This essay should be read in conjunction with Essays Five and Six.
Readers need to make note of the fact that this Essay does not represent my final view on any of the issues raised. It is merely 'work in progress'.
If you are viewing this with Mozilla Firefox, the codes that Microsoft have put into FrontPage (the editor I have employed) appear to have made many of the font colours and some of the formatting in the second half of this Essay change erratically. In addition, you might not be able to read all the symbols I have used.
This Essay is over 50,000 words long; a summary of its main ideas can be found here.
Quick Links
Anyone using these links must remember that they will be skipping past supporting argument and evidence set out in earlier sections.
[DL = Dialectical Logic; FL = Formal Logic; TAR = The Algebra of Revolution; i.e., Rees (1998).]
(1) FL Versus DL
(2) FL And Change
(3) FL Allegedly Uses 'Fixed' Definitions And Categories
(b) Static Terms Or Slippery Arguments?
(d) An Annoying Counter-Example
(e) Other Systems Of Logic Unknown To Dialecticians
(a) Dialectical Change: Conceptual Or Material?
(b) Conceptual Change -- Or Conceptual Distortion?
(c) Logic and Change
(5) Merely Academic?
(6) Is DL A Higher From Of Logic?
(7) Was There Any Logic After Aristotle?
(9) Thesis, Antithesis, Synthesis Debunked
(10) The Crass Things Dialecticians Say About FL
(11) And About Ordinary Language
(b) Descent Into Hegelian Confusion
(c) Ordinary Language Is Not A Theory
(d) Ordinary Language Does Not 'Assume' Things Are Static
(e) Ordinary Language Different From 'Commonsense'
(f) Ordinary Language Not Ideological
(12) Notes
(13) References
Abbreviations Used At This Site
Formal Logic Vs Dialectical Logic
The relationship between DL and FL has not been without its problems. Notwithstanding this, dialecticians in general (and TAR's author in particular) take great pains to make it clear that while they do not reject FL, they regard its scope as somewhat limited. For example, John Rees comments as follows:
"[T]he dialectic is not an alternative to 'normal' scientific methods or formal logic. These methods are perfectly valid within certain limits…. [But] formal logic…has proved inadequate to deal with the 'more complicated and drawn out processes'." [Rees (1998), p.271.]
The problem seems to be that even though it is admitted that FL works well in certain areas, it appears that it cannot cope with change or with the contradictory nature of reality. This is because it supposedly operates with a "static" view of the world --, or at least with "fixed and immobile" concepts. Nevertheless, as we will soon see, when examined closely, these claims bear little resemblance to the truth.
In fact, as is well known, Rees's comments echo Hegel's own criticisms of the FL of his day, which unfortunately was itself a garbled and bowdlerized version of Aristotelian FL.1
The reasoning behind this attitude is outlined in TAR:
"Formal categories, putting things in labelled boxes, will always be an inadequate way of looking at change and development…because a static definition cannot cope with the way in which a new content emerges from old conditions." [Ibid., p.59.]
Again, the claim that concepts are not 'static' but develop and change was central to Hegelian Idealism. At any rate, DM-theorists are careful to emphasise the fact that even though their ideas have been derived from one of the most notorious sources of AIDS ever written, their theory is in reality an inversion of that system, one that puts it "back on its feet", and has extracted its "rational core". This enables DM provide a materialist account of change through contradiction, tested in practice.
[AIDS = Absolute Idealism.]
Whatever merit that claim turns out to have (which is zero, as we will see in Essay Eight Parts One and Two), here I propose only to examine the idea that FL cannot cope with change because it relies on a "fixed" and "static" view of the world. Again, to quote Rees:
"The reason why formal logic is often forced to abandon its own procedures in the face of the facts is that it attempts to analyze a living, evolving reality with static concepts. Formally things are defined statically, according to certain fixed properties -- colour, weight, size, and so on…. [This] is satisfactory only under conditions where the scale of change is not vital to our understanding…. But for more complex tasks in politics, history, and science generally, this will not do. Common sense and formal logic are agreed on static definitions…. But 'dialectical thinking analyzes all phenomena in their continuous change….'" [Ibid., pp.272-73.]
However, consistent with other dialecticians (who make similar assertions), Rees failed to substantiate these allegations with quotations from (or citations to) a single ancient or modern logic text. In fact, DM-authors in general rely on little other than unsupported claims like these, and, as we will see, they fail to explain how it is that AFL is limited in precisely the way they say -- save they merely repeat the same baseless allegations year on year.
And they all seem to make the very same claims. Little change there, then.
[AFL = Aristotelian Formal Logic; MFL = Modern Formal Logic.]
Indeed, as is easy to confirm, the revolution that transformed MFL over 120 years ago -- which was itself largely the result of the work of Frege -- has gone almost completely un-noticed by the majority of dialecticians.2 The old Aristotelian syllogistic, which DM-theorists almost universally confuse with the whole of FL, is now merely of interest to antiquarians, historians and traditionalists -- and, of course, to dialecticians who are sublimely unaware of the profound changes that have transformed MFL.
Admittedly, throughout its history Logic had been confused by many with an assortment of unrelated disciplines -- such as, Metaphysics, Epistemology, Ontology, Theology, Psychology (and the so-called "Laws Of Thought"), Mathematics, and Science. Under such circumstances it is understandable that the only legitimate role that FL could play -- the study of inference -- was all too easily forgotten. This is, alas, one more tradition DM-theorists have been happy to maintain.3
One explanation for this sorry state of affairs is that DM-theorists have been led astray by an elementary mistake -- one that novices often make --, that is, of confusing validity with truth. Hence, as will become apparent, the limitations DM-theorists attribute to FL merely arise from their own misidentification of rules of inference with logical and/or empirical truths, but not from the inability of FL to accommodate change.4
Unfortunately, this accusation is far easier to make than it is to substantiate. This is not because it is incorrect, but because dialecticians rarely bother to explain why they regard FL as defective -- that is, over and above merely asserting that it is, copying the idea from one another generation upon generation, without making any attempt to justify it.
Neither is it to claim that DM-theorists fail to make the point that FL is defective because it deals with "static" forms, etc. Far from it, they all join in the chorus. It is simply to underline the fact that they are quite happy to rely on the mere repetition of this empty claim without ever bothering to check whether it is correct -- or, for that matter, without explaining what it could possibly mean.5
To be sure, the confusion between rules of inference and logical/metaphysical truths dates back to Aristotle himself. This error merely re-appeared in Hegel's work as part of a mystical/ontological doctrine connected with the alleged self-development of concepts, itself the result of an egregious error over the nature of predication (examined in Essay Three Part One), and an even worse one with respect to the LOI.
[LOI = Law of identity.]
However, once this misbegotten 'ontological' interpretation of FL is abandoned, the temptation to identify logic with science (or with the "Laws of Thought") loses whatever superficial plausibility it ever seemed to have. If FL is solely concerned with inference then there would be no reason to saddle it with metaphysical baggage of this sort, and every reason not to. On the other hand, if there is a link between FL and metaphysical/scientific truths -- as legend would have it --, then that fact (if it is one) needs substantiation. It is clearly not enough to assume such a link exists, as is generally done in DM-circles.
In addition, the idea that truths about fundamental aspects of reality can be uncovered by an examination of how human beings reason is highly suspect in itself; but, like most things, so much depends on what allegedly follows from that assumption. As we will see, the line taken on this issue sharply distinguishes materialist thought from Idealist myth-making. Unfortunately to date, DM-theorists have been more content with following traditional Philosophers in supposing that logic can function as a sort of earth-bound cosmic code-cracker, capable of unmasking profound truths about hidden aspects of reality -- aka "essences" -- than they have been with bothering to justify this entire line of thought. Nor have they been keen to examine the motives that gave birth to this aristocratic approach to Super-Knowledge in Ancient Greece.6
Of course, modern logicians are much clearer about the distinction between rules of inference and logical truths than their ancient counterparts were, but that fact just makes the criticisms that DM-theorists level against FL even more anachronistic and difficult to justify.
However, if in the end materialists are to reject Hegelian Ontology -- as surely they must -- then the idea that FL is a part of science becomes much harder to sustain.
Indeed, how is it possible for language reflect the logic of the world if the world has no logic to it?
If the development of nature is not in fact the disguised development of Mind, how can concepts drawn from the development of Mind apply to nature, unless nature is Mind?
Of course, dialecticians have responded to this with an appeal to the RTK; but, as we shall see (in Essays Three and Twelve), that too was an unwise move.
[RTK = Reflection Theory of Knowledge.]
This means that if FL is solely aimed at the study of the inferential links between propositions -- and is not concerned with the status of their truth-values -- then the criticism that FL cannot account for change becomes all the more misguided.
It is instructive to recall that over the last few hundred years or so humanity has (largely) learnt to separate religion from science, and to the extent that the sorts of things that used to be said about science (for example, that it was the "systematic study of God's work", etc.) look rather odd today. In a similar fashion, previous generations of logicians confused logic with science and the "Laws of Thought" (and they did this for theological/ideological reasons, too); one would have thought that avowed materialists (i.e., dialecticians) would be the last ones to perpetuate this ancient confusion.
Clearly not.
Indeed, as will be argued at length later, only if it can be shown (and not simply assumed) that nature has a rational structure to it, would it be plausible to suppose that there is a connection between the way human beings think and reason and the structure of reality. Short of that, the idea that there is a link between the way we draw conclusions and fundamental aspects of reality loses all credibility. Why should the way we knit premises and conclusions together mirror the structure of the universe? Why should our use of words have 'ontological' implications?6a And, how is it that certain metaphysical truths are derivable only from Indo-European grammar? Was this group of humans blessed by the gods? Are there really "subjects" and "predicates" in nature -- features found in only one family of languages, and even then, features which only a tiny proportion of its sentences express?
On the other hand, if it could be shown that the universe does have an underlying 'rational' structure, then the conclusion that nature is Mind (or that it has been constituted by Mind) would be difficult to resist. If all that is real is indeed rational, then the identification of rules of inference with the "rules of thought" -- and with metaphysical truths about "Being" -- becomes more all the more natural.
As the histories of Philosophy, Theology and Mysticism have shown, from such esoteric assumptions it is but a short step to the derivation of truths from thought alone. A priori thesis-mongering and Idealism thus go hand-in-hand; if nature is Ideal, then truths can follow from thought/language alone. In other Essays posted here (for example, here and here) we will see that this is a step DM-theorists (and metaphysicians of every stripe) have been only too happy to take -- and many times.
Nevertheless, there is precious little evidence to suggest that DM-theorists have ever given much thought to this particular implication of the idea that DL reflects the underlying structure of reality -- i.e., that this logic itself clearly implies that reality is Ideal. If logic does indeed reflect the structure of 'Being', then 'Being' must be Mind. [On this, see Essay Twelve Part Four, to be published soon.]
This conclusion only strengthens further the suspicion that the much-vaunted materialist "inversion", supposedly carried out by early dialecticians on Hegel's system, was merely formal --, which can only mean that DM is just an inverted form of Idealism. If this is so, then questions about the nature of Logic cannot but be related to the serious doubts raised here about the scientific status of DM. In that case, if Logic is capable of revealing scientific truths about nature -- as opposed to its being a systematic study of inference, and only that -- then it becomes harder to resist the conclusion that DM is indeed just a rotated form of Idealism. [Inverted here as in a camera not so very obscura, to paraphrase Marx.]
Anyway, since the aim of this section is to examine the specific allegations DM-theorists level against FL, that particular topic will be addressed in other Essays posted here (in this case Essay Three Part One, and Essay Twelve Parts One and Four).
FL And "Static" Definitions
As it turns out, there is good reason to question the usual claim made by dialecticians that FL deals only with "static" definitions (etc.).
Far from it being the case that FL is wedded to changeless forms, even traditional AFL employed variables to stand for propositions and predicates (general terms) long before they appeared in mathematics. This fact alone shows that traditional AFL was no more incapable of handling change than is modern Mathematics.7
[FL = Formal Logic; AFL = Aristotelian Formal Logic; MFL = Modern Formal Logic; TAR = The Algebra of Revolution, or Rees (1998); DM = Dialectical Materialism.]
As Engels himself pointed out, the introduction of variables into Algebra allowed mathematicians to cope with change; if that is so, it is difficult to understand why DM-theorists believe that traditional FL cannot cope with change, too. If mathematicians are currently able to depict change by their use of variables, why deny this capacity of traditional formal logicians who used the very same device 2400 years ago?
Of course, it could always be argued that variables that relate to quantities (as they feature in mathematics) are not at all the same as the variables that relate to concepts, properties or qualities (as they are employed in FL). This is undeniable, but not relevant. The point is that either sort of variable allows for change, even if this is in different ways.
Static Terms Or Slippery Arguments?
Despite this, does the charge that FL cannot cope with change itself hold water? In order to answer this question, consider a valid argument form taken from AFL:
L1: Premiss 1: No As are B.
L2: Premiss 2: All Cs are B.
L3: Ergo: No As are C.8
In this rather uninspiring valid argument schema the conclusion follows from the premisses no matter what legitimate substitution instances replace the variable letters.
So, L3 follows no matter what. But the argument pattern this schema expresses is transparent to change: while it can cope with change, it takes no stance on it. Some might regard this as a serious drawback, but this is no more a failing here than it would be for, say, Electronics to take no stance on the evolution of Angiosperms (even though it can be used to help study them). Otherwise, one might just as well complain that FL cannot predict the weather or kill MRSA.
Moreover, the truth-values of each of the above premisses do depend on the interpretation assigned to the schematic letters. Hence, these premisses are not actually about anything until they have been interpreted; before that they are neither true nor false. Not only that, but the indefinite number of ways there are of interpreting schematic letters like these means that it is possible for changeless and changeable items to feature in any of this argument's concrete instances.
[This was the point behind the observation made earlier that dialecticians (and logical novices) often confuse validity with truth; the above schema is valid, but its schematic propositions can neither be true nor false, for obvious reasons.]
To illustrate the absurdity of the idea that just because FL uses certain words or letters it cannot handle change (and uses nothing but rigid terms), consider this parallel argument:
(1) If x = 2 and f(x) = 2x + 1, then if y = f(x), y = 5.
(2) Therefore x and y can never change or become any other numbers.
No one would be foolish enough to argue this way in mathematics, for that would be to confuse variables with constants. But, if this is so in mathematics, then DM-inspired claims about the alleged limitations of FL seem all the more bizarre -- to say the least.
Of course, it would be naïve to assume that the above considerations address the problems worrying DM-advocates. As TAR itself points out:
"Formal categories, putting things in labelled boxes, will always be an inadequate way of looking at change and development…because a static definition cannot cope with the way in which a new content emerges from old conditions." [Rees (1998), p.59.]
But, as a criticism of FL this is entirely misguided. FL does not put anything into boxes, and its practitioners do not deny change as a result.
[Sure, some of them might have had metaphysical reasons for denying change, but these cannot be blamed on AFL.]
Indeed, without an ability to reason discursively (along lines that have been formalised in FL), dialecticians would themselves find it impossible to argue rationally.
For example, the argument above (from TAR) appears to draw certain conclusions from apparently 'fixed definitions' (or fixed/relatively fixed uses) of words, like "change" and "static", in order to make certain points about change itself. If, however, Rees's argument is now deliberately interpreted uncharitably (copying the tactic used by DL-theorists when they (deliberately) misconstrue FL) it would soon turn into a self-refutation. Thus, in order to point out the supposed limitations of FL, Rees found he had to use the sorts of things he accused FL of employing: i.e., "static" terms.
Of course, if this unsympathetic way of reading Rees's book were correct -- or fair -- then it would mean that if he or other DM-theorists want to argue validly about the limitations of FL using "static" categories such as these, their arguments would rapidly self-destruct.
If, on the other hand, dialecticians were to employ non-static categories consistent with their own precepts, then that would equally undermine any conclusions they 'derived'. This is because such categories (having no fixed meanings) would sanction no inferences, for it is not possible to decide what follows from what if the meaning of the terms employed is indeterminate. So, while it is unwise of DM-theorists to criticize FL for employing allegedly changeless categories, it would be even more inept of them to do this while using terms whose meanings are apt to change unpredictably. Hence, in practice, DM-theorists must either ignore their own principles and argue from 'fixed categories' about the limitations of FL, or they must construct a case against FL using 'slippery' terms, which would establish nothing whatsoever.
Like it or not, rational criticism of FL cannot succeed if either tactic is adopted.9
The schematic letters employed above do not in fact possess "definitions" (only interpretations), hence questions as to their 'fixity' or otherwise are entirely misplaced. The flexibility of interpretation permitted here -- even with respect to traditional schematic argument patterns like the one given above -- enables change to be accommodated by the simple expedient of varying the substitution instances of each and every schema. Such moves will have the effect of re-distributing truth-values among the constituent sentences without affecting the associated inferences.
Unfortunately, this might still not appear to address the worry exercising DM-theorists, which seems to revolve around the alleged superiority of DL over FL, especially in its ability to depict change through contradiction.
Admittedly, whatever one thinks of the ability or inability of FL to handle change, few question its intolerance of 'true contradictions'. However, since this section of the Essay is concerned largely with a narrow range of logical issues, I will postpone the examination of DM-theorists' appeal to dialectical change through contradiction until later Essays.10
Nevertheless, a more effective way of rebutting the claim that FL cannot handle change would be to provide a counterexample to it. The one given below is based on a very simple pattern drawn from MFL, which employs a valid argument form, despite the changes it records. This is an example of the schema known as Modus Ponendo Ponens (MPP):
|
1 (1) P®Q. A. 2 (2) P. A. 1,2 (3) Q. 1, 2, MPP11 |
The following is an apt interpretation of MPP:
|
1 (1) If atoms of 64Cu undergo beta decay then 64Ni atoms, positrons and neutrinos are formed. A 2 (2) Atoms of 64Cu undergo beta decay. A 1,2 (3) Therefore, 64Ni atoms, positrons and neutrinos are formed. 1, 2, MPP |
This simple interpretation of MPP (and one involving reasonably rapid change) is perhaps as good a counterexample as one could wish to find that refutes the claim that FL cannot handle transformations in nature and society. Not only that, there are countless other inferences that MPP itself can instantiate, and many inferential forms other than MPP, all depicting change equally well, when suitably interpreted.
This indicates that DM-theorists' accusations aimed at MFL are even less accurate than the ones they direct at AFL. Of course, the example above will hardly satisfy dialecticians, since no "new content" has been added in the conclusion. Fortunately, this is relatively easy to fix. Consider this one premiss argument:
Premiss 1: All dialecticians are human beings.
Ergo: The refutation of a dialectician is the refutation of a human being.
Here, the conclusion contains more than the premiss, so new content has 'emerged', with no dialectics anywhere in sight. [And, as an additional bonus, it depicts change to our dialectical friends into the bargain.] This argument form is used in Mathematics and in Science all the time to derive results not available to those who are still super-glued to the old logic -- and who are not aware of this fact.
However, dialecticians will still wonder if the changes above are at all relevant to their concerns. DL is said by them to be superior in that it can account for social change, that is, changes of far greater complexity than the above examples illustrate.
Nevertheless, these examples were aimed at countering the specific claim that FL cannot handle change. In later Essays we will see that DL cannot account for change of any sort -- whether these are simple or complex, or whether they occur in nature and society. In that case, no matter how poorly FL copes with change (if that is the case), DL does incomparably worse.
Of even greater significance is the fact that over the last hundred years or so theorists have developed several post-classical systems of logic, which include (among others), modal, temporal, deontic, imperative, epistemic and multiple-conclusion logics. Several of these sanction even more sophisticated depictions of change than are allowed for in AFL or even MFL (i.e., so-called 'Classical Logic').12
Notwithstanding all of this, the feeling may perhaps persist that the above examples still employ "fixed concepts" and "definitions". Unfortunately, because DM-theorists seldom (if ever) provide examples of what they mean by a "fixed concept" -- or what they imagine formal logicians take these to be, should the latter even accept/recognise this descriptor -- it is not easy to make much sense of their complaints.12a
However, there are several confusions that might lie behind, or which might be motivating this odd belief in 'changeable' concepts.
Change In DM -- Conceptual Or Material?
The first confusion involves DM-theorists' own analysis of material change; they frequently depict it in terms that are highly reminiscent of the Hegelian doctrine which holds that change is fundamentally conceptual. How else are we to interpret the following words from TAR that any account of change must explicate how: "…new content emerges from old conditions"? [p.59.] Admittedly, Rees appealed to the usual materialist twist that has allegedly been imposed on Hegel's system (to turn it into a "materialist dialectics"), but he pointedly failed to explain how conceptual change is related to material change. How is it possible for a concept or a category to change if neither of them is material? [And it won't do to suggest that concepts, for example, change because the objects they 'reflect' do, since that would be to confuse a concept with an object. We saw that was a dead end in Essay Three; we will meet it again a few paragraphs below.]
[It is worth pointing out here that I am not denying conceptual change, merely questioning what dialecticians mean by 'fixed concepts'.]
Furthermore, how can change to material objects be recorded by our use of concepts? In DM-writings, as already noted, the impression is given that these two sorts of change are simply the same, or that one is a reflection of the other. Or, to be more honest, the impression is that little thought has actually gone into either sort of change (that is, over and above the regurgitation of the mystical ideas dialecticians borrowed from Hegel).
[RTK = Reflection Theory of Knowledge.]
It could be objected to the above that it ignores the dialectic that operates between the "knower and the known" and the fact that our concepts change as material and social reality develop, and as technique advances. Admittedly, DM-theorists have made attempts to account for the relationship between these two sorts of change (material and conceptual) along such lines, but, as noted above, they have done so by means of a detour into the RTK, buttressed by an appeal to practical activity, linked to a materialist analysis of the dialectical relationship between the abstract and the concrete. Since these topics are addressed in other Essays posted at this site, no more will be said about that here.
Conceptual Change -- Or Conceptual Distortion?
A second source of confusion could be the fact that conceptual change is not at all easy to picture. Indeed, if it should turn out that conceptual change cannot be depicted using traditional (or even DM) terminology then the accusation that DL is superior to FL would become even less easy to sustain. In order to motivate this line of investigation, a brief discussion of some of the problems involved in expressing conceptual change is in order. Consider, therefore, the following sentence:
C1: Green has changed.
The word "Green" in such circumstances would normally be understood as name of a person (as opposed to it being seen as denoting a concept). However, if it were clear that C1 related to the colour green it would probably be re-interpreted in the following way:
C2: This patch of green has changed.
This is because little sense can be made of the idea that the concept green could have changed (for reasons that will be explored below). In which case, C1 (interpreted now as C2) would be understood as referring to a change in the colour of a material object, or part of an object -- but not to the concept green itself. This can be seen if the following sentence is substituted for C1:
C3: The concept green has changed.
Despite what C3 seems to say, the phrase "the concept green" no longer operates as an expression for a concept, but as a singular term.
In that case, it would be difficult to say what "the concept green" now designates -- at least not without completely misconstruing what C3 is attempting to say about the concept green itself. Indeed, "the concept green" could not in fact name the very concept it appears to name since that would transform its supposed target (the concept green) into an object -- now designated by the definite description "the concept green". Naturally, that would fatally blur the distinction between concepts and objects, all the while failing to pick out the original concept intended.13
The paradoxical nature of sentences like C3 can be illustrated by a consideration of the following example:
C4: The concept green is a concept.
If it is first of all assumed that C4 is well-formed, then it looks like it is analytically true. In fact, and on the contrary, C4 is analytically false! This is because "the concept green" is a singular expression, and as such it refers to an object, and an object is not a concept.14
Alas, absurd sentences like this are to metaphysicians what carrots are to donkeys; based on linguistic monstrosities like C4, some thinkers hastily conclude that language -- or 'thought' (or 'reality', or 'everything') -- must be defective, or must be contradictory. With reasoning like that you might as well argue that if a metre rule, say, has been made incorrectly the same must be true of all it measures!
From linguistic sins such as these, committed by our philosophical ancestors, most of Metaphysics has descended without modification by unnatural selection; DM is unfortunately not the only progeny of mutant syntax like this.15
In that case, it is not possible to specify how concepts change by means of sentences like C3; in such contexts the logical role of terms designating concepts alters them in such a way that they no longer work as concept expressions.16
[It is important to note that I am not denying here that concept expressions can be nominalised, only that nothing 'ontological' follows from that superficial linguistic manoeuvre.]
Of course, it could be objected that the mere fact that we can't express conceptual change in the manner specified does not mean that it does not happen; after all, reality is not constrained by the limitations of language. Maybe not, but if an option of this sort cannot be put into language (or if when it is, what it appears to say undoes what it attempts to say) then no option has been presented for anyone even to begin to consider.
Not only that, the above response clearly trades on the supposition that there are indeed concepts in reality that can change; but that would be true only if reality were mind-like. No one supposes, it is to be hoped(!), that concepts pre-date the evolution of sentient life, and they did so in a sort of limbo world waiting to be thought about, and only then begin to change.
On the other hand, if reality is not mind-like then there can be no concepts in nature for our minds to reflect.
Alternatively, if it is claimed that the mind does indeed reflect reality, and it uses concepts to do this, it must distort reality by so doing (that is, it must do so if there are no concepts 'out there' for it to 'reflect').
Now, we saw in Essay Three Part One that the defective logic that dialecticians inherited from Hegel (where the misconstrual of the "is" of predication as an "is" of identity was based on an earlier confusion over the nature of predicate expressions, re-interpreting them as the names of abstract particulars) has already predisposed them toward making this latest mistake: that which confuses objectual with conceptual change. For if concepts are viewed as abstract objects of some sort, then it becomes natural to jumble-together these two sorts of change. So, no wonder that that dialecticians copy Hegel and talk about concepts developing, and how FL is hamstrung because of its fixation with 'fixed' concepts. Only now can we see where the real problem lies; it is not with the 'fixed' concepts of FL, but with the slippery terminology of DL, which is, in turn, based on a crass syntactical error committed by ancient Greek ruling-class theorists. And they did this because it was conducive to their world-view to see reality conceptually. [Until Essay Twelve is published in full, there are brief explanations why I say this here and here.]
In that case, it still remains unclear what exactly is being proposed by those who speak of 'changing' or 'developing' concepts. This is not to suggest that we cannot make sense of conceptual change. Far from it; it is a constant feature of our social life. But we cannot do so by means of a philosophical theory that relies on an egregious distortion of language, and on doctrines heavily infected with AIDS.
[AIDS = Absolute Idealism.]
Despite the above, it is possible to express conceptual change in FL by means of an ascent into Second Order Logic.
Now, this latest twist does not contradict the observation made above (i.e., that what seem to be empirical truths about concepts cannot be expressed in language -- it was in fact maintained that they cannot be directly expressed by means of distorted sentences), since higher order logic is a calculus that expresses rules of inference, not logical (or other) truths.
In Second Order Logic, expressions for concepts become variables ranged over by Third Order quantifiers, and so on.17
Even so, such systems only indirectly relate to our ordinary use of words for change. Indeed, despite what certain Philosophers (and DM-theorists) claim, ordinary language is perfectly capable of expressing change; this is partly because the word "change" is a vernacular term itself, and partly because ordinary language was invented by those who daily interface with material reality in collective labour (etc.) -- i.e., workers. In fact, as will be demonstrated in Essay Six, ordinary language is capable of expressing change far better than the obscure language found in Hegel, and in DM. The vernacular contains literally thousands of different words that are capable of depicting change and development in almost limitless detail.17a
Again, it could be objected that the above considerations all revolve around the linguistic expression of change; whether or not the latter is possible is not relevant to the concerns expressed by DM-theorists. Their interest lies in material change in the real world, verified by practice, intervention and experiment. If this is so, then most of the above comments appear to be entirely misguided -- or so it could be claimed.
Nevertheless, it is worth noting once more that the points raised earlier were specifically aimed at the DM-thesis that FL cannot handle change, not at whether material change is or is not different from any of our attempts to depict it. Hence, the complaint is itself misplaced. Since FL expresses only some aspects of the inferences we make in ordinary life -- formalising a fraction of the discursive principles implicit is our capacity to reason, and to picture the world, truly or falsely -- a defence of FL cannot suddenly pretend that our powers of depiction are not relevant. [Nor indeed can any attempt to show the opposite.]
Anyway, the DM-account of material change is analysed in detail in several of the Essays posted here (for example, Essays Five, Seven and Eight Parts One and Two); there it will be shown that dialecticians themselves are incapable of doing the very thing they find fault with in FL -- that is, accounting for change.
A Purely Academic Issue?
At first sight, it would seem obvious that a logical system based on a static view of the world -- as it is alleged of FL -- would have few if any practical consequences. On the other hand, it would appear equally clear that a different logical system based on the opposite view of reality -- as is also claimed of DL -- should have countless practical applications in science and technology.
Oddly enough, the exact opposite is the case: DL has no discernible practical or scientific applications, and has featured in none of the advances in the natural or physical sciences (and arguably none even in the social sciences) -- ever. Worse, DL has made no contribution to technological innovation.
In stark contrast to this, FL has played an invaluable role on the development of science and mathematics, and has featured in countless applications in technology and the applied sciences.18
Indeed, one excellent example (among the many) of the impact FL on technology is the development of computers. Their origin goes back many centuries, but advances in mathematical logic (post 1850) proved to be decisive. The invention of Boolean and Fregean Logic, the mathematical logic of Russell, Whitehead, Hilbert, Peano, von Neumann and Church (etc.) -- along with the logico-mathematical work of Alan Turing -- all helped to make the development of computers possible. FL has not only contributed to the evolution of software and of computer languages, the principles of Propositional Calculus govern the operation of all standard processors (etc.).19
In addition, there are numerous other examples of the practical applications of FL, ranging from Cybernetics to Code Theory and from Linguistics to Game Theory and Discrete Mathematics. The question is: Can DM-theorists point to a single successful application of DL in technology, or in the natural and physical sciences? The answer is reasonably plain; they can't. But this glaring failure becomes all the more revealing when it is remembered that dialecticians repeatedly claim that their 'logic' is superior to FL when it is applied to the material world.
This is perhaps one paradoxical mismatch between DM and recalcitrant reality that cannot be solved by the simple expedient of "grasping" it.20
What then of the general boast that DL is a superior form of logic? Is there any way of confirming this? Perhaps there is; TAR's author claims that DL does not reject FL, and neither is it:
"[A]n alternative to 'normal' scientific methods or formal logic…. Formal Logic, like Newtonian physics, has proved inadequate to deal with 'more complicated and drawn out processes.' So the dialectic stands in the same relation to formal logic as Newtonian physics stands to relativity theory or, as Trotsky puts it, as 'that between higher and lower mathematics'." [Rees (1998), p.271.]
If it can be shown that DL does all that Rees claims for it, then perhaps the academic quibbles noted above can be set aside. The rest of the Essays posted at this site are aimed at testing these claims, and more. However, a few awkward initial problems need to be addressed before the main picture can begin.
First of all, while it is clear that Relativity has largely superseded Newtonian Physics it is a little less obvious how this was related to the latter's inability to deal with "drawn out processes". Still less clear is what exactly FL and DL have in common that makes Trotsky's analogy with higher and lower mathematics at all apt. If anything, the opposite appears to be the case: DM-theorists are only too happy to begin their discussions of FL by pointing out that many of what they (but no one else) take to be its central tenets are fundamentally defective. This includes the LOI, the LOC and the LEM (among others). [This allegation is documented below, and in Note 23.]
Although lower mathematics is clearly limited in scope, none of its precepts are defective and professional mathematicians do not criticise it in any way --, quite unlike the attitude adopted toward FL by DM-theorists, who continually excoriate it.
[LOI = Law of Identity; LOC = Law of Non-Contradiction; LEM = Law of Excluded Middle.]
Secondly, and as will be demonstrated in Essays Five and Six, Trotsky's attempt to criticise the LOI rapidly collapses into incoherence, as does Engels's 'analysis' of motion. In stark contrast, higher mathematics does not disintegrate when we pass beyond its 'lower' forms. In fact, far from being able to handle "more complicated and drawn out processes", DL has great difficulty in coping with an ordinary bag of sugar and with the movement of the average cat!
Furthermore, higher and lower mathematics are not inconsistent with each other. Hence, we do not find mathematicians correcting ordinary addition or multiplication, nor do we find them expanding on the limitations of, say, the equal sign, the cube root function or quadratic equations. Admittedly, higher mathematics contains concepts and rules not found in lower mathematics, but there is never any suggestion that the latter's procedures and symbols are defective, or that they are the very opposite of what they are normally taken to be. Compare this with the sort of comments made by DL-enthusiasts about FL:
"Trotsky saw that it was the inadequacies and contradictions of formal logic that drove theorists toward dialectical formulations. Even those who pride themselves on a 'deductive method', which proceeds 'through a number of premises to the necessary conclusion,' frequently 'break the chain of syllogisms and, under the influence of purely empirical considerations, arrive at conclusions which have no connection with the previous logical chain.' Such ad hoc empirical adjustments to the conclusions of formal logic betray a 'primitive form of dialectical thinking.'" [Ibid., p.272.]
Again, it is worth pointing out that fundamental criticisms of FL (like these) advanced by DL-fans are seldom if ever substantiated with examples drawn from the work of a single logician.21 Add to this Lenin's remarks:
"The inaneness of these forms of formal logic makes them deserving of 'contempt' and 'derision'…. Hegel shrewdly adds [concerning the Syllogism]: 'Boredom immediately descends when such a syllogism is heard approaching.'" [Lenin (1961), pp.93, 177.]
It would be difficult to find a single mathematician who is as dismissive of lower mathematics as Lenin is of FL, or any modern scientist for that matter who would be prepared to call Aristotle or Newton's work "inane" and fit only for "contempt" and "derision".22
Was There Logic After Aristotle?
As already noted, DM-theorists (but particularly those who are revolutionaries) almost invariably identify FL with AFL -- and, worse, with that bowdlerized version found in Hegel's two badly misnamed books on logic. DM-theorists of earlier generations (such as Engels) may perhaps be excused in this regard, since they largely wrote before the revolution that took place in Logic after the 1870s; later Marxists are not so easy to exonerate.
[AFL = Aristotelian Formal Logic.]
For example, we find Trotsky (who was otherwise reasonably up-to-date in his knowledge of the sciences) writing the following in his "Open Letter to Burnham" -- approximately 60 years after MFL was founded by Frege, and approximately 30 years after Russell and Whitehead's Principia Mathematica was first published:
"I know of two systems of logic worthy of attention: the logic of Aristotle (formal logic) and the logic of Hegel (the dialectic). Aristotelian logic takes as its starting point immutable objects and phenomena…. [P]lease take the trouble to inform us just who following Aristotle analysed and systematized the subsequent progress of logic." [Trotsky (1971), pp.91-92.]
To which Burnham not unreasonably replied:
"[A]part from Aristotle, the only 'logic worthy of attention' is that of -- Hegel…. Comrade Trotsky, as we Americans ask: where have you been all these years? During the 125 years since Hegel wrote…[,] after 2300 years of stability, logic has undergone a revolutionary transformation…in which Hegel and his ideas have had an influence of exactly zero….
"In a most sarcastic vein, you keep asking me to 'take the trouble to inform us just who following Aristotle analysed and systematized the subsequent progress of logic'…as if this demand were so obviously impossible of fulfilment that I must collapse like a pricked balloon before it…. Do you wish me to prepare a reading list, Comrade Trotsky? It would be long, ranging from the work of the brilliant mathematicians and logicians of the middle of the last century to…the monumental 'Principia Mathematica' of Russell and Whitehead…." [Burnham (1971), pp.236-37.]
Unfortunately, wilful ignorance like this among dialecticians has not noticeably changed since Trotsky's day (with the notable exception of the work of logicians like Graham Priest, of course). Hence, we still find socialists of otherwise impeccable dialectical credentials repeating Trotsky's ill-informed opinions time and again, still confusing FL with AFL, still clinging to the dogma that Aristotle is and always will be the last (and only) word on the subject.
Worse still, many Marxists compound this inexcusable ignorance with an open failure to grasp even the few degenerate logical ideas they mistakenly attribute to Aristotle.23
Turning to specifics: according to its supporters, the superiority of DM arises partly from its ability to explain change and partly from the understanding it gives of the contradictory behaviour of nature and society, thus assisting in the revolutionary transformation of the latter. This, it is claimed, FL cannot adequately do.
However, not even mathematics can provide a scientific account of change -- even if it does play a major role in science. Mathematical objects have no causal impact on reality; they nowhere appear in nature.24 And yet, this does not mean that mathematics is inferior to a 'higher' brand of 'Dialectical Mathematics'. Why DM-theorists use an analogous argument to depreciate FL is therefore something of a mystery.
Of course, some DM-theorists have attempted to offer their own account of the superiority of 'higher' over 'lower' mathematics, based, for example, on Engels's interpretation of Descartes's introduction of variables into Algebra, as well as on some rather obscure notes left by Marx on the nature of Differential Calculus.25
Nevertheless, DM-apologists claim that when linked to a detailed analysis of material causes, DM can provide a scientific account of change. This idea is discussed in detail in Essays Five and Eight, Parts One and Two, and then systematically dismantled.
1. Aspects of Hegel's 'logic' are taken apart here -- more will be when the rest of Essay Twelve is published (summary here).
Nevertheless, dialecticians tend not only to confuse FL with the garbled version of AFL extant in Hegel's day, but they disregard, ignore or underplay the significant advances in FL that have taken place over the last 125 years. It is no exaggeration to say that more than 95% of FL is less than 150 years old. But you would not be able to guess that by reading any randomly chosen DM-text. Quite the opposite in fact; naïve readers would perhaps conclude from what they find there that FL has stood still for over 2400 years! And this from the self-styled 'Apostles of Change'.
[These comments do not, of course, apply to the work of Graham Priest. His work will be the subject of a special Essay to be published later. In the meantime, readers should consult Goldstein (1992) and Slater (2007b), as well as this review.]
On the subject of Hegel's dismissal of, say, the LOC, see Hanna (1986) and Pippin (1978). The views of these two authors will also be critically examined in a later Essay.
[LOC = Law on Non-contradiction; FL = Formal Logic; AFL = Aristotelian Formal Logic.]
2. These accusations will be substantiated presently.
3. Again, these assertions will be substantiated later in this Essay.
4. Validity is a formal property of argument schemas, whereas truth is a 'property' of propositions. [The word "property" is in 'scare' quotes since it is being used technically -- if not figuratively -- here.] The proper role of FL is the study of patterns of inference, and as such it is only indirectly related to the 'search for truth'. Logic is therefore a science only in the wider (German) sense of that term.
The definition here is incorrect, as I have pointed out in the discussion pages.
[The confusion of FL with science is discussed below, in Note 5.]
For a clear definition of validity, see, for example, Tomassi (1999), pp.2-19.
5. DM-theorists in general labour under the widespread illusion that FL is the study of the "Laws of Thought" -- that is, that it is one of the sciences proper. For example, consider Lenin's description:
"Logic is the science of cognition. It is the theory of knowledge…. The laws of logic are the reflections of the objective in the subjective consciousness of man." [Lenin (1961), pp.182-83.]
And we find Novack defining logic as:
"…the science of the thought process. Logicians investigate the activities of the tho