"): in its simplest form, all it says (once more!), is that a proposition and its negation cannot both be true and cannot both be false at once. [This characterisation can even be found in Aristotle's famous "Square of Opposition".]  Nothing here about what must or must not exist, or about "non-being".

 

Admittedly, some propositions are 'about' existence, or about what does or does not exist, but that is an entirely separate matter.

 

However, when put into conjunction, even that observation is controversial. For example:

 

C1: Tony Blair exists and Tony Blair does not exist.

 

In many systems of logic, if there is and never has been a Tony Blair, then "Tony Blair does not exist" is truth-valueless. On the other hand, if there is a Tony Blair "Tony Blair exists" would be a logical truth! In such systems, C1 is not even a contradiction, since the second half lacks a truth value. In that case, even this 'contradiction' is not about "non-being", since it isn't a contradiction to begin with. And, even if it were a contradiction, as noted above, it would have no implications for the LOC in general. [More about this in Essay Twelve. Until then, see Williams (1981), and Miller (2002).]

 

To be sure, in certain forms of traditional logic, a non-empty universe must be assumed if the Square of Opposition is to work. But, even here, the LOC itself is not about what exists, or about "non-being" (since the former has already been assumed).

 

Now, it is also true that there are many different characterisations of contradictions in MFL. For example, Grimm [in Grimm (2004), pp.51-55] lists 19 different definitions of the LOC, and when he combines these with other factors, he tells us that there are at least 240 different ways of depicting this 'law' [p.55]!

 

It is worth pointing out, however, that not only are most of the above definitions virtually indistinguishable, with respect to many of them it is also clear that their originators have confused contradictions with inconsistencies. Indeed, in his opening sentence, Grimm commits that very error himself!

 

Out of those he lists, only a handful are described by Grimm as 'ontological' (i.e., are about 'existence', etc.).

 

"On an ontological outline, a contradiction would be neither a single statement nor a pair of statements, neither a proposition nor a pair of propositions, but a state of affairs. A contradictory state of affairs would be one in which something had a particular property and also an incompatible property, or in which something both had a particular property and lacked that property." [Grimm (2004), p.53.]

 

Even so, the only modern logicians Grimm references for this definition are Arthur Prior and the two Routleys (p.52) -- i.e., the late Richard and Val Routley, who later changed their names to Richard Sylvan and Val Plumwood. Their definition goes as follows:

 

"A contradictory situation is one where both B and ¬B (it is not the case that B) hold for some B". [Quoted from Grimm (2004), p.52. I have used a different sign for negation here.]

 

This is not a happy definition, since it seems to treat the letter "B" as a substantival term/variable (i.e., an expression capable of being quantified -- as, for example, in "some B"), but not as a proposition. Of course, if "B" is a predicate letter, then this definition relies on second order logic, and is thus controversial. [I won't try to defend or justify that assertion here.]

 

When interpreted, their example in fact cashes out as one or other of the following:

 

S1: A contradictory situation is one where both Paris is in France and it is not the case that Paris is in France hold for some Paris is in France.

 

S1a: A contradictory situation is one where both "Paris is in France" and "It is not the case that Paris is in France" hold for some "Paris is in France".

 

[Interpreting "B" as "Paris is in France", with or without the quotes. It won't do to object that this is unfair, since, if this is indeed a definition, it should hold for all propositions and/or indicative sentences -- i.e., all interpretations.]

 

But, this is just plain gibberish; I'm surprised Grimm even gave it the time of day.

 

Putting this to one side, we would need to know what these two meant by "situation" before we could decide if this is indeed "ontological". For example, if "situation" means "formulae in the context of a theory", then it wouldn't be "ontological". Unfortunately, the original article in which this 'definition' appears was published in an obscure Colombian mathematics journal (Revista Colombiana de matemáticas), to which I do not have access, so I can't say much more about it. Anyway, as should seem obvious, even this unfortunate 'definition' isn't about "non-being".

 

However, the two Routleys were both radical activists, and Sylvan himself was also a Paraconsistent logician who collaborated with Graham Priest in that endeavour. In that case, it isn't difficult to conclude that Hegel's baleful influence lies behind their definition. [This suspicion is in fact confirmed by the existence of Routley and Meyer (1976) (no irony intended).]

 

[On this, see Graham Priest and Dominic Hyde's brief biography of Sylvan in Hyde and Priest (2000), pp.1-3. Indeed, in Hyde and Priest (p.13), Sylvan pointedly recommends 'dialethic logic' (often spelt "dialetheic logic", a family of non-standard logics which is openly dependent on Hegel), and the many essays published in Priest, Routley and Norman (1989). Background material can be found in Franklin (2003).]

 

Prior's 'ontological' definition goes as follows:

 

"The law of contradiction asserts that a statement and its direct denial cannot be true together ('not both p and not-p') or, as applied to terms, that nothing can both be and not be the same thing at the same time ('Nothing is at once A and not-A')" [Prior (1967). I have relied on the quotation found in Grimm, p.50.]

 

This is an appallingly bad definition from a leading logician (on a par with the lamentably poor 'dialectical definitions' we met in Essay Four Part One)! I will not try to defend it. Even so, there is nothing here about what must exist, or about "non-being", and Prior's 'definition' does not seem to conform to Grimm's typology, anyway.

 

Now, I suspect Prior would have paraphrased this definition (maybe in a longer article) in terms of modern quantification theory, thus removing the apparent existential implications it seems to have. Indeed, this guess is partially confirmed by the other definition Grimm quotes from Prior (1967) [on p.51], which is far superior, and much closer to the one adopted here.

 

Grimm also quotes Aristotle's alleged 'ontological' definition (pp.49-50):

 

"For a principle which every one must have who understands anything that is, is not a hypothesis; and that which every one must know who knows anything, he must already have when he comes to a special study. Evidently then such a principle is the most certain of all; which principle this is, let us proceed to say. It is, that the same attribute cannot at the same time belong and not belong to the same subject and in the same respect; we must presuppose, to guard against dialectical objections, any further qualifications which might be added. This, then, is the most certain of all principles, since it answers to the definition given above. For it is impossible for any one to believe the same thing to be and not to be, as some think Heraclitus says. For what a man says, he does not necessarily believe; and if it is impossible that contrary attributes should belong at the same time to the same subject (the usual qualifications must be presupposed in this premiss too), and if an opinion which contradicts another is contrary to it, obviously it is impossible for the same man at the same time to believe the same thing to be and not to be; for if a man were mistaken on this point he would have contrary opinions at the same time. It is for this reason that all who are carrying out a demonstration reduce it to this as an ultimate belief; for this is naturally the starting-point even for all the other axioms." [Aristotle (1984b), p.1588. In the internet version, this can be found in Book IV, at the end of section 3. Bold emphases added.]

 

This is not much better than Prior's attempt, and will not be defended here, either. The only thing that can be said in Aristotle's defence is that he was writing 2400 years ago, and attempting to initiate the study of logic almost from scratch. The same excuse cannot be extended to Hegel and his many dialectical dupes. Even so, Aristotle's 'definition' does not mention "non-being", either. To be sure, Aristotle says: "For it is impossible for any one to believe the same thing to be and not to be", but this is far too vague to co-opt to Hegel's defence -- since Aristotle might have meant: "For it is impossible for any one to believe the same thing to be and not to be true of a man/a cat/a number...". This interpretation is confirmed by the next sentence in the above passage:

 

"For what a man says, he does not necessarily believe; and if it is impossible that contrary attributes should belong at the same time to the same subject...." [Ibid. Bold added.]

 

In any case, even if (per impossible) it were clear what 'dialectical contradictions' are, FL would need neither it, nor DL, to help explicate, or apply, the LOC.

 

After all, does Astronomy need Astrology?

 

At last we are nearing the dialectical denouement:

 

"For our purposes, this illustration is sufficient to show that while the term 'contradiction' as used here does not have the seemingly 'full' sense of logical contradiction, nevertheless it is not reducible to some 'clash' of externally related 'positives.' Nor is it equivalent to some 'tranquil' association of mutually exclusive logical contraries, such as odd and even numbers, male and female persons, or north and south poles of a magnet -- unless these are in fact understood dialectically…. It is necessary to understand the mutual relation and opposition that constitutes the inner dynamic of the terms in opposition. This opposition may contain the possibility of developing into 'full' contradiction, i.e., into real destruction. However, the real potentiality for the development of dialectical contradiction is not to be seen in this possibility of destruction, but in a potentiality for transformation where only the 'immediate forms' of opposing phenomena are suppressed -- while other, often more developed forms are realised through essential 'internal' interconnections." [Lawler (1982), pp.37-38.]

 

All this a priori jargon is standard fare in HCD texts, but that doesn't imply it means anything. Indeed, it is a sure sign of the opposite. [Irony intended.]

 

But, why is "full contradiction" equated with "real destruction"? Now, the LOC was (and still is) connected with all manner of things in the bad old logic (Lawler himself seems to think it has something to do with "cancelling out" -- although he doesn't use those exact words, as far as I can ascertain (but Hegel certainly does -- he copied this way of talking from Kant), and yet he does speak of negatives in mathematics cancelling; see below --, or as "self-nullifying", as he puts it on page 16). As we will see in Essay Twelve (and here), card-carrying HCDs also think likewise.

 

However, neither the contradictions of FL nor those of ordinary language have anything to do with "cancelling out", or "nullifying". If a proposition "p" is true, its contradictory "not p" is false, not "cancelled out".

 

Look, it is still there on the page/screen, unharmed!

 

This odd idea is connected with the equally bizarre notion that 'negative' propositions are all false (or 'defective' in some other unspecified way). But, 'negative' propositions can be, and often are true. For example, "Blair isn't a socialist" is true, as is "Anyone who reads the Daily Mail, and doesn't reject much of what it says, is no Marxist."

 

And, not even the content of "not p" is "cancelled", for whatever it is that "not p" says is still up for consideration; it is just false if "p" is true -- true if "p" is false. Nor is it "nullified", for (and once more) "not p" could one day become true and "p" itself false, or vice versa. For example, "Blair hasn't resigned" is the contradictory of "Blair has resigned"; the first is false, but, hopefully, it will become true one day -- it could hardly do that if it had been "cancelled", or "nullified". [Needless to say, this was written before Blair finally went!]

 

Moreover, every proposition is paired/pairable with its negation; does that mean that they have all been "cancelled"/"nullified"?

 

Anyway, what would count as the "nullification" of "Blair has not resigned"? One could try to nullify Blair's actual resignation (or its effects), but what could one do to nullify "Blair has not resigned"? Prevent this message getting out? Silence whoever might want to utter it? [If this sentence is false, then what it says has not even happened, so nothing can nullify it, surely?] Even so, that proposition is still there, on your screen, annoyingly mocking any attempt to "nullify" it.

 

Those who talk this way have clearly confused FL-contradictions with contradictory orders or instructions, like "Open the door!"/"Close the door!", which, if acted upon, undo each other, etc. But, the propositions of FL and ordinary language are neither instructions nor orders.

 

Lawler does, however, try to illustrate this sort of negation by appealing to negatives in mathematics (a common ploy used by, among others, Engels):

 

"From the 'thoughtless' viewpoint of abstract understanding, A is conceived of as simply given, and the implicit relation to not-A does not get the trouble of a serious consideration. Just as in mathematics two negatives make a positive, in which they are thought of as cancelling out, here abstract understanding makes the journey from A to not-A and back again without noticing that any movement has taken place." [Ibid., p.22. Italic emphases in the original.]

 

For sure, Lawler then proceeds to sort of reject this view (or, rather, he aims to transcend this approach since it is 'formalistic'), but he doesn't repudiate the idea that it is correct to regard formal negation as a sort of "cancelling-out". He then uses this 'analysis -- beloved of the "abstract understanding" -- to develop a dialectical account of negation. So for Lawler, this sort of 'negation' isn't just "cancelling-out", it has moved beyond it.

 

However, if formal negation is not, and never has been, a "cancelling-out", then the dialectical moves that allegedly follow from (or seek to transcend) it cannot use it as a launch pad for such an aimless 'logical' journey to nowhere.

 

But, and to spoil the fun, not even in mathematics -- if we adopt for the moment this primitive way of talking -- is it always true that two negatives give a positive. For example: -1 + -2 = -3. [Notice, no "cancelling-out" here, either!]

 

Exactly why Lawler only considers multiplication (and perhaps, by implication, division, too) in order to illustrate this obscure point is somewhat unclear, but, even there, the results are not always as he imagines: in the Complex Plane, -i x -i = i = (-1)1/2, which is still negative!

 

Of course, it could be objected that (-1)1/2 isn't negative (even though it contains a negative sign!), but what about -(i1/2)/-i = i-1/2; is that negative? Maybe so, maybe not. Well then what about -(a - b) x -1 = (b - a), where b>a? Or -a x -a = a, where a<0? Or, (x2 - 3x - 1) x -1 = 1 + 3x - x2. Are any of these 'negative'?

 

[I have highlighted "x" in bold when it represents a letter in order to distinguish it from its use as a multiplication sign.]

 

In which case, it seems reasonably clear that this quasi-Hegelian 'rule' is far too crude to use even in lower mathematics. But, when we come to more complex areas (such as matrices and their inverses, groups or infinite series), the whole idea becomes ridiculous.

 

Anyway, negatives in mathematics don't "cancel-out"; what happens is that certain functions take negative numbers as arguments and yield positives as images (but, the domain set of negatives still exists -- it has not been "cancelled-out", or even "nullified").

 

In that case, there is no good reason to connect the "full" contradictions of FL with "destruction".

 

Well, not for us materialists there isn't.

 

Lawler continues:

 

"Real opposition must be understood as dialectical contradiction." [Ibid., p.38. Italic emphasis added.]

 

And that's it! A plain "must" after a lengthy detour through this sub-Aristotelian wasteland.

 

The rest of Lawler's article is just further window-dressing. We are left with this counterfeit "must" here, backed neither by logic nor fact. Exactly why we "must" see these obscure creations of Hegel's Hermetic Hallucinations in this way is left entirely mysterious.

 

To be sure, there is no problem with the phrase "real opposition". But, the phrase "dialectical contradiction" is still lost in the same impenetrable fog Hegel left it in 200 years ago. Precisely why the word "contradiction" has to be super-glued to the other term ("dialectical") is still a mystery -- except that Lawler might have hoped that some of the clarity associated with the former word might rub off onto the latter.

 

[However, I offer a materialist explanation for this odd phenomenon in Essay Twelve (summary here), and I advance much more political reasons in Essay Nine Part Two.]

 

To be sure, Kant introduced into Philosophy the concept of "real opposition" and "real negation", an idea that was also present in embryo in Aristotle:

 

"Two things are opposed to each other if one thing cancels that which is posited by the other. This opposition is two-fold: it is either logical through contradiction, or it is real, that is to say, without contradiction." [Kant (1763), p.211. Emphasis in the original.]

 

However, as we have seen in this Essay, the idea that these 'cancel' each other is completely misguided. [I will say more about this idea of Kant's in a later re-write of Essay Eight Part Two.]

 

Lawler now quotes the following prime example of a priori Superscience from Hegel:

 

"Instead of speaking by the maxim of Excluded Middle (which is the maxim of abstract understanding) we should rather say: Everything is opposite. Neither in heaven nor in earth, neither in the world of mind nor nature, is there anywhere an abstract 'either-or' as the understanding maintains. Whatever exists is concrete, with difference and opposition in itself. The finitude of things with then lie in the want of correspondence between their immediate being and what they essentially are. Thus, in inorganic nature, the acid is implicitly at the same time the base: in other words its only being consists in its relation to its other. Hence the acid is not something that persists quietly in the contrast: it is always in effort to realize what it potentially is. Contradiction is the very moving principle of the world: and it is ridiculous to say that contradiction is unthinkable. The only thing correct in that statement is that contradiction is not the end of the matter, but cancels itself. But contradiction, when cancelled, does not leave abstract identity; for that is itself only one side of the contrariety. The proximate result of opposition (when realised as contradiction) is the Ground, which contains identity as well as difference superseded and deposited to elements in the completer notion." [Lawler (1982), p.38; partially quoting Hegel (1975), p.174, §119. I have used the online version and given a fuller quotation than Lawler.]

 

Considering this famous (but no less dogmatic) assertion: it is nevertheless true that either Hegel wrote it or he didn't. If either (but not both) of these is the case, then Hegel was mistaken since there is just such an "either-or", thanks to Hegel himself -- namely here!

 

Worse: in heaven, hell or high water, there is an "either-or" or there isn't. So, if Hegel was right (and there isn't an "either-or"), he was thereby wrong, since one of these would be the case, not both, nor neither. On the other hand, if he was wrong, then he was wrong anyway. Either way, he was wrong. [There is a longer version of this argument, here.]

 

How did Lawler miss this obvious inference? Has the bad old logic "nullified" his brain? Has Hermetic Hype "cancelled" his ability to use/understand a simple "or"?

 

The rest of what Hegel says should now be consigned to one of Hume's bonfires.

 

I'll get the matches and petrol...

 

 

Acid Finally Corrodes Hegel's 'Logic'

 

Hegel's acid example is none-too-clever either. Lawler commented on it as follows:

 

"…the acid is only an acid through its implicit relation to what negates it…." [Ibid., p.38.]

 

But acids burn the skin not because a base exists (which negates nothing, since a base is not a sentential/phrasal operator; neutralise is not negate) -- which would counteract it if they came into contact --, but because of its corrosive properties. And, if there were no bases anywhere in existence, acids would still do what acids do. Anyway, in what sense is a base (like NaOH -- Sodium Hydroxide) the opposite (the 'other') of an acid (like HNO3 -- Nitric Acid)?

 

Figure Two: A Match Made In Hegelian Heaven?

 

But, Nitric acid is 'neutralised' by countless bases, and not just Sodium Hydroxide. The same is true of other acids. Do they all have countless 'others', as well, contrary to what Hegel assured us must be the case? Of course, if these were genuine 'dialectical opposites', they'd turn into each other, as the classics assure us they must. Does Nitric Acid turn into Sodium Hydroxide? Or vice versa? If they do, Inorganic Chemistry textbooks have been remarkably secretive about it.

 

Of course, modern definitions of acids do not mention bases. The Brønsted-Lowry definition says that acids are proton donators, while the Lewisian definition tells us that an acid is an electron-pair acceptor. To be sure, bases are still defined as the 'opposite' of each of these, but acids and alkali's are no longer defined in terms of each other, but in terms of a third item (or a third and a fourth term, if we lump the lot together). [On this, see Zumdahl (1989), pp.654-56 and Shriver and Atkins (2001), pp.143-76.]

 

So, it seems that Chemistry has taken a decidedly reactionary turn since Hegel attempted to pontificate on the subject.

 

But, this is a specially-chosen example. It won't work in cases that DM-fans conveniently ignore. Many of these are listed in Essay Seven; others have been itemised above. Here are several new examples: voltage, current and resistance are all interlinked, but no single one has its 'being' defined in terms of any one "other" (but two "others"); this is also true of pressure, volume and temperature in an ideal gas, just as it is true of the items found in the traditional Square of Opposition (where implications, contraries (two propositions which can't both be true but can both be false), subcontraries (two propositions which can't both be false but can both be true) and contradictories (two propositions which can't both be true and can't both be false) are interdefined among four "others"). What are we to say of the US Constitution (and many other countries), which sees the State separated into three main branches: The Executive, the Legislature and the Judiciary?

 

Lest these be rejected as 'abstract' (a fine accusation to be levelled by anyone impressed with Hegel!) consider this: in the Periodic Table, none of the Halides (Chlorine, Bromine, Fluorine, Iodine, etc.,) is defined in terms of a significant "other", and neither are salts, proteins, enzymes, catalysts, alcohols, or Aldehydes.

 

And, what are we to say of "buffer solutions", which can be both acid and alkaline?

 

Furthermore, this entire topic is aggravated by Hegel's mystical musings about "finitude" and "infinity"; Lawler quotes him as follows:

 

"Thus essentially relative to another, [something -- Lawler's addition, RL] is virtually against it: and since what is passed into is quite the same as what passes over, since both have one and the same attribute, viz., to be another, it follows that something in its passage into other only joins with itself. To be thus self-related in the passage, in the other, is the genuine Infinity." [Lawler (1982), p.39, quoting Hegel (1975), p.139, §95; Lawler's italics. Again, I have used the on-line version.]

 

Well, that certainly clears things up!

 

But, how is self-relation a "genuine Infinity"? Lawler just accepts this mystical missive and fails to explain it -- except he expands on it with yet more obscure jargon:

 

"…in speaking of the chemical relation of an acid and an alkali, where he notes that 'the negation of the negation is not a neutralization: the infinite is the affirmative, and it is only the finite that is absorbed' [Lawler is quoting Hegel from here -- RL]. The 'absorption' of finite objects consists in the transition implicit in the 'want of correspondence between their immediate being and what they essentially are,' which leads to the realization of that essential being or to the 'genuine Infinite' which Hegel calls being 'self-related in the passage' into the other. In other words, since the other is essential to the original being, there is a form of relating to that other which is not a relation to something 'alien' but a 'self-relation' -- a relation in which the being, at first seemingly self-sufficient, finds its 'self' in and through the other (its other, some definite other)." [Ibid., p.39. Italic emphasis in the original.]

 

I think I have passed enough derogatory remarks about verbal Knotweed like this, but what is a materialist like Lawler (I am assuming, of course, that he is one!) doing assisting in the spread of this Idealist pest as if it helps account for a single thing?

 

We seem, therefore, to be going backwards in our "passage" away from the clarity to be found in FL (and, potentially, in ordinary language) toward the infinite non-sense of dialectics.

 

However, we now get a flash of sense (or do we?), for Engels relates this 'infinity' to "law":

 

"'[F]undamentally we can know only the infinite.' In fact all real, exhaustive knowledge consists solely in raising the individual thing in thought from individuality into particularity and from this into universality, in seeking and establishing the infinite in the finite, the eternal in the transitory. The form of universality, however, is the form of self-completeness, hence of infinity; it is the comprehension of the many finites in the infinite. We know that chlorine and hydrogen, within certain limits of temperature and pressure and under the influence of light, combine with an explosion to form hydrochloric acid gas, and as soon as we know this, we know also, that this takes place everywhere and at all times where the above conditions are present, and it can be a matter of indifference, whether this occurs once or is repeated a million times, or on how many heavenly bodies. The form of universality in nature is law, and no one talks more of the eternal character of the laws of nature than the natural scientists." [Engels (1954), pp.234; quoted in Lawler, pp.39-40. Italic emphases in the original. I have used the on-line version, again.]

 

Lawler comments on this idea as follows:

 

"While rejecting Hegel's ultimately idealist interpretation of 'self-relation' or 'reflection' in the other as 'ideality,' Engels' treatment of 'infinite' as law-governed process, 'absorbing' finite moments into itself, is faithful to Hegel." [Lawler (1982), p.40.]

 

At the risk of repeating myself, how is it possible to translate the word "infinite" as "law-governed process"? Are the rest of us using the wrong Gobbledygook Into English dictionary?

 

Now, Engels certainly tries to equate/relate these two terms, but, for those still in command of the language, neither an "always" nor an "at all times" is an "infinite".

 

[In Essay Thirteen Part Two, we will see that this view of scientific/physical law is a left-over from ancient, animistic ideas about nature, so it is no surprise to find this doctrine re-surfacing here in such mystically-motivated company. On this, see here and here; the first is Swartz (2009), the second Swartz (2003). (See also Guy Robinson's Essays.)

 

Certainly, a weak case could be made for linking "general" with "law-governed" -- but, given the fact that Hegel's 'logic' destroys generality, no Hegelian (drawn either from the 'upside down' wing or the 'right way up' tendency) is free to make this connection.]

 

As noted in Essay Three Part One, from simple sentences like "John is a man" (and now in Lawler's case "Socrates is mortal") we can -- if we are so minded -- 'derive' the thesis that the world is a 'law-governed' "Totality", and that knowledge is an 'infinite' asymptotic journey into oblivion. As Lawler now explains (beginning with a quotation from Hegel):

 

"'Outside one another as the phenomena in this phenomenal world are, they form a totality, and are wholly contained in their self-relatedness. In this way the self-relation of the phenomenon is completely specified, it has Form in itself: and because it is in this identity, has it as essential subsistence. So it comes about that the form is Content: and in its mature phase is the Law of the Phenomenon.'

 

"It is clear from these passages that 'ideality' is not derived by Hegel from the simple suppression of distinct phenomena but from the interaction and dialectically negative interpenetrations which result in their law-governed transformations. The explosive combination of hydrogen and chlorine is more than the 'clash' of two externally related beings. It is the negation of their 'immediate' form as self-subsistent 'free' entities, and the realization of their inner or essential connectedness with each other (under the necessary conditions). The result is not their mutual annihilation, but their transformation." [Ibid., p.40, quoting Hegel (1975), p.189, §133. Lawler has italic emphases; the original has bold.]

 

But, this rather poetic description of a chemical reaction is far from being even metaphorically 'true'. Since when has Chlorine ever been a 'free entity'? At the very least, as a gas, under normal temperature and pressure, it exists as a diatomic molecule, and in solution as an ion -- nowhere in nature does it subsist as a 'pure' element, so far as we know.4

 

And, we note once again that the mystical/Hermetic typology of the "other" has now been dropped, since Chlorine reacts with practically everything. In fact, it has more "others" than Tony Blair has excuses.

 

By way of contrast, if we choose a far less 'dialectically-accommodating' element -- say one of the 'Noble gases' (Helium, Neon, Krypton, etc.), which seem in comparison to be rather stand-offish -- loners, as it were, with no "others" to speak of -- the above comments become all the more apposite. That is because, except under the most extreme conditions, these gases react with nothing at all, and have to be dragged, kicking and screaming down the "passage". So, even this reluctant 'logical' object, this "other", Chlorine, has to be forced into adopting its dialectically-determined fate with respect to these inert elements, and react with them. [Are these "others", therefore, dependent on human intervention?]

 

But, even if this mystical fairytale (about the formation of HCL) were correct, exactly how this is an internally-driven process is still unclear. Surely, Chlorine isn't to be regarded as not-Hydrogen? If it were, then everything in the universe that is not Hydrogen (or not-Hydrogen) would be Chlorine! Conversely, everything that is not-Chlorine would be Hydrogen. [In which case, you, dear reader, in so far as you are 'not Hydrogen', you must be Chlorine, and Zinc, and pencil shavings, and poisonous reptiles, and used bus tickets..., since all of these are 'not Hydrogen', too.]

 

Of course, that is why the significant "other" myth (we met earlier) was invented by Hegel -- to block this very objection, and these countless 'others' --, but as noted above, Chlorine reacts with so many things we would have to use a veritable via negativa to 'identify' it (e.g., Chlorine is not-this, not- that, not-this, not-...); indeed, in the limit, it would be not-anything. Trapped in this Hermetic Hell Hole, Chlorine should disappear about as quickly as the Cheshire Cat's smile!

 

[The same is true (only more so) of Fluorine --, and even more so of Hydrofluoric Acid.]

 

And, as we saw in Essay Eight Part One, these 'internal relations' in fact turn out to be mis-described 'external relations'. It is little wonder then that we need the assistance of Super-Duper 'Logic' to appreciate such verities, courtesy of Hegel. Ordinary language, FL, and the good old-fashioned material world are dialectically most uncooperative.

 

But, we now encounter this:

 

"However, if their identity is narrowly or abstractly defined by the superficial features of their original phenomenal form, the result appears to be annihilation. And this annihilation seems to 'realize' a formal contradiction: for example, 'hydrogen exists independently of chlorine' and 'hydrogen does not exist independently of chlorine.' Following the law of noncontradiction, both of these statements can only be true if we distinguish the 'different respects' in which independence of chlorine can be asserted and then denied of hydrogen. Thus, in the original free state hydrogen is independent of chlorine, while in the chemical reaction or in the hydrochloric acid gas it is not. The logical contradiction in the original crude statements seems to be resolved by qualification of the different respects or conditions in which the seemingly contradictory assertions hold." [Ibid., p.40.]

 

The first example (i.e., "Hydrogen exists independently of chlorine") is of the form:

 

L11: E(x) E(y) [(Hx & Cy) & Fxy].

 

Or perhaps:

 

L12: (x)(y) [(Hx & Cy) ® Fxy].

 

L13: (x) E(y) [(Hx & Cy) ® Fxy].

 

[Where "E" is the existential quantifier, "" is the universal quantifier; "®" is the implication arrow (i.e., "if...then"); "H(ξ)" and "C(ξ)" are one-place, first level predicate expressions/predicables, standing for "ξ is Hydrogen" and "ξ is Chlorine", respectively; and "F(ξζ)" is a first level, two-place predicate (in this case, a binary relation), standing for "ξ is independent of ζ"; "x" and "y" are bound variables, ranging over elements, in these examples.]

 

L11 roughly reads: "There are two elements, Hydrogen and Chlorine, which are independent of each other". In that event, its contradictory would be: "No two elements, which are Hydrogen and Chlorine, are independent of each other".

 

L12 translates out approximately as: "Take any two elements, if they are Hydrogen and Chlorine, then they are independent of each other". If so, the contradictory would be something like: "For any element there is some other element, which, if the first is Hydrogen and the second is Chlorine, then there is at least one example where the latter is not independent of the former."

 

L13 is roughly "For any element, if the first is Hydrogen and there is a second which is Chlorine, then they are independent of each other". The contradictory here would be something like: "For any element, there is no other element, which, if the first is Hydrogen and the second is Chlorine, the latter is independent of the former."

 

If, on the other, hand Lawler's example were of the following form:

 

L14: E(x) E(y) [(Hx & Cy) & Fxy].

 

where "F(ξζ)" is a first-level two-place predicate, standing for "ξ exists independently of ζ", not much would change.

 

Of course, it is unlikely that this method of analysing propositions will be accepted by dialecticians; indeed, there is nothing that forces any of us to adopt this way of looking at language, or logic, or both (except perhaps the fact that it prevents this sort of a priori Idealism and Superscience from establishing even a slender toe-hold in our brains, as was pointed out in Essay Three Part One, here and here). Anyway, if for some reason this more precise and modern method of analysis is rejected, then Lawler's example would be a contradiction only if someone asserted both conjuncts, and held both to be true at once, but who also denied both could be false at once. But, who on earth would want to do that?

 

[In all his talk about "respects", I suspect Lawler realised this, but seemed to want to ignore it.]

 

In that case, this latest example is a logical flop, too.

 

 

Two Senses Of "Independent" Conflated

 

Well, perhaps not -- for Lawler continues:

 

"We should first of all note that the above reformulation of the apparent contradiction implicitly depends on the general proposition, formulated according to the law of noncontradiction, that something, at any one time or in one respect, is either independent or not independent (dependent). But for something which is independent to become dependent, it must have within it the potential to become dependent. It was therefore relatively, not absolutely independent. The potentiality for the chemical reaction was present in the hydrogen in its free state. To follow Hegel's form of expression, in its free state hydrogen was all the while 'repelling' or negating possible reactions with other elements with which it was nevertheless related. Its 'independence' was maintained in its state of interdependence under certain conditions where this was possible." [Ibid., pp.40-41.]

 

Unsurprisingly, there are several highly dubious moves in the above argument. The original claim that "Hydrogen is independent of Chlorine" has now morphed into "Hydrogen is independent, period" -- that is, it now seems to be independent of everything. Moreover, the meaning of the word "independent" has altered in like manner. From "independent" implying "not linked to" (or "isolated from"), it has become "does not depend on", and this slide is what allows the idea that one item can and does depend on the other to be smuggled in while no one is looking.

 

But, it is surely possible for Hydrogen to exist totally isolated from Chlorine (this is the first sense of "independent"), but for it still to be capable of reacting with it if and when its quarantine-like status was terminated.

 

Indeed, scientists invent new compounds all the time (about which they might know very little), which are in fact isolated from other compounds (some of which they will never encounter), but with which they would/could react if given the chance.

 

Let us assume, therefore, that one day some scientists create a new compound called "Hegelase" (a new form of poison -- apparently it blocks certain "passages", and cripples a victim's powers of reason before brain death finally sets in), which they keep isolated from everything else as best they can, for obvious reasons. However, let us further imagine that some of this compound escapes and kills a dialectician, who, for the sake of mischief, we will call "Lawless".

 

Now, did Hegelase have the potential to kill Lawless before it reached him? Was Lawless Hegelase's significant "other"? Well, in the sense that this poison will kill him if it reaches him, it most certainly had this potential. That is why it had to be isolated (and not just from Lawless). On the other hand, in the sense that Lawler (not Lawless) needs, the answer must be, no it doesn't because it isn't his 'other'. If it were, then we must argue that Hegelase has nearly 7 billion "others" out there (i.e., the rest of the human race currently alive), which it has the potential to kill 'programmed' into it. And if we now assume that Hegelase is able to kill all living things, then 7 billion "others" would in comparison amount to a tiny fraction of all of its countless "others".

 

Does this one chemical have so much 'programmed' into it? So many significant "others"?

 

For those who look upon "potentialities" as "actualities" in disguise --, or, at least, as very well hidden "actualities" --, the above example presents serious problems. Every time a new life comes into the world, Hegelase would gain a new "potentiality", for free, and without moving a muscle.

 

Let us now imagine a new strain of bacterium coming into existence (which, for the sake of further mischief, we will christen "Grantococcus Woodsonii B#2", or "GWB2", for short), by whatever avenue such cells have for evolving. Let us further suppose that Hegelase can (i.e., has the potential to) kill GWB2. When GWB2 came into existence, Hegelase has thus gained a new potential to kill GWB2 (say, "PGWB2", for short). But, to do that it must have had the potential to develop this potential (or it wouldn't have happened, given the traditional way of looking 'potentiality'). So, before PGWB2 came into existence, Hegelase must have had a potential to develop PGWB2 (say, "PPGWB2"), too. But, once more, in order for that to happen, PGWB2 must have had a further potential to develop PPGWB2 (say "PPPGWB2"), too. Well, it doesn't take very much Diabolical Logic to see where this is going if we insist on regarding potentialities as the disguised/hidden properties of bodies (governed by those ill-defined 'dialectical negations'), and not just our way of making sense of what they do, or can do.

 

We have to conclude this or imagine that Hegelase has an (actual?) potential to kill things that do not now exist (and perhaps might never exist). But, what kind of 'potential' is that?

 

However, even if the above is rejected for some reason (perhaps, by the use of a complex counterfactual, or the deployment of the Nixon defence), what is all this "repelling" that Hegel thinks things engage in?

 

"To follow Hegel's form of expression, in its free state hydrogen was all the while 'repelling' or negating possible reactions with other elements with which it was nevertheless related. Its 'independence' was maintained in its state of interdependence under certain conditions where this was possible." [Ibid. Bold emphasis added.]

 

It is worth noting that in the highlighted parts of the above passage Lawler implicitly admits that Hydrogen, for example, has no significant "other" (but many "others"). With that we can now see that Hegel's account of change "repels" even his own logic, and collapses under the weight of its own 'internal contradictions'.

 

A rather ironic, but fitting fate for such a confused 'theory'.

 

Be this as it may, is Hydrogen really that intelligent and/or focussed? Can it "repel" each and every "possible" reaction -- even those on the far side of the universe? [This mighty atom is clearly master of all it cannot survey.] But, apart from sounding profound, what sense can be made of this rather odd claim?

 

Perhaps this:

 

"Within this analysis, the concept of independence and nonindependence as mutually exclusive states applies primarily or most adequately to the surface distinction between the phenomenal states of hydrogen (classification of phenomena) but does not apply, at least with the same ease, to the law of hydrogen's development and its internal structure. In this deeper analysis it is necessary to see 'independence' as a form of interdependence ('nonindependence'). The conception of the categories 'independence' and 'dependence' as mutually exclusive and so not applicable to the same thing -- in the same respect -- is more difficult to defend." [Ibid., p.41.]

 

And yet, the above only works because of the ambiguous way that the words "independence" and "dependence" have been understood. As noted earlier: one minute the "independent" means "isolated", or "free and unconnected", the next it means "not dependent on".

 

Lawler now proceeds to discuss a few technical notions connected with "form" and "essence":

 

"One might argue that Hydrogen in its free state is independent 'in respect to' its actual form and dependent 'in respect to' its essential relations (or its potential). But this analysis only postpones the problem, for it implies that 'form' and 'essence' or 'actuality' and 'potentiality' can be distinguished as 'respects' [sic] of the object -- in a manner at least analogous to the way we can distinguish the two distinct states of Hydrogen.  But 'phenomenal form' cannot be distinguished from 'essence' in the way in which two phenomenal states can be distinguished. The form is the form only through the essence and vice versa -- but the one is not the other. Although 'essence' and 'form' are mutually exclusive categories there is no possibility of adequately separating the phenomenal 'respect' from the essential 'respect' -- so as to permit one to say, unproblematically, that hydrogen in its phenomenal form is independent while in its essential properties it is not independent. Such a distinction of respects superficially applies to the two phenomenal states of hydrogen ('superficially' in the sense that it is necessary to go on from the distinction to understanding the law relating to the phases of hydrogen's transformations). But in understanding the essential nature of hydrogen there can be no comparable distinguishing of 'respects' -- except as an abstract or formal approximation of the dialectical unity of opposites." [Ibid., pp.41-42. Italic emphasis in the original.]

 

What exactly the "unity of opposites" amounts to here is left tantalisingly vague, hence the whole passage is about as clear as London smog.

 

 

Figure Three: Dialectical Clarity, At Last!

 

A Few Loose Threads Left

 

Mercifully, we are nearing the end. Lawler now tries to draw several (formally or phenomenally) disconnected threads together:

 

"Thus the process of chemical reaction demonstrates the inner connectedness as well as relative opposition of hydrogen and chlorine which must be taken into account and explained in a scientific theory of the law of chemical reactions and in an understanding of the particular properties of these elements. The 'finitude' that is suppressed is the particular state of the element as 'free,' as existing (relatively) independently of other elements while being essentially related to them.  Realisation of the reaction constitutes at least some approximation to the 'self-relatedness' which Hegel calls 'genuine infinity'. (This amounts to the claim that the essential nature of elements consists in their reactions and combinations rather than in their relative independence in a free state.)" [Ibid., p.42.]

 

However, all that Lawler has done here is connect these elements (Hydrogen and Chlorine) with talk about potentialities, those that cannot be regarded as physically real, but which can perhaps be regarded as a metaphoric/poetic way of depicting their capacity to react. And, all of this was based on the seemingly random juggling of a few letter "A"s, themselves of a somewhat 'mercurial' disposition (or, indeed, "potential").

 

[As we will see in Essay Twelve Part Four (when it is published), all this dialectical talk about 'independence' and 'relatedness' (relative or not) is no less confused. Discussion will therefore be postponed until then, since it is far from clear what the above comments have got to do with 'dialectical contradictions'.]

 

As far as the laws governing nature are concerned, they can't be seen as decrees written into matter, which all things have to obey (as it seems Lawler's line-of-thought implies). To be sure, Hegel himself could adopt such an animistic way of viewing things, but no materialist can or should -- unless, that is, they subscribe to the non-materialist doctrine that the universe is governed by a cosmic will of some sort. [Again, on this see here and here.]

 

In fact, Lawler admits as much in his final paragraph:

 

"It seems that the main reason why Hegel terms the essential relatedness of one element to another and their lawful connectedness as their 'ideality' is that Hegel regards matter as inherently incapable of such relations and transformations. Matter is conceived of as the embodiment of the principles of abstract understanding. In other words, Hegel accepts the mechanistic or atomistic theory of matter, and so any discovery nonmechanistic, nonatomistic properties of reality is interpreted as evidence of the operation of a nonmaterial force -- the Idea." [Ibid., p.42. Bold added.]

 

And there we have it in a nutshell; Hegel's Idealism prevented him from seeing the material world as it is, sufficient to itself, and capable of doing all the things we have seen Idealists deny for centuries it is capable of doing unaided -- since that would not be 'rational'. [We have seen Lenin take the side of the Idealists against the materialists, too (here and here) -- just as we have seen other dialecticians tell us that matter is just an abstraction, in need of the help of 'abstractions' for it to work!] This alone explains all the desperate word-magic and symbol-juggling aimed at re-enchanting nature in order to make it in effect the development of Idea, since plain-and-simple, common-or-garden, boring old matter isn't good enough on its own.

 

But, how does Lawler square all this with Marxist materialism?

 

"But the fact that Hegel sees in natural laws a manifestation of this Idea makes possible materialistic interpretations which reverse this scheme -- interpreting the 'idea' as the subjective image of the material law. This reinterpretation requires a rejection of the mechanistic form of materialism and the development of a more advanced theory of matter." [Ibid., p.42.]

 

And yet, how can this work if the belief that there are laws in nature is itself based on an Ideal view of reality? We have seen how the quirky 'logic' Hegel employed helped conjure these mythical beings (these "laws") into existence solely from a handful of words and/or concepts; merely reversing our perspective (putting it 'on its feet') in no way changes such bogus moves into valid alternatives. Without the Ideal background Hegel attempted to provide, these (allegedly) materialist 'laws' would have no ontological basis, except perhaps in a more deflationary sense as part of the way we make sense of nature -- a materialist sort of Positivism.5

 

 

What A Dialectical Dog's Dinner!

 

That's it! This article is the best defence/explanation of these obscure 'contradictions' that I have read in over 25 years rummaging through the ruins of this Dialectical Disaster Area!

 

Read it again, dear reader, and scratch your rather 'inadequate', material head.

 

WTF is a 'dialectical contradiction'?

 

Are you any the wiser? If you are, please help me out, for I am, if anything, even more in the dark!

 

Now, in many places throughout this work I have advanced the claim that the slur that dialectical mystics often throw in the faces of us genuine materialists (i.e., that we do not "understand dialectics") also applies in reverse to those very same mystics, since they clearly do not understand this phrase, and have been incapable of explaining a single dialectical concept in over 150 years of not trying very hard. Perhaps readers can now see why I have said this.

 

Finally: reading through the many papers and books (like Lawler's essay), written by Dialectical Marxists who still think we can learn anything from Hegel, one is struck by the similarity between their approach to truth and that adopted by, say, Roman Catholic Philosophers who, nearly a thousand years ago, began the process of trying to render Aristotle's theories consistent with Christianity, then later with science -- who are still endeavouring to do so --, and who even now attempt to defend Papal Infallibility in the face of the countless Pontifical screw-ups we have witnessed over the centuries.

 

The 'logical' contortions DM-fans have to inflict on language and thought is somewhat similar to the linguistic gyrations perfected by the above theologians and casuists. Indeed, the somersaults the former perform merit some sort of International Gymnastics award. Dialectically double-jointed comrades should, in my view, receive Gold every time.

 

Lawler is no exception. In order to make Hegel's jargon 'work', he has to twist language way beyond even the knotted pretzel stage, rather like the aforementioned Roman Catholic Contortionists.

 

 

Figure Four: Compared To Dialectics -- Remarkably Straight And True!

 

Now, I do not expect dialecticians to accept the above criticisms since they are still locked on the ancient idea that human discourse, at some level, contains the key to the inner secrets of 'Being'. Given this view of language, all that such Philosophical Alchemists have to do is find the right formula -- the right key --, and linguistic dirt can be turned into Philosophical Gold, the whole transformation achieved without so much as leaving one's non-dialectical armchair. As Lenin (inadvertently) admitted:

 

"The identity of opposites…is the recognition…of the contradictory, mutually exclusive, opposite tendencies in all phenomena and processes of nature…. The condition for the knowledge of all processes of the world in their 'self-movement', in their spontaneous development, in their real life, is the knowledge of them as a unity of opposites. Development is the 'struggle' of opposites…. [This] alone furnishes the key to the self-movement of everything existing…." [Lenin (1961), pp.357-58. Bold emphasis alone added.]

 

Dialecticians are indeed the philosophical equivalent of those whom Marx called revolutionary alchemists; only, in this case, finding the right verbal formula will enable the aspiring adept to unlock the mysteries of 'Being', allowing these Dialectical Magi to construct an ideal world to suite themselves. Up to now, they have manifestly failed to transform the class structure of the planet, but they've made up for this by withdrawing into an Ideal World where they can juggle with 'reality' to their class-compromised hearts' content, and ignore all criticism along with each and every political screw-up.

 

And this is partly why they cling to this mystical theory for dear life -- and resist all attempts to prize their fingers loose. Indeed, they do this for reasons Feuerbach exposed 160 years ago. That is because this theory 'allows' them to see the world as the opposite of what it really is -- consolation from linguistic contortion.

 

There is no arguing with Hermetic faith such as this. As I have pointed out elsewhere:

 

The founders of this quasi-religion weren't workers; they came from a class that educated their children in the classics and in philosophy. This tradition taught that behind appearances there is a hidden world, accessible to thought alone, which is more real than the material universe we see around us.

This way of seeing things was concocted by ideologues of the ruling-class, who viewed reality this way. They invented this world-view because if you belong to, benefit from or help run a society which is based on gross inequality, oppression and exploitation, you can keep order in several ways.

The first and most obvious way is through violence. This will work for a time, but it is not only fraught with danger, it is costly and it stifles innovation (among other things).

Another way is to persuade the majority (or a significant section of "opinion formers", administrators, bishops, 'intellectuals', editors, teachers, lawyers, philosophers, and the like) that the present order either works for their benefit, is ordained of the 'gods', or is 'natural' and cannot be fought against, reformed or negotiated with.

Hence, a world-view is necessary for the ruling-class to carry on ruling in the same old way. While the content of this ruling ideology may have altered with each change in the mode of production, its form has remained largely the same for thousands of years: Ultimate Truth can be accessed by thought alone, and can therefore be imposed on reality dogmatically.

So, these non-worker founders of our movement, who had been educated as children to believe there was just such a hidden world that governed everything, when they became revolutionaries, looked for principles in that invisible world that told them that change was inevitable and part of the cosmic order. Enter dialectics, courtesy of the dogmatic ideas of that ruling-class mystic, Hegel.

That allowed the founders of this quasi-religion to think of themselves as special, as prophets of the new order, which workers, alas, couldn't quite grasp because of their defective education and reliance on ordinary language, 'abstract understanding', and the 'banalities of commonsense'.

Fortunately, history has predisposed these prophets to ascertain the truth about reality on their behalf, which means they are their 'naturally-ordained' leaders. That in turn means these 'leaders' are the rightful teachers of the 'ignorant masses', who could thus legitimately substitute themselves for the unwashed majority -- in 'their own best interests', you understand.

And that is why 'Materialist Dialectics' is a world-view.

It is also why dialecticians cling to this theory like grim death (and become very emotional (and abusive!) when it is attacked (by yours truly)), since it provides them with a source of consolation that, despite appearances to the contrary, and because this hidden world tells them that Dialectical Marxism will one day be a success, everything is in fact peachy, and nothing in the core theory needs changing -- in spite of the fact that the core theory tells them that everything changes!

 

Hence, this 'theory' is ossified into dogma, and imposed on reality. A rather nice unity of opposites for you to ponder.

And that is how this 'theory' insulates the militant mind from reality.

In which case (to paraphrase Marx): Dialectics is the sigh of the depressed dialectician, the heart of a heartless world. It is the opiate of the party. The abolition of dialectics as the illusory happiness of the party hack is required for their real happiness. The demand to give up the illusion about its condition is the demand to give up a condition which needs illusions.

Unfortunately, these sad characters will need revolutionary workers to rescue them from themselves.

 

Changing the material conditions that give rise to such alienated thought-forms is the only way that Dialectical Day-Dreaming like this will be brought to an end.

 

I stand no chance!

 

Dialectical Mystics are just going to have to rely on the material force of the working class to save them from the consequences of their unwise adoption of this virus of the mind.6

 

 

Neo-Hegelian Attempts To Dispel The Fog

 

I will add several comments on this topic over the next few years.

 

 

Kosok's Kooky 'Logic'

 

Preliminary Points

 

Remember: (1) If you are viewing this with Mozilla Firefox, you might not be able to read all the symbols I have used (I have no idea if other Browsers are similarly affected), and (2) If you are using Internet Explorer 10 (or later), you need to follow the advice given at the top of this page, otherwise many of the links I have inserted won't work properly.

 

Kosok (1966) represents a 'bold' attempt to 'formalise' Hegel's dialectical 'logic' (and one that has been recommended to me by various Marxist dialecticians, perhaps in order to 'put me straight'; here is Chris Arthur's advice to that end), but, before I examine it in detail I need to make three preliminary points:

 

[1] Kosok's article consists of little other than page after page of dogmatic, a priori assertions/theses (most of which are in fact non-sequiturs) -- of the sort that were shown to be both non-sensical and incoherent in Essay Twelve Part One. In which case, I won't be examining his more substantive 'philosophical' ideas in this Essay. Most of my comments would have overlapped, anyway, with what will appear in Essay Twelve Parts Five and Six, when they are published, where I will be subjecting many of Hegel's core ideas to prolonged and destructive criticism.

 

So, in what follows I will largely be concerned with Kosok's claim to have formalised Hegel's 'logic'. Hence, I will be subjecting his work to detailed logical scrutiny (and, as far as I can determine, this is the very first detailed, logical examination it has ever received), which approach some readers might regard as excessively pedantic. Any who do so think are encouraged to read this first, and then maybe think again. Or, perhaps proceed no further!

 

Recall, Kosok claims to have formalised Hegel's 'logic', so it is appropriate to test that claim to the limit. To that end, only a detailed analysis will suffice.

 

Of course, a critique like this doesn't make for easy reading -- certainly no more than the original article by Kosok himself. In fact, anyone who can stomach Kosok's article should find my critique 'a walk in the park' in comparison.

 

Incidentally, in what follows, I have used the on-line version of Kosok's article. Unfortunately, when the latter is compared with the published version, it soon becomes obvious that it contains numerous minor typos, and several more serious transcription errors, all of which I have corrected in the quotations I have used.

 

[2] In order to show how far short even of an undergraduate attempt at formalisation Kosok's rendition falls, it might be useful to remind ourselves what a formalisation actually looks like in genuine logic and/or mathematics.

 

[A far more competent (but no less incomprehensible) attempt to formalise Hegel's Logic can be found in McCumber (1993), pp.123-78. I will examine McCumber's work in a later re-write of this Essay.]

 

The following has been adapted from Hunter (1996), pp.54-62 (but, for an on-line example, see Shapiro (2009)), and represents only the initial stages of a formalisation of the Propositional Calculus. I won't provide a full formalisation since my aim here is merely to show how lamentable Kosok's rather pathetic attempt actually is. Indeed, Kosok's work falls short to such an extent that the only honest way to describe it would be to call it a joke.

 

Any who think that allegation excessively harsh, if not downright impertinent, should read on, where those qualms will soon be laid to rest.

 

[In what follows, I have added one or two comments which wouldn't normally appear in a formalisation. This has been done in order to assist those who might not be familiar with modern logic understand what is going on.]

 

Formal Language L:

 

Symbols of L:

 

1. Propositional variables:

 

a. 'p', 'q', 'r'.

 

2. Connectives of L:

 

a. '¬' -- negation (interpreted below);

b. '®' -- 'if...then'.

 

3. Punctuation for L:

 

a. Left and Right brackets: '(', and ')'.

 

4. Meta-symbols of L:

 

a. 'Γ', 'Δ', 'Ω' -- these stand for any wff (short for "well formed formula" -- that is, formulae that conform to the formalisation rules --, pronounced 'woof') of L.    

 

Formulae (wffs) of L:

 

a. Any propositional symbol is a wff of L.

b. ¬Γ is a wff of L.

c. (Γ® Δ) is a wff of L.

d. Nothing else is a wff of L.

 

Semantics of L:

 

1. An interpretation, I, of L is an assignment to each propositional symbol of L one or other (but not both, nor neither) of the truth-values T (true) or F (false), and an assignment of truth-functional meanings to the connectives of L. [In other formal languages, naturally, these stipulations often vary.]

 

2. For one proposition there are only two (i.e., 21) distinct interpretations:

 

a. p is assigned T, or

b. p is assigned F.

 

For two propositions, p and q, there are four (i.e., 22) possible interpretations:

 

c. p is assigned T and q is assigned T.

d. p is assigned T and q is assigned F.

e. p is assigned F and q is assigned T.

f. p is assigned F and q is assigned F.

 

For three there are eight interpretations (i.e., 23), for four there are sixteen (24), ..., for n propositions there are thus 2n distinct possible interpretations.

 

3. If Γ is true in I then ¬Γ is false in I.

 

[In other words, in L, '¬' is a truth-functional operator mapping a proposition onto its negation. Normally, one would also stipulate that in L, "false" means the same as "not true", and vice versa. In other formal languages, naturally, this, too, could vary.]

 

4. (Γ® Δ) is true in I iff (i.e., if and only if) either Γ is false in I or Δ is true in I.

 

[This might seem somewhat counter-intuitive, but it follows from something we want to rule out: the case where Γ is true but Δ is false. Condition 4, above, achieves this. (Why that is so I won't enter into here; recall, this isn't meant to be a logic lesson!)]

 

The formalisation would normally add more detail, but for present purposes this is as far as I need to go.

 

[For more on formalisation, see, for example, here and here -- or even better, here (this links to a PDF) --  or the rest of Hunter (1996). See also Sider (2010), and Bostock (1997) -- this also links to a PDF.]

 

[It is worth pointing out once more that there are numerous transcription errors in the on-line version of Kosok's article. Clearly, those who posted it on the Internet failed to notice these errors; perhaps they too regarded such careful attention to detail as "pedantry", and skipped the proof-reading phase? But, this is just par for the course with DL-fans.]

 

 

An Elaborate Hegelian Hoax?

 

[3] Lastly, it is highly unusual for the vast bulk of a formalisation to consist of prose (with a few symbols thrown in for good measure) -- in fact, I have never seen a formalisation like Kosok's, and I doubt anyone else has, either.

 

[Recall: much of the prose I added to the formalisation above was to assist the comprehension of those who are unfamiliar with Pure Mathematics or Symbolic Logic; normally, most of it would be omitted.]

 

Indeed, when I first read Kosok's article (back in the 1990s), and I encountered page after page of dense prose, peppered with an idiosyncratic and wildly inconsistent use of 'symbols', my first reaction was one of incredulity. In fact, I had to resist the temptation to conclude this 'formalisation' was a deliberate hoax. I even wondered whether Kosok wasn't trying to see how many Hegel-fans, ignorant of genuine logic, would buy into this convoluted con-trick, as a sort of dialectical version of The Emperor's New Clothes Parable.

 

After all, another mischievous Mathematician/Physicist, Alan Sokal, published a similar hoax only a few years back. [Of course, he owned up to it soon after, otherwise he might never have been found out.]

 

Anyway, Kosok has since apparently disappeared (according to his leading disciple, the 'Marxist' mystic, Peter Wilberg):

 

"The larger-than-life man to whom this essay is dedicated and without whose genius and inspiration it could not possibly have been written, is in all likelihood long dead. I first encountered Michael Kosok in 1975, when he was still professor of physics and mathematics at Fairleigh Dickinson University, New Jersey. For over two decades now he has disappeared from trace, his extraordinary writings on philosophy and science now seemingly consigned to oblivion -- never published save for a few articles in the journal Telos." [Quoted from here.]

 

Otherwise, I would have asked Professor Kosok directly whether or not his 'formalisation' was genuine. In fact, I tried to e-mail him using the address given at his site, but my e-mail was returned "undeliverable". I have been able to ascertain no more details about this maverick 'logician' (although Peter Wilberg's hagiographical site tells us that Kosok's passed away in 2015, and this appears to be a notice of his death).

 

In what follows I will, however, assume that this 'formalisation' wasn't meant as a hoax.

 

To date, I have encountered few attempts by Marxist Dialecticians to make use of or appropriate Kosok's work. Roy Bhaskar (in Bhaskar (1993), pp.30ff) describes Kosok's article as a "path-breaking study". However, Bhaskar has clearly failed to notice the glaring errors and confusions in Kosok's 'formalisation' (described in painful detail in what follows); in which case, one can only assume he didn't read it with due care. Even so, Bhaskar has attempted to construct his own quasi-formalisation (although I don't think he actually used that word to describe his particular approach), in that he has made use of various diagrams and symbols (of dubious import) throughout his impenetrable and largely unreadable book -- a study that fellow mystic, Terry Eagleton, called a "massively important work".6a

 

[I have now added several comments (to Note 6a) concerning Bhaskar's attempt to develop Kosok's "path-breaking study".]

 

Others have certainly referred their readers to this 'formalisation', though; for example, James E Hansen -- Hansen (1977), p.105 (footnote 11). Plainly, Hansen either failed to read this 'formalisation' with any care, or he doesn't know the difference between formalisation and Shinola.

 

Petru Ioan has also referenced Kosok's work (calling it a "generalisation of Hegelian dialectics" -- Ioan (1990), p.141 -- however, mis-spelling Kosok's name as "Korok")), but he failed to notice the egregious errors and confusions readily apparent in Kosok's work (again, exposed below). Could he be yet another DM-fan who failed to read Kosok's work with due care, or at all? In places, Ioan's book reveals that he appears to be a competent logician, but anyone who can reference the dialectical dog's dinner that is Kosok's 'formalisation' only succeeds in raising serious doubts about their competence in this area -- or their academic honesty.  

 

 

One Man's Formalisation Is Another's Rat's Nest

 

With the above in mind, what do we actually find in Kosok's 'formalisation'?

 

To start with, this:

 

"The generating principle, called the principle of Non-Identity, acts as a recursive formula producing a sequence of self-expanding terms. The sequence begins with a singular indeterminate primitive element e standing for any type of entity capable of being reflected upon (i.e. any object, structure, relation, or more generally, any event present to a field of consciousness). The process of reflection, R, is an operation transforming e into e′ -- i.e. (R)e = e′. Reflection of e into e′ will produce three terms for the first reflection or level. Repeating this operation on e′, i.e., (R)e′ or (R)(R)e for a second reflection, will give three times three or a matrix of nine terms called e″. The nine term structure has qualitatively different modes of interrelation present than in the initial three term sequence." [Kosok (1966), p.238. In all the passages I have quoted from this article I have altered the spelling to conform to UK English, modified the quotation marks in line with the conventions adopted at this site, and corrected the many minor typos I discovered in the on-line version (when compared with the published version). I have also altered the prime notation (i.e., e′) to conform to the published version. Unless otherwise stated, all italic emphases are those found in the original.] 

 

Is this meant to be serious? Irony and deliberate hoax aside, how on earth did this joke survive the peer review system for the journal in which it was first published, let alone the peer review system for the book in which it later appeared (always assuming it had one)? I can only think this article was passed by those who knew very little logic -- or those who cared even less about it.

 

Be this as it may, and as we will see, throughout his article Kosok introduced his 'symbols' in a piecemeal manner; these 'symbols' are almost without exception ill-defined (or not defined at all). Even worse, their meaning slides backwards and forwards between several different interpretations -- rather like those we met above, in connection with Lawler and Hegel's use of those chameleonic letter "A"s --, often on the same page, or even in the same paragraph!

 

Kosok added no list of symbols, and no indication what the designation was of those he did use -- i.e., he presented his readers with no formal vocabulary. In addition, he stipulated no axioms, no rules of inference, no punctuation protocols, no way of assigning interpretations to the wffs, no rules for the formation of wffs, no semantics, no model (i.e., no interpretation under which every wff is true), no hint as to what connectives he was using, and no way of determining what even constituted a wff, etc., etc.

 

Hence, this can only be called a "formalisation" by those possessed of an odd sense of humour, or those who have no idea what a formalisation even looks like.

 

Moreover, Kosok introduced considerations into his 'formalisation' that made it look like an unwise return to psychologism -- for example, where he confuses an operation in a formal language with what goes on in someone's head (i.e., what is "present to a field of consciousness" -- whatever that means!):

 

"The process of reflection, R, is an operation transforming e into e′ -- i.e. (R)e = e′." [Ibid.]

 

We are given no idea what this could possibly mean. "Reflection" apparently covers anything from an idea that fleetingly crosses the mind to an extended cogitation on any subject that happens to enter an individual's thoughts, deliberately or accidentally. Nor is there any attempt to standardise this 'process'; in which case, the thoughts of a complete novice seem to be on a par with those of an expert 'reflector'.

 

Moreover, there is no attempt either to avoid all the pitfalls Wittgenstein highlighted  concerning 'private languages' (which, after all, seems to be what Kosok has cobbled together here) --, something brought out, but not solved by Bertell Ollman (in relation to that other obscure 'mental'/'intellectual' process called "abstraction"):

 

"What, then, is distinctive about Marx's abstractions? To begin with, it should be clear that Marx's abstractions do not and cannot diverge completely from the abstractions of other thinkers both then and now. There has to be a lot of overlap. Otherwise, he would have constructed what philosophers call a 'private language,' and any communication between him and the rest of us would be impossible. How close Marx came to fall into this abyss and what can be done to repair some of the damage already done are questions I hope to deal with in a later work...." [Ollman (2003), p.63. Bold emphases added.]

 

As I pointed out in an earlier Essay:

 

Well, it remains to be seen if Professor Ollman can solve a problem that has baffled everyone else for centuries -- that is, those who have even so much as acknowledged it exists!

 

It is to Ollman's considerable credit, however, that he is at least aware of it.

 

In fact, Ollman is the very first dialectician I have read (in well over twenty five years) who is cognizant of this 'difficulty'!

 

[I have devoted Essay Three Parts One and Two, and Essay Thirteen Part Three to a lengthy discussion of this topic; the reader is referred there for further details.]

 

So, it rather looks like Kosok's approach to 'logic' has been compromised in the same way -- except he, unlike Ollman, appears not to have been aware of it. [In fact, it is possible to show that much, if not all of Hegel's work is susceptible in this regard -- as is Ollman's, too.]

 

The implicit psychologism here is further underlined by what Kosok goes on to say about 'reflection':

 

"It is possible to give a non-contradictory account of the process of reflection. Being called the Principle of Non-Identity, it serves to determine and delineate the first universe of discourse out of the originally indeterminate posit called 'e,' and at the same time set up the conditions for the negation and transcendence of the very universe generated. In a sense, the process of reflection transforms a pre-formal indeterminate posit e into a formal determinate universe, such that a meta-formal perspective of the formal universe called e′ appears. Reflection is thus a shift from a pre-formal to post-formal situation, wherein a well-formed universe appears as an intermediate stage. The second reflection then regards this meta-formal e′ as a new pre-formal posit, ready for further determination, producing new relations within an expanded universe of discourse. Reflection is therefore a generating process in which an initially unformed element becomes formed, making reference to the element impossible without reference to the act of reflection. The activity of reflection becomes an integral aspect of the element reflected, and a process of continual reflection amounts to self-reflection -- the initial element embodying reflection as its form." [Kosok (1966), p.239.]

 

So, it seems that only expert 'reflectors' are allowed an input here -- although how one decides who is an expert and who is a charlatan is still up for grabs. Just as it is up for grabs how it would be possible to decide whether or not the (hidden) cogitations of, say, 'reflector' NN were the same as, or were different from those of 'reflector' NM -- although, Kosok's commitment to something he calls non-identity must surely weigh the dice heavily against a positive answer in this regard. Indeed, given his approach to 'reflection', no one could possibly mean the same as anyone else even about the word "same", let alone "word", "logic" or "reflection"!

 

[Of course, this opens Kosok's psychologism to all of Frege's criticisms of this trend in 19th century logic. On that, see Frege (1953, 1977b, 1979b), Dummett (1981a), pp.678-82, (1981b), pp.64-73, and (1991), pp.13-21, 31-32. Having said this, no one should assume that I agree with Frege's Platonism (far from it!) -- on this see Baker and Hacker (1984), pp.28-46 --, or with Dummett's ideas about the 'theory of meaning'. (See also, Coffa (1991), and Shanker (1998), especially Chapter Three.)]

 

Be this as it may, one thing is reasonably clear: all that Kosok has done (in this 'formalisation') is take a few ill-defined symbols (but they can't even be symbols if their mode of signification slides about all over the place) -- or, more accurately, he has taken a handful of inconsistently applied inscriptions --, and thrown page after page of half-digested Hegel-speak at them.

 

This 'formalisation' would give even the term "rat's nest" a bad name!

 

 

Slippery Syntax And Shifty Semantics

 

An early sign that the denotation of Kosok's letter "e"s is, shall we say, somewhat mercurial, is given by the following:

 

"The initial step of reflection R(e) is called the Assertion of e, written (e) or +e, which announces (affirms) something present in the field of consciousness, the parenthesis or plus sign indicating the act of reflection. However, the very fact that (e) or +e is different from e (as, e.g., the positive integer +4 is different from the natural number 4) implies that something other than +e must exist, from which +e is distinguished by being only the positive or assertive form of e, otherwise there would be no point in regarding +e and e distinctly. This 'other-than-positive' is defined as its co-relative contrary e (minus e), or, in opposition to (e), we can call this the logical Negation of e, written (-e) and called 'not e,' the parentheses about both e and -e indicating that a reflection has been taken, producing two terms as a result. [Added in a footnote: The short dash in -e means 'not e,' while the longer dash in ―e means 'minus e' such that +e = (e) and ―e = (-e).] This means that unlike e, -e does not explicitly appear as an immediate pre-reflected given, but only makes its appearance through reflection, appearing as a reflected term (-e) after a reflection on e, producing (e), has implied that something other than e must exist permitting e to appear as a mediated term. Indeed, the notion of negation is regarded as the essence of reflection and mediation (and the act of questioning), since to mediate or reflect is to remove (negate) oneself from a situation of immediacy. The immediacy of -e is implicit, for by definition that which is immediate, and therefore starting our analysis, has been called e." [Ibid., pp.239-40. The on-line version has the wrong 'sign' in front of the first occurrence of "minus e"; I have corrected it. It should be "―e" not "-e".]

 

[When using "e", I will put that letter in bold-type; when quoting/mentioning it, I will use ordinary type, as I did in the first part of this Essay with "A".]

 

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

 

So, e can be asserted, which means that it must be a proposition, indicative sentence or clause, but not:

 

"a singular indeterminate primitive element...standing for any type of entity capable of being reflected upon (i.e. any object, structure, relation, or more generally, any event present to a field of consciousness)." [Ibid., p.238.]

 

Try asserting any of the following (which are items "capable of being reflected upon"): a coffee grinder (an "object"), "...is bigger than..." (a "relation"), or a headache (an "event present to the field of consciousness").

 

Can't do it?

 

Now, there's a big surprise...

 

To be sure, one can assert that a certain item is a coffee grinder, or that an elephant is bigger than a mouse, or even that one has a headache, but these assertions are all expressed by propositions or indicative sentences, not objects, relations or events "present to the field of consciousness". It is not possible to assert an object, relation or "event present to the field of consciousness". In which case, Kosok must mean that e is a proposition or indicative sentence and not an object, relation or "event present to the field of consciousness", after all.

 

This interpretation is supported by what Kosok goes on to say about his morphoholic letter "e"s:

 

"This 'other-than-positive' is defined as its co-relative contrary e (minus e), or, in opposition to (e), we can call this the logical Negation of e, written (-e) and called 'not e,'..." [Ibid., p.240.]

 

If "e" is indeed the "logical negation of e", then e must be a proposition, sentence or clause, as suggested earlier. Of course, Kosok might mean something a little more 'dialectical' by "negation" (and, as it turns out, he does), but in terms of "logical negation" there is no such thing as the logical negation of a coffee grinder, or even a headache.

 

So, it now looks like "minus e" (i.e., "―e") is the assertion of -e. Although from the above passage, it also looks like Kosok intends (-e), but not e -- as we were led to believe -- to be the "logical negation of e":

 

"This 'other-than-positive' is defined as its co-relative contrary e (minus e), or, in opposition to (e), we can call this the logical Negation of e, written (-e) and called 'not e,' the parentheses about both e and -e indicating that a reflection has been taken, producing two terms as a result." [Ibid.] 

 

Unless, that is, we assume (-e) = e. Kosok is far from clear here. For example, he seems to say -- and rather fittingly for a Hegel-fan -- the opposite later on. [But, that's Diabolical Logic for you!]

 

Even so, several other things Kosok says are decidedly odd. As is the case with far too many 'dialectical logicians', and as we will see below, Kosok's sloppy use of 'symbols' -- here in particular in relation to, for example, "+" and "" -- prompts him into confusing them with mathematical operations (or the symbols thereof). [We can see this by the way he calls the "" sign, "minus".] This then leads him into conflating e (and several other letters) with numbers (not to be confused with "E numbers"!).

 

This would mean, of course, that e can't be a proposition, after all!

 

Any who doubt this are invited to try to assert six, or one hundred and forty-two.

 

However, Kosok does say this:

 

"Thus the very act of affirming an immediacy, asserting or announcing a given, or recognizing what is present, is to set up the condition for its negation, since to affirm is to reflect, and allow for the possibility of its negation. Both +e and e, or the assertion of and negation of e, are functions of e, which is to say that the content or reference-base e of assertion and negation is the same, expressed however, in contrary forms. That which is initially given can be referred to positively as that which is present (called 'positive presence') and negatively as that which is lacking (called 'negative presence,' since the given makes itself evident as a lack). The concept of negation viewed dialectically as a type of 'negative presence' is therefore qualitatively different from the standard notion of logical negation. Given a term A, its negation not-A is usually interpreted to be a positive presence of something other than A, '-A,' called, e.g., 'B,' such that A and B are not only distinct but separable 'truth values.' However the form 'other than A' is actually a referral to A since no content different from A has been posited: to simply deny A is not to assert anything else in its place. Not A is indeterminate as to what is asserted positively, referring only to the denial of that which was intended. A genuine negation is a negative presence which cannot without transformation be replaced by an affirming presence. If asked, 'Where are you going?' and you respond: 'I am not going to the theatre,' this is a reference to the theatre in the mode of rejection." [Ibid., pp.240-41. Again, the on-line version has "-e" instead of "―e" in the second sentence. I have followed the original.]

 

Here, it is plain that for Kosok 'dialectical negation' isn't the same as logical negation. Even so, Kosok introduces two new letters, "A" and "B", which he tells us are "terms". But then, we are told that they are also "separable truth values"! And yet truth values aren't terms, they are part of the semantics of a formal system (see my formalisation above). [Unless, of course, Kosok means something different by "truth value". In that case, he clearly prefers to keep his readers in the dark.] So, if these letters are terms, then they can't be truth values -- nor vice versa. Perhaps he means that they are propositions or indicative sentences which can be given an interpretation among the truth-values? Who can say?

 

[I have used Kosok's phrase "truth value" here, not my own preferred "truth-value".]

 

In addition, Kosok tells us that "other than A" is a "referral to A", in which case A and/or "A" must be or must designate an object. If so, A can't be a proposition, or clause. [This might be Kosok's way of telling us that 'truth values' are objects. Again, who can say? (Why a proposition can't be an object was explained in Note Two.)]

 

Even so, Kosok then tells us that to deny A is not to "assert anything else in its place", which can only mean that A is a proposition (or clause), after all! This is confirmed by the following comment:

 

"Not A is indeterminate as to what is asserted positively, referring only to the denial of that which was intended." [Ibid.]

 

Once again, this can only mean that A and B are propositions, indicative sentences or clauses -- not 'terms', or objects! So, not only do Kosok's fickle letter "e"s appear to swap denotations with each change in the wind, these new 'terms', A and B, do likewise.

 

[When using "A" or "B", I will put them in bold-type, too; when quoting/mentioning them, I will use ordinary type. I will do the same for any other letters Kosok introduces.]

 

However, we are then told:

 

"The notions of assertion and negation, mutually implying each other as possibilities, must both appear in a single act. Reflection is a questioning process producing determination by setting an element in opposition with itself: +A is seeing the element 'from within' or 'in-itself' as Hegel would put it, while A is seeing the element 'from without' or 'for-itself.' +A is a given object or system and A is its co-determinate context or space, existing 'for' the object, defining the object negatively." [Ibid., pp.241-42. Once more, the on-line version has "-A" instead of "―A" in the second sentence. I have followed the original, again.]

 

Here, A is an "object", and A is no longer "minus A", but an object's "co-determinate context or space, existing 'for' the object, defining the object negatively" (whatever that means!). So, A is no longer a proposition!

 

Kosok now goes into what can only be described as 'let's confuse-the-reader' hyper-drive:

 

"Thus there is one content (the original e), two forms, and three phases present in the initial act of reflection (R)e: (e); (e) → (-e); (e) (-e) or Assertion of what is (Ae or +e), Assertion implying Negation (Ne or e), and Negation in turn implying Assertion, making both co-relative, such that the negation of e is still a reference to its assertion, something which we shall call the Self-Negation of e (Se or +e). Reflection, in attempting to determine or assert e, produces a self-negation of e, involving a coupling of contraries: the original pre-formal non-positive and non-negative e becomes transformed into a formed self-relation between itself (now appearing as +e) and its other e, which as a whole is written +e, i.e. something which is neither +e nor e as such -- neither 'within' nor 'without,' but their mutual 'boundary' state of mutual implication as possibilities. This now makes Se or +e a meta-formed relation about the co-relativity between +e and e, which cannot consistently be expressed by +e or e themselves, regarding them as separable distinctions. Se or +e thus expresses explicitly that which the original e was only implicitly, namely something neither positive nor negative, but rather both 'in and for-itself' as possibilities. Reflection brings out (expresses) the original ambiguity of the pre-formal element, but can only remain true to this ambiguity by expressing the formed + and aspects on a meta-formal, self-negative level, wherein the original immediacy or e now  appears self-mediated through its co-relative mediation with its negation. (e) is the assertion of immediacy, which, however, because assertion is a reflection, gives us (e) → (-e), which mediates the immediacy, but, since mediation is doublefaced, (e) (-e) expresses the condition that while e is a function of (implies and therefore is mediated by) -e, -e is in turn a function of e, such that e becomes a function of itself through -e: e becomes self-mediated or self-negated. A cyclic triad of assertion, negation and self-negation, or immediacy, mediation and self-mediation, is produced through a single act of reflection: i.e. the so called thesis, antithesis and 'synthesis' of Hegelian dialectic. The movement is directly from a pre-reflected, preformal thesis e, to a reflected, meta-formal synthesis +e, producing a formed or reflected thesis +e and reflected antithesis e along the way. The synthesis term then serves as a new pre-reflected thesis e΄ for higher reflections." [Ibid., pp.242-43. In the on-line version, every occurrence of "―" is misrepresented as "-". I have corrected that systematic error in the above.]

 

[Much of this, in fact all of it, is merely asserted and not proven from any stated premisses by means of explicit rules of inference. Sceptical readers are invited to derive much (any?) of the above from Kosok's non-existent formal vocabulary, unstated premises, missing rules of inference and defective 'formalisation' -- and good luck with that one!]

 

Independently of this, Kosok introduces two new, undefined 'symbols', "" and "". And, as if that weren't enough, he now uses the letter "A" to stand for "assertion"! So, A is no longer a "term"!

 

He also introduces the letters "N" and "S" to stand for "negation" and "self-negation", respectively. It also looks like the negation of e is "e", after all -- although it is unclear whether or not this is 'dialectical' or logical negation. [Perhaps we are meant to guess?]

 

If, however, we interpret "" and "" in the standard way (to mean implication ("if...then"), and biconditional implication ("if and only if"), respectively), then e must be a proposition or indicative sentence, again! But, Kosok then ruins it all by telling us that:

 

"...the original pre-formal non-positive and non-negative e becomes transformed into a formed self-relation between itself (now appearing as +e) and its other e, which as a whole is written +e, i.e. something which is neither +e nor e as such -- neither 'within' nor 'without,' but their mutual 'boundary' state of mutual implication as possibilities. This now makes Se or +e a meta-formed relation about the co-relativity between +e and e, which cannot consistently be expressed by +e or e themselves, regarding them as separable distinctions." [Ibid.]

 

If e and +e can stand in some sort of relation to each other (or to themselves), they must be objects, not propositions or sentences! [Why that is so was established earlier. See also Note 2.] In addition, we are told they also mutually imply one another, so they must be propositions or sentences, once more! And yet, they are also called "possibilities".

 

With the worst will in the world, it isn't possible to make any sense of this.

 

As if to cap it all, Kosok now informs us that:

 

"A cyclic triad of assertion, negation and self-negation, or immediacy, mediation and self-mediation, is produced through a single act of reflection: i.e. the so called thesis, antithesis and 'synthesis' of Hegelian dialectic." [Ibid.]

 

But, this triad has nothing to do with 'the Hegelian dialectic', which perhaps tells us all we need to know about Kosok's knowledge of Hegel and his own 'careful attention to detail'.

 

The interpretation of "" and "" along standard lines suggested above seems to be substantiated by the following comments:

 

"The mutual implication which results (e) (-e) is called the principle of Non-Identity, which is not necessarily contradictory since the form 'p q' has two possible modes: either p and q are both (positively) present in one and the same notion, or p and q are both lacking (negatively present) in a single notion. If (e) and (-e) are both positively present, then this would violate the law of contradiction. However, if (e) and (-e) are mutually in a state of negative presence (regarding +e as the boundary state between +e and e which is neither as such) -- i.e. if it is the case that 'not(e) and not(-e)' or '-(e) and -(-e)' exists, then the law of contradiction is not violated, but the law of the excluded middle is. Put in this form, the principle of Non-Identity says that it is impossible to have both the law of contradiction and the law of the excluded middle, or it is impossible to be both consistent and complete at the same time since (as Quine points out) the notion of consistency demands that an element and its negation cannot both be present, while the notion of completeness demands that an element and its negation cannot both be absent. The law of Non-Identity hence states that it is not possible to regard (e) and (-e) as strict contradictories as initially intended, due to the coupling relation discovered between (e) and (-e) producing a term, which, while having a (negative) reference to (e) and (-e), is nevertheless different from either: they are either contraries or sub-contraries. The law of Non-Identity couples an element and its negation together in such a way that it is not possible for a completely determined system to appear -- i.e. a system in which reference to either an element or its negation, but not both, can be made: ambiguity in some form must be present because no final distinction into separable compartments such as A and -A, 'true' and 'false,' or present and absent, can be achieved." [Ibid., pp.243-44. Once again, the on-line version has misrepresented every occurrence of "―" as "-". The occurrences of "-" in the above now agree with the published version.]

 

Despite what Kosok says (or, rather, despite what he just asserts with no proof), the LOI (or, indeed, its Kosokean alter ego, "the principle of Non-Identity") has nothing to do with the "mutual implication" of propositions or indicative sentences. [That was also demonstrated earlier.] Even so, Kosok now introduces two new inscriptions, "p" and "q", but with no indication what they designate. We are left to assume they are propositional variables, which fact, if this were a genuine formalisation, would have been made explicit from the start.

 

[It is also worth noting that the "principle of Non-Identity' has been promoted by Kosok so that it has now become the far more exalted 'law of Non-Identity' -- again with no proof. (This shambles would fail even the introductory class to Logic 101!)]

 

Be this as it may, exactly what "positively present" has got to do with the LOC is a mystery that Kosok evidently preferred to keep to himself. As we have come to expect, he doesn't even attempt to derive this 'result' from any declared premisses by stated rules of inference. In which case, like most of the other 'results' we have so far encountered, this latest claim in fact amounts to a stipulation, which, unfortunately, fixes the meaning of the terms 'defined'. But, since, Kosok is using what look like familiar words (such as "contradiction", "identity", and "implication") in a totally new way, and despite what he thinks he is doing, he can't mean by these terms the same as other logicians -- and, while we are at it, since Hegel does none of these things, either, he can't even mean the same as Hegel!

 

That is, of course, why competent logicians construct their formalisations with care and attention to detail -- even at the risk of being accused of 'pedantry'.

 

For example, Kosok tells us the following:

 

"...if it is the case that 'not(e) and not(-e)' or '-(e) and -(-e)' exists, then the law of contradiction is not violated, but the law of the excluded middle is. Put in this form, the principle of Non-Identity says that it is impossible to have both the law of contradiction and the law of the excluded middle..." [Ibid.]

 

As is well known, the LEM and the LOC are inter-derivable (by De Morgan's Laws -- that is, if we also allow ¬¬p p):

 

(1) ¬(p & ¬p) ¬p v ¬¬p

 

(2) ¬p v ¬¬p ¬p v p

 

(3) Ergo: ¬(p & ¬p) p v ¬p

 

[I explained what these symbols mean earlier on in this Essay.]

 

If so, whatever is (logically) true of the LOC is (logically) true of the LEM, too. This can only mean that Kosok intends something different by one or both of these 'laws'.

 

It is also worth noting that Kosok speaks of consistency and completeness here, but he makes no attempt anywhere in his article to show that his 'formalisation' is either complete or consistent.

 

[But it can't be, can it? It is full of contradictions! Of course, a consistent dialectician would lose his/her licence to confuse.]

 

However, in relation to the letter "A" used in the quoted passage above, Kosok tells us the following:

 

"...ambiguity in some form must be present because no final distinction into separable compartments such as A and -A, 'true' and 'false,' or present and absent, can be achieved." [Ibid.]

 

This confirms the suspicions aired above that A isn't in fact a proposition, it is a "truth value". But, what is the "-" sign doing in front of a truth-value! If this 'symbol' -- i.e., "-" -- is a truth-functional operator (as it seems it might be), then it can only attach to propositions, sentences, or clauses, but not the (assumed) syntactic apparatus of this (supposed) 'formal system'. [Kosok might in fact be using it a term modifier. Again, who can say? (On that, see here.)]

 

 

Plumbing New Depths

 

Kosok now adds this comment:

 

"The expression -(e) is not the same as (-e), nor is -(-e) the same as (e): if either or both were the case, a contradiction would result in the form '-(e) and -(-e).' Regarding (e) and (-e) as contraries we can then say that (e) -(-e) or 'the presence of (e) implies the lack or negative presence of (-e)' and (-e) -(e) or 'the presence of (-e) implies the lack or negative presence of (e).' It cannot then be the case that the converse is true, namely -(-e) (e) and -(e) (-e). Since -(e) is distinct from (-e), dialectic logic cannot dispense with parentheses in the formulation of negation operations." [ibid., p.244.]

 

But, we already know the following:

 

(α) (e) (-e) (from here).

 

(β) (e) -(-e) (from here).

 

(γ) (-e) -(e) (from here).

 

In which case, it is relatively easy to obtain these:

 

(1) (e)        Assumption

 

(2) (-e)       From (α) and (1)

 

(3) (e)        Assumption

 

(4) -(-e)     From (β) and (3)

 

(5) (-e)      Line (2) repeated

 

(6) -(e)      From (γ) and (5)

 

Ergo:

 

(7) -(-e) & -(e)     From (4) and (6)

 

So, from (e) it is possible to derive a 'Kosokean contradiction'. In which case, Kosok's own half-baked, totally garbled 'syntax' and (assumed) 'rules of inference' lead to the very thing he says we can't have, a contradiction:

 

"The expression -(e) is not the same as (-e), nor is -(-e) the same as (e): if either or both were the case, a contradiction would result in the form '-(e) and -(-e).'" [Ibid.]

 

Again, this is just one more reason why genuine logicians are careful when setting up a formalisation.

 

However, the plot thickens:

 

"Analyzing the coupling relation +e in this way indicates that we have already begun a reflection on our initial reflection (R)e. For regarding the meta-formal relation +e as e΄, a new pre-formal posit, (R)e΄ produces two new expressions, (e΄) and (-e΄). But since e΄ already represents the inseparable relation between (e) and (-e), the new reflection (R)e΄ generates four terms: (e΄) involves a relation between ((e)) and ((-e)) and (-e΄) a relation between (-(e)) and (-(-e)). It should be noted that the first parenthesis about e was an indication that e co-exists with its negation -e, each term therefore appearing with a parenthesis, i.e. (e) and (-e), since each co-exists with the other. Similarly two parentheses about e, i.e. ((e)), indicates that not only do (e) and (-e) co-exist, but their negations -(e) and -(-e) exist, all four of which co-exist, producing the four terms ((e)), ((-e)), (-(e)) and (-(-e)). Thus a second reflection on e gives us the four expressions (e), (-e), -(e) and -(-e) originally implicit in the self-negation relation (e) (-e) except that now a second parenthesis appears indicating a completed second order reflection. A self-negation thus represents a transition state from one level of reflection to another. For example, the formed (e) and (-e) elements of the first reflection produced a universe of discourse which included a non-determinate relation (e) (-e) within it, which, however, could only consistently be expressed on a second level, where not only the (e) and (-e) terms appear (now as ((e)) and ((-e))) but also their negations (-(e)) and (-(-e)) implicit in (e) (-e)." [Ibid., pp.245-46. Once again, I have corrected the on-line misconstrual of "―" with "-".]

 

In relation to this, I can only repeat what I alleged earlier:

 

Much of this, in fact all of it, is merely asserted and not proven from any stated premisses by means of explicit rules of inference. Sceptical readers are invited to derive much (any?) of the above from Kosok's non-existent vocabulary, unstated premises, missing rules of inference and defective 'formalisation' -- and good luck with that one!

 

Except we now seem to have several new rules (introduced out of thin air, and just when they were needed -- this is surely logic-on-the-hoof!) for the manipulation and iteration of parentheses, which rules we have also had to guess, since Kosok nowhere tells us what they are (that is, other than in his attempt to distinguish them from the parentheses found in FL).

 

Moreover, all this talk of relations once again shows that these letter "e"s (bracketed or not) can't be propositions, indicative sentences or clauses, but objects of some sort. In which case, and once more, the implication and biconditional 'inscriptions' (which is all we can call them) Kosok uses can't stand for implication or equivalence, as they do in FL, but for 'implication' and 'equivalence', expressions whose meanings have yet to be explained.

 

Readers are free to make whatever sense they can from the next few paragraphs of Kosok's article -- which, by the way, introduce yet another letter, "X", which is similarly left undefined (I won't quote them all):

 

"On a second level, for example, ((-e)) can be called the second level assertion of an original first level negation, while (-(e)) in turn would be the second level negation of a first level assertion. The former, could, for example, be interpreted to mean that a certain X 'is not moral' in the sense that X (is (not-moral)) while the latter might be interpreted to mean that the X which is not moral implies that X (is not (moral)). Hence the expression 'X is not moral' can appear as an assertion or negation: i.e. we can say that 'X is not-moral' (which could mean 'X is immoral,' equating immoral with not-moral) or 'X is not moral,' and it becomes meaningful to distinguish these otherwise obscure alternatives, for to state that X is not moral does not make a commitment: X could be neither moral nor not-moral (immoral) -- being rather a-moral or in doubt as to the resolution of a certain issue." [Ibid., p.246.]

 

Even though some of the above comments represent valid observations concerning the difference between predicate and predicate term negation (on that, see here) -- something Lawler, for example, ignored (but Hegel did not) -- it is worth pointing out that "X 'is not moral'" is not at all the same as "X is not moral". The second says something about whoever "X" designates, whereas the first simply attaches a quoted verb phrase to a letter/name variable, and, as such, says nothing! [Compare it to this: "Hegel 'is not competent'." (Of course, this might be to highlight what someone has said about Hegel and/or X; if so, who?)]

 

Earlier, Kosok informed us that:

 

"The expression -(e) is not the same as (-e), nor is -(-e) the same as (e): if either or both were the case, a contradiction would result in the form '-(e) and -(-e).'" [Ibid., p.244.]

 

But, a page or so later we are told the following:

 

"...as for example, the initial coupling of (e) (-e) gave rise, relative to the first level, to the indeterminate expression '-(e) and -(-e)'...." [Ibid., p.247.]

 

One minute "-(e) and -(-e)" is a contradiction, the next it is "indeterminate". But, if it is indeed "indeterminate", then it would surely be impossible to decide whether or not it is a contradiction. On the other hand, if it is a contradiction, it can't be "indeterminate". Unless, of course, Kosok now means something different by "indeterminate" and/or "contradiction". Who can say? Kosok certainly doesn't.

 

[Then again, this is a 'dialectical formalisation', so it would be unwise to expect too much in the way of clarity.]

 

Kosok's problems do not stop there, either:

 

"Everything indeterminate and immediate (such as e, e΄, e˝) is unstable, becoming negated and mediated by its own opposition, only to yield a higher mode of immediacy, having negatively present the previous modes of opposition it has negated. Only through a process of continual reflection are all oppositions and contradictions negatable, but this process cannot be completed at any single stage for new indeterminacies always appear. The e΄ as (e) (-e) would be a complete resolution, but expressed as merely the positive terms '(e) and (-e)' e΄ is a contradiction. To cancel the contradiction demands the negation of the co-relative terms, giving '-(e) and -(-e),' but now, while consistent, the expression e΄ is incomplete. For now a new level has been started, namely (-e΄) in opposition to (e΄), requiring a new resolution e˝ = (e΄) (-e΄) which repeats the above condition. The movement of reflection is therefore a continual movement of self-cancelling self-contradictions. Reflection is an infinite movement of self-realization that can never resolve itself in the form of a completed product: the whole as a process is incomplete; only the process as a whole or an infinite totality and not a product is complete. In this infinite process, no particular term remains as a non-negative term, each expression appearing only as a transitory step in a continual process of negation. Arresting the process at any point will result in a finite sub-set of opposites, the resultant term of which can only consistently express its component parts as negatively present due to the coupling of all contraries." [Ibid., pp.248-49.]

 

Apart from the fact that the above is as clear as non-dialectical mud, this can't be correct:

 

"For now a new level has been started, namely (-e΄) in opposition to (e΄), requiring a new resolution e˝ = (e΄) (-e΄) which repeats the above condition." [Ibid.]

 

If "=" is meant to be the sign for identity, flanked by singular terms (Proper Names or Definite Descriptions), then there is no way that it can also be flanked by propositions, sentences or clauses. This can only mean that e˝, (e΄) and (-e΄) aren't propositions, sentences or clauses, but are the names of objects (or they are the objects themselves!). But, if that is the case, the 'biconditional sign' can't be a biconditional sign, and as such remains undefined.

 

[Any who doubt this should try making sense of "Socrates if and only if Socrates", or "The 43rd president of the United States if and only if The 43rd president of the United States"!]

 

On the other hand, if e˝, (e΄) and (-e΄) are propositions, sentences or clauses, after all, then the 'sign for identity' can't be a sign for identity!

 

[That was established earlier on in this Essay.]

 

 

Time -- Not On Kosok's Side

 

Kosok now introduces into his 'argument' what, in effect, amounts to a Trojan Horse, in the shape of a reference to time and memory:

 

"What makes the above sequence of coupled contraries possible without explicit contradiction is the notion of negative-referral: i.e. realizing that an expression of the form '-(e)' is a referral to the lack of (e). The notion of negative presence hence involves the presence of a memory process in which something is capable of being referred to in its negated state as a negative-presence. Indeed, the past is referred to through our memory process as that which once was and hence is not, but yet is capable of being referred to qua past. This must not be confused with the act of producing a memory, appearing in 'the present': the content of the memory, or the memory itself is, however, a negative referral to a previously but now non-existing state. Hence dialectic logic is a type of 'temporal' logic involving a memory system in which the negation of an element preserves the negated element as that from which the negation appeared. For this reason, not (notA) cannot be the same as A since not (notA) while negating the negation of A nevertheless has preserved within the parenthesis the fact that A was negated in the activity of a double negation. Thus negations are 'non-conservative,' since an attempted return or repetition from the initial A to notA and back to the initial A by means of a double negation retains within its representing structure the activity of movement that has generated the A which appears as a result of negation: one cannot return unmodified to the original state. In this way negated elements are preserved within the parentheses as reference points for all future activity." [Ibid., pp.249-50.]

 

Before we examine the substantive, if not suicidal implications of the introduction of temporal considerations here, it is worth noting that these inchoate "A"s have turned up again. The only way to make sense of them in this novel incarnation is to view them as meta-logical symbols that allow Kosok to talk about his letter "e"s. [But, and once again, we are left to guess.]

 

Be this as it may, and as we are about to find out, for Hegel-fans the introduction of memory and temporal considerations is about as wise as quaffing orange juice laced with Potassium Cyanide in order to quench a thirst.

 

That is because anyone who casts doubt on the LOI (or who extols the 'Law of Non-Identity') has no way of knowing that any of the words they use (such as: "identity", "contradiction", "reflection", "time", "irreversibility", "memory", "word", "same", "different", etc.), or the 'concepts' to which they supposedly 'refer', are the same, or mean the same, from moment to moment. In fact, given the Hegelian commitment to the universal Heraclitean Flux, they can't be the same.

 

Now, the only way that Hegel-fans can escape from this fatal implication of their 'theory' is to appeal to the 'relative stability' of words and/or concepts. But, that can't work, either, since, given this 'theory', Hegel-fans have no way of knowing whether or not the words "relative" and "stability" mean the same from moment to moment! The relative stability of words/concepts can't even be assumed for the purposes of the argument, since there is no way of knowing from moment to moment that "assumed" means the same, let alone "for the purposes of the argument". Or, for that matter, that any of the above words mean the same to different 'reflectors' at the same time, or from moment to moment. [This argument is developed more fully in Essay Six.]

 

[This is, of course, just another (but less well appreciated) consequence of the Private Language Argument we met earlier.]

 

And, the same problem will afflict any attempt to respond to this fatal objection that (1) Uses words, and (2) Is advanced by anyone who accepts the Heraclitean Flux and/or the 'Law of Non-Identity'.

 

So, far from DL being a "temporal logic", as Kosok fondly imagined, it more closely resembles an intellectual suicide note.

 

 

Psychotic Semantics

 

Kosok now proceeds to argue as follows:

 

"It is important to recognize that the indeterminate nature of negation (i.e. notA is a referral to the absence of A and is indeterminate as to what is present) has as its intuitional foundation the notion of time. Since we are considering the process of reflection to be an asymmetric process appearing through time (and indeed, as we shall see, defining the very nature of time) this implies that the various elements to be generated cannot at any stage all be present. Hence we are not dealing with an already formed and determined universe of discourse, but with one that is in the process of being formed, and therefore the system is intrinsically incomplete and must exhibit this incompleteness through the indeterminacy of its variables. Only within a completed system (and hence one that is essentially finite in description) is it possible to state that the negation of a given element x is all that which is 'left over,' namely an un-ambiguous 'not-x' such that not-notx is in turn x! Since we are dealing with a continually expanding universe of discourse, not-x is an indeterminate reference to what is present, having only a determinate reference to that which has been excluded. Once a negation has been determined and de-limited within a given frame of reference (as for example -e appearing as (-e)) [this second bracket has been correctly added in the on-line version -- RL], and thus binding or coupling -e in relation to what is excluded, namely e, giving (e) (-e), this then implies that the entire universe of discourse (now called e΄) can be negated, producing higher order negations that initially are likewise indeterminate (i.e. giving us -e΄ or -(e) and -(-e). It thus important to distinguish between the genuine indeterminate negation, opening a system up to elements beyond those already formed, and a determined negation expressing a previous act of negation, and which co-exists with and is thus bound to its co-relative assertion within an already formulated universe. Thus –(A) is open and (–A) is closed: the former states that an x does not have a property A, while the latter states that an x has a property notA. In sequence, the negation of an element A as notA gives the indeterminate form -A, but recognizing that reflection yields notA determines the negation as (-A), permitting not (-A) or -(-A) to appear and its determination not(-A) or (-(-A)) etc. The genuine indeterminate negation produces levels of negations (and co-relative levels of assertions such as (A), ((A)), ((-A)) etc.), and ignoring this distinguishing nature of dialectic negation reduces negative presence to positive presence, and 'spatializes' time: non-dialectic logic is a-temporal, corresponding to a view of the universe as essentially determined and given 'in space,' and in need of description." [Ibid., pp.251-52. Alas, there were more typos in the on-line version of this paragraph than there were in the rest of the article to this point!]

 

Earlier, I questioned whether these "A"s were truth-values (as Kosok seemed to think they were), and pointed out that they were in fact propositional variables. But, they now morph into properties!

 

"Thus –(A) is open and (–A) is closed: the former states that an x does not have a property A, while the latter states that an x has a property notA." [Ibid.]

 

[So, they can't be meta-logical symbols, after all! And, what exactly is the "property notA?" While a leaf might be green, and thus possess the property 'greenness', or of 'being green', but if the leaf in question isn't red, what property of 'not-redness' does it have? Do you, dear reader, have the property of 'not being able to eat the Moon'?]

 

But, there is more, and worse, to come:

 

"In sequence, the negation of an element A as notA gives the indeterminate form -A, but recognizing that reflection yields notA determines the negation as (-A), permitting not (-A) or -(-A) to appear and its determination not(-A) or (-(-A)) etc." [Ibid.]

 

In the above, A can't be a property -- since it can take the negative particle (when was the last time you saw the word "not" glued to the property (not the word for this property, but the actual property itself of) redness?); so A must be a property token (possibly a predicable?).

 

But, what is this new 'symbol' "x"? Is it the same as the "X" from earlier? Well, it seems these "x"s are either buried inside these chameleonic letter "A"s, or A is predicable of them:

 

"Thus –(A) is open and (–A) is closed: the former states that an x does not have a property A, while the latter states that an x has a property notA." [Ibid.]

 

In fact, the above suggests those "x"s are both inside these "A"s and not inside them! If, according to Kosok, -(A) states that x does not have the property A, then x must both be contained in the proposition -(A) and not contained in it -- since we were told that A is a property, not a proposition!

 

[Perhaps the reader can now see what I meant earlier when I called this 'formalisation' a "joke".]

 

And yet, these mercurial "A"s now turn into propositions again! This latest hermeneutic twist is confirmed by the following passage:

 

"The genuine indeterminate negation produces levels of negations (and co-relative levels of assertions such as (A), ((A)), ((-A)) etc.)...." [Ibid.]

 

But, if (A) is an assertion, it (or A) must be a speech act, or it must stand for one. One presumes that Kosok meant to say "when these are asserted". Either way, this implies that these "A"s must be propositional or sentential variables, not properties, or property tokens!

 

[Try asserting "hardness" simpliciter, for example. To be sure, it is possible to assert that diamonds are hard, but not hardness on its own. One can assert hardness of diamonds, too, but Kosok doesn't say that these "A"s are asserted of anything. So, they must stand for propositions, sentences or clauses, as already noted.]

 

Returning to those pesky "x"s, we are now told the following:

 

"...(and hence one that is essentially finite in description) is it possible to state that the negation of a given element x is all that which is 'left over,' namely an un-ambiguous 'not-x' such that not-notx is in turn x!" [Ibid.]

 

So, these letter "x"s are "elements"; but they can also be negated, so they must in fact be phrases, clauses, sentences, or propositions, or they must stand for them!

 

 And yet, earlier they seemed to be singular term variables:

 

"Thus –(A) is open and (–A) is closed: the former states that an x does not have a property A, while the latter states that an x has a property notA." [Ibid.]

 

Here, Kosok tells us that an x has a property A -- or, rather, notA. [Compare that with "Hegel has a headache" -- probably induced by reading Kosok! -- or, rather, "Kosok hasn't a clue".]

 

And, while we are at it, what is the significance of gluing a "not" to a letter -- as in "notx", or "notA"? Is it the same as "not x", or "not A" (which format Kosok used in the first part of his article), or different? Again, we are left to guess.

 

I won't pass comment on the egregious non-sequiturs that litter the above paragraph (indeed, the rest of the article), since it is possible that they might not be non-sequiturs, and actually follow from certain premisses and/or rules of inference -- which we'd be able to decide for ourselves had Kosok bothered to provide us with a genuine formalisation as opposed to this running joke.

 

The equivocations continue:

 

"The synthesis or self-negation of a term, resolving itself into a negative unity of opposites, thus illustrates that the definition of dialectic opposites are 'positive contraries which become negative subcontraries upon their mutual implication in a non-identity relation.' Thus (e) and (-e) are positive contraries meaning that they cannot both appear together in any one relation. However the very act of writing the denial of inconsistency or contrariness '-(e) and -(-e)' allows us to consider the negative presence of (e) and (-e), wherein they now appear as negative sub-contraries. This means that as negative relations, they cannot both be absent in any one relation. Thus, the first term (e) implies -(-e) or the negative referral to its opposite (-e), and the second term (-e) implies ‑(e) or a negative referral to its contrary (e), while the synthesis term (e) (-e) is a negative referral to both, i.e. it is '-(e) and -(-e).' Being negative sub-contraries is the other side of the coin of being positive contraries, and in this way we guarantee a condition of negative completeness: there will always be a negative reference to either (e), (-e) or both. Hence the dialectic of a synthesis term lies in the fact that it is both terms (negatively) yet neither (positively) at the same time, spelling out the essence of dialectic opposites: to be inseparable yet distinct. We can now construct a table of opposition, showing how dialectic opposites complete an otherwise incomplete structure. It also illustrates that dialectic opposites, like contradictories, are a combination of contraries and sub-contraries but in a different way. Let X stand for impossible, and / for possible...." [Ibid., pp.254-55.]

 

Here, the "X" from earlier has now morphed into the modal operator "impossible"! And, these "e"s have now become propositions, sentences or clauses once more.

 

Except, the dialectical parade has been rained on once again, because of this comment:

 

"Thus (e) and (-e) are positive contraries meaning that they cannot both appear together in any one relation." [Ibid.]

 

If these letter "e"s, or what they stand for, can enter into relations with one another, they must have reverted back to being objects (or the names thereof), not propositions, sentences or clauses, as before. That suspicion is confirmed by the following:

 

"Regarding the dialectic process intuitively, reflection takes an immediately given entity called e, and 'places' this entity e in context with its other called not e or o, implicitly present within itself as the entity's potentiality for being questioned or reflected (i.e. negated as an immediacy), such that the result is now neither e nor o as such but the transcending and unifying movement or relation eo. In this relationship of context, e itself becomes transformed and determined as (e) and not e or o likewise becomes determined as (o), while the relationship eo is the co-relativity and hence transcendence of these individual determinations. The basic structure of reflection can now be intuited as a movement from a singular indeterminate term e, to a singular meta-determined relationship eo, the process (R)e = (e o: eo) being called e΄, indicating that reflection has been a self-determining process of e. The negating o term represents the expansion brought about by the explicating reflection process, and is not something alien to e. To reflect on something is to view that element and not some other element from a plane of perspective and hence a reflection is a double negation whereby the original immediate posit disappears and reappears in context with the implicit negation inherent in the process of reflection, i.e. with the questioning of the given. If we did not have a temporal logic, a reflection on e would simply be e itself. But a temporal logic regards reflection as an activity in which the very questioning of an initial posit changes the nature of the posit present. Thus we have a conceptual counterpart to the indeterminacy principle in physics, which states that the very activity of a subject measuring an object modifies the object (and also subject) involved. For example, reflection on or thinking about a conceptual object changes the way in which the object appears to the field of consciousness, and reflection or thought about an emotional state itself transforms that state from one of bare immediacy to reflective mediation, bringing to bear implicit associated feelings. Reflection on a perceptual object will alter the frame of reference with which the object is viewed and hence will alter the relevant information that the subject takes as essential for the perceived object, since perception involves not only seeing, but also the operation of looking-for, i.e. discovering 'in' that object an example of some conceptualized relation forming part of the evaluative perspective negatively present in the field of viewing consciousness. Experiments indicate that an altered perceptual mode even transforms what is seen." [Ibid., pp.255-57.]

 

These letter "e"s have now returned to base, and are "entities" again (as they were at the start), which can stand in relation to other "entities". Alas, Kosok now introduces a new 'symbol', "o", and he does so in the piecemeal manner we have come to expect. These lower case letters are gregarious, too, and can appear together, holding hands, for example, in "eo". What the significance is of this touching moment is somewhat unclear, and (as if to be rigorously consistent) Kosok failed to tell us.

 

[This is where you at home can join in -- and simply guess.]

 

It is also worth noting that the word "not" has retreated somewhat and is no longer glued to a letter -- before it was "note" now it is "not e". Maybe Kosok realised that "note" would be misunderstood! Even so, how can a word like "not" modify an "entity"? We are once more left in the dark. [Can "not" really modify the Moon (not the word, but the planet)?]

 

However, this passage is rather puzzling:

 

"The basic structure of reflection can now be intuited as a movement from a singular indeterminate term e, to a singular meta-determined relationship eo, the process (R)e = (e o: eo) being called e΄, indicating that reflection has been a self-determining process of e." [Ibid.]

 

As I pointed out earlier (here modified slightly):

 

If "=" is meant to be the sign for identity, to be flanked by singular terms (Proper Names or Definite Descriptions) then there is no way that it can also be flanked by propositions, sentences or clauses. This can only mean that e and o aren't propositions, sentences or clauses, but are the names of objects (or they are the objects themselves!). But, if that is the case, the 'conditional sign' can't be a conditional sign, and as such remains undefined.

 

On the other hand, if e and o are propositions, sentences or clauses, after all, then the 'sign for identity' can't be a sign for identity!

 

And, while we are at it, what is the logical significance of this inscription ":" (as it features in "(R)e = (e o: eo)"? We aren't told whether it is a punctuation mark or some other logical symbol, in this non-pedantic 'dialectical formalisation'.

 

Once more, the reader is left to guess.

 

 

Sesame Street 'Logic'

 

In Essay Seven Part One, I called the amateurish evidential display (apparent in the writings of DM-fans when they make some attempt to substantiate the hyper-bold claims they advance on behalf of their 'theory'), "Mickey Mouse Science". In view of the sub-amateurish attempt made by Kosok to 'formalise' Hegel's 'logic' we might want to call this a paradigm example of "Sesame Street Logic".

 

Kosok continues, further undermining his credibility, in the following convincing manner:

 

"The principle of Non-Identity holds that entities appear as events within a field of consciousness and are basically neither determined nor not-determined, but rather in a process of being-determined: e.g. e is being determined to be e΄. This implies that the problem of Identity or defining 'what is' must include the negation of reflection as an integral aspect: what is defined cannot be severed from the act of definition. In a non-temporal structure, the principle of Identity would hold: once something is given, e.g. an object A, reference can be made to the same A despite modifications of context. Thus it would be possible to write 'A is A' or 'A A.' However, to say that 'A is A' is to give an answer to an implied question, namely 'A is ?' since the statement 'A is A' is a reflection on the immediately given A and in effect becomes 'A is (A).' Reflection, reveals A co-existing with -A, such that (A) -(-A): 'A is A' means that A is A and not something else. Recognition of immediacy or a reference to it, transforms it into mediation. Within a temporal context, the very fact that A reappears (i.e. appears twice in 'A is A') means that the unquestioned immediacy of an original A has been modified by the questioning process: it appears as something mediated (i.e. it appears a second time, now in relation to -A) and not immediate (appearing only a first time). The dialectic of something appearing a second time is therefore based upon the dialectic of the notion 'to reappear.' For something to reappear means on one level that it indeed does appear again, but in that it reappears, means that the mode of appearance transforms the object present and appearing into something mediated and not immediate: all repetition is therefore transformation since a repeated state has negatively present in its memory structure the fact that it has already happened in the past. The law of Identity is not false: it is simply empty since 'A is A' is not definable within a temporal context." [Ibid., pp.257-58.]

 

So, these eternally plastic "A"s have evolved once more; they are no longer property tokens, or propositional letters -- nor do they stand for "assertion" --, they have become "objects"! Except, they can't be objects since the following is also true of them:

 

"In a non-temporal structure, the principle of Identity would hold: once something is given, e.g. an object A, reference can be made to the same A despite modifications of context. Thus it would be possible to write 'A is A' or 'A A.' However, to say that 'A is A' is to give an answer to an implied question, namely 'A is ?' since the statement 'A is A' is a reflection on the immediately given A and in effect becomes 'A is (A).' Reflection, reveals A co-existing with -A, such that (A) -(-A): 'A is A' means that A is A and not something else." [Ibid.]

 

If it is indeed the case that 'A A', then A can't be an object, but must be a proposition, indicative sentence or clause. [Any who doubt this are invited once more to make sense of the following 'sentence': "Mount Everest if and only if Mount Everest".] Either that or "" can't be a biconditional sign. But, if not, what is it? [Yes, you guessed it! We are supposed to guess!]

 

Somewhat similar questions can be asked about the following:

 

"Reflection, reveals A co-existing with -A, such that (A) -(-A): 'A is A' means that A is A and not something else." [Ibid.]

 

However, when we try to take note of the given meaning of these brackets (they stand for assertion -- or so we were told near the beginning of Kosok's article -- pp.239-40), we obtain some rather bizarre 'sentences' from "(A) -(-A)" --, for example: "If asserted Mount Everest then not asserted (not Mount Everest)" (interpreting A as a singular term variable), a string of words that Hegel fans are invited to try to make sense of.

 

[The brackets I have used in this 'translation' are ordinary, non-logical brackets. The reader should assume the same is the case in all subsequent attempts at 'translation'.]

 

On the other hand, if A is a predicate expression, then "A = A" (or "A is A") is no less nonsensical. What, for instance does this mean: "...is red is identical to ...is red"?

 

Alternatively, if A is a propositional or sentential variable, that would transform propositions, indicative sentences and clauses into objects, which, of course, say nothing -- yielding, for instance, "Paris is in France is identical with Paris is in France" (for "A = A" -- or "A is A", where the "is" here is one of identity). [On that, see here.]

 

And, "(A) -(-A)" would turn out to mean something like: "If asserted Paris is in France then not asserted (not Paris is in France)."

 

If Hegel-fans (or even Marxist dialecticians) think this is an advance over AFL (to say nothing of MFL), then they are welcome to it!

 

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

 

The other things Kosok says about the temporal constraints on repeating these "A"s are susceptible to the comments I made in Essay Four Part One:

 

Nevertheless, even if their (collective) analysis of the LOC were correct, and it was true that "A is A and at the same time non-A", it would be impossible for dialecticians to begin to express their criticisms of even their own garbled AFL-principles. That is because it would be impossible to state the following:

 

B1: "A is A and at the same time non-A".

 

If it were indeed true that "A" is at the same time "non-A", then the first half of B1 would have to be re-written as:

 

B2: "Non-A is non-A".

 

Or, more accurately, the whole of B1 would become:

 

B3: "Non-A is non-A and at the same time non-(non-A)".

 

That is, if each "A" in B1 is replaced with what it is supposed at the same time to be (i.e., "non-A"), B1 would 'dialectically disintegrate' into B3. Or, perhaps worse, into the following:

 

B3a: "A and non-A is A and non-A and at the same time non-(A and non-A)".

 

Depending on how radically we interpret this dialectical re-write of the LOC.

 

[In B3a, I have replaced each occurrence of "A" with a "A and non-A", since we have been told that each "A" is at the same time "A and non-A".]

 

Now, this fatal result can only be avoided by those who reject the DM-inspired version of the LOC (i.e., those who reject this dictum: "A is at the same time non-A"), and who thus do not think that the first half of B1 is false, or both false and true -- or even that "It depends...".

 

B1: "A is A and at the same time non-A".

 

Even worse still, if every "A" is at the same time "non-A", then these would surely follow from B3:

 

B4: "Non-(non-A) is non-(non-A) and at the same time non-(non-(non-A))."

 

B5: "Non-(non-(non-A)) is non-(non-(non-A)) and at the same time non-(non-(non-(non-A)))."

 

And so on, as each successive "A" in B3, and then B4, is replaced with the "non-A" that dialecticians insist they (at the same time) are. Once more, this untoward result can only be avoided by those who reject standard DM-criticisms of the LOC.

 

Or, even worse:

 

B4a: "A and non-A and non-(A and non-A) is A and non-A and non-(A and non-A) and at the same time non-(A and non-A and non-(A and non-A))".

 

[B3a: "A and non-A is A and non-A and at the same time non-(A and non-A)".]

 

Replacing each "A" in B3a with "A and non-A" once more. I won't even attempt B5a!

 

[Of course, it won't do to claim that all these "non-"s cancel out (an odd notion in itself; on that see here), since if they did we would have to reject the idea that each "A" was at the same time a "non-A". Thus, if each "A" were at the same time a "non-A", then, when we formed a "non-(non-A)" from a "non-A" in the above manner, and if this could be 'cancelled' back to an "A", the "A" in "non-A" would no longer be a "non-A", since these two "non-"s would ex hypothesi have cancelled, wiping out that "non-A"!]

 

As should now be apparent, the LOC has an annoying way of hitting back in a most un-dialectical manner when challenged. In which case, as noted above: it is impossible for dialecticians to say what they mean!

 

So, anyone reading Kosok's 'formalization' today would have to do the same to each occurrence of his quirky letters all the way though his article -- turning each and every simple occurrence of "A", for example, into the potentially infinite string: "Non-(A and non-(A and non-(A and non-(A and non-(A and...)...)...)...)...)", before they could even begin to understand his point!

 

Of course, if they can't do this, that would be an implicit admission that not even they could make sense of Kosok's (or, indeed, Hegel's) whacko 'logic'.

 

 

Sinking Deeper Into Semantic Quicksand

 

Alas, things only seem to deteriorate:

 

"We could of course say that 'A was A' meaning that the present state of what is is being bracketed, and the temporal aspect introduced by taking into consideration the effects of an observing and persisting field of consciousness is ignored. In that case, with the suspension of the on-going temporal process, we have a hypothesized past which qua-being-past remains unchanged. Thus the law of Identity operates for a system whose members are taken to be already fixed by definition: it operates within a system in which the ambiguity of definition is eliminated by fiat. Thus, every element is well-formed in-itself, and is not influenced by contextual relatedness: the A within a formula 'x + A = y' is the 'same' A as within a formula 'z + A = w,' since 'A A' rejects any coupling A may have with a contextual '-A.' Thus the law of Identity can be regarded as a type of sub-set within a law of Non-Identity, referring to the past aspect of the time process. This can be formally stated in the form of a meta-principle of Non-Identity called -I΄: calling the principle of Identity I (e e or (e) (e)) and the principle of Non-Identity -I (-(e e)) or (e -e) or ((e) (-e)), a meta-principle of Non-Identity would read -I΄ = (I) (-I). Therefore Identity can be expressed as a function of some higher order Non-Identity; being appears as a function of time and becoming, and the past appears as a function of an enlarged temporal structure which includes the negating present. Indeed, the very attempt to show that a law of Non-Identity negates itself by a self-reflection reestablishes a higher form of Non-Identity. Calling the law of Non-Identity N, a coupling of N with its negation -N gives us N΄ = (N) (-N). Unlike a law of Identity, the law of Non-Identity expresses itself through its opposite, and ceases to express itself if it is not related to its opposite." [Ibid., pp.258-59. There are several serious typos in the on-line version of this passage, which I have corrected.]

 

This is easily the most confused paragraph we have stumbled across so far. Earlier, I made the prediction that Kosok would conflate his loosely-defined (or, rather, more often undefined) letters with numbers, and so it has proved to be:

 

"Thus, every element is well-formed in-itself, and is not influenced by contextual relatedness: the A within a formula 'x + A = y' is the 'same' A as within a formula 'z + A = w,' since 'A A' rejects any coupling A may have with a contextual '-A.'" [Ibid.]

 

We have already seen these hyper-plastic "A"s (and "x"s!) effortlessly traverse the entire semantic spectrum, ranging from objects to predicables, and then on to propositions or indicative sentences -- now they have been magicked into numbers (or, perhaps other mathematical objects). How else are we to interpret this new, and yet-to-be-defined 'symbol', "+"? And, what does the biconditional sign now mean? What sense can be made of a string of inscriptions like this: "2 if and only if 2"?

 

If at all possible, things appear to deteriorate even further:

 

"This can be formally stated in the form of a meta-principle of Non-Identity called -I΄: calling the principle of Identity I (e e or (e) (e)) and the principle of Non-Identity -I (-(e e)) or (e -e) or ((e) (-e)), a meta-principle of Non-Identity would read -I΄ = (I) (-I)." [Ibid.]

 

But, the above could only be "formally stated" if this 'formal language' had been set up correctly, which it manifestly hasn't. Hence, the above farrago simply amounts to a few 'symbols' thrown at the page, then drowned in a sea of obscure waffle and egregious non-sequiturs.

 

In the above, "I" is supposed to be "Identity", but this means that the following:

 

T1: -I΄ = (I) (-I),

 

pans out as:

 

T1a: Reflected upon negation of identity is identical with asserted identity if and only if asserted negation of identity.

 

On the other hand, since there are no propositions or clauses either side of the bi-conditional sign, the latter can't mean "if and only if". What then does it mean?

 

Furthermore, each expression either side of the "=" sign must be a singular term; in which case, neither can feature either side of the bi-conditional! Conversely, if either is meant to feature on opposite sides of the bi-conditional, they must be propositions or clauses; if so, they can't flank the "=" sign!

 

Of course, Kosok might have invented a whole new logic here where all of the above are possible and legitimate; but, if so, he should have formalised it properly so that, as is the case in every other branch of logic and mathematics, his work would be crystal clear and could be checked.

 

[Having said this, the way that Kosok's symbols constantly change their denotations suggests that if this is indeed a 'new logic', then he will have been single-handedly responsible for putting the discipline back more than 2500 years!]

 

I won't comment on the other unfortunate 'formulae' in the above paragraph; that would merely amount to repeating myself for the umpteenth time. However, give-or-take a few changes in the lettering, these comments still apply -- as they do to this passage:

 

"Calling the law of Non-Identity N, a coupling of N with its negation -N gives us N΄ = (N) (-N). Unlike a law of Identity, the law of Non-Identity expresses itself through its opposite, and ceases to express itself if it is not related to its opposite." [Ibid.]

 

But, the 'formula', "N΄ = (N) (-N)", can only 'translate' out as "Reflected upon Law of Non-Identity is identical with asserted Law of Non-Identity if and only if asserted Non-law of Non-Identity", or some such. [If anyone has a better 'translation', please e-mail me!]

 

Now, I have said several rather unkind things about this sub-logical shambles, but the above passage takes the biscuit (or even, the non-biscuit).

 

[Alas, there is worse to come!]

 

One would also like to know what the "=" sign is doing in such inhospitable company, surrounded on all sides by letter "N"s (or, possibly by what they mean -- 'Non-identity'). And yet, we are also told that identity always implies Non-Identity (in temporal contexts):

 

"Therefore Identity can be expressed as a function of some higher order Non-Identity; being appears as a function of time and becoming, and the past appears as a function of an enlarged temporal structure which includes the negating present." [Ibid.]

 

If so, then this should be the 'right formula': " (N) (-N)". And if that is so, the following can't be correct:

 

"...the law of Non-Identity expresses itself through its opposite, and ceases to express itself if it is not related to its opposite." [Ibid.]

 

Since my 'corrected formula' above explicitly rules it out.

 

Such are the consolations of Diabolical Logic...

 

There is very little worth commenting on in the next few pages, other than, perhaps, this:

 

"Consciousness is thus a co-relativity between the contraries S and O (subject and object) giving rise to the form (S) (O) and, as we shall see later, capable of expressing levels of subject-object relation, S΄, O΄, S˝, O˝ etc. Dialectics, phenomenologically based, avoids being either a subject-centred idealism or an object-centred materialism. The subject-object relation of phenomenology is the content of the dialectic process, which as a structure in turn is the very form of the subject-object phenomenology of consciousness: Dialectic Phenomenology is what results." [Ibid., pp.259-60.]

 

Well, we aren't told what constitutes either a legitimate "subject" or a kosher "object", but the use of a biconditional sign (if, that is, it is one!) implies that both S and O must be propositions -- so O can't be an object, after all!

 

On the other hand, if S and O are what we are told they are, and the above 'formula' applies to them -- i.e., "(S) (O)" -- then the following (interpreted) 'dialectical' monstrosity will emerge as a result: "Socrates if and only if Mount Everest", or, perhaps, "I (Rosa, or whoever) if and only if Mt Everest" (depending on what Kosok means by "subject"), or some such.

 

[Of course, the "I" here is the first person, personal pronoun, not Kosok's 'Identity', from earlier!]

 

Once again, Kosok might mean something different by all this, but until someone succeeds in formalising his work for him, it is impossible to say.

 

 

Old MacDonald's Farm

 

We now encounter this rather odd passage:

 

"Recognition of differentiation implies the existence of negating events (events that take on a determining, negating characteristic) within a field of presence such that a meaningful contrast appears between something given and something not-given; between a sustaining and persisting field of conscious presence preserving what has already been given within its memory field (reflective of its continuity of presence), and a non-persisting and hence 'fleeting' or negating set of events as something not-given but 'happening' and therefore in contrast to the persistency of the field. This can then be shown to yield the triadic relation: (the negated yet preserved given) (the negating not-given) : (the process of the given being negated by the not-given) as (e o: eo)." [Ibid., p.260.]

 

It is a pity Kosok didn't throw in a few more symbols, to yield "e-i-e-i-o", or we could all have joined in a familiar kindergarten sing-along.

 

Be this as it may, we have been left in the dark once more over the meaning of the colon -- i.e., the ":" in the above passage.

 

However, and once again, the conditional sign Kosok used here can't be an ordinary conditional sign since it is flanked by verb phrases, not clauses, sentences or propositions:

 

"(the negated yet preserved given) (the negating not-given)...." [Ibid.]

 

But, what then is it?

 

On the other hand, if the above is an ordinary conditional sign (and the brackets are interpreted as a sign for assertion, as we had earlier been told), then this odd passage will read as follows: "If asserted (the negated yet preserved given) then asserted (the negating not-given)."  

 

 

Matrix Re-Loaded

 

Moving on:

 

"...the development of the dialectic matrix, representing the form in which levels of reflection appear, will be presented as a formal structure of A (Assertion), N (Negation) and S (Self-Negation) operators, a logical interpretation as assertion, (e) or +e, negation, (-e) or e, and self-negation, (e) (-e) or +e, and an intuitive process using the e, o and eo symbols. As intuitive symbols, e and o are to be regarded as elements-in-continual-transformation, capable of having a reference to formal counterparts, but essentially symbolizing that which is in a state of continual temporal self-transformation." [Ibid., p.263. Once again, the minus sign, "―", was misrepresented as, "-", in the on-line version, and the biconditional sign, "", was simply omitted. I have corrected both errors.]

 

We have already seen how A oscillates erratically between its role standing for an 'object', a predicable, a proposition (or indicative sentence), a "truth-value", and "Assertion", but now "S" has changed its denotation, too. Earlier it stood for "Subject", now it stands for "Self-negation"!

 

Surely, this is 'formalisation' for fools.

 

 

Ordinary Versus Dialectical Logic

 

Kosok now introduces Gödel's Theorem as a way of promoting/advertising the superiority of DL over FL. I won't comment on Kosok's remarks in this regard, except to say that Gödel's results aren't quite as sound as most suppose them to be -- on that, see here.

 

Be this as it may, we soon find Kosok's slippery semantics spoiling the dialectical fun, once more:

 

"The above situation appears as a limitation of expression only if we view formal structures merely from the perspective of the law of Identity, wherein we regard the essence of a given term as already fixed and formed, independent of the activity of reflection. Reflection, however, opens up any given X to an indeterminate -X, placing the given thus in a new context, within which both the given X and the -X become transformed due to the mutually limiting nature of the coupling relation expressing the co-existence of X and -X. Hence X appears determined as (X) in relation to an equally mediated (-X), productive however, of a transformed X called X΄ representing the coupling (X) (-X). The coupling relation thus acts to delimit and form both X and -X by a relation of mediation (i.e. X mediated by -X gives (X) and -X mediated by X gives (-X)), yet is itself a transcendence of that which it forms, standing as it does for the act of formation. Thus, of necessity, reflection will always produce potential contradictions, for a contradiction is always a contradiction in terms, and the terms formed by the coupling relation, while delimited by a mutual limiting relation and thus excluding ambiguity in themselves, have nevertheless only achieved this determination by a coupling relation which as a meta-determination to the determined forms itself exhibits the ambiguity it has eliminated from the formed terms. Thus the only way out of the contradiction of terms resulting from delimited terms exhibiting the ambiguity of the act that produced them, namely the co-relativity relation (X) (-X), is a redefinition of terms, allowing for an expansion of the universe of discourse: instead of merely (X) and (-X), we have ((X)), ((-X)), (-(X)) and (-(-X))." [Ibid., pp.264-65.]

 

Earlier, we were told that "X" stood for the modal operator "impossible", but it now seems to have undergone yet another radical semantic make-over. As things stand (and I am guessing again, since Kosok's understanding of "formalisation" appears to be synonymous with "keeping everything secret"), X seems to be a meta-theoretical 'symbol' allowing Kosok to refer to any sign that takes his fancy -- even those drawn from other formal languages, or from mathematics.

 

In which case, in relation to the match between FL and DL, the score so far is:

 

FL 1 -- DL 0.

 

[That is because those competent in this area not only know what a formalisation is, but also how to construct and then employ one. Those knobbled by DL don't.]

 

Once more, I won't comment on Kosok's rather confused 'dialectical' remarks on the development of number theory (pp.265-66), except to say that his 'symbols' "(X)" and "(-X)" mean that "X" and "-X" have been asserted (recall the brackets signify assertion for Kosok, that is, they did in the first half of his article -- elsewhere, they seem to mean "reflected upon"!), but in relation to the indirect proofs to which Kosok refers (for example, in the proof that the (positive) square root of some (positive) integer is irrational), the discharged premiss (i.e., that p/q is rational, where "p" and "q" are integers, and "/" is the sign for division) isn't asserted merely assumed. A small point? Not at all. There is no point trying to derive a proposition that none has asserted. There is if it merely assumed for the purposes of the proof.

 

However, the "X" we met above, not content to be limited in this way (that is, by having the word "formalisation" insincerely waved at it), soon undergoes yet another chameleonic denotational change:

 

"From the law of Identity perspective, Gödel's theorem would regard an expression such as Dem(G) Dem(-G) or (X) (-X) as giving rise to only two alternatives: (a) either we get '(X) and (-X)', expressing a contradiction in that while inseparable, (X) and (-X) are also indistinct, or (b) '-(X) and -(-X)' expressing incompleteness in that, while distinct, (X) and (-X) are also separable, productive of a formed relation that is neither (X) nor (-X), but a third alternative. This alternative goes beyond (X) and (-X) and has no reference to them, since they have been rejected. This type of reasoning leads to a meta-level analysis in which there is no continuity of content from level to level: each new level becomes a completely distinct and separable formed expression which does not retain a reference base to that which has been transcended." [Ibid., pp.266-67.]

 

"X" now seems to mean a 'symbol' designating "demonstrations" in Gödel's theorem! If so, while it is certainly the case that the (linguistic) results of one demonstration might contradict those of another (or allegedly those of the same 'demonstration'), a demonstration itself can't contradict anything, since it isn't a proposition. Of course, and once again, Kosok might mean by "contradiction" something new or something different, but since neither he nor anyone else has been able to say with any clarity or consistency what this 'something new or something different' is, I can't comment on it any further. That is, of course, just another reason why this pigs ear can't be called a formalisation.

 

FL 2 -- DL 0.

 

This entertaining farce continues:

 

"Calling A by the symbol p, and notA by q, we can construct, according to the standard meaning of operations in classical logic, the following relations...." [Ibid., pp.267-68.]

 

So, "p" no longer stands for a number, or even a proposition, but has morphed into a meta-theoretical 'symbol' that stands for yet another 'symbol', "A", which itself sometimes means an 'object', sometimes a predicable, sometimes a proposition (or, indeed, indicative sentence), sometimes a truth-value, and sometimes simply "Assertion".

 

FL 3 -- DL 0.

 

And now we meet some old friends:

 

"However, if we deny the law of Identity, holding that p is not self-identical (because reflection relates p to q), or deny the condition of strict Contradiction we get -I -(p --p) [-(-(p & q)) or -(p or q)]. In other words, the possibilities open are either inconsistency or incompleteness: the law of Identity is not only a necessary condition for a well determined system, but its negation leaves us right in the beginning with the notions of consistency and completeness set against one another." [Ibid., p.268.]

 

We have already seen that the LOI has got nothing to do with the alleged identity or otherwise of propositions, and that the LOC has got nothing to do with the LOI ("stated negatively"), either, so the first half of the above 'formula' (or K1, below) is defective (that is, if we are ever told what the brackets Kosok uses here mean -- earlier the round brackets stood for "assertion", but that can't be the case in this instance --, and we have yet to be told anything about those square brackets!):

 

K1: -I -(p --p) [-(-(p & q)) or -(p or q)].

 

K2: -(p --p) [-(-(p & q)) or -(p or q)].

 

If we consult only the first line of a truth-table test applied to K2, we obtain the following (using "v" for "or"):

 

      p  ,  q :    -  ( p    -   -   p )      [ -  ( -  ( p   &  q ))   v   -  ( p   v   q ) ]

 

  T     T :    F   T   T   T   F  T      F     T    F    T   T   T      T   F   T   T   T

 

[The final result for the main connective is in red; the truth-values of the two connectives that have been used to decide this are in purple.]

 

This shows that K2 can't be a theorem in Kosok's 'formal language', otherwise the main connective would yield "T" on every line, and never an "F" -- that is, unless he means something different by the 'symbols' he uses. [But, we have been here several times, already!]

 

This result isn't all that surprising since the LHS of K2 does not have a "q", while the RHS does! [This is sub-sub-Logic 101! In fact, it is so far south of Logic 101, its nearest neighbour is the Earth's core.]

 

In which case, Kosok is the very last person to be lecturing us about "consistency" and "completeness".

 

[Of course, it might be possible to rescue Kosok's non-theorem here if we knew what the semantics of the mysterious "I" in K1 amounted to. That is because the conditional (between I and the rest) allows for an F in the consequent (i.e., 'the rest'), yielding T for that conditional if the proposition(s) on the extreme left (in this case, buried in that I) permit it. But, we can't conclude anything until we are informed about I's internal structure (if it has one). (Perhaps his mystical acolytes can 'summon' Kosok in a séance and find out for us?)]

 

FL 4 -- DL 0.

 

Alas, the slippery semantics and shifty syntax do not stop there:

 

"Thus the essence of dialectic analysis lies in the fact that it forces reformulations and transformations of presently accepted and artificially fixed conceptualizations. It is opposed to any type of fixed substance notion, whether the concepts apply to the self, world or self-world interaction. Identity is not something given or defined: it is something that has to be continually achieved and reaffirmed, involving the anxiety of non-identity and self-negation. The act of definition itself, i.e. that X is A, which underlies the basic structure of formal systems, is what must be transformed: upon reflection X is also A΄ or (A) (-A)." [Ibid., pp.268-69.]

 

Perhaps this gives us all the clues we need in order to understand why this 'formalisation' wouldn't pass even a basic course in High School logic.

 

"...dialectic analysis forces reformulations and transformations of presently accepted and artificially fixed conceptualizations." [Ibid.]

 

So, a 'dialectic formalisation' is nothing like a formalisation in genuine logic; not a bit of it! Dialecticians are allowed to make stuff up as they go along, switching the denotation of whatever takes their fancy, and as the fancy takes them, using 'symbols' inconsistently (since to do otherwise would be to give in to those tedious "fixed conceptualisations" that hamstring those less adventurous, slaves to pedantry).

 

In which case, Kosok-fans will be glad to hear that the letter "X" has now cast off yet another "fixed conceptualisation". Earlier, it was that boring, stick-in-the-mud modal operator, "impossible". It then bravely stripped away these conservative shackles and became a meta-theoretical 'symbol' that could refer to any other 'symbol' in this 'formal language'.

 

However, this Heraclitean gem of a letter soon grew tired of this dusty persona, and within minutes (but, isn't even that a little tardy in Heraclitean Hell?) it then assumed a shiny new 'identity' (a status it is "continually achieving" in a most impressive manner), beginning its new life as a 'symbol' designating "demonstrations" in Gödel's theorem. Hardcore Heraclitean Honchos will also be glad to hear that this rebellious X quickly turned its face against all attempts to tie it down to any suggestion of consistency, rapidly evolving into a singular term designating anything that can be defined: "X is A" -- i.e., as in "Kosok is a rather poor logician".

 

Not to be outdone by X, the morphoholic letter "A" has now reverted to one of its earlier personas (but isn't that against the spirit of "dialectic analysis"?), and is now..., er..., a boring predicable. Perhaps the "anxiety of non-identity" was just too much for it?

 

Well, maybe not, for in the very same sentence A, cocking yet another snoop at convention, has morphed into a proposition again, something that can be asserted: "(A) (-A)".

 

[If A were still a predicable, we'd have: "Asserted is green if and only if asserted isn't green", or some such.]

 

But, this rebel without a cause -- this devil-may-care X -- ever keen to live on the edge, has now transformed itself into an..., er..., stick-in-the-mud predicable, again:

 

"When a predicate X such as 'is in motion' is analyzed from a formal perspective, it is important to introduce levels (meta-levels) wherein it is necessary to distinguish motion taken in different senses, i.e. motion1, motion2, motion3, etc. in order to avoid contradiction. However, this is but another form of the consistency-completeness conflict, since one is forced either to (a) consider one expression such as motion, as complete and including all its variations within its scope with the result that inconsistencies occur, or (b) consider any one expression such as motion, as well defined and incomplete regarding other senses of the term in order to maintain consistency. However, all the various senses of motion are nevertheless still references to an overall idea of motion (otherwise we would not refer to them as motion with subscripts), which as an idea undergoes self-transformation in its identity as further reflections are made." [Ibid., p.269.]

 

[This topic was explored at length in Essay Five, but, as we saw, we certainly do not need the help of loopy logic like this to analyse motion. Quite the reverse in fact.]

 

The pressing question now is: What form will these masters of disguise (X and A) assume next?

 

Watch this space...

 

FL 5 -- DL 0.

 

 

Kosok Elevated To A Higher Plane?

 

Kosok now ascends to a higher level of 'consciousness'; it mightn't prove possible for us mortals to follow in his hallowed footsteps...

 

"We will now briefly indicate, given the principle of Non-Identity, how higher order levels of reflection manifest themselves as dialectic matrices displaying triadic movement in several dimensions simultaneously. Calling the self-negation term (e) (-e) by the symbol (--e), thus reflecting the double-implication and double-negation structure of the self-negation operation (negating both e and -e), the initial triad obtained through (R)e involves the terms (e); (-e) and (--e). The expression (--e) also indicates that the synthesis term +e is a negation of the negation of the original e, in that it is a return to the non-positive and non-negative nature of the original e, seen however on a more developed plane. We can now write: (R)e = (A N: S)e = (Ae Ne: Se) = ((e) (-e): (--e)) = e΄, where A, N and S stand for the assertion, negation and self-negation operators." [Ibid., pp.271-72. I have once again corrected the "―" sign, which has been misrepresented in the on-line version as "-".]

 

So, it now turns out that "--e" is now a meta-theoretical term representing the following formula: "(e) (-e)". But, and alas, the iterated sign "--" hasn't yet been defined for this 'meta-language'. No surprise there, then.

 

But, what the George W is this supposed to be?

 

"(R)e = (A N: S)e = (Ae Ne: Se) = ((e) (-e): (--e)) = e΄, where A, N and S stand for the assertion, negation and self-negation operators." [Ibid.]

 

Earlier on, brackets indicated assertion, but here assertion is marked by "A", so what do the above brackets now mean?

 

For example, does (A ...) mean "assertion of an assertion"? And we are still in the dark about the meaning of the colon, ":". Normally, it is short for "such that"; is that what it signifies here?

 

While we are at it, what on earth does this mean: (A N: S)e = (Ae Ne: Se)? The transition from the LHS to the RHS suggests that the "e" outside the first set of brackets (highlighted in red) has multiplied the contents of the bracket to its left to yield the RHS of this 'identity'! [If so, an earlier allegation that Kosok has conflated mathematics and logic has been confirmed yet again.] This means, of course, that A, N, and S must be mathematical objects/symbols, too, and thus no longer stand for "assertion", "negation" and "self-negation", contrary to what Kosok himself asserts. [If not, what do they mean?] On the other hand, if they still mean "assertion", "negation" and "self-negation", how can these terms (or "operators") be multiplied in this way? What on earth does "Assertion x entity" (i.e., "Ae") mean?

 

[My "x" here is the multiplication sign!]

 

True to form, we are given no rules sanctioning the expansion of 'dialectical brackets', which means that Kosok is simply making stuff up as he goes along, again.

 

However, if we assume that ":" stands for "such that" and "A", "N" and "S" signify "assertion", "negation" and "self-negation", respectively, then the above 'formula' must 'mean' something like the following:

 

"Reflection on an entity is identical to (if assertion then negation such that self-negation) multiplied by entity is identical with (if assertion multiplied by entity then negation multiplied by entity such that self-negation multiplied by entity) is identical to (if asserted entity then not asserted entity such that double negated entity) is identical with reflected entity."

 

Ah, so, that is what Hegel meant!

 

It is all so clear now...

 

On the other hand, Kosok might have meant by (A N: S)e a sort of functional relationship (rather like f:x 2x +1 in mathematics). If so, the above formula will come out something like the following:

 

"Reflection on an entity is identical to (if assertion then negation such that self-negation) applied to an entity is identical with (if assertion applied to an entity then negation applied to an entity such that self-negation applied to an entity) is identical to (if asserted entity then not asserted entity such that double negated entity) is identical with reflected entity."

 

Not much of an improvement, I venture to suggest.

 

Of course, Kosok mightn't have meant this, but without a full formalisation, who can say?

 

[Once more, if anyone has a better 'translation' of this 'formula', please e-mail me.]

 

 

Welcome To The Twilight Zone

 

We are now about to enter a sort of Kosokean Twilight Zone:

 

"The problem remains as to what the second order reflection e˝ = (R)e΄ = (R)(R) e = (A N: S)(A N: S)e entails. Let us write (R)e΄ = (Ae΄ Ne΄: Se΄), and since e΄ = (A N: S)e, we get the following: e˝ = (R)e΄ = (A(A N: S)e N(A N: S)e: S(A N: S)e). This can be better seen as a two-dimensional structure or matrix:..." [Ibid., p.272. I have collapsed a few gaps between several letters which don't seem to be doing any work.]

 

Of course, the "second order reflection e˝ = (R)e΄ = (R)(R)e = (A N: S)(A N: S)e" entails nothing of the sort since we have yet to be given a single rule of inference, nor are we told what an "e" situated outside a bracket means.

 

[This confirms the suspicion that when Kosok says things like "Let us write...", what he really means is "Let's make some more stuff up...".]

 

And, what do two bracketed expressions like this mean: "(A N: S)(A N: S)e"? Are they like those we find in algebra -- such as (x + y )(x - y)? It seems so, since, 'multiplied out', these Kosokean brackets yield: A(A N: S)e N(A N: S)e: S(A N: S)e, which is how they'd be expanded in mathematics.

 

But, what does the following monstrosity mean: e˝ = (R)e΄ = A(A N: S)e N(A N: S)e: S(A N: S)e)?

 

Perhaps this:

 

"Doubly reflected upon entity is identical with reflected upon reflected upon entity (sic) which is identical with if assertion multiplied by (if assertion then negation such that self-negation) multiplied by entity then negation multiplied by (if assertion then negation such that self-negation) multiplied by entity such that self-negation multiplied by (if assertion then negation such that self-negation) multiplied by entity."

 

Yep, that certainly captures the essence of what Hegel was banging on about...

 

As we saw earlier, not much will improve if we replace "multiplied by" with the more functional "applied to". [The reader is left to work that out for herself.]

 

 

Matrix Revolutions

 

We are now introduced to a 'matrix' (p.272), which I won't even attempt to reproduce here (it can be found on-line, or in the printed version (p.272)), but I will draw the bemused reader's attention to some new and unexplained 'symbols' Kosok again just throws at the page, apparently, perhaps, for good luck (since they don't seem to mean anything, and they do no work). Here are just two examples:

 

(1)   Ae΄

        ↓

       Ne΄

 

(2)  (--(ë))

 

There is absolutely no indication what those two dots mean above that "e". In mathematics, they often indicate that some expression or other has been differentiated twice with respect to time -- i.e., they express the second derivative; Newton used it that way. Nor is any help offered the reader in understanding the vertical arrow. I suppose it must mean "implies" again, but that is just another guess on my part. Nor are we told what the rules are that govern these 'matrices'.

 

Kosok now adds the following comment:

 

"Thus levels of assertion, negation and self-negation correspond to writing levels of e, -e and --e within ordered parentheses. The immediate observation is that nine terms appear, involving four non-synthesis terms (AA, AN, NA, NN), four partial syntheses (AS, SA, NS, SN) and one complete synthesis SS. The diagonal of the matrix AA, NN, SS represents the complete second level Thesis, Antithesis and Synthesis." [Ibid., p.273.]

 

We have already seen that "Thesis, Antithesis, Synthesis" has nothing to do with Hegel's method.

 

The next passage worth quoting is the following:

 

"Starting with e as an unreflected term, the sequence Ae, Ne, Se of the first reflection can intuitively be written as e(e), o(e), eo(e) respectively, indicating that the triple sequence (e o: eo) originated from an unreflected e (now appearing within parentheses) by a single act of reflection, giving us (R)e = (e(e) o(e): eo(e)). Thus, remembering that the A operator leaves present any symbol combination, the N operator replaces any e symbol by an o, and any o by an e, and finally that the S operator combines the result of A and N together in the order A + N (i.e. Se is the relation eo and not oe, indicating that (R)e = (e o: eo) is a transition from e, the initially present, to eo), we are now prepared to interpret the second order matrix in terms of the intuitive symbols e and o...." [Ibid., pp.274-75.]

 

It looks like the implication sign (i.e., "") has now become a sign for the "transition from e"! We are also left to guess once again what the "+" sign in "A + N" amounts to; is it a mathematical "+", or merely a common-or-garden "and"?

 

And, this 'formula', (R)e = (e(e) o(e): eo(e)) must translate out as follows:

 

"Reflected entity is identical with (if asserted entity then opposite asserted entity such that entity opposite asserted entity)" -- or some such.

 

Which only prompts the obvious question: "WTF were the peer reviewers high on when they approved this syntactic and semantic Midden?!"

 

Well, whatever it was, it obviously wasn't strong enough.

 

There is very little left worth commenting on in the next ten or twelve pages of Kosok's 'formalisation' (that hasn't already been remarked upon, several times), except perhaps this:

 

"A third order reflection would make every e and o another double term, giving us a movement from e o o e to eo oe oe eo, or a movement from E to O, where O is the self-determination of o: oeeo. Just as the second reflection eooe or E is a negation of the negation of the zero order e, the third reflection EO is a negation of the negation of the first order eo: even number reflections are e-directed and odd numbered ones are o-directed." [Ibid., p.277.]

 

Here we have yet another term, "E", which has just been lobbed into the 'argument' with no indication what it might mean. Context suggests it is the 'self-determination of e' (which seems to imply that e is an agent of some sort!), but that is just another guess.

 

And, finally we run into this pièce de résistance:

 

"However, once the Absolute is revealed, a new level of infinite valued relations appear[s]. For a reflection on the Absolute itself reveals three component Absolutes within the Absolute, i.e. each of the three generating components S, O and SO is itself infinite, reflecting the entire S, O dialectic within itself from its own perspective. The nth level of reflection (S, S΄, S˝... Sn), Sn On: SnOn, will give S O: SO as n goes to infinity (). Now the nth level of reflection generates the n+1 level (e.g. e΄ o΄: e΄o΄ is called e˝). A reflection (meta-reflection) on S would thus give S+1, which is however still S since infinity plus one is still infinity. Indeed, the S+1 term is formed by combining the three S, O, S O, terms together (as e.g. the nine terms of e˝ is the combination of the three three-termed e΄ o΄ and e΄o΄ elements), but three infinities still give infinity: 3 = . (sic)" [Ibid., pp.279-80. I have replaced the word "infinity", which appears in the on-line version, with an "", which features in the published version, and have corrected several important typos.]

 

Alas, the symbol "" isn't a number, it is simply shorthand for a process without limit, and/or for the word "infinite" itself. [Unfortunately, mathematicians are rather careless with the use of this word and this symbol, too. Often, they seem to mean by their use of "" something like "We haven't a clue what results from this calculation" -- for example, if/when they write "2/0 = ".]

 

Ào (the smallest transfinite cardinal), on the other hand, is a number, but isn't. In which case "3" makes no sense, nor does "S+1. Moreover, Kosok seems to think that 3 means "three infinities" when it actually means 3 x 3 an 'infinite number' of times -- and Kosok is supposed to be a Professor of Mathematics. It was blatant gaffs like this that suggested to me that this was an elaborate hoax.  

 

[ isn't a number since there is no way of constructing it, whereas there is a way of constructing Ào. On that, see, for example, Moore (2001), and Lavine (1994). Of course, Kosok might be using "" in place of "Ào", i.e., as shorthand for it; but if this were a properly constructed formalisation, we'd have been told.]

 

Moreover, the prime symbol (i.e., "΄") isn't a number, either, so the series S, S΄, S˝... Sn makes no sense -- unless, that is, this series of symbols were to be replaced by numbers, as is the case in function theory --, e.g., where, for example, "f(3)(x)" is short for "f(f(f(x)))".

 

Had he reflected a little more about what he was doing, Kosok would surely have replaced this prime symbol with numbers from the get-go.

 

[The many other non-sequiturs that litter each paragraph of the last ten pages (and indeed the entire article) will be considered if and when they crop up in connection with my demolition of Hegel's even more obscure system, in Essay Twelve Parts Five and Six.]

 

It is no surprise, however, to find Kosok later descended into open and honest mysticism -- on that, see much of his site, but more particularly Kosok (2003).

 

So, other than the possibility that this was indeed an elaborate hoax, the only viable conclusion is to agree with the following comment from Monty Python (paraphrased):

 

Formalisation my foot!7

 

Notes

 

01. The latest example of this sort of allegation can be found in Molyneux (2012). This comrade has been told several times (by yours truly) that not even AFL is based on the LOI, nor yet even on the other two 'laws', but I might as well have been talking to the cat for all the good it does. [Molyneux's other attempts to put logic back over 3000 years were discussed here.]

 

1. Some readers unfamiliar with Analytic Philosophy might find this way of analysing propositions rather odd, if not downright perverse. It was briefly explained and justified here and here. It isn't the only way to look at such sentences, nor is it mandatory, but it is extremely difficult to make these points in any other way. How, for example, would it be possible to distinguish "ζ is identical with ξ" from "ξ is identical with ξ" if simple gaps were used, as in "...is identical with..."?

 

We could, of course, use Quine's dodge: "➊ killed ➋" and "➊ killed ➊", for example. The numerals are in circles to distinguish them from numbers proper. Or, we could employ different style dots and dashes, as in: "--- killed ...", and "--- killed ---".

 

Part of the reason why those using the sort of logic that preceded Frege made so many mistakes is that they didn't have access to the sophisticated tools we now possess for making such distinctions -- the dialectical mess Hegel and Lawler find themselves in being a prime example of this malady.

 

2. It might be wondered why a proposition can't be a singular term, object, or name thereof -- nor vice versa. Neither an object nor a singular term says anything (in the sense that a sentence says something, or can be used to say something, true or false) -- unless, of course, that object or singular term is part of some pre-arranged code. But, even then, that code will say something (factual) if and only if it can be translated into indicative sentences. [On this, see the section on signs in Essay Thirteen Part Three.]

 

[In what follows I will confine my comments to explaining why a proposition can't be a name (or even a Proper Name).]

 

An indicative sentence can't be the name (or Proper Name) of an object, fact or truth-value ('The True', or 'The False', as it was for Frege). [On this, Geach (1972b).] There are at least four reasons why:

 

(1) If sentences were Proper Names (in the above sense), it would be possible to substitute the one for the other (salva congruitate) and still make sense. But, that isn't so. For example, if we replace "Paris" by "The Capital of France is a city" in the following, we end up with unvarnished nonsense:

 

S1: Paris is a city. 

 

S2: The Capital of France is a city is a city.

 

Of course, it could be argued that "The Capital of France is a city" does not name "Paris" so the one can't be substituted for the other. But, that is beside the point. Any name can be substituted for "Paris" and S1 would still make sense:

 

S1a: London is a city.

 

S1b: Tony Blair is a city.

 

So, if "The Capital of France is a city" were a name it should make sense if it were substituted for "Paris" in S1 to give S2.

 

It could be objected that S1b makes no sense since "Tony Blair" is the name for a man not a city. [On the distinction between "name for" and "name of", see Essay Twelve Part One.]

 

Indeed, but there is nothing to stop human beings naming a city after Blair, which would give S1b a sense; but no one is going to use "The Capital of France is a city" as a name for a city. And even if they were to do that, it would make "The Capital of France is a city" logically simple. From that 'name' it wouldn't be possible to infer that France had a capital which was a city, or, indeed, even that it had a capital, without that 'name' ceasing to be a name and reverting to a proposition again.

 

Let us suppose that Rouen were re-named "The Capital of France is a city". In that case, these would make sense:

 

S2a: Rouen's Cathedral has just collapsed.

 

S2b: The Capital of France is a city's Cathedral has just collapsed.

 

But, for S2b to make sense, "The Capital of France is a city" would have to be regarded a syntactically and logically simple.

 

[Anyone who thinks differently is invited to regard "The Capital of France is a city" itself as a subject/predicate proposition (that is, as logically and syntactically complex) and then explain what "The Capital of France is a city's Cathedral has just collapsed" could possibly mean (without reverting to interpreting "The Capital of France is a city" as a logical unit -- i.e., as logically simple again). (On why names can't be logically complex, even if they are typographically complex, see (4) below.)]

 

(2) It is possible to assert a sentence, or clause, but not a name.

 

S3: The council for the defence asserted that the Police officer was lying.

 

S4: The council for the defence asserted that Margaret Thatcher.

 

(3) Indicative sentences are capable of being true or false, names aren't.

 

S5: Is it true that Paris is in France?

 

S6: Is it true that Socrates?

 

S6 makes no sense at all.

 

(4) Names, even if they are physically complex, are syntactically and logically simple (and thus have no parts that signify separately), sentences aren't syntactically or logically simple (and do have parts that signify separately).

 

Consider a typographically complex name such as, "The Duke of York" -- which is, say, the name of a public house. In relation to the following sentence, no one would argue as follows:

 

S7: The Duke of York is a pub, therefore York has a Duke who is a pub.

 

Contrast that with this:

 

S8: The Duke of York has just got married, therefore York has a Duke who has just got married.

 

In S7, "The Duke of York" is name whose parts do not signify separately -- which is what makes the inference "therefore York has a Duke who is a pub" fail --, whereas in S8, "The Duke of York" is a definite description whose parts do signify separately, allowing the inference to go through.

 

[Of course, in both S7 and S8, the sentences as a whole are syntactically complex, whose parts signify separately -- i.e., the nouns signify separately from the verbs, etc. (I owe some of the above points to Geach (1972b) and Geach (1972c,d), pp.59-60, 290-91.)]

 

Moreover, if a proposition is understood as "That which is being proposed, or which has been put forward for consideration (as true or false)", then it can only be called an object if it is confused with a propositional sign (i.e., with a set of conventionalised inscriptions on a page or screen). [On that see Glock (2003), pp.102-36, and Hacker (1996), p.288, n.65.]

 

If, on the other hand, a propositional sign is treated as a series of names (or physical objects, written in ink), it would become a list, or a collection of objects, and, as we saw in Essay Three Part One, lists and collections of objects say nothing.

 

~~~~~~oOo~~~~~~

 

[This forms a continuation of Note 2.]

 

Remember: if you are viewing this with Mozilla Firefox, you might not be able to read all the symbols I have used.

 

In what follows, I am assuming that an answer can be found to the fatal objection I raised earlier. If that isn't possible, much of what follows in this particular Note is beside the point.

 

It could also be argued that we might be able to define, formulate, or stipulate a rule or axiom that licences the derivation of the LOC from the LOI 'stated negatively'; H3 and H4 might suffice to that end:

 

H1: "A is A" implies and is implied bydf "A cannot at the same time be A and not be A."

 

H2: "A = A" implies and is implied bydf "A cannot at the same time be A and not be A."

 

H3: df(p) [(p = p) º ¬(p ≠ p)].

 

H4: df(p = p) º ¬(p ≠ p).

 

[Henceforth, I will omit the "df" sign, unless I need to add any new definitions.]

 

However, we have already seen that H3 and H4 present problems of their own over the nature of propositions, so we might find it useful to concentrate on revamping H1 and/or H2, instead -- or, rather, H2 alone, since it is less controversial (in that it uses the equal sign between two singular terms).

 

But, once more, the fourth and fifth of those "A"s in H2 are, or are parts of predicate expressions, namely: "...cannot at the same time be A" and "...(cannot at the same time) not be A," -- even though the first "A" (in the expression "A = A" (in H2)) isn't a predicate expression, while its "A"s are singular terms. If, for present purposes we overlook this annoying 'difficulty', and ignore the modal expression, "cannot", in H2, the latter might then be an instantiation the following form:

 

H5: (x) [Ax ® ¬(Ax & ¬Ax)].

 

[This reads, "Anything which is A is not both A and not A."]

 

But, this is no help either since all three "A"s are predicate expressions, and thus not part of a relation (of identity), which is what was required.

 

Perhaps the following will suffice?

 

H6: (A = A) ® ¬[(A = A) & (A ≠ A)].

 

This reads, "If A is identical with A, then it is not the case that it is both identical and not identical to A" (paraphrasing slightly).

 

Again, we have already considered a version of H6, here. So, once again, if we replace "(A = A)" with "Γ" and "(A ≠ A)" with "¬Γ" (creating a rule here where there was none before, allowing us to derive ¬(A = A) from (A ≠ A), thus permitting the replacement of "(A A)" with "¬Γ"), we could obtain the following:

 

H7: Γ ® ¬(Γ & ¬Γ).

 

H7a: (A = A) ® ¬(Γ & ¬Γ)

 

The consequent of H7 (i.e., "¬(Γ & ¬Γ)") is indeed the LOC. No problem with that.

 

Alas, however, this is not what Lawler tells us Hegel was arguing, which was that the LOI stated negatively (i.e., ¬(A = A)) implies the LOC. Moreover, H8 below, which is what Lawler wanted, isn't the same as H7 or H6.

 

H8: ¬(A = A) ® ¬(Γ & ¬Γ).

 

With respect to the following:

 

H8a: (A ≠ A) ® ¬(Γ & ¬Γ); and

 

H9: ¬(A = A) ® ¬[(A = A) & (A ≠ A)],

 

the consequent of H8a would follow if we allowed the required rule (i.e., ¬(A = A) º (A ≠ A)), but this rule (if it is one) presents problems of its own. H9 is also problematic. [On this, see the end of this Note.]

 

It could be objected that the negation of the LOI is not the same as the LOI "stated negatively", so the above response is misguided. But, we weren't told with any clarity what "the LOI stated negatively" actually is, so who can say they aren't the same? Certainly Hegel doesn't tell us, and neither does Lawler. [Even so, I will also return to this objection at the end of this Note.]

 

Anyway, it might prove useful if we re-examined an earlier point:

 

H6: (A = A) ® ¬[(A = A) & (A ≠ A)].

 

H7: Γ ® ¬(Γ & ¬Γ).

 

H7a: (A = A) ® ¬(Γ & ¬Γ).

 

We derived H7 (or H7a) from H6 by the introduction of the following rule (which we didn't even attempt to justify):

 

H10: (A ≠ A) º ¬(A = A).

 

To be sure, H10 might seem 'intuitively obvious', but the negative particle on the RHS is a propositional operator, while that on the LHS isn't (i.e, that which is buried in the "≠" sign) -- or it isn't obviously one. Even so, I'll put that minor niggle to one side.

 

Recall, "A" here isn't a proposition, but an object (or the name of an object) of some sort. If so, we can only use H10 as a rule if it possesses generality, which takes us back to H5:

 

H5: (x) [Ax ® ¬(Ax & ¬Ax)].

 

Again, this reads, "Anything which is A is not both A and not A." However, as we saw earlier, all three "A"s in H5 are predicative, and thus aren't (and can't be) part of a putative relation of identity. They would have to be singular terms if that were the case. So, H5 is no use, either.

 

Well, we might be able to circumvent this obstacle by means of the following:

 

H11: (x)(y) [(x = y) ® ¬{(x = y) & ¬(x = y)}].

 

This reads: "If any two objects are identical then it is not the case that they are both identical and not identical."

 

This at last looks like a general version of the rule that Lawler requires; in fact it is better, since it doesn't confuse predicates with relations.

 

But, is the consequent of H11 (i.e., "¬{(x = y) & ¬(x = y)}") an example of the LOC? No, it isn't, since the LOC is not about objects but about propositions (or clauses)! We kept hitting this brick wall in the main body of this Essay, and here it is again.

 

[To be sure, "¬{(x = y) & ¬(x = y)}" might be a contradiction (but, then again, it might not!), and yet it still isn't the LOC.]

 

It could now be argued that if we replaced "(x = y)" with "Γ", and "(x ≠ y)" with ¬(x = y), and hence with "¬Γ", in H11, we might be able to obtain a contradiction -- perhaps that expressed in H12:

 

H11: (x)(y) [(x = y) ® ¬{(x = y) & ¬(x = y)}].

 

H12: (x)(y) [Γ ® ¬(Γ & ¬Γ)].

 

But, this is a syntactical mess! The prenex quantifiers have no variables to latch onto.

 

Furthermore, if we now try to isolate the consequent of H12:

 

H12a: Γ ® ¬(Γ & ¬Γ)

 

we would simply lose the generality we possessed before we did this, and which generality is required if this is to be a rule. In addition, we would re-introduce all the problems we faced earlier.

 

Moreover, we can't go back to quantifying across propositions again, for reasons outlined in the main body of this Essay, here. [Sure, some logicians do indeed attempt to quantify across propositions, but they can only do so by treating them as objects, and not propositions.]

 

We hit the same brick wall again!

 

Objectors might be tempted to return to H5 to try to explain what Hegel and/or Lawler meant:

 

H5: (x) [Ax ® ¬(Ax & ¬Ax)].

 

[Again, this reads, "Anything which is A is not both A and not A."]

 

But, the "is" here is predicative and not one of identity, as noted earlier (here and here) -- where it was also demonstrated that any attempt to turn it into an "is" of identity will always hit yet another brick wall.

 

It might be objected that the consequent of H11 (i.e., H14) is indeed the LOC.

 

In fact, it is the apparent negation of a contradiction (i.e., H13) -- I use "apparent" since it isn't the LOC (and H13 isn't even a contradiction -- on why that is so, see below, and the end of this Note), which, once more, concerns propositions, not the identity of objects.

 

H11: (x)(y) [(x = y) ® ¬{(x = y) & ¬(x = y)}].

 

H13: (x = y) & ¬(x = y).

 

H14: ¬{(x = y) & ¬(x = y)}.

 

H13 isn't a contradiction, either. That is because it, too, is a syntactical mess; as noted earlier, it has lost its prenex quantifiers!

 

As I commented earlier in relation to this passage of Lawler's:

 

"The other principles follow from this basic one. The principle of noncontradiction, Hegel argues, is the principle [of Identity -- RL] stated negatively. 'A is A' implies 'A cannot at the same time be A and not be A,' or one cannot assert something to be true and at the same time, and in the same respect, assert it to be false. The principle of excluded middle is that something must either be A or not be A: there is no third possibility. By extension, the law of noncontradiction implies that 'A cannot be non-A', where 'non-A' is something that is not A, or some part or property of A." [Lawler (1982), p.19. Italic emphasis in the original; middle set of quotation marks (around the LEM) missing in the original.]

 

Now, in relation to the LOC, if these letters refer to propositions (i.e., if they are propositional variables), no problem. "One cannot assert something to be true and at the same time, and in the same respect, assert it to be false" would at least be a passable first stab at a definition of the LOC (in urgent need of improvement, however -- on this, see here and here); but by no stretch of the imagination can these letters refer to propositions when they appear in the LOI. That 'law' is not about the identity of a proposition with itself.... The LOC does not rule out propositions being non-identical..., since it doesn't concern the identity of propositions to begin with. So, the LOC neither rules such an identity in nor does it rule one out. Indeed, if a proposition lacked identity it wouldn't be a proposition to begin with. And if it possessed identity it would be an object, not a proposition.

 

To be sure, ¬(Γ & ¬Γ) is the LOC, but we have been here already...

 

It could be objected that it is intuitively obvious that (A ≠ A) and ¬(A = A) are one and the same. So, this is a safe rule:

 

H10: (A ≠ A) º ¬(A = A).

 

Well, think about it: no follower of Hegel could possibly admit they are one and the same, could they?

 

Quite apart from that, as the above shows, even if they are one and the same (that is, if we (temporarily) ignore what Hegel had to say about the LOI in our endeavour to save this part of the argument from easy self-refutation, all the while catapulting right into just such a self-refutation!), Hegel's 'derivation' of the LOC from the LOI "stated negatively" would still fail. [The reasons for this have been spelt out many times; the latest attempt can be found a few paragraphs back.]

 

At this point, it could be pointed out that this seriously misrepresents what Hegel and Lawler were actually trying to argue. Neither of them is claiming that the LOI stated negatively is the same as "(A ≠ A)" or "¬(A = A)". What they are maintaining is that the LOI stated negatively is ipso facto the LOC:

 

H15: "A cannot at the same time be A and not be A."

 

H15 is the LOI stated negatively, and it is also the LOC. Nothing needs to be done to it, or derived from it.

 

Or, so it could be argued.

 

If so, we can represent H15 as follows (if we ignore the modal term, "cannot"):

 

H16: ¬[(A = A) & (A ≠ A)].

 

Or, perhaps better:

 

H17: ¬[(A = A) & ¬(A = A)].

 

But, neither of these is an accurate translation of H15. They are translations of:

 

H18: It is not the case that ((A is identical with A) and it is not the case that (A is identical with A)).

 

Or, perhaps:

 

H19: It is not the case that ((A is identical with A) and (A is not identical with A)).

 

I will ignore this minor 'difficulty', too, and take H19 as a more accurate version of H15. Now, while H19 might be a particular contradiction (but, that is controversial; we'll return to this presently), it isn't the LOC. As noted several times already, the LOC concerns the truth-functional relation between a proposition and its negation. It isn't about the alleged identity or non-identity of objects. So, the LOI stated negatively might imply a contradiction (but, as has already been noted, that is controversial, too), but it doesn't imply the LOC, which is a general rule about a proposition and its negation.

 

The reason why H18 and H19 (and many others listed above) might not be contradictions is that the last clause (in H19) -- "(A is not identical with A)" -- implies a change of denotation for the letter "A". If A isn't identical with A, then it must be something else, perhaps B.

 

H20: It is not the case that ((A is identical with A) and (B is not identical with A)).

 

H21: It is not the case that ((A is identical with A) and it is not the case that (B is identical with A)).

 

And by no stretch of the imagination are these contradictions!

 

The negation clause outside the first set of brackets makes no difference; if A is not identical with A then it must be B (or, C, or...), or it must be replaced by the letter "B". The supposed proposition "(A is identical with A)" is what is being negated by that clause, but that is precisely what undermines the denotation of "A".

 

[Incidentally, the same comments (no pun intended!) apply to H15, H9, and all the others left over from earlier. Naturally, this depends on how we view the construction of propositions like H16 and H17. I won't enter into this knotty problem here, unless the above is challenged in some way.]

 

Indeed, this isn't something dialecticians should wish to deny (i.e., the change in denotation of the letter "A"), since, according to them, everything is always changing (into its opposite), and nothing remains the same, including letter "A"s! [I went into some detail on this in Essays Four and Six.]

 

If A does change into B, its opposite, it must be identical with it (in an 'identity-in-difference' sort of way), if we apply a little 'dialectical logic' here. If so, the following must be 'dialectically true':

 

H22: It is not the case that...it is not the case that (B is identical with A).

 

Which is the equivalent of "B is identical with A"; i.e., A is identical with that which it has changed into, B, -- the "Identity of Opposites"!

 

Even so, it still isn't a contradiction...

 

But, what about this:

 

"[O]ne cannot assert something to be true and at the same time, and in the same respect, assert it to be false." [Lawler (1982), p.19.]

 

This is indeed one version of the LOC, but it can't be the same as the following (contrary to Lawler's assumption indicated by the "or" he uses):

 

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

 

It might have been had Lawler argued as follows:

 

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

 

But, he didn't.

 

And even if he had have argued this way, he'd have been mistaken, since it isn't possible to assert a name or a singular term, which is how those "A"s function in "A = A".

 

[Any who doubt this should try to assert "Socrates" or "The President of the United states of America" -- that is, they should try to assert these phrases, and not try assert something of the individuals concerned.]

 

Once again, we smack right into yet another non-dialectical brick wall!

 

2a. Conclusions can, of course, follow from actions or states, but even then, they will have been based on a certain interpretations of those actions or states, which interpretations will be framed linguistically. For example, "I conclude from your silence that you have no excuse for your behaviour." Or, "From your anger, I can only conclude you disagree with the results of the ballot." Or, "I conclude from the state of your car that you have been in a serious accident."

 

3. As noted in Essay Six (more specifically here), it looks like modern logicians are at last taking a hard look at the complexities inherent in our use of words/phrases like "diverse", "same but distinct", "identical but not the same" and "identical but distinguishable". (Many examples of these were given in that Essay). [On this see Sanford (2005).] This issue has now become important in QM. [On this, see French (2015), French and Krause (2006), Ladyman and Bigaj (2010), Muller and Seevinick (2009), and Muller and Saunders (2008). See also the Wikipedia entry here.] One thing is reasonably clear, few, if any, will be consulting Hegel's badly misnamed books on this subject in order to learn anything useful -- except, perhaps, how not to approach this topic.

 

3a. Hegel appears to have appropriated this odd idea from Kant, who introduced a new piece of jargon -- "real negation" -- to distinguish it from formal negation  (and possibly also from the use of the negative particle in the vernacular). The problem is that Hegel (and now Lawler, and, indeed, other DM-fans) run these two (or three) notions together. [On this, see Redding (2007), although it should be pointed out that Redding presents a completely different view to that which has been outlined here.] I will criticise Kant's novel use of "negation" in Essay Four Part Two. However, my line-of-attack there will simply be an extended version of the comments I now proceed to make in the main body of this Essay.

 

4. On this, see, for example, van Brakel (2000).

 

5. Hegel's (anthropomorphic) way at looking at nature is traced back to its roots (as part of 'Divine'/ruling-class law, etc.) in Essay Twelve (summary here).

 

6. There is more on this in Essay Nine Parts One and Two. My comments on Lawler's other significant contributions to this topic can be found here, and here.]

 

6a. Bhaskar clearly accepts the fractured 'logic' one finds in Kosok's pseudo-formalisation of Hegel's dialectic:

 

"Now from the consideration that the Hegelian determinate negation is simultaneously both a transformation in the observer's consciousness and an expansion of the whole conceptual field it follows that the latter can only be held in the mode of 'negative presence' -- what I am going to call, following Kosok's path-breaking study, 'negative referral'." [Bhaskar (1993), p.30. Italic emphases in the original.] 

 

We have already seen that Kosok oscillates alarmingly over his characterisation of the letters and symbols he employs. For example, concerning "e", we are told that it can be asserted, so it must be a proposition, indicative sentence, or clause -- but then we are told that it is also:

 

"a singular indeterminate primitive element...standing for any type of entity capable of being reflected upon (i.e. any object, structure, relation, or more generally, any event present to a field of consciousness)." [Kosok (1966), p.238.]

 

Here e has now changed into an "entity". However, as I have pointed out in the main body of this Essay, it isn't possible to assert an "entity" -- try asserting, for example, a planet or a mouse. Sure, one can assert that this or that object in space is a planet, but it isn't possible to assert a planet simpliciter. Go on, try it: "I assert Jupiter".

 

Again, one can assert this in reply to a question such as "Which planet is the largest in the Solar System?", but in that case that assertion would be an elliptical form of "I assert that Jupiter is the largest planet in the Solar System" (although the use of "assert" here would be decidedly odd -- one would normally just say "Jupiter is the largest planet in the Solar System"). Without such a background the assertion of "Jupiter" on its own would create nothing but puzzlement.  

 

Kosok also seems to think e is a number term!

 

"This 'other-than-positive' is defined as its co-relative contrary e (minus e), or, in opposition to (e), we can call this the logical Negation of e, written (-e) and called 'not e,' the parentheses about both e and -e indicating that a reflection has been taken, producing two terms as a result." [Ibid.]

 

For what else is this "minus" sign supposed to operate upon? It should hardly need pointing out, but the minus sign and the sign for negation aren't at all the same. "-2" designates a negative integer not the negation of 2; "-Socrates" does not designate an individual other than Socrates; it is just plain gibberish. -2 + -2 = -4 doesn't designate the addition of the 'negation of 2' to itself, either. [On this topic, see above.]

 

In relation to another passage in Kosok's pseudo-formalisation, I pointed out the following:

 

If, however, we interpret "" and "" in the standard way (to mean implication ("if...then"), and biconditional implication ("if and only if"), respectively), then e must be a proposition or indicative sentence, again! But, Kosok then ruins it all by telling us that:

 

"...the original pre-formal non-positive and non-negative e becomes transformed into a formed self-relation between itself (now appearing as +e) and its other e, which as a whole is written +e, i.e. something which is neither +e nor e as such -- neither 'within' nor 'without,' but their mutual 'boundary' state of mutual implication as possibilities. This now makes Se or +e a meta-formed relation about the co-relativity between +e and e, which cannot consistently be expressed by +e or e themselves, regarding them as separable distinctions." [Ibid., pp.242-43.]

 

If e and +e can stand in some sort of relation to each other (or to themselves), they must be objects, not propositions or sentences! [Why that is so was established earlier. See also Note 2.] In addition, we are told they also mutually imply one another, so they must be propositions or sentences, once more! And yet, they are also called "possibilities".

 

With the worst will in the world, it isn't possible to make any sense of this.

 

And, in connection with this passage:

 

"Analyzing the coupling relation +e in this way indicates that we have already begun a reflection on our initial reflection (R)e. For regarding the meta-formal relation +e as e΄, a new pre-formal posit, (R)e΄ produces two new expressions, (e΄) and (-e΄). But since e΄ already represents the inseparable relation between (e) and (-e), the new reflection (R)e΄ generates four terms: (e΄) involves a relation between ((e)) and ((-e)) and (-e΄) a relation between (-(e)) and (-(-e)). It should be noted that the first parenthesis about e was an indication that e co-exists with its negation -e, each term therefore appearing with a parenthesis, i.e. (e) and (-e), since each co-exists with the other. Similarly two parentheses about e, i.e. ((e)), indicates that not only do (e) and (-e) co-exist, but their negations -(e) and -(-e) exist, all four of which co-exist, producing the four terms ((e)), ((-e)), (-(e)) and (-(-e)). Thus a second reflection on e gives us the four expressions (e), (-e), -(e) and -(-e) originally implicit in the self-negation relation (e) (-e) except that now a second parenthesis appears indicating a completed second order reflection. A self-negation thus represents a transition state from one level of reflection to another. For example, the formed (e) and (-e) elements of the first reflection produced a universe of discourse which included a non-determinate relation (e) (-e) within it, which, however, could only consistently be expressed on a second level, where not only the (e) and (-e) terms appear (now as ((e)) and ((-e))) but also their negations (-(e)) and (-(-e)) implicit in (e) (-e)." [Ibid., pp.245-46. Once again, I have corrected the on-line misconstrual of "―" with "-".]

 

I pointed out the following:

 

All this talk of relations once again shows that these letter "e"s (bracketed or not) can't be propositions, indicative sentences or clauses, but objects of some sort. In which case, and once more, the implication and biconditional 'inscriptions' (which is all we can call them) Kosok uses can't stand for implication or equivalence, as they do in FL, but for 'implication' and 'equivalence', expressions whose meanings have yet to be explained.

 

Later, I considered this passage:

 

"For now a new level has been started, namely (-e΄) in opposition to (e΄), requiring a new resolution e˝ = (e΄) (-e΄) which repeats the above condition." [Ibid., pp.248-49.]

 

If "=" is meant to be the sign for identity, flanked by singular terms (Proper Names or Definite Descriptions), then there is no way that it can also be flanked by propositions, sentences or clauses. This can only mean that e˝, (e΄) and (-e΄) aren't propositions, sentences or clauses, but are the names of objects (or they are the objects themselves!). But, if that is the case, the 'biconditional sign' can't be a biconditional sign, and as such remains undefined.

 

[Any who doubt this should try making sense of "Socrates if and only if Socrates", or "The 43rd president of the United States if and only if The 43rd president of the United States"!]

 

On the other hand, if e˝, (e΄) and (-e΄) are propositions, sentences or clauses, after all, then the 'sign for identity' can't be a sign for identity!

 

[That was established earlier on in this Essay.]

 

The confusion continues:

 

"Regarding the dialectic process intuitively, reflection takes an immediately given entity called e, and 'places' this entity e in context with its other called not e or o, implicitly present within itself as the entity's potentiality for being questioned or reflected (i.e. negated as an immediacy), such that the result is now neither e nor o as such but the transcending and unifying movement or relation eo." [Ibid., p.255.]

 

These letter "e"s have now returned to base, and are "entities" again (as they were at the start), which can stand in relation to other "entities".

 

Later still, I pointed out the following:

 

Kosok now ascends to a higher level of 'consciousness'; it mightn't prove possible for us mortals to follow in his hallowed footsteps...

 

"We will now briefly indicate, given the principle of Non-Identity, how higher order levels of reflection manifest themselves as dialectic matrices displaying triadic movement in several dimensions simultaneously. Calling the self-negation term (e) (-e) by the symbol (--e), thus reflecting the double-implication and double-negation structure of the self-negation operation (negating both e and -e), the initial triad obtained through (R)e involves the terms (e); (-e) and (--e). The expression (--e) also indicates that the synthesis term +e is a negation of the negation of the original e, in that it is a return to the non-positive and non-negative nature of the original e, seen however on a more developed plane. We can now write: (R)e = (A N: S)e = (Ae Ne: Se) = ((e) (-e): (--e)) = e΄, where A, N and S stand for the assertion, negation and self-negation operators." [Ibid., pp.271-72. I have once again corrected the "―" sign, which has been misrepresented in the on-line version as "-".]

 

So, it now turns out that "--e" is now a meta-theoretical term representing the following formula: "(e) (-e)". But, and alas, the iterated sign "--" hasn't yet been defined for this 'meta-language'. No surprise there, then.

 

But, what the George W is this supposed to be?

 

"(R)e = (A N: S)e = (Ae Ne: Se) = ((e) (-e): (--e)) = e΄, where A, N and S stand for the assertion, negation and self-negation operators." [Ibid.]

 

Earlier on, brackets indicated assertion, but here assertion is marked by "A", so what do the above brackets now mean?

 

For example, does (A ...) mean "assertion of an assertion"? And we are still in the dark about the meaning of the colon, ":". Normally, it is short for "such that"; is that what it signifies here?

 

While we are at it, what on earth does this mean: (A N: S)e = (Ae Ne: Se)? The transition from the LHS to the RHS suggests that the "e" outside the first set of brackets (highlighted in red) has multiplied the contents of the bracket to its left to yield the RHS of this 'identity'! [If so, an earlier allegation that Kosok has conflated mathematics and logic has been confirmed yet again.] This means, of course, that A, N, and S must be mathematical objects/symbols, too, and thus no longer stand for "assertion", "negation" and "self-negation", contrary to what Kosok himself asserts. [If not, what do they mean?] On the other hand, if they still mean "assertion", "negation" and "self-negation", how can these terms (or "operators") be multiplied in this way? What on earth does "Assertion x entity" (i.e., "Ae") mean?

 

[My "x" here is the multiplication sign!]

 

True to form, we are given no rules sanctioning the expansion of 'dialectical brackets', which means that Kosok is simply making stuff up as he goes along, again.

 

Well, we needn't labour the point (especially since I have devoted tens of thousands of words to this topic already), Kosok is serially careless and hopelessly inconsistent in his employment of letters and symbols, but what use does Bhaskar make of some of them? Here is one rather confusing attempt to appropriate Kosok:

 

"Take a triadic dialectic, where (e) is the determinate negation of the originating conceptual or social form e, and o is the sublation of (e) and (e). In principle it seems that we have a choice: either (α) we can say neither (e) nor (e) apply in the transition state or boundary zone, rejecting the law of excluded middle and/or bivalence, assigning a third value (e.g., ontologically, indeterminate/undetermined/fuzzy; epistemologically, undecidable); or (β) we can say that both (e) and (e) apply, thereby rejecting the law of non-contradiction." [Bhaskar (1993), p.31.]

 

So, for Bhaskar, e has now morphed into a "conceptual or social form" (whatever that means!) -- studiously ignoring what Kosok had to say about this mercurial letter (see above) -- , which, of course, means that it can't feature in the LEM or the LOC, as it seems it can (sometimes!) for Kosok. And, as far as can be determined, "o" for Kosok doesn't mean the "sublation of (e)", but e's 'opposite'.

 

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

 

Be this as it may, Bhaskar is totally silent about the semantic and syntactic mess Kosok presented his readers. To be sure, we can agree that Kosok's is "path-breaking" work -- it breaks new ground in reducing 'the dialectic' to the status of a joke.

 

Bhaskar also uses the bracket sign in a different way to Kosok (so far as can be ascertained, that is!). The latter 'explains' his own use of this symbol as follows:

 

"The initial step of reflection R(e) is called the Assertion of e, written (e) or +e, which announces (affirms) something present in the field of consciousness, the parenthesis or plus sign indicating the act of reflection." [Kosok (1966), p.239.]

 

 He then adds:

 

"However, the very fact that (e) or +e is different from e (as, e.g., the positive integer +4 is different from the natural number 4) implies that something other than +e must exist, from which +e is distinguished by being only the positive or assertive form of e, otherwise there would be no point in regarding +e and e distinctly. This 'other-than-positive' is defined as its co-relative contrary e (minus e), or, in opposition to (e), we can call this the logical Negation of e, written (-e) and called 'not e,' the parentheses about both e and -e indicating that a reflection has been taken, producing two terms as a result. [Added in a footnote: The short dash in -e means 'not e,' while the longer dash in ―e means 'minus e' such that +e = (e) and ―e = (-e).] This means that unlike e, -e does not explicitly appear as an immediate pre-reflected given, but only makes its appearance through reflection, appearing as a reflected term (-e) after a reflection on e, producing (e), has implied that something other than e must exist permitting e to appear as a mediated term. Indeed, the notion of negation is regarded as the essence of reflection and mediation (and the act of questioning), since to mediate or reflect is to remove (negate) oneself from a situation of immediacy. The immediacy of -e is implicit, for by definition that which is immediate, and therefore starting our analysis, has been called e." [Ibid., pp.239-40. The on-line version has the wrong 'sign' in front of the first occurrence of "minus e"; I have corrected it. It should be "―e" not "-e".]

 

It is far from clear that Bhaskar is employing brackets in the same way as Kosok -- who, it is worth adding, later uses brackets inconsistently himself -- for example, here).

 

If I can summon up the will to do so, I will add a few more comments here about Bhaskar's fluent gobbledygook in the next few months.

 

7. This is an allusion to the following scene from Monty Python:

 

INTERVIEWER: How do you get along with French people?

 

PEPPERPOTS: Oh very well! Yessss. So do I, yes! So does Mrs. E! I like them... They think well, don't they... I mean, be fair: Blaise Pascal, Jean Paul Sartre, Voltaire, Rene Descartes...

 

INTERVIEWER: What do think of the Germans?

 

PEPPERPOTS: RUBBISH!! Rubbish! Emmanuel Kant Bloody "Ego posits itself!" My foot! Nietzsche?! HAH!

 

 

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French, S., and Krause, D. (2006), Identity In Physics: A Historical, Philosophical And Formal Analysis (Oxford University Press).

 

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--------, (1972b), 'Why Sentences Are Not Names', Studia Semiotyczna 3, pp.13-21.

 

--------, (1972c), 'History Of The Corruptions Of Logic', in Geach (1972a), pp.44-61.

 

--------, (1972d), 'Nominalism', in Geach (1972a), pp.289-301.

 

Glock, H-J. (1996),  A Wittgenstein Dictionary (Blackwell).

 

--------, (2003), Quine And Davidson On Language, Thought And Reality (Cambridge University Press).

 

Goble, L. (2001) (ed.), The Blackwell Guide To Philosophical Logic (Blackwell).

 

Grimm, P. (2004), 'What Is A Contradiction?', in Priest et al (2004), pp.49-72.

 

Hacker, P. (1996), Wittgenstein's Place In Twentieth Century Analytic Philosophy (Blackwell).

 

--------, (2007), Human Nature, The Categorial Framework (Blackwell).

 

Hahn, S. (2007), Contradiction In Motion. Hegel's Organic Concept Of Life And Value (Cornell University Press).

 

Hansen, J. (1977), 'Terrorism And political Activism', in Parsons and Somerville (1977), pp.101-11.

 

Hegel, G. (1975), Logic, translated by William Wallace (Oxford University Press, 3rd ed.).

 

--------, (1995a), Lectures On The History Of Philosophy Volume One: Greek Philosophy To Plato, translated by E. S. Haldane (University of Nebraska Press).

 

--------, (1995b), Lectures On The History Of Philosophy Volume Three: Medieval And Modern Philosophy, translated by E. S. Haldane (University of Nebraska Press).

 

--------, (1999), Science Of Logic (Humanity Books).

 

Horn, L. (1989), A Natural History Of Negation (University of Chicago Press).

 

Hunter, G. (1996), Metalogic. An Introduction To The Metatheory Of First Standard First Order Logic (University of California Press).

 

Hyde, D., and Priest, G. (2000) (eds.), Sociative Logics And Their Applications. Essays By The Late Richard Sylvan (Ashgate Press).

 

Ioan, P. (1990), Logic And Dialectics, translated from the Rumanian by Carmen Monoliu-Ciobanu and Silvia Manoliu (University Press).

 

Kant, I. (2003), Theoretical Philosophy, 1755-1770, translated and edited by David Walford and Ralf Meerbote (Cambridge University Press).

 

--------, (1763), Attempt To Introduce Negative Magnitudes Into Philosophy, reprinted in Kant (2003), pp.203-41.

 

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--------, (2004), The Singularity Of Awareness. From Mystical Theology Through Contemporary Cosmology (Author House).

 

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Lawler, J. (1982), 'Hegel On Logical And Dialectical Contradictions, And Misinterpretations From Bertrand Russell To Lucio Colletti', in Marquit, Moran, and Truitt (1982), pp.11-44.

 

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--------, (1972), Materialism And Empirio-Criticism (Foreign Languages Press).

 

MacIntyre, A. (1976) (ed.), Hegel. A Collection Of Critical Essays (University of Notre Dame Press).

 

Marquit, E., Moran, P., and Truitt, W. (1982) (eds.), Dialectical Contradictions And Contemporary Marxist Discussions, Studies in Marxism, Volume 10 (Marxist Educational Press).

 

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McCumber, J. (1993), The Company Of Words. Hegel, Language, And Systematic Philosophy (Northwestern University Press).

 

McGill, V., and Parry, W. (1971), 'The Unity Of Opposites: A Dialectical Principle', in DeGrood et al (1971), pp.183-208.

 

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Parsons, H., and Somerville, J. (1977) (eds.) Marxism, Revolution And Peace: From The Proceedings Of The Society For The Philosophical Study Of Dialectical Materialism (B. R. Grüner Publishing Company).

 

Priest, G., Beall, J., and Armour-Garb, B. (2004) (eds.), The Law Of Non-Contradiction. New Philosophical Essays (Oxford University Press).

 

Priest, G., Routley, R., and Norman, J. (1989) (eds.), Paraconsistent Logic. Essays On The Inconsistent (Philospohia Verlag).

 

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Sanford, D. (2005), 'Distinctness And Non-Identity', Analysis 65, 4, pp.269-74.

 

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Shanker, S. (1998), Wittgenstein's Remarks On The Foundations Of Artificial Intelligence (Routledge).

 

Shapiro, S. (2009), Classical Logic, in The Stanford Encyclopedia of Philosophy (Winter 2009 Edition, Edward N. Zalta (ed.)).

 

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Trotsky, L. (1971), In Defense Of Marxism (New Park Publications).

 

Van Brakel, J. (2000), Philosophy Of Chemistry. Between The Manifest And The Scientific Image (Leuven University Press).

 

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Williams, C. (1981), What Is Existence? (Oxford University Press).

 

Zumdahl, S. (1989), Chemistry (D C Heath and Company, 2nd ed.).

 

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