Well

Essay Eight Part Three -- 'Dialectical Contradictions'

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

If you are viewing this with Mozilla Firefox, you might not be able to read all the symbols I have used.

(1) This Essay began life as a footnote to Essay Eight Part Two ("Forces and 'Contradictions'"), and as such it assumes the results of that Essay, and those of Essay Eight Part One ("Change Through Internal Contradiction")'

(2) The central concern of this Essay largely revolves around the arguments found in the best article I have ever read on this topic (written by James Lawler).

(3) The ideas of other dialecticians in this area are covered in other Essays published at this site (but their comments are nowhere near as clear and comprehensive as Lawler's).

(4) Hegel's actual arguments will be considered in Essay Twelve Parts Five and Six (but they differ little from those reproduced below, as far as I can tell).

(5) A later re-write of this Essay will consider the arguments and explanations given in best Hegelian account of 'dialectical contradictions' I have so far read -- Hahn (2007).

This Essay is over 28,500 words long; a summary of its main ideas will be published at a future date.

Quick Links

Anyone using these links must remember that they will be skipping past supporting argument and evidence set out in earlier sections. [If your Firewall has a pop-up blocker, you will need to press the "Ctrl" key at the same time or these and the other links here won't work!]

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

(a) The Best Article I Have Read

(b) Science Of Thought?

(c) Yet Another Syntactic Mess

(d) Rosa's "Pedantry"?

(e) Hegel Screws Up Big Time

(f) Law Of Identity Mis-Identified

(g) More Dark Sayings From Hegel's Dialectical Dungeon

(h) 'Difference' Made Unrecognisable

(i) The Fog Thickens

(j) Zeno: No Help At All

(k) A Unity Of Opposites?

(l) The Magical Use Of 'Negation'

(m) Hegel's Hermetic House Of Horrors

(n) Acid Corrodes Hegel's 'Logic'

(o) Two Senses Of "Independent" Confused

(p) Threadbare

(q) What A Dialectical Dog's Dinner!

(2) An Hegelian Attempt To Dispel The Fog (not yet published)

(3) References

Abbreviations Used At This Site

Well, What Are 'Dialectical Contradictions'?

The Best Article I have Ever Read

Easily the best (Marxist) account of 'dialectical contradictions' I have come across in my trawl through the desert 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 piece of Hegelian gobbledygook is no better than his analysis of Bertrand Russell's criticism of Hegel for confusing the "is" of identity with that of predication, discussed in Essay Three Part One.

In fact, there are so many logical errors in Lawler's article that any conclusions he draws are not really worth the paper they were printed on.

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 of this very idea:

"Modern materialism is essentially dialectical.... What independently survives of all former philosophy is the science of thought and its laws -- formal logic and dialectics." [Engels (1976), p.31, quoted in Lawler (1982), p.14; Lawler's added italic emphasis here.]

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, the passage from Engels seems to identify formal and dialectical logic (indeed, he lumps them together as "the science of thought and its laws -- formal logic and dialectics"). In that case, far from making the said distinction so plain that it could not have been clearer, had Engels actually said they were distinct, that would have been clearer.

Hence, it is obvious from the beginning that Lawler's aim is to defend a view consonant with tradition, rather than read even Engels with any accuracy.

As noted in Essay Two, when it comes to Philosophy, dialecticians are as tenaciously traditional as they are consistently conservative. Indeed, they are quite happy to copy and then recapitulate the errors of Ancient Greek (and now modern-day Hermetic) thinkers, spinning their own webs of a priori Jabberwocky-lore, using obscure jargon they struggle to explain to bemused onlookers.

[How they do this is the subject of Essay Three Parts One and Two, and Essay Twelve Part One. Why they do it is outlined in Essay Nine Part Two and Essay Fourteen (summary here).]

Sure, we have no evidence that Marx himself was this confused over the nature of logic, but there is enough in Engels's writing to indicate that he was no clearer than Hegel -- indeed, Hegel was less clear than Aristotle (who tended to confuse logical with psychological and ontological issues far less than did this modern-day, Hermetic 'genius') --, which makes the logical views of these two completely worthless.

And, as we have already seen (in Essay Four), Logic cannot be counted as a science of thought, for if it were, logicians would perform brain scans, psychometric testing and surveys (etc.), and wouldn't waste time with all those useless definitions, rules of inference and proofs.

Nevertheless, we should not let these relatively minor deficiencies detract from the more serious errors to come.

Another Syntactic Mess

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 later), Hegel's criticism of the LOI is worthless, since he confused predication with the relation of identity, which then 'allowed' him to conjure his 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".]

[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 cannot be implicated in the latter'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 turn to more substantive issues, we find Lawler is just as slip-shod in his use of 'logical' terms as other dialecticians are. Indeed, this is the only way he and they can make Hegel's 'theory' seem to work (upside down or the 'right way up').

First of all, as we have already seen with respect to other DM-fans, Lawler is decidedly unclear about the denotation of the letter "A"s he uses. [Why this isn't a minor, 'pedantic' detail will become clear before too long.]

For example, on pages 18-19, in reference to Hegel's discussion of Identity, Lawler has 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, three different kinds of 'things'.

[LEM = Law of Excluded Middle.]

But then 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 middle set of quotation marks here (around the LEM) are missing in the original.]

As we will soon see, the principle of identity does not imply what Hegel says it does (or even what Lawler himself says it does -- since he nowhere corrects Hegel), but that is not of immediate concern here. However, when Lawler qualifies what he takes Hegel to mean, he clearly 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.]

So, they are no longer the names of objects or concepts, they are (the names of, or proxy letters for) propositions. That's 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 its name (but that is hardly likely; Lawler and/or Hegel were not bothered to discover alleged truths about names, one supposes). But even if this were so, in the above passage, "A" itself would be an object and what can be asserted of an object (i.e., a predicate expression, say). So, this response would be at once to defend Lawler and convict him in the same move.

Despite that, his wording does not support this contention. Lawler 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 his "A"s to be named objects, say, then he would have used the latter phrasing.

[Anyway, as we shall soon see, later on in Lawler's Essay these accommodating letters are unambiguously propositions.]

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?); that's 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 could be that Lawler is merely adopting a tradition in ancient/early modern logic that treats all logical expressions equally sloppily (which, as it turns out, is the tradition that presided over the creation of the bowdlerised version of AFL that Hegel was taught at University (the kind of sloppy 'formalism' one finds in Kant's Logic, for example), and which he then put to no good), which seems to be the most likely explanation for Lawler's confusion here, given the other things we are about to discover (and to which we have already drawn attention, in Essay Three Part One, and Essay Four).

[AFL = Aristotelian Formal Logic.]

Nevertheless, it is this slip-shod approach to logic 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.]

And this is somewhat reminiscent of the sort of word-juggling which allowed, say, St Anselm 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., p21. Italic emphasis in the original.]

Although Lawler does not mention those "A"s here, they have now clearly become "things" once again. However, on page 22, they quickly 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 soon morph into "beings" (or what it true of them):

"…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 more, 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 does not imply Bush no longer exists. Anti-imperialists would surely have consigned one or both of these war-mongers and mass murderers 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 indeed 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", and 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 [an Italian Marxist, who Lawler is criticising in this article, RL] deny Hegel's point that asserting 'A' is equivalent to saying 'not-not-A'" [Ibid., p.24. Italic emphases in the original.]

If something is capable of being asserted, it 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 if predicative expressions are completed with names, or with other singular terms (or indeed with the linguistic equivalents of the bound variables of quantifiers). As should seem obvious to any language-user, it is not possible just to assert a bald "term", predicate or concept. Uttering "ξ is a cat" (or "...is a cat", or even "is a cat") is to assert nothing (i.e., it is to make no assertion) -- and the same is true of merely uttering the word "cat".

Of course, one can point at an animal and utter this word, but that is the equivalent of saying "That is a cat". Without the pointing gesture, the use of that word would be to assert nothing (i.e., it is to make no assertion, once more). 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?"

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.]

Unfortunately, detailed consideration of the above will take us into areas that will be discussed in Essay Twelve (when it is finally published); suffice it to say here that Hegel's confusions on this score 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.]

The conflation of "terms" with "things", and then with linguistic expressions that can be asserted of named individuals (or once again perhaps better: true or false sentences can be formed by the completion of predicative expressions with names, or with other singular terms (or indeed with the linguistic equivalents of the bound variables of quantifiers, etc., etc.)), 'allows' Lawler (just as it 'allowed' Hegel) to derive the sort of "interesting" results we have come to know and loathe.

So, that's nine sorts of things these "A"s are.

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 named relational expressions(!):

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

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

And it will not do to say that Lawler is merely reporting what Hegel's opponents might say, since he nowhere tries to pull these miscreants up for their syntactical sins.

At the very least these morphoholic letter "A"s now stand for propositions again, since here 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 two hundred years ago Hegel was indeed faced with such simple-minded opponents, then no wonder he got away with so many logical howlers. But even so: 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 example (i.e., as a change of mind) that does not treat Hegel's opponents as sub-literate morons.

Nevertheless, Lawler's "A"s have been transmuted once more into either propositions or predicates -- or perhaps even into properties(?) --, or maybe all three(?).

On the very next page (but in the same paragraph), it becomes a little clearer that these highly plastic "A"s are indeed relations, or nominalised relational expressions (or maybe nominalised relational phrases(?)); in fact it's quite plain that this is indeed 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 nor false, Lawler's reasoning is, shall we say, 'innovative'. Nevertheless, these busy little "A"s have plainly had yet another denotational make-over, and now stand for "identity held aloof from difference".

[The phrase "identity held aloof from difference" might appear to make sense to some, but that is only because they have become inured to this odd way of talking -- perhaps as a result of reading far more Hegel, or "systematic dialectics", than is good for any human to have to endure --, a use which pretends that relational expressions can be named and still remain relational. (This Ancient Greek ploy 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 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"s and "not-A"s now plainly stand for "here" and "not-here", respectively. A change of identity perhaps, but no less of an example of lamentably poor logic for all that.

That's now at least thirteen different identities for these impressively fluid letters!

As we saw in Essay Five, the above 'analysis' of motion had more holes in it than a lorry load of Polo Mints. There is no 'common sense definition' of the items Lawler mentions; ordinary language (let alone 'common sense') easily allows for the sorts of place and motion in the material world that Idealists like Hegel ignored --, and they do this with relative ease, too.

Nevertheless, on page 32, these change-oholic "A"s go into morphological hyper-drive as they become parts (or perhaps 'reflected' parts) of one another:

"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 seem to work. Above, I have 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 some of the best.

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 have then been 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 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 thus by traditional styles-of-thought (which they had no hand in creating, but into which they had been educated and which they were only too happy to appropriate), DM-theorists found there was no easy way out of this traditionalist 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 deny that dialecticians are aware of the Idealism implicit in traditional thought; on the contrary, their excuse for ignoring its pernicious influence on their own ideas is that the materialist flip they say they inflicted on Hegel is deemed capable of transforming theoretical dirt into philosophical gold.

However, flip or no flip, their own thought is still thoroughly traditional in style: it is dogmatic, a priori, and couched 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 copying its conservative approach to 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 reality. 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 such a sloppy use of words, where predicate expressions are turned into names, objects, terms, indexicals and possibly relations themselves -- and which can thus stand in some relation to other similarly deformed linguistic expressions, or suitably 'processed' objects.

Indeed, this is the only way that 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 with any urgency.]

But, because of this 'innovative' use of language, Lawler's explanation of 'dialectical contradictions' falls completely flat, as we will see.

Now it could be argued that these syntactical niggles are not 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, of course, remains to be seen. But since Lawler's article is by far and away the best defence of this incomprehensible Hegelian notion (i.e., 'dialectical contradiction') I have so far seen from a Marxist, this should indicate to the reader just how bad things are in this back-water of traditional myth-making. In that case, a dialectical rescue is highly unlikely from this stubborn wing of Idealism. Even academic dialecticians regularly make serious errors of this sort, and worse -- and they all fail to notice them, let alone acknowledge them, even after they have been exposed. That is how logically purblind this ruling-class gobbledygook has rendered them. [The latest examples of this can be found here (halfway down the page), here, here, here, here, here and here.]

[Indeed, Rosenthal (1998, 2001) also fell upon deaf dialectical ears. The above allegations, however, will be substantiated in Essay Twelve, where Hegel's work in this area (along with that of his 'Marxist' groupies) will be taken apart.]

Naturally, I exclude Graham Priest's work from these impertinent indictments since it is far from clear whether the 'contradictions' he considers are 'dialectical' to begin with (even if we could tell!), or are even contradictions to begin with -- and he is generally very careful with his syntax. 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 those who think that this sort "pedantry" (or "semantics") can be ignored it is worth pointing out that that would be the only way they could excuse their own sloppy thinking, and the only way they could make their ideas appear to work.

This sort of attitude would not 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 does not matter what the Magna Carta said, or when the Battle of the Nile was fought, or what the Declaration of Independence actually contained, or what the exact wording of Newton's Second Law was, or whether "G", the Gravitational Constant, was 6.6742 x 10^-11 or 6.7642 x 10^-11 Mm²kg^-2, or indeed something else? Would we accept this sort of excuse from someone who said it did not matter what the precise wording of a contract in law happened to be? Or, that it was of no real concern what Marx meant by "variable capital", or who claimed that he had "pedantically" distinguished use-value from exchange-value -- or more pointedly, the "relative form" from the "equivalent form" of value --, the distinction is merely "semantic"? And how would we react if someone said, "Who cares if there are serious differences in the evidence given by two cops against some strikers"? Or if someone retorted "Big deal if there are a few errors in this or that e-mail address/web page URL, or in that mathematical proof! And who cares whether there is a difference between rest mass and inertial mass in Physics! What are you, some kind of pedant?"

You can be sure such 'non-pedants' will be examining these Essays with well-focussed magnifying glasses, nit-picking the detail, having turned their selectively pedantic eyes on all I have written in order to locate the tiniest of assumed errors --, all the while refusing to examine anything in the DM-Grimoire with a tiny fraction of such attention to detail. [In fact, they already have.]

With such a sloppy regard for logic and fondness for Mickey Mouse Science, is it any wonder that genuine ruling-class theorists regard Dialectical Marxists with undisguised contempt, and workers in their billions ignore all they have to say?

Hegel Screws Up Big Time

Nevertheless, in order to consider every option open to Dialectical Mystics to say what they mean by 'dialectical contradictions', Lawler's argument will be considered on its own merits. This is where we will see how and why Lawler's syntactic sins have led him astray.

Early on, Lawler tries to revamp Hegel's criticism of the LOI by arguing thus:

"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 thinkers got themselves into over precisely this in Essay Three Part One, and Essay Four.

[LOI = Law of Identity; FL = Formal Logic.]

To be sure, Hegel was writing at a time when little work had been done on this 'law', but Lawler isn'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 mystical joke that it is. [On this, see here, and here.]

Putting this to one side for now, Lawler proceeds to argue as follows:

"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 it being stated "negatively". The latter principles comprise the LOC and the LEM –- but notice once again the common error dialecticians make (exposed in Essay Four) of thinking that FL has just three fundamental principles.

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 is itself not 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. MFL = Modern Formal Logic.]

Hegel (and now Lawler) offers no proof of this '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 is not about the truth-functional links between propositions, which is what concerns those other 'laws'.

Lawler thus reports the following:

"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 these letter "A"s (which explains why I went into all that 'pedantic' detail over making this very point!).

Now, in relation to the LOC, if these letters refer to propositions, no problem. The above would at least be a passable definition of the LOC; but under 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 (which means that the LOI is not a tautology -- on that, see below), but even if it were, that would have no implications for the LOC. The LOC does not rule out propositions being non-identical (but see below), since it doesn't concern the identity of propositions to begin with. So, the LOC neither rules this in nor rules it out. Indeed, if a proposition lacked identity it would not be a proposition in the first place. And if it possessed identity it would be an object, not a proposition. [On why propositions aren't objects, see Note Two.]

To be sure, we can speak about two propositions saying the same thing, but that would not 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, or the sounds involved when it is spoken) or the name of a proposition with what a proposition expresses. [On this, see below.]

We have already seen (here, here and here) that the LOI cannot be about the alleged identity between concepts, or even between predicates (since if it were, the latter would be objects too, and cease to be predicative); the LOI can only apply to objects (or perhaps their names), 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.

This is partly because an identity statement isn't molecular --, that is, it expresses a relations of an objects to itself, and thus doesn't contain sub-clauses, or simpler propositions. [On this, see Glock (1996), pp.164-69.] Identity statements cannot be expressed as tautologies by the truth tables. And even in predicative sentences, tautologies (at a discursive level) merely "say the same thing", or involve the use of synonyms. They do not involve identity statements, since the latter are not predicative, but relational. At best, a proposition expressing identity contains a relational expression which is symmetrical, reflexive, and transitive (among other things).

In short, identity statements cannot be tautological (in the sense of "saying the same thing") because both halves do not "say the same thing" -- since those halves do not say anything at all. "A", in "A = A", if it is a name, or other singular term, does not say the same thing as "A" since "A" says nothing. Only clauses, propositions or sentences can be used to do that. On the other hand, if "A" is a proposition, or clause, it cannot be put into a relation with itself, since it is not an object.

Discursively, an example of a tautology would be something like "A vixen is a female fox", which expresses a rule of language, and so cannot be true or false (this was argued at length in Essay Twelve Part One). On the other hand, "A vixen is a vixen" is not a rule of language. However, if this sentence is interpreted predicatively, "ξ is a vixen" cannot be saying the same thing as "A vixen", for the latter is plainly not of the form "ξ is a vixen". Moreover "A vixen" is not saying anything determinate, so "A vixen is a vixen" cannot be saying 'the same thing'. Moreover, "'ξ is a vixen' is a vixen" is not a tautology, and "...is identical with ξ" does not "say the same thing" as "ζ is identical with...".¹

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

Indeed, and that is why this sentence was called a rule, since it expresses a pattern for replacing synonymous terms in English, so that anyone who used "a vixen" in a sentence" would be saying the same as anyone using "a female fox" (in non-opaque contexts).

[MFL = Modern Formal Logic; wff (pronounced "woof") = well formed formula.]

It could be argued that an identity statement is predicative, or could at least be put into predicative form. Moreover, an identity statement -- for example, "ξ is identical with ξ" --, always gives the value true for any legitimate substitution instance. Maybe so, and in that sense, it would be a tautology in MFL (if the latter is defined as any wff that always maps onto the true). But this is not a necessary adjunct to logic, as Wittgenstein showed. In a properly constructed formal language, identity would be expressed by the use of the same sign, so we do not in fact need this formal relation. [More on this, here.]

But this is certainly not what Hegel and Lawler were talking about.

Anyway, even as predicative propositions, identity statements would still not be tautologies in the discursive sense Lawler and Hegel need (i.e., in the sense of "saying the same thing"). This is because the predicate here would be a two-place linguistic function "ζ is identical with ξ" (it cannot be "ξ is identical with ξ", for that prejudges the substitutional instances allowed), 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, such functions are analogous to mathematical functions, except, in this case, they map linguistic expressions (of a certain sort) onto linguistic expressions (of another sort). (The latter sense is not intended here). For example, the linguistic function "ξ wrote Das Kapital" maps "Karl Marx" onto "Karl Marx wrote Das Kapital".]

Finally, even if the predicate were "ξ is identical with ξ", this would be no use, either, for "...is identical with ξ" does not "say the same thing" as "ξ is identical with...".

The Law Of Identity Mis-Identified

But, even if we were to concede that the LOI were the following:

L1a: p = p,

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

or perhaps:

L1b: ∀(x) [Fx = Fx],

[Where "∀(ξ)" is the universal quantifier, and "F(ξ)" a one-place, first-level predicate expression], neither of these would have any bearing on the relation they are supposed to have with their alleged negative/'opposite' -- as Lawler alleged --, 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.

This is because there are no rules for deriving either L2 or L3 from L1a or L1b (or from the less formal versions of these two), or indeed from anything analogous. And it is not hard to see why. [More on this presently.]

[Of course, L3 could itself be correct (I will pass no opinion on it here), but L2 and L3 certainly do not follow from L1a or L1b, or from their alleged negative versions (or from the less formal versions of the two, as we will soon see).]

Now, if L2 had been:

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

the problems associated with Hegel's 'derivation' would have been a little easier to see. 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."]

Or, perhaps just this:

L4a: [(p = p) ® ¬(p ≠ p)].

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

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

L5: ¬(p = p) v ¬(p ≠ p),

and thus (by De Morgan's rules):

L6: ¬[(p = p) & (p ≠ p)],

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

L7: ¬(Γ & ¬Γ).

But, 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 is another fatal defect with this 'derivation'; on that see Note 2.

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

Even if we did have such rules, 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. But, as we have seen, it is not too clear how L7 can be derived from "p = p" on its own, or even from its alleged negative form.

However, it is worth pointing out again that if a proposition is not identical with itself, it cannot be a proposition (at least, not one with a determinate content). In that case, nothing could follow from it. On the other hand, if it is identical with itself, it would be an object, not a proposition -- and, plainly, nothing follows from an object.²

Either way, we hit another brick wall.

Nevertheless, it could be argued that in logical stencils 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 at least between their signs. So the earlier claims cannot be correct.

But, logicians who use either the equal or the equivalence sign between propositional tokens do not imagine that these physical objects 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 as 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, and so on.

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

[To be sure, some philosophers have held such views, but they too confused propositions with objects.]

Indeed, the second of the above (L10) shows that this is so by implicitly interpreting the equivalence sign as expressing an identity between objects of some sort. In that case, stencils like L9 and L10 do not contradict what was maintained earlier, which was that where the sign for identity (etc.) is used, it expresses a relation between objects (or an object and itself -- or between its names), not between concepts, predicates or propositions. Sure, we can introduce a sign that it typographically identical with the identity sign (no pun intended), and place it between concepts and propositions. But if this is not interpreted as the identity sign, then that would be to treat concepts and propositions as objects again.

Moreover, in L10, the "=" sign appears between quantified variables (the interpretation of which will depend on the domain of quantification, so this might not even be an example of the use of that sign between propositional tokens).

Now, whether this employment of signs captures the full range of meanings available in scientific contexts -- or even in ordinary language --, I will leave to one side for the present (but, it is worth adding here that Essay Six delivers a negative judgement in this regard).

[Of course, in stencils like L9, the "=" sign would be replaced by an "º", that is, by a biconditional sign. This is because "=" is a sign for two-place predicate/linguistic function (i.e., "ξ = ζ"), which can only take names or singular terms as arguments.]

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 syntactical mess we find in DL. In fact, as Essays Three through Seven show, DL cannot handle the simplest of ideas/objects (such as a bag of sugar!), let alone anything more complicated.

[DL = Dialectical Logic.]

Hence, once more, the suggested Hegelian 'derivation' of the LOC (i.e., the one expounded by Lawler) cannot work if these "A"s are read as objects (since objects cannot be true or false), nor, indeed, if propositions are viewed as objects, either (and, for the same reason).

This is why it is so important to be clear about the denotation of these letters, and (once more!) why such a fuss was made earlier.

Alas, there is not much that can be done with this:

Here, the letter "A" oscillates between predicative and naming roles (it seems), and if so, the LEM as stated above cannot be correct. [Even Aristotle saw through that one!]

[Nevertheless, as with most topics in logic, things are not quite so simple. We need to distinguish between sentential negation (i.e., "not p"), predicate negation (i.e., "not F") and predicate-term negation (i.e., "not-F" or "non-F"). It is unclear which form Lawler intends to use in the above passage (but his indiscriminate employment of "not A" and "not-A" suggests he is either unaware of this distinction, or he considers it unimportant -- the same unfortunately seems to be true of Hegel and his many groupies), so I have not dwelt on this difference in this Essay (nor on its alleged double negated form --, as in "non-non-F"). This topic will, however, loom large in Essay Twelve, where the deleterious effects of suicidally sloppy syntax like this will be exposed.

More details on this distinction can be found in Horn (1989) and Wansing (2001).]

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 "…is red" cannot be "…is non-red" (if viewed traditionally --, but as "ξ is red" cannot be "ξ is non-red", otherwise). But, since these are not even sentences, it is impossible to make sense of them.

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 predicates allegedly designate.

But, in that case, Lawler's "A cannot be non-A" would yield "C cannot be D". This is because Lawler clearly sees these "A"s here as the names of properties (and if these are expressed as predicate expressions, then the latter will become names once more). 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 obtain "C cannot be D". And that is because, "...is red" must name something different from "...is non-red".

Of course, this will be so unless "…is red" is viewed as the same name (say "E") as "…is non-red" (also "E"). If so, 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 sense of what Lawler is trying to say here.

That is because Lawler's 'definition' tries to relate a term to its negated 'other', but his own (sloppy) syntax prevents him from doing this. The reader will note that at the beginning of this passage "A" is a predicate letter, but by the end it has become 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.} So, this is just another example of the confusion I tried to highlight 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 cannot say since he does not say. [And no one else has.]

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

P1: Non-A is not A,

or:

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

Where B is the "something" that is not A. But Lawler immediately qualifies this by saying that "non-A" is "something that is not A, or some part or property of A". In which case he appears to mean:

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

or perhaps:

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 conceptual and logical tools Hegel passed on to the unfortunates who look to him for inspiration.

So, as things stand, it seems this logical sow's ear cannot be made even into a plastic purse...

More Dark Sayings From Hegel's Dialectical Dungeon

Now Lawler moves on to consider several other dark sayings he rescued from 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, since it can only 'work' if propositions, predicates and objects are confused one with another, as we have seen. This means that we can only make sense of 'dialectical contradictions' if we pretend that the denotation of words and letters does not matter. In which case, we should openly remove the word "logic" from its already precarious presence in Hegel's method, and rename it perhaps "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?

As we saw in Essay Three Part One, this inept trick was invented by ancient Greek philosophers: nominalise anything and everything in sight. In fact, they had to do this to try to make their a priori 'theories' seem to work (and this in turn was done for ideological reasons, explored in Essay Twelve (summary here)).

The problem is that this move changes propositions into lists, which destroys their capacity to say anything at all. [Why that is so is demonstrated here.] Any 'contradiction', or, indeed, conclusion that 'follows' from this Stone Age segue is therefore entirely bogus, since nothing can legitimately follow from a named abstract object like "identity". [Conclusions can only follow from propositions, or clauses.]

Well, perhaps Hegel meant that the practice of referring to identity statements tended to exclude those that expressed difference; 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 not an object, but a relation), and yet it is quite plain that both Hegel and Lawler need this 'abstraction' to be an object so that it can serve as the denotation of those annoyingly plastic letter "A"s we met earlier. However, if identity isn't an object (abstract or otherwise), then neither of these two can extract a contradiction from their idiosyncratic version of the LOI:

Here, plainly, "A" stands for "identity" and "not-A" for "difference". But, once again, it's only sloppy syntax like this that allows Hegel's argument to gain even so much as a pretend toehold. 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 the passage quoted earlier, 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 can derive all sorts 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 as supposed to exclude, namely difference." [Ibid., p.20.]

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 his straw opponents: 'abstract identity' can only be conjured into existence if relational expressions are transmogrified into names. This is what is actually happening in the theories of those he was criticising; Hegel does not question these moves, he just compounds the problem with novel confusions of his own.

How could he possibly have missed this obvious response?

[Hint, fill in the missing letters in the following: "Hegel was a logical inc*m*et*nt."]

Insults aside, can any sense be made of this?

Not much, it seems, since the whole topic (indeed, the whole of Hegel's work) is a direct result of a systematic capitulation to the misuse of language on a grand scale.

And, of course, it is possible to identify something (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 variables; "®" is the implication arrow, equivalent to "if...then"; "x" and "y" are bound variables.]

To be sure, different signs are used 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" (and what they say is hypothetical): it sets conditions on objects being the same, not different. The same applies to the others -- they were all translated here.

Moreover, it is worth noting that Hegel (and perhaps Lawler) slides between two uses of the word "identity/identify" -- that is, between this word when it is used (1) to provide an empty (or perhaps significant) identity statement for any given object, and (2) in relation the capacity most of us have of being able to identify (in the sense of being able to pick out, or to recognise perhaps) a person, property, process or object.

So, if, say, squaddie NN is asked whether or not he can identify Osama bin Laden in a line-up, and he replies, "Osama is identical to Osama", 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!", he would not.

Naturally, the latter use could in some circumstances involve the capacity to differentiate among objects, but this is not necessarily so in every case (as was pointed out here).

By running these two senses together, Hegel demonstrated he was even more confused than this dim squaddie. Lawler might well be advised, therefore, to resign his role as defence counsel.

[Admittedly, there are three uses of this word (indeed, in ordinary language, there are countless -- on that, see here), the third being found in more 'philosophical' contexts, connected with an attempt to provide a comprehensive description of a substance, a là Leibniz.]

Of course, to do the former (i.e., (1) above) we do not 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 this Hegelian wild-goose chase can only get started if we are prepared to become linguistic philistines, or if we 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 Absolute Idiots, not Idealists!

Lawler now inflicts 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 since 'subjects' (I assume Lawler means names here, or some other singular designating expression) assert nothing (and neither can we assert anything merely by the simple use of a name, or any other singular term), then the employment of names (or other singular terms) can assert nothing different from that of predicates if they do not assert anything to begin with. [All this was argued in detail in Essay Three Part One.]

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 cannot -- so, there is a difference.

This is undeniable, but it's not 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 was 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 also something different from each other. But, since, only one is capable of asserting anything, we cannot even derive an 'identity' (in what is asserted) here, never mind a 'difference'.

It is not easy to credit such an 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 or phenomenological differences between subject and predicate terms, it would plainly be based on the crass confusion noted above -- in that it runs together identity with being able to identify, difference (i.e., lack of 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 need not be physically different from 'subjects' (nor even divorced from them in time); so Lawler's 'argument' is hopeless from beginning to end.

Once again, we can see that it is quite clear that 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 dialectically-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 here, 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 is not a relation, but an object, or a name of an object. Now, this is about as crass 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 dialectically-annoying riposte is effective only because it makes hay of Hegel's dim-witted confusion of relational terms with singular designating expressions, or, indeed, with abstract particulars, and/or the names thereof --, a trick, of course, he learnt from equally confused Ancient Greek theorists.

In fact, this manoeuvre does not just relate to, but helped create the empty Idealist flap over 'Subject/Object identity', which was the main problematic of German Idealism. Hence, if names and predicates are both objects of some sort (or they designate them), then their inter-identity (or lack of it) naturally becomes a 'problem'. But, if only names that actually name things --, whereas predicates merely describe the objects so named --, then the centuries devoted to solving this bogus 'problem' can be seen for what they are: a monumental waste of time. 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' -- but, there's no seeming about it; it does, and good riddance, too.

Indeed, we will see later (in Essay Twelve Part Six) that this doctrine arose from within ancient Greek ideas concerning 'non-propositional' thought (in Aristotle and Plotinus, for example), and the relation of the mystical knower to the Hermetic unknown. It is this ancient doctrine that lies behind all the nominalisations we have seen, as well as the Identity Theory of Predication that Hegel was taught and which he needed to make his 'theory' 'work'.

[On the Greek end of this sorry tale, see the Owen (1966) -- 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 by a seemingly insignificant syntactical error, and by supposedly intelligent theorists!

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

In that case, Marx did not go far enough: ruling ideas do not just rule such minds, they ruin them.

Hence, Lawler's conclusion:

"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.]

is so wide of the mark it is lodged in the next star system.

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

This 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 no better; if anything, it's worse. Exactly who wants to "banish" difference is unclear -- and how they might manage to pull this trick off is even less obvious; take out a court order, perhaps? Utter a spell?

Nevertheless, such conveniently fictional characters and their impossible antics need not bother us for now. What's 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 is this no longer 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 concluded from this latest 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) neglected to say.³

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 the word in question cannot 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 would not need to appeal to this 'entity' (indeed, we would be wise to ignore it) in order to understand how to make identity statements.

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

The Fog Thickens

From here, Lawler's attempt to clarify the meaning of the fog-bound 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.]

As we have seen, if this is an implication, then the required relation can only be forged out of it if the propositions involved are nominalised. But, once that is done, no inference is possible; objects do not and cannot imply other objects, and neither can expressions that have been nominalised.

But, 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" does not in fact imply that A is not also not-A; indeed, it could be the case that even while "A is A", A could also be B (which is not-A).

Taking 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 syntactic 'looseness' of this counter-example, for the "A"s they use are subject to no little dialectical double-dealing themselves. Hence, dialecticians have no more right to complain about sloppy syntax when it used against them that George W Bush has a right to moan about "terrism". If this counter-example is to be ruled out on syntactic grounds, then much of Lawler's (and hence Hegel's) argument must 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 since, as we have seen, Lawler's As can be anything we please.

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 see, the required relation can only be forged if the propositions involved are nominalised. And, as we also saw earlier, even if the "is" here is treated 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.

More-or-less the same comment applies to this example of 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.]

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

However, as we have just seen, there is no "negative relation" of A to not-A, and that means that it is not the case that "A is itself in not being not-A". The whole passage is thus about a genuine as one of George Brown's smiles.

In that case, the NON here is just as fabulous a beast as the Jabberwocky ever was. Hence, if the NON works, it can't apply to negation; on the other hand, 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 above examples of reconstructive linguistic surgery, as he turns to Hegel's use of contradictions, beginning with a consideration of Zeno's paradox of motion:

"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 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 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 excluded 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.]

But, this is of no use at all in helping anyone understand the term "dialectical contradiction" since Zeno's 'paradox' is no paradox, as we saw in Essay Five (or, rather, it is only a paradox for those Idealists who are determined to think and speak like linguistic Philistines).

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…, 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.]

Here, it seems, the terminally unclear (i.e., "dialectical contradiction") can be explained by means of the hopelessly obscure (i.e., "unity of opposites").

Nevertheless, at the risk of further annoying those who, even now, are content to stumble about in this Hermetic Haze, this alleged 'unity' 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 as soon as that is done, these 'terms' either cease to be predicates, or they are no longer general (depending, of course, on how this Hegelian fairy tale is finally unwound -- that is, whether it is interpreted as applying to 'things' or 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 terms changes dramatically. Traditional theorists in general ignored this glaringly obvious fact. They still do.]

As we noted in Essay Three Part One, this remarkable a priori 'truth' is one such solely because Hegel's system depends on a methodology derived from an ancient ruling-class tradition, one that systematically distorts ordinary material 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, see here.]

Lawler then notes that Hegel's analysis of 'dialectical contradictions' begins from the 'commonsense' view of motion and place, and proceeds from there. He adds that it is not relevant to argue that modern definitions of motion are more precise -- or rather, that this would be 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 -- 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., abstract particulars once more).

Now, as we approach the seemingly impossible goal -- that of trying to find some 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.'" [Ibid., p.32. Italic emphases in the original.]

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

[Indeed, "A and not-A" is a non-contradiction, unless, that is, "A" is no longer an object, or name of an object, but a proposition, and as such stands 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 of 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…. 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, 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 cannot 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 supposed. 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. However, on this see here.]

Unity Of Opposites?

Now, Lawler rejects the open insertion of "not-A" for "A" (which, if correct, as we saw in Essay Four (here), would in fact be bad news for Diabolical Logicians) with an obscure quotation from Hegel that seems to be devoid of earthly sense (omitted here, to help conserve the reader's sanity), but he then goes on to say:

"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." [Ibid., pp.32-33. 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." [Ibid., p.33.]

Now, as we saw in Essay Seven, this example of homespun neo-Romantic pseudo-science won't work; 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 (which was current in Hegel's day) than it is an accurate reflection of living things themselves.

And 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'? Did it gain an 'identity' only when the first living things evolved? In that case, was life bound to evolve, just to help identify, or 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' must exist somewhere if all things, including matter, are to have an 'identity' only in and because of its 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, 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 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 the 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 this he would not have been able to spin any of his elaborately convoluted dialectical fairy tales, since ordinary speakers do not confuse predicate expressions with 'beings', sentences with objects, objects with relations, and "not" with 'negativity', in their everyday use of language.

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

The Magical Use Of 'Negation'

But, is this once again a little too hasty? We will soon 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 see an HCD like Lawler make all the same old sophomoric mistakes. What the dialectics has "formal" negation got to do with any of this? Precisely which non-existence of what entities 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 that it was that easy to consign Hegel's confused book to logical limbo!

Or, what does the existence of the Eiffel Tower imply the non-existence of? It could be argued that had the Eiffel Tower never been built, something else would occupy its place, which, of course, now it 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) prevents anything else occupying the same space.

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 list the Eiffel Tower first in their list of favourite structures, and the Great Pyramid as first in their list of place to visit next. Here, these two would then occupy the same place in both lists, namely, first.

Someone could object that this example merely concerns the appearance of names in two lists, 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). 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 this for herself), it's 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.

[LCD = Low Church Dialectician; HCD = High Church Dialectician; LOI = Law of Identity.]

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

Of course, ordinary negation is very complex -- on this 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' might seem to allow this virulent strain of Hermetic Herpes to proliferate.

Lawler continues:

"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.... 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 (also) intrinsic to that constitution. The negativity is not an unfortunate by-product, which one might possible eliminate, of the positive relations necessary for the things development. It is intrinsic to that positive connection." [Ibid., pp.35-36.]

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 aren't external (extrinsic), but are internal (intrinsic)? 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 more. So, apart from an appeal to yet more sloppy logic, there is nothing to indicate that '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:

"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.]

But, the "dialectical negativity" of "certain thought processes" is a genuine as a thirteen dollar bill. So, unless the physical world 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) which 'support' such hyper-bold claims?]

Well, here it is; here is the missing 'evidence' -- and, surprise, surprise, it is just as watery-thin as the 'data' produced in support of the sort of Mickey Mouse dialectical superscience we met in Essay Seven, scraped-together by the aforementioned, conceptually-benighted 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 does not work, howsoever they are re-packaged. But, flowery language aside, the forces at work here are all manifestly external; there are no internal relations (except, of course, those conjured into existence by Hegelian Hocus Pocus, once more).

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.]

But, here we are confronted by "forces" (plural) that oppose life. So life, it seems, is exempt from that earlier Hegelian caveat, in that it appears to have hundreds, if not thousands of "others". Of course, this 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 must not expect answers to such questions; this is Mickey Mouse a priori superscience, after all.

But, 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." [Ibid. p.36.]

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

Of course, heat is not a force; it is in such contexts merely a shorthand for the energy with which certain molecules have been accredited. 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?

However, 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 "others"? How might we tell?

Despite this, the processes Lawler describes are all causal; there are, once again, no Hegelian concepts here for Biophysicists to study.

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." [Ibid., p.37.]

[There then follows a few hundred words of fluent Martian (aka, hardcore Hegelian gobbledygook) I haven't the heart to inflict on the reader -- she has suffered enough.]

So, how precisely does heat 'mediate' here? Unfortunately Lawler neglected to say.

No doubt, some day soon a Biophysics department, somewhere, will commission a PhD student to fill in the gaps...

To be sure, Hegel did argue as follows:

"...[E]ach 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." [Hegel (1999), p.441; §960.]

This paragraph highlights Hegel's warped and prejudicial thinking quite nicely. 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. What about tripartite relations (like speed, distance and time, or mass, density and volume)? Or multivariate relations like the points on a compass?

Figure One: Hegel Loses His Bearings

And if this example is regarded as 'abstract' (but those who think so should check out the next 'abstract compass' they use on a walk in the mountains, say, and it will 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. This might be regarded as unfair, since the latter was invented after Hegel's day -- but that just shows, once more, what hopelessly limited the 'logic' Hegel used.]

And do not even begin to think about large finite relationships, such as "the millionth woman to give birth to a child", or "the ten thousandth man to visit the USA", who are only such because of the ordering relations we have among our numbers; each is only what he or she is because of the 999,999 or the 9999 individuals/'others' they are related to respectively as their predecessors.

And 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 be between here because it has at least two 'others'. And if we move into three dimensions once more, something can be both to the right and left of an 'other', if it is on a globe, while being between at least eight others (which reside at the vertices of a cube which surrounds it).

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 through 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." [Ibid., p.37.]

And, earlier we had this:

But, while we are clear about the nature of contradictions (in ordinary language and FL at least), we are still in the dark as to what 'dialectical contradictions' are --, other than their merely being the products of Hegel's insecure grasp of even the primitive logic of his day, and (at least in his theoretical deliberations) of ordinary language -- 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 is not about "non-being"): all it says (once more!), and in its simplest form, 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 a separate matter.

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

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

In many systems of logic, if Tony Blair does not exist, then "Tony Blair does not exist" is truth-valueless. On the other hand, "Tony Blair exists" would be a logical truth if he does exist! In such systems, C1 is not even a contradiction, since the first half lacks a truth value. In that case, even this 'contradiction' is not about "non-being", since it is not a contradiction. 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. But even there, the LOC is not about what exists, or about "non-being".

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

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

Out of these, only a handful are described by Grimm as 'ontological':

"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 is 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., capable of being quantified: in "some B"), and 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.]

Putting this to one side, we would need to know what these two mean 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 would not be "ontological". Unfortunately, the original article in which this 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. Anyway, even this unfortunate definition is not 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 this endeavour. In that case, it is not difficult to believe that Hegel's baleful influence lies behind their definition. This is in fact confirmed by Routley and Meyer (1976).

[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 and heavily dependent on Hegel), and the many essays 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, here --, p.50.]

This is an appallingly bad definition from a top 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, 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 create logic almost from scratch. The same excuses 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/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]

In any case, even if it were clear what 'dialectical contradictions' are, FL would need neither this notion nor dialectics 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." [Ibid., pp.37-38.]

All this a priori jargon is standard fare in HCD texts, but that doesn't imply that 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 does not use those words, as far as I can tell, but 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 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 belief that 'negative' propositions are all false (or 'defective' in some other way). But, 'negative' propositions can be, and often are, true. For example, "Blair is not 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 "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 has not resigned" is the contradictory of "Blair has resigned"; the first is false, but hopefully it will become true one day -- it could not 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 it is false, what it says has not 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 sort of rejects this view (or, rather, he aims to transcend this formalist approach), but he does not 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, the latter is not 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 this pointless 'logical' journey to nowhere.

Well, 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!]

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

Of course, it could be objected that (-1)^1/2 is not negative (even though it contains a negative sign!), but what about -(i^1/2)/-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'?

In that case, it seems 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 do not "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. Emphasis added.]

And that is it! A plain "must" after this long detour through this sub-Aristotelian wasteland.

The rest of the article is merely window-dressing. We are left with this counterfeit "must" here, backed neither by logic nor fact. So why we "must" see these obscure creations of Hegel's Hermetic Hallucinations in this way is 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 dense fog Hegel left it in 200 years ago. Exactly why the word "contradiction" has to be super-glued to the other term ("dialectical") is a mystery -- except that Lawler might have hoped that some of the clarity associated with the former might rub off onto the latter.

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

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

"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 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." [Ibid., p.38; quoting Hegel (1975), p.174. I have used a different edition from Lawler.]

Considering this famous (dogmatic) assertion: either Hegel wrote it or he did not. If either (but not both) of these is the case, then Hegel was mistaken since here there is just such an "either-or".

Worse: in heaven, hell or high water, there is an "either-or" or there isn't. So, if Hegel was right (and there wasn't an "either-or"), he was wrong, since there would be (i.e., here!). And if he was wrong, then he was wrong anyway. Either way, he was wrong.

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

I'll get the petrol...

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"?

Acid Corrodes Hegel's 'Logic'

The acid example is none-too-clever either. Lawler comments 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 it 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.

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, if we lump the lot together).

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, some have been 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, subcontraries and contradictories are interdefined among four "others"). Lest these be rejected as 'abstract' (a fine accusation to have levelled at one by a Hegelian) 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, and Aldehydes.

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

Furthermore, this entire topic is mixed up with Hegel's mystical fugue on "finitude" and "infinity"; Lawler quotes him thus:

"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." [Ibid., p.39, quoting Hegel (1975), p.139; Lawler's italics. Again, I have referenced a different edition from that used by Lawler.]

Well, that certainly clears things up!

But, how is self-relation "the genuine Infinity"? Lawler just accepts this mystical missive, and does not explain it -- except he expands on it with yet more 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' [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.]

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

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

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

"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 is the form of completeness, hence of 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....The form of universality in nature is law." [Engels (1954), pp.234; quoted in Lawler, p.39-40. Italic emphases in the original.]

Lawler comments on this 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 tries to equate these two, but, for those still in command of their reason, neither an "always" nor an "at all times" is an "infinite".

[In a later Essay, we will see that this view of scientific/physical law is a carry-over from ancient animistic ideas about nature, and so it's no surprise to find this doctrine re-surfacing here, in such mystically motivated company. On this see here and here; the first is Swartz (2006), the second Swartz (2003).]

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:

"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.]

But, this poetic description of a chemical reaction is far from being even metaphorically 'true'. Since when has Chlorine ever been a 'free' being? 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 more that the semi-religious typology of the "other" has now been dropped, since Chlorine reacts with practically everything. In fact, it has more "others" than 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. This 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, this 'logical' object, this "other", has to be forced into adopting its dialectically-determined fate.

But, even if this mystical fairytale (about the formation of HCL) were correct, exactly how this is an internally-driven process is somewhat unclear. Surely, Chlorine is not to be regarded as not-Hydrogen? If it were, then everything in the universe that is not Hydrogen (or not-Hydrogen) would be Chlorine! Or, conversely, everything that is not-Chlorine would be Hydrogen. [In which case, you, dear reader, are Hydrogen, and Chlorine, and Zinc, and pencil shavings, and poisonous reptiles, and...!]

Of course, that is why the significant "other" myth was spun earlier (to block this very objection), but as we 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-...); indeed, in the limit, it would be not-anything. In this Hermetic Hell Hole, Chlorine should disappear like 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' turn out to be mis-described 'external relations'. It is thus no wonder that we need Super-duper logic -- courtesy of Hegel -- to assist us; ordinary language, FL, and good old-fashioned matter are 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.]

Well, Lawler's 'contradiction' isn't one if the word "exist" is a quantifier, and the first (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; "H(ξ)" and "C(ξ)" are one-place, first level predicate expressions, 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 be different.

Of course, this method of analysing propositions could be rejected; there is nothing that forces 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 this 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, and who denied both could be false at once. But who 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 example is a dud too.

Two Senses Of "Independent" Confused

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.]

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 is independent of everything. Moreover, the meaning of the word "independent" has altered, too. From "independent" implying "not linked to" (or "isolated from"), it has become "does not depend on", and this is what allows the potential for one item to 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 in the first sense of "independent"), but still for it to be capable of reacting with it if and when this state is altered.

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 react if given the chance.

Let's assume, therefore, that one day a group of scientists create a new compound called "Hegelase" (a new form of poison -- apparently it blocks the "passages", and cripples its 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's further imagine that some of it 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 has 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 does not. If it did, then we must argue that Hegelase has over 6 billion "others" (i.e., humans) out there, 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 that 6 billion "others" would amount to a mere fraction in comparison.

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 will gain a new "potentiality", for free, without moving a muscle.

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

We have to say 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? How is it able to kill things that do not, and perhaps will not ever exist?

However, even if this is rejected for some reason (perhaps, by the use of a complex counterfactual), 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 sentence Lawler implicitly admits that Hydrogen, for example, has no significant 'other'. With that Hegel's account of change "repels" even his own logic, and collapses under the weight of its own 'internal contradictions'. A rather fitting fate for such a useless 'theory'.

But, despite this, is Hydrogen that intelligent and 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 any of this?

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 dos 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.]

But, this only works because of the ambiguous way that the words "independence" and "dependence" have been used (as noted above: one minute the first is understood to mean "isolated", or "free and unconnected", the next it means "not dependent on").

Lawler then goes on to discuss more technical notions connected with "form" and "essence", which add little to the above -- except, perhaps, this:

"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, and so the whole passage is as clear as dialectical mud.

A Few Threads Left

Mercifully, we are nearing the end; Lawler now tries to draw several 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." [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 perhaps can be thought of as a poetical sort of way of depicting their capacity to react. And all of this is based on the earlier word-juggling of a few letter "A"s, themselves of a somewhat 'mercurial' disposition (or, indeed, "potential").

As far as the laws governing nature are concerned, these cannot be seen as decrees written into matter, which all things have to obey (as it seems this line of thought implies). To be sure, Hegel could accept such an animistic idea, but no materialist 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.] Lawler almost 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.]

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 it is capable of doing unaided -- since that would not be 'rational'. 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, common-or-garden, boring old matter is not 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 used helped conjure these mythical beings (these "laws") into existence; merely reversing our perspective in no way changes these bogus moves into a valid alternative. If it did, we should have to start believing that the Brothers Grimm were first-rate scientists. Without an Ideal backdrop, 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.

[This (i.e., 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).]

What A Dialectical Dog's Dinner!

That's it! This is the best defence 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 genuine materialists (i.e., that we do not "understand dialectics") also applies in reverse to those very 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 been saying 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, and then later with science -- who are still endeavouring to do this --, 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 these comrades have to inflict on language is somewhat similar to the linguistic gyrations perfected by the above theologians and casuists. Indeed, the somersaults these comrades 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, just like the aforementioned RC contortionists.

Now, I do not expect dialecticians to accept the above criticisms since they are still wedded to the ancient idea that human discourse, at some level, contains the key to the inner secrets of 'Being'. Given that view of language, all that these philosophical alchemists have to do is find the right formula -- the right key --, and linguistic dirt can be turned into theoretical Gold, the whole transformation achieved without leaving one's non-dialectical armchair.

Such theorists are indeed the philosophical equivalent of those whom Marx called revolutionary alchemists; only here the right verbal formula is capable of unlocking the mysteries of 'Being', allowing such Dialectical Magi to invent an the ideal world to suite themselves. Up to now they have plainly not transformed the class structure of the planet, but they have 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 and political failure.

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 so for reasons Feuerbach exposed 160 years ago. This is because this theory allows them to see the world as the opposite of what it really is -- consolation from convolution.

There is no arguing with faith like this. As I have pointed out elsewhere:

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

This way of seeing things was invented by ideologues of the ruling class, who originally 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" and administrators, at least) that the present order either works for their benefit, is ordained of the 'gods', or is 'natural' and cannot be fought, 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 changed with each change in the mode of production, its form has remained largely the same for thousands of years: Ultimate Truth is ascertainable by thought alone, and it can therefore be imposed on reality dogmatically.

So, these non-worker founders of our movement, who had been educated to believe there was just such a hidden world that governed everything, 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 a ruling-class mystic called Hegel.

That allowed the founders of this quasi-religion to think of themselves as special, as prophets of the new order, which workers, alas, could not quite grasp because of their defective education and reliance on ordinary language and 'common sense'.

Fortunately, history has predisposed these prophets to ascertain the truth about reality for the rest of us, which meant they were our 'naturally-ordained' leaders. That in turn meant these 'leaders' were the rightful teachers of the 'ignorant masses', and thus who could thus legitimately substitute themselves for the unwashed majority -- in 'their own interests', you understand . This is because the masses are too caught up in 'commodity fetishism' to see the truth for themselves.

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

It is also why dialecticians cling on 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 outward 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 this core theory says everything changes! Hence, it is ossified into a dogma, and imposed on reality. A rather nice unity of opposites for you to ponder.

So, this 'theory' insulates the militant mind from reality.

In that case: 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 (materialist) workers to rescue them from themselves.

Changing the material conditions that gave rise to such alienated thought-forms is the only thing that will finally bring Dialectical Day-Dreaming to an end. RL stands no chance!

Dialectical mystics are just going to have to rely on the material force of the working class to save them from themselves and from this virus of the mind.

[More on this in Essay Nine Part Two. My comments on Lawler's other significant contributions to this topic were posted here, and here.]

Notes

1. Readers may find this way of analysing propositions rather odd. It was briefly explained and justified here. It isn't the only way to do this, 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...", for instance? Part of the reason why those using the traditional logic that predated Frege made so many errors is that they did not possess the sophisticated tools we now have for making such distinctions, the dialectical mess Lawler gets into being a prime example.

2. It might be wondered why a proposition can't be an object, nor vice versa, but an object says nothing (in the sense that a sentence says something, or can be used to say something). [On this, see the section on signs in Essay Thirteen Part Three.]

If a proposition is interpreted as "That which is being proposed, or put forward for consideration", then it can only be confused with an object by conflating it with a propositional sign (i.e., marks on the page, or screen).

If, on the other hand, a propositional sign is treated as a series of objects, it becomes a list, and, as we saw in Essay Three Part One, lists say nothing.

It could also be argued that we should create a rule that licences the derivation of the LOC from the LOI stated negatively; that is, one of the following:

H1: 'A is A' implies 'A cannot at the same time be A and not be A.'

H2: 'A = A' implies 'A cannot at the same time be A and not be A.'

H3: ∀(p) [(p = p) ® ¬(p ≠ p)].

H4: [(p = p) ® ¬(p ≠ p)].

We have already seen that H3 and H4 present problems for the nature of propositions, so we might find it useful to concentrate on H2 and H2 -- or, rather, on H2, since it is less controversial (in that it uses the equal sign). But, once again, this interprets the second and third of the As in H2 each as part of a predicate expression: "...cannot at the same time be A" and "...(cannot at the same time) not be A," while the first A is not part of a predicate expression. H2 would then have the form (if we ignore the modal version for now):

H5: ∀(x) [Ax ® ¬(Ax & ¬Ax)].

This reads, "Anything which is A is not both A and not A."

But, this is no good either since this treats all three "A"s as predicative, and not part of a relation, which is what was required. Perhaps then this will do:

H6: (A = A) ® ¬[(A = A) & (A ≠ A)].

Again, we have already seen a version of this (here), so once again, if we now 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 us to replace "¬(A = A)" with "¬Γ"), we could obtain the following from H6:

H7: (A = A) ® ¬(Γ & ¬Γ).

Which is the LOC. No problem with that.

Alas, however, this is not what Lawler tells us Hegel is arguing, which was that the LOI stated negatively implies the LOC. But H8, which is what Lawler wanted, cannot be derived from H7:

H8: ¬(A = A) ® ¬(Γ & ¬Γ).

Nor can this:

H9: ¬(A = A) ® ¬[(A = A) & (A ≠ A)].

Nor can ¬(Γ & ¬Γ), be derived from ¬(A = A) on its own.

Anyone who thinks otherwise is welcome to try.

It could be objected that the negation of the LOI is not the same as the LOI "stated negatively", so the above response is beside the point.

So, returning to an earlier point:

H6: (A = A) ® ¬[(A = A) & (A ≠ A)].

H7: (A = A) ® ¬(Γ & ¬Γ).

We derived H7 from H6 by the introduction of the following rule (which we did not attempt to justify):

H10: (A ≠ A) º ¬(A = A).

But, we can only use this rule if it is true for all objects, which takes us back to H5:

H5: ∀(x) [Ax ® ¬(Ax & ¬Ax)].

This reads, "Anything which is A is not both A and not A." However, as we saw earlier, the As here are predicative, not part of a relation. Well, we might be able to circumvent this obstacle by the use 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 identical and not identical."

This at last looks like a general version of the rule that Lawler requires; if fact it is better, since it does not confuse predicates with relations.

But, is the latter half of H11 the LOC? No, it isn't, since the LOC is not about objects but about propositions (or clauses).

We might now think that by H11, replacing "(x = y)" with "Γ" and "(x ≠ y)" with ¬(x = y), and hence with "¬Γ", we can obtain a contradiction:

H12: ∀(x)∀(y) [Γ ® ¬(Γ & ¬Γ)].

But, this is syntactically ill-formed, But, if we focus on:

H12a: Γ ® ¬(Γ & ¬Γ),

we lose the generality we once had.

We can't do back to quantifying across propositions, for reasons stated in the main body of this Essay, here.

We hit the same brick wall.

Finally, we might be tempted to go back to H5:

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 -- where we also demonstrated that any attempt to turn it into an identity hits a brick wall.

It might be felt that the back end of H11 (i.e., H14) is indeed the LOC. In fact, it is the negation of a contradiction, but it's not the LOC, which concerns propositions not the identity of objects.

H11: ∀(x) ∀(y) [(x = y) ® ¬{(x = y) & ¬(x = y)}].

H13: (x = y) & ¬(x = y).

Hence, if H13 is a contradiction then the following is a tautology (but only in the context of the quantifiers in H11):

H14: ¬{(x = y) & ¬(x = y)}.

[Incidentally, this does not contradict the earlier claim that an identity is not a tautology since the above is clearly a negated conjunction of an identity with its negation.]

But, this is still not the LOC, as noted earlier. As I commented 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, no problem. The above would at least be a passable definition of the LOC; but under 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..., but even if it were, that would have no implications for the LOC. The LOC does not rule out propositions being non-identical...since it doesn't concern the identity of propositions to begin with. So, it neither rules this in nor rules it out. Indeed, if a proposition lacked identity it would not be a proposition in the first place. And if it possessed identity it would be an object, not a proposition.

3. As noted in Essay Six (more specifically here), it looks like modern logicians are at last taking a hard look at the complexities 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 (2006), French and Krause (2006), 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 the subject.

4. On this, see, for example, van Brakel (2000).

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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).

Prior, A. (1967), 'Negation', in The Encyclopedia Of Philosophy, edited by Paul Edwards (Macmillan).

Quine, W. (1974), Methods Of Logic (Routledge, 3^rd ed.).

Rosenthal, J. (1998), The Myth Of Dialectics (Macmillan).

--------, (2001), 'Hegel Decoder: A Reply To Smith's "Reply"', Historical Materialism 9, pp.111-51.

Routley, R., and Meyer, R. (1976), 'Dialectical Logic, Classical Logic, And The Consistency Of The World', Studies in Soviet Thought 16, pp.1-25.

Russell, B. (1961), History Of Western Philosophy (George Allen & Unwin).

Sanford, D. (2005), 'Distinctness And Non-Identity', Analysis 65, 4, pp.269-74.

Schofield, M., and Nussbaum, M. (1982) (eds.), Language And Logos. Studies In Ancient Greek Philosophy (Cambridge University Press).

Sorabji, R. (1982), 'Myths About Non-Propositional Thought' in Schofield and Nussbaum (1982), pp.295-314.

--------, (2005) (ed.), The Philosophy Of The Commentators. A Sourcebook 200-600AD, Volume One, Psychology, Ethics And Religion (Duckworth).

Swartz, N. (2003), The Concept Of Physical Law (Cambridge University Press, 2^nd ed.); this is a PDF file.

--------, (2006), 'Laws Of Nature', Internet Encyclopedia of Philosophy.

Van Brakel, J. (2000), Philosophy Of Chemistry. Between The Manifest And The Scientific Image (Leuven University Press).

Wansing, H. (2001), 'Negation', in Goble (2001), pp.415-36.

Williams, C. (1981), What Is Existence? (Oxford University Press). [This book can be accessed at Google Books, but the link is too long for me to embed it in this page!]

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