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

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

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

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

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

Clearly, using the right language was important to Lenin.

Unsurprisingly, Trotsky concurred:

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

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

Hegel Screws Up Big Time

Identifying The Problem

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

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

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

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

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

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

[LOI = Law of Identity.]

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

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

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

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

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

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

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

Lawler follows up with this remark:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

This is neatly summed up for us by Henri Lefebvre:

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

Indeed, Hegel himself clarified his position in like manner:

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

Lawler also says as much:

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

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

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

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

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

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

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

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

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

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

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

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

"In brief, dialectics can be defined as the doctrine of the unity of opposites. This embodies the essence of dialectics...." [Lenin (1961), p.222. Bold emphases added.]

"The identity of opposites…is the recognition…of the contradictory, mutually exclusive, opposite tendencies in all phenomena and processes of nature…. The condition for the knowledge of all processes of the world in their 'self-movement,' in their spontaneous development, in their real life, is the knowledge of them as a unity of opposites. Development is the 'struggle' of opposites…. [This] alone furnishes the key to the 'self-movement' of everything existing…. The unity…of opposites is conditional, temporary, transitory, relative. The struggle of mutually exclusive opposites is absolute, just as development and motion are absolute…." [Ibid., pp.357-58. Bold emphasis alone added. Paragraphs merged. Quotation marks altered to conform with the conventions adopted at this site ]

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

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

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

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

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

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

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

"Formal logic, which is based on abstract, or simple, identity (A equals A), is too one-sided to explain this negation of one state of matter and its transformation into its opposite, in this case the lifeless into the living, because it excludes from its premises real difference and contradiction, which is the extreme development of difference. But the unity of opposites (A equals non-A), which makes contradiction explicit and intelligible, can explain this transition, which actually occurred on earth. The emergence of life from the nonliving in turn substantiates the objective basis in nature of this law of concrete contradiction, a cornerstone of dialectical logic." [Novack (1978), p.239 and Novack (2002), p.196. (This links to a PDF.)]

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

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

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

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

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

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

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

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

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

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

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

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

With that observation, the entire 'dialectic' implodes.

Lawler sort of half recognises this when he says:

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

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

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

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

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

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

Not A Tautology

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

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

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

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

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

T1: A vixen is a female fox.

T2: A regicide is a king-killer.

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

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

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

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

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

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

T1: A vixen is a female fox.

T2: A regicide is a king-killer.

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

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

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

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

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

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

T1: A vixen is a female fox.

T2: A regicide is a king-killer.

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

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

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

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

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

T1: A vixen is a female fox.

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

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

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

F1: A vixen turned the bins over last night.

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

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

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

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

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

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

F1a: Cicero turned the bins over last night.

F2a: Tully turned the bins over last night.

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

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

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

[MFL = Modern Formal Logic.]

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

F3: A vixen is a female fox.

F4: A regicide is a king-killer.

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

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

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

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

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

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

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

The Law Of Identity Mis-Identified

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

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

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

L1a: p = p.

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

Or, perhaps even:

L1b: ∀(x)[Fx = Fx].

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

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

L1c: ∀(x)[Fx º Fx],

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

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

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

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

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

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

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

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

P1: N*(A) º ¬*A.

Or even:

P2: N*(A) = ¬*A.

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

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

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

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

P3: N(A) º ¬A.

P4: N(A) = ¬A.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The dilemma facing DM-fans is now quite stark:

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

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

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

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

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

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

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

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

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

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

L4: ∀(p) [(p = p) ® ¬(p ≠ p)].

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

Or, perhaps more simply:

L4a: [(p = p) ® ¬(p ≠ p)].

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

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

L5: ¬(p = p) v ¬(p ≠ p),

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

L6: ¬[(p = p) & (p ≠ p)].

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

L7: ¬(Γ & ¬Γ).

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

Which, of course, looks like the LOC.

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

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

L7: ¬(Γ & ¬Γ).

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

Either way, we hit a brick wall.

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

L9: ∀(x)[Fx = Fx],

and:

L10: (∀x)(∀y)(∀F)[(Fx º Fy) ® (x = y)],

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

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

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

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

L9a: ∀(x)[Fx º Fx].

L9b: ∀(x)(∀F)[Fx º Fx].

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

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

L9: ∀(x)[Fx = Fx].

L9a: ∀(x)[Fx º Fx].

L9b: ∀(x)(∀F)[Fx º Fx].

L10: (∀x)(∀y)(∀F)[(Fx º Fy) ® (x = y)].

L10a: (∀x)(∀y)[(Fx º Fy) ® (x = y)].

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

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

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

L9: ∀(x)[Fx = Fx].

L9a: ∀(x)[Fx º Fx].

L10: (∀x)(∀y)(∀F)[(Fx º Fy) ® (x = y)].

L10a: (∀x)(∀y)[(Fx º Fy) ® (x = y)].

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

However, I suspect the above should really have been:

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

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

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

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

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

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

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

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

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

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

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

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

otherwise.

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

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

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

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

B3: "A cannot be non-A",

would in fact yield:

B4: "C cannot be D".

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

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

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

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

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

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

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

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

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

P1: Non-A is not A.

Or, it could be:

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

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

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

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

Or, perhaps even:

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

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

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

More Dark Declamations From Hegel's Dialectical Dungeon

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

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

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

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

However, Lawler continues:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

(1) (∀x)(∀y)((x = y) º (Fx ® Fy)).

(2) (∀x)(∀y)((∀F)(Fx º Fy) ® (x = y)).

(3) j(y) º [(∃x)((x = y) & j(x))].

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Surely this is philosophy for Idiots, not just Idealists!

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

Lawler now piles yet more confusion on his unfortunate readers:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

'Difference' Rendered Unrecognisable

Unfortunately, there is more:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

This misbegotten tale continues:

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

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

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

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

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

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

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

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

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

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

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

Lawler continues:

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

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

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

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

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

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

The Fog Thickens

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

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

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

That is so for at least two reasons:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[NON = Negation of the Negation.]

Zeno -- No Help At All

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

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

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

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

But what about these words:

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

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

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

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

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

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

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

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

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

As we have seen, Engels asserted the following:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[Irony intended.]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Consider, therefore, the following example:

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

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

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

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

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

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

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

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

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

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

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

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

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

L45: Workers move about in factories.

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

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

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

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

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

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

That appears to contradict Engels:

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

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

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

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

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

Or, so some might like to think.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[SC = Spatial Co-ordinate.]

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

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

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

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

We seem to be going round in circles.

[No irony or pun intended.]

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

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

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

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

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

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

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

But that is just Option (1), again!

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

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

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

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

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

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

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

[Iterated version of Option (1)!]

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

Perhaps this is the direction we need to take?

[No pun intended.]

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

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

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

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

Consider, then, Option (4a):

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

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

[Modified Option (2)!]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Figure One: At Last! An Organism That

'Understands' Dialectics

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

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

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

[DL = Dialectical Logic.]

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

Back to the main feature...

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

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

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

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

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

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

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

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

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

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

[On this in general, see here.]

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

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

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

Every Magic Trick Requires A Diversion Of Some Sort

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Lenin wrote in the margin:

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

To which he added:

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

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

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

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

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

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

The most relevant and important part of which is this:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The Real Main Feature

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

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

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

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

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

He does so as follows:

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

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

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

Unity Of Opposites?

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

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

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

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

Lawler continues:

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

This represents Hegel's way of:

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

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

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

In relation to that we read:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Well, maybe not Hegel, but certainly Lawler should.

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

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

The Magical Use Of 'Negation'

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

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

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

With such 'logic', when someone, for instance, says you don't own the Taj Mahal, they must mean that amazing building has just disappeared. Indeed, if you want to get shut of your neighbour's tall trees (that are maybe blocking your daylight), just try saying to yourself that you don't own those trees. If that doesn't inspire you, then maybe reflect on the fact that Tony Blair isn't a socialist.

Problem solved...

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

But, the above use of "not" isn't an example of "formal negation", I hear someone say. That is undeniable. In that case, we should perhaps consider the following question: What 'non-existence' is implied by ¬p? Of course, it is impossible to say before symbols like this have been interpreted. But, as soon as that has been done, the negative particle ceases to be formal! In which case, it is impossible to make sense of Lawler's "negation cannot be understood in the formal sense".

It could now be objected that if Blair doesn't own a copy of the said book then it doesn't exist on his shelves, or in his possession. So, non-existence is implied after all.

But, is it? Isn't it possible that even though Blair doesn't own a copy of the said book, it still sits on his shelves because he borrowed it from the library or from a friend, or he was sent a copy by the publishers for him to review? So, even if it were true that Blair doesn't own the said book, that doesn't imply it isn't on his shelves or in his possession. So, the proposition "Blair does not own a copy of Hegel's Logic" does not of itself imply the non-existence of anything.

Someone could now object that the sentence "There is no copy of Hegel's Logic anywhere in Blair's house, office, car, garage, potting shed, or any property he owns" --  this use of negation does imply nonexistence, the nonexistence of a copy of that book in any property owned by Blair.

Not so fast! Nonexistence here is built into that sentence by the use of a quantifier expression qualifying a general noun -- i.e., "no copy" -- not the use of the negative particle itself. So, no wonder it is implied by that sentence -- which we can see for ourselves when it is expanded into what it is really saying: "There isn't a copy of Hegel's Logic in any property owned by Blair." The use of a quantifier expression that explicitly implies non-existence hardly shows that non-existence is implied by negation as such! Indeed, we can achieve the same result by using a sentence with no negative particle anywhere in such a sentence. For example: "Everything Blair owns has just been blown to pieces." That sentence implies the non-existence of the said book in anything Blair owns, but there is no negative particle anywhere in sight.

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

However, given the complexities involved in our use of the word "place" (on that, see Essay Five), not even that is as secure an inference as it might seem at first. For example, someone could put the Eiffel Tower first in (i.e., at the top of) their list of favourite structures, and then The Great Pyramid first in their list of places to visit. Here, these two structures, or their names, would then occupy the same place in both columns -- namely, first in each list -- at the same time. And that doesn't even necessarily involve the use of their names (i.e., their physically written names), since both lists could be committed to memory. In that case, we would have two things in the same place at the same time -- and possibly even two 'intentional objects' occupying the same place that the same time.

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

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

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

[LOI = Law of Identity.]

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

Of course, ordinary negation is very complex -- on that, see Horn (1989/2001) -- but, formal negation is the result of either the use of sentence-forming, or clause-forming operators, in a formal language. That's it! Anything else ain't formal negation, howsoever much this "anything else" allows this virulent strain of Hermetic Herpes to proliferate. [However, so-called "predicate term negation" will be ruled out of court in Essay Twelve Part Five -- but even if that ruling were quashed on appeal for some reason, it isn't too clear how it might be of any assistance to Hegel, or even Lawler.]^3a

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

"In the first place, negation cannot be understood in the formal sense, according to which the existence of some entity implies the nonexistence, pure and simple, of another. [We have just seen that neither 'formal negation' nor ordinary negation imply this -- RL.] And yet intuitively we recognize in real life some entities do destroy others, or less radically, they 'clash,' collide or struggle. It is common to regard such practical negativity as external or accidental to the nature of the entity or entities involved. The entities are regarded as in themselves self-subsistent 'positives' which may 'interact,' modify, and sometimes interfere with or destroy one another." [Ibid., pp.35-36. Bold added.]

If so, the mere existence of one object does not automatically imply the non-existence of another. If it did, there would be nothing for A to struggle against or interfere with, would there? So, it seems this odd form of negation would make the existence of 'dialectical opposites' (i.e., 'not-A', where the 'not' here is understood 'dialectically') impossible. [I return to this topic again, below.]

Lawler continues:

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

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

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

Perhaps because he recognises the bogus nature of this derived-out-of-thin-air sort of 'necessity', Lawler now retreats into the subjunctive mood:

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

But, the "dialectical negativity" of "certain thought processes" is about as genuine as a $17 bill (even if we knew what the obscure phrase, "dialectical negativity", meant!). So, unless the universe is itself as logically-challenged as this passage clearly is, such 'innovative' reasoning will find no easy correlate in nature.

[Perhaps Lawler has access to the missing container-loads of evidence that went 'walk-about' soon after Lenin made similar, but even more grandiose claims over a century ago, and that lend 'support' to such hyper-bold claims?]

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

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

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

And, like it or not, life arose because of the operation of real material, causal factors at work in nature, not logical principles inherent in Hegel's 'concepts' (upside down or 'the right way up').

But what, we might ask, has become of those eternally-malleable letter "A"s, which were said to have one, and only one, "other"? Wonder no more:

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

That is puzzling, to say the least. We have just been informed there are numerous "forces" that oppose life. So it seems that life must be exempt from the Hegelian caveat -- that each object or event has a 'unique other' --, since it appears to have hundreds, if not thousands of them. Of course, that depends on how we differentiate or count forces. For example, is each molecule of Carbon Monoxide, or Ozone, or Chlorine, or Phosgene, or Hydrogen Cyanide a single opposing force, or do they count as many such? Perhaps they work in gangs? Is every poison a separate force that opposes life? Or are they all to be lumped together as a sort of collective 'unique other'? What about other lethal forces, like extreme cold or a raging fire? What about tsunamis, avalanches, earthquakes, landslides, icebergs, volcanoes and meteor strikes (like the one that we are told wiped out the dinosaurs)? What of the countless bacteria and viruses that can cause death (and not just to humans)? What of diseases like cancer, heart attacks, strokes, diabetes, and multiple sclerosis? Are car crashes part of this 'dialectical assault' on life? If so, what about other accidental causes of death, like falling off a ladder, drowning, electrocution or medical incompetence? What about the deliberate taking of life, say, by the cops, the US Marines, the Saudi execution machine, or a drone strike? Is each natural predator (all those wolves, lions, tigers, sharks, etc.) to be counted? If so, are herbivores to be lumped in or left out? Or is plant life exempt? Do serial killers count as 'dialectical enemies' of life? And, what about suicide? Do successful attempts imply that those who take their own lives are their own 'unique others'?

Once more: so many questions, so few answers...

Of course, we mustn't be foolish and expect answers to such impertinent questions. After all, we are dealing with Mickey Mouse Superscience, here, where any request for detail will be labelled "pedantry", "semantics" or "academic nit-picking".

Fortunately, Lawler does have an answer (of sorts):

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

But, what "imprint" does a meteor strike imply? Or an earthquake? And is there a different "imprint" for each virus type? If so, there must be countless trillions of such "imprints", now that we know there are more (vastly more!) different strains of virus out there than there are stars in the entire universe:

"An estimated 10 nonillion (10 to the 31st power) individual viruses exist on our planet -- enough to assign one to every star in the universe 100 million times over." [Quoted from here; accessed 30/05/2022. Link in the original.]

Of course, not all those viruses are lethal or a threat to life (human, animal or plant), but that is surely because life can fend them off because it has an "imprint" for each. Why then do we need vaccines?

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

Of course, heat isn't a force; the word is, in such contexts, merely shorthand for the energy we accredit to certain molecules. Hence, it is even more difficult to see how the vibrational energy of, say, a Carbon-Carbon bond could be the unique "other" of..., well what? And, isn't heat simply our subjective impression of molecular motion (which was unknown in Hegel's day)? Shouldn't, therefore, its opposite, its 'other', be no motion at all? Disappointingly, Lawler is silent on this important issue, as, indeed, are other DM-fans -- perhaps wisely so.

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

Despite this, the processes Lawler describes are all causal. So, there are no Hegelian concepts here for Biophysicists to study. Even less surprising in the fact that, as far as is known, no PhD thesis has ever been commissioned to study these Hegelian fantasies scientifically -- not even by Haldane, Bernal, Levins, Lewontin or Rose. [If anyone knows of one, please email me with the details!]

Nevertheless, this might be to miss the point:

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

So, how precisely does heat 'mediate' here? Unfortunately, Lawler neglected to say, just as he neglected to say how organisms know when, where or how it is possible to dial-down the negations they encounter so that they don't experience the full fury of all those nasty, destructive 'contradictions'. Maybe they know more logic than Hegel?

[Incidentally, Lawler also forgot to include anything resembling a vague demonstration -- or even a weak argument -- that made some attempt to show that logical contradictions have anything to do with destruction (which they don't). (On that, see above, and again, below.)]

To be sure, Hegel did offer his readers this rather weak argument:

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