Formal Logic



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; AFL = Aristotelian Formal Logic; TAR = The Algebra of Revolution; i.e., Rees (1998).]


(1) FL Versus DL


(2) FL And Change


(a) Unfounded Allegations


(b) Validity And Truth


(3) FL Allegedly Uses 'Fixed' Definitions And Categories


(a) Variables And Change


(b) Static Terms Or Slippery Arguments?


(c) Change Of Denotation


(d) An Annoying Counter-Example


(e) Other Systems Of Logic Unknown To Dialecticians


(4) Conceptual Change


(a) Dialectical Change: Conceptual Or Material?


(b) Conceptual Change -- Or Conceptual Distortion?


(c) Logic and Change


(d) Real Material Change


(5) Merely Academic?


(6) Is DL A Higher From Of Logic?


(7) Was There Any Logic After Aristotle?


(8) Explaining Change


(9) Thesis, Antithesis, Synthesis Debunked


(10) The Crass Things Dialecticians Say About FL


(11) And About Ordinary Language


(a) Mistaken Assumptions


(b) Descent Into Hegelian Confusion


(c) Ordinary Language Is Not A Theory


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


(e) Ordinary Language Different From 'Commonsense'


(f) Ordinary Language Not Ideological


(12) Notes


(13) References


Abbreviations Used At This Site



Formal Logic Vs Dialectical Logic


The relationship between DL and FL has not been without its problems. Nevertheless, 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 immutable" concepts. Nevertheless, as we will soon see, when examined closely these claims bear little resemblance to the truth.



FL And Change


Unfounded Allegations


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 AFL.1


The reasoning behind this attitude is outlined in TAR:


"Formal categories, putting things in labelled boxes, will always be an inadequate way of looking at change and development…because a static definition cannot cope with the way in which a new content emerges from old conditions." [Ibid., p.59.]


The claim that concepts are not 'static' but develop and change was central to Hegelian Idealism. Even so, dialecticians 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 an inversion of that system, one that in fact puts it "back on its feet", and which has extracted its "rational core". This enables DM-theorists to provide a materialist account of change through contradiction, tested in practice.


[AIDS = Absolute Idealism.]


Whatever merit this claim turns out to have (which is zero, as we will see in Essay Eight Parts One and Two), I propose only to examine here 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, in relation to FL, 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 in fact 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 sort of 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 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 invariably confuse with the whole of FL, is in fact now merely of interest to antiquarians, historians and arch traditionalists -- and, of course, to dialecticians who are sublimely unaware of the profound changes that have transformed logic into 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



Validity And Truth


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.).



Variables And Change


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


[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



Change Of Denotation


The schematic letters employed above do not in fact possess "definitions" (only interpretations), hence questions as to their 'fixity' or otherwise are entirely misplaced. The flexibility of interpretation permitted here -- even with respect to traditional schematic argument patterns like the one given above -- enables change to be accommodated by the simple expedient of varying the substitution instances of each and every schema. Such moves will have the effect of re-distributing truth-values among the constituent sentences without affecting the associated inferences.


Unfortunately, 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



An Annoying Counterexample


Nevertheless, a more effective way of rebutting the claim that FL cannot handle change would be to provide a counterexample to it. The one given below is based on a very simple pattern drawn from MFL, which employs a valid argument form, despite the changes it records. 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.



Other Systems Of FL


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



Conceptual Change


Notwithstanding all of this, the feeling may perhaps persist that the above examples still employ "fixed concepts" and "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.]



Logic And Change


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


Now, this latest twist does not contradict the observation made above (i.e., that what seem to be empirical truths about concepts cannot be expressed in language -- it was in fact maintained that they cannot be directly expressed by means of distorted sentences), since higher order logic is 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



Real Material Change


Again, it could be objected that the above considerations all revolve around the linguistic expression of change; whether or not the latter is possible is not relevant to the concerns expressed by DM-theorists. Their interest lies in 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



DL -- A Higher Form Of Logic?


What then of the general boast that DL is a superior form of logic? Is there any way of confirming this? Perhaps there is; TAR's author claims that DL does not reject FL, and neither is it:


"[A]n alternative to 'normal' scientific methods or formal logic…. Formal Logic, like Newtonian physics, has proved inadequate to deal with 'more complicated and drawn out processes.' So the dialectic stands in the same relation to formal logic as Newtonian physics stands to relativity theory or, as Trotsky puts it, as 'that between higher and lower mathematics'." [Rees (1998), p.271.]


If it can be shown that DL does all that Rees claims for it, then perhaps the academic quibbles noted above can be set aside. The rest of the Essays posted at this site are aimed at 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



Explaining Change


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. The author of that review has now published a book on Paradox, where he shows that the Dialetheic and Paraconsistent Logic Priest favours cannot handle the paradoxes of truth, which had in fact been one of the main motivators of this sort of logic: Field (2008), pp.36-92.]


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


Lenin and Novack have clearly confused logic with psychology. If logic were the science of what went on in people's heads, then logicians would busy themselves with brain scans, surveys, psychometric testing, and the like. They certainly would not bother with proofs.


Do dialecticians seriously think that people actually cogitate in syllogisms, or that they use the formal calculi found in Principia Mathematica when they reason? They must do if they believe that logicians study how people in fact think.


On the basis of passages like these it is not easy to contradict those who conclude that the above two comrades did not know what they were talking about. But what they say is in fact quite representative of opinion in dialectical circles. In their defence, though, they inherited this idea from an ancient tradition in logic (also found in Kant and Hegel) that logic is indeed a sub-branch of Philosophical Psychology.


However, FL is no more the science of thought than Geometry is the study of where to stand -- or the rules of Cricket/Baseball represent the science of ball hitting. Science is descriptive, explanatory and predictive. The theorems of FL are constitutive and normative.


This topic is extensively discussed in Shanker (1998), pp.63-120. Cf., Coffa (1991), pp.113-67, Baker (1988), and the general comments in Button, et al. (1995). Cf., also Brockhaus (1991), pp.65-106. [I discuss this topic in more detail in a later Essay.]


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


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


[LIE = Linguistic Idealism.]


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


This is what Professor Nidditch had to say:


"One has to give Aristotle great credit for being fully conscious of this [i.e., of the need for a general account of inference -- RL] and for seeing that the way to general laws is by the use of variables, that is letters which are signs for every and any thing whatever in a certain range of things: a range of qualities, substances, relations, numbers or of any other sort or form of existence....


"If one keeps in mind that the Greeks were very uncertain about and very far from letting variables take the place of numbers or number words in algebra, which is why they made little headway in that branch of mathematics...then there will be less danger of Aristotle's invention of variables for use in Syllogistic being overlooked or undervalued. Because of this idea of his, logic was sent off from the very start on the right lines." [Nidditch (1998), pp.8-9. Italic emphasis in the original.]


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


8. With respect to this argument schema, the only condition validity requires is the following: if, for a given interpretation, the premisses are true then the conclusion is true. This claim is not affected by the fact that schematic premisses themselves cannot be true or false, since such schema express rules, and the above depiction is hypothetical. [A clear explanation can be found here.]


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


Premiss 1: No moving object is stationary.


Premiss 2: All objects with zero velocity are stationary.


Ergo: No moving object is one with zero velocity.


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


The above syllogism is valid, and would remain valid even if all motion ceased. But, it also 'copes' with movement, and hence with change, as is clear from what it says.


And we do not have to use what seem to be necessarily true premisses to make the point:


Premiss 1: All human beings are aging.


Premiss 2: All Londoners are human beings.


Ergo: All Londoners are aging.


Admittedly, the term "aging" is not of the type Aristotle would have countenanced in a syllogism, so far as I can determine. However, if we free Aristotle's logic from his metaphysics, the inference is clearly valid, and based on a syllogistic form. Anyway, the term "aging" can easily be replaced by a bona fide universal term (such as "the class of aging animals"), to create this stilted but genuine syllogism:


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


Premiss 2: All Londoners are human beings.


Ergo: All Londoners are members of the class of aging animals.


There is an excellent account of Aristotelian Logic in Smith (2004), here.


And there is an equally useful account of MFL (i.e., now confusingly called "Classical Logic") in Shapiro (2000), here.


Readers should also consult Hirsch (2004), which, while deeply flawed itself, represents a major step in the right direction. The editors of this on-line journal did not publish my reply; it will be published at this site, in 2008.


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


It also raises questions about the relative stability of meaning in language. That topic is dealt with in more detail in Essay Six, which is devoted to the LOI and to change.


[LOI = Law of Identity.]


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


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


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


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


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


Unfortunately(!!), Gentzen was either a Nazi, or had clear Nazi sympathies. On this, see here.


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


Despite this embarrassment of riches, freely available on the internet, DM-fans stoutly maintain their pose of self-inflicted ignorance, all the while pontificating about FL as if they were latter-day Aristotles.


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


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


[This topic is discussed in more detail in Essay Three Part One (and briefly below, in Note 14). Many of the issues raised here are outlined with admirable clarity in Gibson (2004).]


Anyway, dialecticians themselves appear to need this distinction, otherwise their theory would be little different from "crude materialism".


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


However, as far as the alleged change to concepts is concerned, and with respect to C2 and C3:


C2: This patch of green has changed.


C3: The concept green has changed.


there seem to be two possibilities; neither one looks at all viable:


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


So much was at least clear to Plato, but he 'solved' this problem by turning general words into the names of abstract particulars (the "Forms"), thereby destroying generality.


Moreover, this alternative would also leave the phrase "the concept green" behaving as a singular term, and not as a concept expression. Concept expressions are descriptive; names and singular terms are designative.


(2) "The concept green" could refer to an 'abstraction', perhaps one residing in some mind or brain (or in all objects sharing that 'property'). But, again, on reflection, it can't designate a 'collective idea of green', for there is no such thing. And, even if there were, calling 'it' a concept would be inept since, ex hypothesi, 'it' would be an 'object', or collection of 'objects', not a concept. And if all green objects share this common property "The concept green", designating it this way would deny them that capacity, since "The concept green" would name an object, not a general property.


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


The problem here is that in language we cannot express in indicative sentences the logical role that, for example, concept expressions play; any attempt to do so simply destroys their capacity to function in this way. While Frege was aware of this 'difficulty', he could not account for it; Wittgenstein, I think, 'solved' this 'problem' by dissolving it. On this see the references given below.


The illusion that conceptual change may be referred to (in the crude manner envisaged in TAR and other DM-texts) is created by the transformation that concept expressions seem to undergo when they are situated in new but non-standard sentential contexts -- for example, if direct reference to them is attempted, and the singular terms that result from this are then situated in indicative sentences.


As C1 and C3 show, the claim that concepts can change rests on a nominalisation of concept expressions (or perhaps their quasi-nominalisation by means of a definite description, as in "the concept green"), which transforms them into singular terms. This then motivates the idea that because singular terms denote objects -- which can and do change -- these newly nominalised 'entities' must similarly be subject to alteration, and in like manner.


C1: Green has changed.


C3: The concept green has changed.


Change to objects thus becomes the exemplar that conceptual change is now modelled upon, but only because, in referring to concepts, it seems we have to nominalise them. Naturally, this linguistic move is the first step in jumbling together these two sorts of change.


In Essay Three Part One we saw how this simple error spawned a 2500 year long philosophical wild goose chase to account for 'Abstract Objects', 'Universals' and 'Concepts'.


However, it is worth noting that this move only appears to work because the distinction between concepts and objects has now been obliterated, again by means of yet another grotesque distortion of language.


Metaphysicians have repeatedly made mistakes like this, constantly falling prey to what might be called the "Nominalisation Fallacy". Those misled in this way seem to think that if a clause (or phrase) can be nominalised then there must be something (visible or invisible) in reality that answers to it.


So, on that basis, it is reasoned that "the concept green" must exist because it has just been designated. But, such inferences have only ever been justified by nominalisations of this sort -- ones that conjure into existence objects at the drop of a noun.


This error also prompts the idea that since the ordinary use of words prevents such linguistic tomfoolery, technical terms must be invented that readily permit it -- and words like "Form", "Concept", "Being", "Nothing" and "Becoming" are then pressed into service. The supposed meaning of such empty phrases now seems to allow profound 'philosophical' truths to be derived at will. In this way, thought (acting alone, and divorced from the constraints social life puts on the use of language) appears to be able to penetrate to the heart of reality, all thanks to a terminological trick motivated by an inept (and ancient) transformation of concept expressions.


In DM, this approach to the vernacular resurfaces as part of the claim that the logic of ordinary discourse (which, it is worth noting, is not that belonging to FL) must be "surpassed" by the use of a highly obscure jargon drawn from Hegel's Logic, which not only permits such 'word magic', it insists on it.


Fortunately, since singular terms are not concept expressions (nor vice versa), manoeuvres like this must always fail.


This is because, in order to pick out the alleged reference of a general term, a singular term supposedly naming it has to be introduced. But, this new term now functions as the name (etc.) of an abstract object -- it has to be abstract, for if it were material there would be no need for this charade in the first place. But, this newly introduced expression does not now operate as a general term (but as a name). Hence, because of this manoeuvre concepts now appear to be strange types of objects -- or, objects look like peculiar sorts of concepts.


Either way, since objects can change, it is assumed that concepts can, too, and in like manner.


As noted above, this 'inference' encourages the additional (and traditional) idea that ordinary language must be "defective" if it prevents 'profound' 'scientific/philosophical' moves like this from being made.


Now, instead of finding fault with the linguistic contortion that created such abstractions in the first place (and which cannot work since it destroys the unity of the proposition -- this was explained in Essay Three Part One), dialecticians assume that reality itself must be 'contradictory', since it is now 'clear' to them that a singular expression cannot be identical with universal. We saw this here in connection with the traditional confusion of general words (concept expressions) with abstract particulars.


This suggests that further adjustments now have to be made to the original 'concepts', indicating to those taken in by this linguistic conjuring trick that there is "movement" in such 'concepts' -- and they are now said to possess "identity-in-difference", which now becomes the basis/motor of universal development. This is because these artificial 'objects' seem capable of change, since they have been altered so that they resemble real material objects.


We can see this is Hegel's confusion of the LOI with the LOC and the LEM; he runs together concepts, objects, propositions, judgements, along with a host of other things -- as do dialecticians in general (whether these be Marxist HCDs or not), whose thinking has been skewed by an uncritical acceptance of this Hermetic bungler's logical blunders.


And so, a bogus (local) change imposed on a handful of words (and one that is supposedly revealed by certain 'concepts' as they 'develop') is said to reflect an 'essential' feature of change for everything in nature, and for all of time --, which is thus promptly imposed on reality.


[In Essay Twelve, a developed version of this dodge will be called the RRT, which is an essential move in setting up more sophisticated versions of LIE. We also saw here and here how the entire dialectic is based on a series of logical howlers like this.]


[RRT = Reverse Reflection Theory; LIE = Linguistic Idealism.]


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


[This 'argument' (unwisely praised by Lenin and Trotsky!) is destructively analysed in Essay Twelve Part Three (summary here).]


This tangled rat's nest (otherwise known as Hegel's Logic) is in fact a sub-Aristotelian Grimoire overflowing with syntactic screw-ups of this sort (and worse!), all piled on top of one another.


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


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


Engels clearly sees objects and concepts as both object-like.


Plainly, these artefacts of the imagination can't undergo change in the material world (at least in the way that objects do), so such manoeuvres must take place in the artificial world of the mind (which is, or is not, assumed to be 'identical' with 'Being', depending on which branch of Idealism this ancient form of mental illness has colonised the thought of one so afflicted), even though we only have these distorted words as 'proof' that any of this has actually occurred.


In that case, the implied reasoning here seems to be that if objects in the real world can change (i.e., just as rivers, say, actually 'flow'), then so can concepts.


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


Now, as noted earlier, Hegel performed this trick on 'Nothing' to produce 'Being' (or vice versa) and hence 'Becoming'. These days, too, DL is supposed to have the 'power' to give life to certain 'concepts' by nominalising them into existence as abstract particulars -- but this merely destroys their capacity to express generality, vitiating the whole exercise.


Hence, and once more: a move in language is held to mirror, or to reveal, movement in reality --, but, as noted above, the former is held (by Idealists and naive DM-fans) to reflect changes which are more profound than mere material development. Indeed, this sort of confused conceptual change is said to drive the latter along. In this way, nature becomes 'dialectical' because a series of logical blunders has allowed Dialectical Magicians to conjure the underlying logic of 'Being' and 'Becoming' into existence literally from nothing, as these merge into and re-emerge from 'Nothing'.


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


As we saw in Essay Three, this is based on the idea that all words are really names, and on the belief that all concepts expressions are really singular terms (i.e., they are the names of abstract particulars -- or they 'designate' them in other ways).


However, what finally emerges at the end of this linguistic make-over is not in fact an account of how concepts change, but how a bogus linguistic ceremony, which conjures into existence these named abstract objects, can be substituted for a genuine account of change in the material world.


This inept syntactical 'research programme' (now over 2400 years old) deliberately jumbles up the logical role played by singular and general terms, names and concept expressions. In Essay Three Part One, this move was linked with Hegel's own confusion of the "is" of predication with the "is" of identity -- seriously compounded by DM-fans with their spurious distinction between "the abstract" and "the concrete".


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


As was also argued in Essay Three Part One, if sentences were composed solely of names (or singular terms), they would be no different from lists. Lists do not actually say anything -- unless they are given a context were they are capable of being used to say something by means of the explicit or implicit use of concept expressions/predicates (but only if these are no longer viewed as the names of abstract particulars).


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


Of course, this is the real reason why in the end DM-'propositions' are just empty collections of words: the inept syntactical theory dialecticians have inherited from Hegel (and from traditional logic) has vacated DM-theses of sense by turning the sentences used to express them into mere lists, thus preventing them from saying anything at all.


14. Compare the following with C3:


C3: The concept green has changed.


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


C5 succeeds in depicting change -– but, plainly, this is not change to a concept, but to an object.


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


By way of contrast, in C3, the phrase "the concept green" operates as a singular term, which cannot express a rule. [A moment's thought should convince the reader of that fact.]  Nevertheless, "the concept green", acting now as a singular term (when coupled with the one-place predicable "ξ has changed"), facilitates the formation of sentences like C3. But, because of this, C3 is no ordinary sentence. While it looks perfectly straight-forward, it cannot now be about the concept green, since the concept green is not an object, and yet the subject of that sentence is an object. This means that C3 is thoroughly perplexing. While C5 succeeds in depicting material change, C3 fails to depict anything because of the distorted linguistic form it 'expresses'.


As was pointed out above, the problem with a nominalisation like "the concept green" is that it cannot actually function as a concept expression. Indeed, in appearing to name (or designate) a concept, it now serves as a singular term, and an empty one at that. It cannot refer to whatever it might at first sight seem to be doing. This is because, as a singular term "the concept green" cannot pick out a concept, just an object, and it can only do so in the context of a mal-formed 'proposition', like C3.


Even if (per impossibile) the phrase "the concept green" could 'refer' to something, it couldn't serve as an archetype for the role that legitimate concept expressions -- such as "ξ is green" -- play in sentences like C5. Once more, this is because a singular term (i.e., "The concept green") cannot express a rule, which is what "ξ is green" actually does. But, the use of "ξ is green" is, ipso facto, part of our understanding how to employ the concept green in ordinary (materially-orientated) sentences.


"ξ is green", as it appears in sentences like C5, is the expression of a rule -- that is, anyone who knows how to utter sentences like C5 will have to know how to complete the stencil "ξ is green", just as the rest of us do. This does not mean that they are aware of this rule, but the stencil "ξ is green" is one way in which we can post facto make sense of what they have done. Nor does it mean that this is the only way that C5 could be built, of that we have to view things this like this, but this way of depicting things is one way of bringing out the rule-governed way we all form sentences like C5. Moreover, this way of depicting things brings underlines the fact that a singular term like "The concept green" cannot express a rule, whereas "ξ is green" can.


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


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


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


The reason for using this Fregean form notation was explained here and here.]


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


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


This is because predicate expressions can only be turned into 'referring' expressions by changing them into singular terms, which is a move that destroys their original non-referential (i.e., descriptive) status. And this is precisely what the use of C3 does: in trying to express in an indicative sentence what the logical role of a concept expression is in C5 (say), that role has to be altered, and by doing that C3 is prevented from saying anything at all about that role, and this about that 'concept'.


Thus, phrases like "The concept green" cannot designate the concepts they were perhaps intended to designate without seeming to transform them into 'objects' 'named' by singular terms, which then prevents such phrases from designating their intended target, since concepts are not objects!


However, that had certainly not been the aim of anyone who might have wanted to use a sentence like C3.  In fact, the use of C3-type sentences (or even the more obscure versions found in DL -- their use in modern philosophical logic is another matter entirely) was aimed at unmasking nature's hidden 'essences', those that that supposedly underpin all of reality. So, if a dialectician wants to say something like:


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


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


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


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


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


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


then he or she will only be able to do so by distorting language to such an extent that they end up saying nothing at all comprehensible (this was discussed in detail here). Hence, "The category 'Man'" cannot tell us anything about the logical role of " a man" (or if you like "ξ is a man") in "John is a man". But this bogus form comrade Jackson uses is typical of the way that DL-fans talk, and the way that traditional theorists have expressed themselves for 2400 years.


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


However, " green" is not a denoting expression.


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


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


[RTK = Reflection Theory of Knowledge.]


To put it another way: if there were any "essences" of this sort 'out there', somewhere in reality (howsoever they are conceived), then they could not be the referents of predicate expressions, since the latter are not singular terms. They are not referring expressions, they are descriptive.


But -- just to continue this metaphysical fantasy a little longer --, if these "essences" encapsulated general features of reality, then none of our general terms could be used to denote them. Any attempt to do so would demote these general terms and would thus turn these allegedly "general features of reality" into abstract particulars (as we saw in Essay Three) --, at the same time as robbing language of its capacity to express generality (by turning predicates into singular terms).


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


Movement in material reality (properly expressed in sentences like C5) is thus conflated with the spurious changes that have been imposed on concept expressions (in 'propositions' like C3). But, as we have seen, movement in material reality cannot be depicted in the latter way, and this is what prevents dialecticians from explicating the very thing they had claimed they wanted to do.


By tinkering around with the capacity that material language already has for expressing change, dialecticians merely produce empty strings of words.


This is the myth-begotten stake that Idealist thinkers, and their latter-day clones -- dialecticians --, have repeatedly driven through the rational heart of material language. And like any stake, it kills.


'Philosophical' sentences like C3 try to reveal the logical role of concept expressions (by constructing what seem to be empirical propositions about language itself, or about concepts themselves); but in order to do this they have to change concept expressions into singular terms, which now allegedly refer to something suitably "abstract", and non-material. But, if predicate/concept expressions do not refer, and never have, and can only be made to seem to do so by altering them in this way, then no wonder sentences like C3 create confusion and generate 'paradox' (and thus provide employment for traditional Philosophers who then to try to 'unravel' them!).


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


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


[Of course, this does not mean that we cannot make sense of conceptual change by other means. How this is achieved will not be entered into in this Essay.]


For example, consider these attempts to state putative truths about concepts:


C6: The concept green is a concept.


C7: The concept green is a concept expression.


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


C9: F is a concept expression.


C10: F is a concept.


C11: "F" is a concept expression.


C12: "F" is a concept.


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


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


[Some might wonder then how we can set-up a syntax; but whatever we set-up when we do that, we are not listing truths, merely expressing rules for the use of symbols.]


The locus classicus of the modern discussion of this topic can be found in Frege (1892), upon which much of my own thinking has been based. Further background to this topic can be found in Geach (1976), and Slater (2000); now in Slater (2007a).


15. Distortions of language like this motivate metaphysical systems in general; indeed, much of traditional Philosophy is based on just such muddles.


[Examples of this sort of confusion are given throughout this site; this particular one was analysed in detail in Essay Three Part One. See also the previous two Notes -- 13 and 14.]


This partly explains why ontological and epistemological fairy tales have had to be invented to provide bogus denotations for the artificial terms introduced as a result.


16. This claim is qualified in a later Essay. But, in order to be clear about its import, the use of the word "true" in such contexts will need clarification. That won't be attempted here.


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


See also here.


17a. Nevertheless, one bemused commentator has attempted to respond to this point (but without checking the much fuller argument presented in Essay Six (reproduced below), or waiting for the detailed argument that will be posted in Essay Twelve), in the following manner:


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


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


Moreover, the above comments reproduce the usual confusion of 'commonsense', or everyday beliefs, with ordinary language. As such, they are worthless. It will be argued in detail in Essay Twelve that the fact that ordinary language allows for every indicative sentence expressing a 'commonsense' belief to be negated shows that ordinary language cannot be identical with 'commonsense' (examples of this are given below).


And since this critic gives no examples himself of the "ideological" contamination of ordinary language with suspect terminology, not much can be made of that baseless allegation, either.


Ordinary Language


Dialecticians' Mistaken Assumptions


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


John Rees put things this way:

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

The problem with this passage is that it gets things completely the wrong way round. It is in fact our use of ordinary language that enables us to refer to change. Technical and philosophical jargon (and especially that which was invented by Hegel) is practically useless in this regard since it is wooden, static and of indeterminate meaning, despite what Rees asserts.

As is well-known (among Marxists), human society developed because of its constant interaction with nature and as a result of the struggle between classes. In which case, ordinary language could not fail to have developed the logical multiplicity to record changes of limitless complexity.

This is no mere dogma; it is easily confirmed. Here is a greatly shortened list of ordinary words (restricted to modern English) that allow speakers to refer to changes of unbounded complexity:

Vary, alter, adjust, amend, make, produce, revise, improve, deteriorate, edit, bend,  straighten, weave, twist, turn, tighten, loosen, relax, slacken, bind, wrap, pluck, tear, mend, repair, damage, mutate, metamorphose, transmute, sharpen, modify, develop, expand, contract, constrict, constrain, widen, lock, unlock, swell, flow, differentiate, divide, partition, unite, amalgamate, connect, fast, slow, swift, rapid, hasty, heat up, melt, harden, cool down, drip, cascade, drop, pick up, fade, darken, wind, unwind, meander, peel, scrape, graze, file, scour, dislodge, is, was, will be, will have been, had, will have had, went, go, going, gone, return, lost, age, flood, crumble, disintegrate, erode, corrode, rust, flake, shatter, percolate, seep, tumble, mix, separate, cut, chop, crush, grind, shred, slice, dice, saw, spread, fall, climb, rise, ascend, descend, slide, slip, roll, spin, revolve, oscillate, undulate, rotate, wave, conjure, quickly, slowly, instantaneously, suddenly, gradually, rapidly, hastily, inadvertently, accidentally,  snap, join, resign, part, sell, buy, lose, find, search, explore, cover, uncover, stretch, compress, lift, put down, win, ripen, germinate, conceive, gestate, abort, die, rot, perish, grow, decay, fold, many, more, less, fewer, steady, steadily, jerkily, smoothly, quickly, very, extremely, exceedingly, intermittent, continuous, continual, push, pull, slide, jump, run, walk, swim, drown, immerse, break, charge, retreat, assault, dismantle, pulverise, disintegrate, dismember, replace, undo, reverse, repeal, enact, quash, throw, catch, hour, minute, second, instant, invent, innovate, rescind, destroy, annihilate, boil, freeze, thaw, cook, liquefy, solidify, congeal, neutralise, flatten, crimple, evaporate, condense, dissolve, mollify, pacify, calm down, terminate, initiate, instigate, enrage, inflame, protest, challenge, expel, eject, remove, overthrow, expropriate, scatter, gather, assemble, defeat, strike, revolt, riot, march, demonstrate, rebel, campaign, agitate, organise…

Naturally, it would not be difficult to extend this list until it contained literally tens of thousands of words all capable of depicting countless changes in limitless detail (especially if it is augmented with the language of mathematics). It is only a myth put about by Hegel and DM-theorists (unwisely echoed by Rees) that ordinary language cannot express change. On the contrary, it performs this task far better than the incomprehensible and impenetrably obscure jargon Hegel invented in order to fix something that was not broken.

It seems that dialecticians like Rees, for example, would have us believe that because of the alleged shortcomings of the vernacular, only the most recondite and abstruse terminology (invented by Hegel, the meaning of much of which is unclear even to Hegel scholars) is capable of telling us what we already know -- and have known for tens of thousands of years -- that things change!

Of course, as Rees himself implicitly conceded, Hegel's leaden language has to be translated into 'ordinary-ish' sorts of words for the rest of us to be able to gain even a dim appreciation of the obscure message it supposedly contains (that was the whole point of his précis of a key Hegelian 'deduction' (discussed in Essay Twelve -- summary here); pp.49-50 of TAR) --, which apparently was that we can't understand change without such assistance!

But, if we already have ordinary terms (like those listed above) that enable us to talk about and comprehend change, what need have we of Hegel's prolix terminology?

Conversely, if according to Rees ordinary language is inadequate when faced with the task of translating Hegel's observations into something we can understand, how would anyone be able to grasp what Hegel meant -- or even determine whether he meant anything at all?


On the other hand, if we are capable of comprehending Hegel's obscure ideas only when they are written in ordinary-ish sort of terms, why do we need his opaque concepts to reveal to us what our language can or cannot express anyway -- when (on this supposition) it must have been adequate enough for just such a successful re-casting of Hegel's ideas for the rest of us to grasp?


If ordinary language is able to capture what Hegel meant, in what way is it defective? If it can't, then how might we understand Hegel?


Not surprisingly, if Hegel were correct, no one (including Hegel himself!) would be able to understand Hegel --, for, ex hypothesi, his words would then be un-translatable in terms that anyone could comprehend. Conversely, once more, if Hegel's words are translatable, that must mean that we already have the linguistic resources available to understand change (etc.) perfectly well. Naturally, this implies that on the one hand, if Hegel were correct, no one would be able to understand him, while on the other, if he were incorrect -- and we could understand him enough to be able to say even that much -- no one need bother.


[QM = Quantum Mechanics.]


It could be objected that it is not necessary to translate Hegel into ordinary language to understand him (any more than it is necessary to understand, say, QM this way); hence the above comments are somewhat misguided.


Descent Into Confusion


In response it is worth making the following points:


1) If that were the case, how would we ever be able to tell if anyone has ever understood Hegel? It would be no use pointing to the many hundreds of books and articles devoted to his work (which books and articles themselves defy comprehension, as I hope to show in Essay Twelve), any more than it would be to point to the many books and articles there are on the Christian Trinity (a doctrine that also originated from the same NeoPlatonic cess pit that spawned many of Hegel's ideas) as proof that that obscure notion is comprehensible. In fact, Hegel scholars are merely expert weavers of jargon; that does not mean that any of it makes a blind bit of sense.


2) The word "understand" is in ordinary language already.


3) The analogy with QM is unfortunate in view of the fact that leading physicists themselves admit that QM is incomprehensible.


"Those who are not shocked when they first come across quantum theory cannot possibly have understood it." Niels Bohr


"If you are not completely confused by quantum mechanics, you do not understand it." John Wheeler


"It is safe to say that nobody understands quantum mechanics." Richard Feynman


"Quantum mechanics makes absolutely no sense." Roger Penrose


Indeed, there is no theory in science that is not shot through with metaphor.


Other points will be dealt with below.


The idea that ordinary language cannot cope with rapid or slow change may perhaps be summarised by the following sentence:

H1a: Ordinary language cannot account for or depict change.

But, is H1a itself written in ordinary language? It certainly looks like it. If it is, it is pertinent to ask what the word "change" in H1a actually means.

If we, as ordinary speakers, do not understand this word, what precisely is it that Hegel and Rees are presuming to correct? We may only be educated if we know of what it is that we are ignorant -- that is, if we already know what change is (so that we can at least say that our word "change" does not match this ideal). But, ex hypothesi, we are not supposed to know this since our language is allegedly inadequate in this area.

[This point shows that the argument here is not solely about language, but about what it conveys to us -- in this case, what our words convey about change. Indeed, if we want to study change, we can only get a handle on it by the use of words (albeit connected with material practice, etc.).]

Contrast H1 with the following:

H1b: Ordinary language cannot account for or depict quantum phenomena.

The situation with regard to change is not at all like that presented in H1b, where technical expertise is required.

"Change", as it appears in H1a (if H1a is in the vernacular), cannot be an example of the technical use of language (as it is in H1b). Of course, if H1a is not in the vernacular, then the technical word "change" it contains will need to be explicated in terms of the ordinary word "change", so that we might grasp what this confusing but typographically identical technical word "change" actually means. And if that is so, the ordinary word "change" would have to feature in that new explication, which, of course, would just take us back to where we were a few paragraphs ago.

Without such an explication, if we don't know what the technical term "change" means, H1a would be incomprehensible. This is because it contains at least one word (i.e., "change") that (on this view) no one -- not a single human being -- yet understands. Unfortunately, this would mean that our re-education cannot be initiated by means of H1a, or, indeed, by any other sentence that uses this as-yet-to-be-explained word (i.e., "change").

Of course, that would also imply that the 'dialectical' development of this word/'concept' cannot begin, for as yet, all that aspiring dialecticians would available to them would be this empty word (i.e., "change"). For all the use it is, it might as well be "slithy tove".

It could be objected here that while our use of ordinary terms help us partially grasp the nature of change, Hegel's language provides the wherewithal to comprehend the concept (or the real processes it depicts) more fully -- 'dialectically' and 'scientifically', as it were.

Perhaps then Rees meant the following?

H2a: Ordinary language cannot fully grasp change.

H2b: A specially created terminology is required to enable its comprehension.

But, once again, what does the word "change" in H2a mean? Is it being used in the same way that we use the ordinary word "change"? Or does it possess its own 'special', technical sense, which has yet to be explained? If it does mean the same as the ordinary term, then where does our common understanding of this word (and what it relates to) fall short? Why do we need a theory to explain something we already understand?

On the other hand, if our common understanding of this word (and what it relates to) is defective -- if users of this word do not understand it -- then H2a is incomprehensible as it stands, since it contains a word (i.e., "change", once again) that no one (as yet) comprehends. Until we know the extent of our ignorance (or where this word falls short) -- or even what the subject of this query amounts to --, all the technical/dialectical terminology in the world is of no use -- even to dialecticians!

Alternatively, if the word "change" in H2a has its own special meaning, what is it? And if that is the case, what sort of criticism of ordinary language do H2a and H2b represent if they do not actually use the vernacular? Indeed, if in H2a the word "change" has a technical sense, how can that word with its special sense be used to criticise the ordinary word "change" (or point out its limitations) if that word is not itself being used?

Furthermore, if the word "change" has a dialectical meaning, how could that meaning possibly help anyone correct the ordinary word if we still do not understand the ordinary word? And how might dialecticians explain to themselves, or even to one another, what this special 'dialectical' meaning is if all they have to begin with is the defective ordinary word "change", a word that no one yet comprehends? This side of a clear answer to these questions, H2a is as devoid of sense as H1a ever was.

Again, in response to this it could be argued that H2a is not about our understanding of the meaning of a word; it is merely reminding us that ordinary language cannot be expected to operate outside its legitimate sphere of application (i.e., "beyond certain limits"). No one expects ordinary language to cope with complex issues found, say, in the sciences, or in philosophy; this does not impugn common understanding, it simply reminds us of its limitations.

Doubtless this is correct, but unless we are told in what way the ordinary term "change" -- as we now understand it -- falls short (of whatever it is supposed to fall short of), a dialectical extension to our knowledge cannot even begin. So, the complicated somersaults that dialecticians subsequently perform (with their words/'concepts') are irrelevant; we still do not know what the initial word/'concept' means.

In fact, if the word "change" is indeterminate as it now stands, dialecticians cannot even begin their warm up exercises, let alone impress us with their complex gyrations.

This shows that H2a is directly about our understanding of this word (and what it relates to), for if the word "change" (as it is used in H2a) does not mean what the ordinary word "change" means, then the meaning of H2a itself must be indeterminate, since the criticism it presents of the vernacular is devoid of content.

Again, it could be objected that no one is claiming that the ordinary word "change" is understood by no one at all (as the above responses would have it), only that it cannot handle complex processes that occur in nature and society.

But if our understanding of the word "change" is even slightly defective, we certainly cannot use it while pretending to correct it. We cannot feign comprehension of a word for the sole purpose of revising its current (supposedly defective/limited) meaning. This is not because this would be a difficult trick to pull off, it is because it is no more of an option than, say, pretending (to oneself) to forget the meaning of a word while actually using it!

Conversely, if the word "change" has no meaning (or if it is unclear what it means), then, plainly, neither that word nor its meaning may be corrected by the use of any sentence that also contains the 'suspect' word (as in H2a). Clearly, any attempt to do so must involve the use of this defective word, thus compromising any sentence in which it appears.

H2a: Ordinary language cannot fully grasp change.

So, if it is true that our grasp of this word is defective (in any way), then those very same imperfections/limitations apply to the sentences used by those who seek to correct it -- such as H2a (or its preferred 'dialectical' equivalent). Clearly, in that case, prospective revisers of the vernacular would not be able to comprehend what they themselves were trying to reform, since they would be in the same position as the rest of us, using a word with unspecified shortcomings.

On the other hand, if such linguistic/conceptual reformers understand the word "change" differently from the rest of us then any proposed modification to ordinary language would clearly apply to their own special use of this novel term -- i.e., to a word that is only typographically similar to the ordinary word "change" (but which novel term is still of undisclosed sense) --, but not to "change" as it is used in ordinary language.

The claim here, therefore, is that with respect to the word "change", it is not possible for anyone even to begin to say in what way it fails to mean what it is ordinarily taken to mean (or by how much or how little it falls short of this), or even to entertain the possibility that it might or might not do whatever it now does, without using that word in any attempt to do so, and in a way that was not also subject to the very same unspecified uncertainties.

It could be objected that this would make the translation of foreign words into, say, English impossible. In addition, it would make dictionaries useless.

Neither of these responses is at all relevant. We translate foreign words into English, for example, using words we already understand. In contrast, the above ruminations revolve around the use of a term in sentences, but by means of which no one could point out its limitations without using this word in that very act. Plainly, any sentence in which this word is used cannot fail to inherit those unspecified limitations, making any sentence in which it appeared equally defective.

On the other hand, if such sentences had a clear sense, the word in question must be alright as it is, vitiating the whole exercise.

More or less the same comments apply to the use of a dictionary, the successful employment of which depends on its authors explicating unknown terms to us in words we already understand. If, however, no one knows what "change" really means (or if it has unspecified shortcomings), then no one would know precisely what was being corrected, or how to go about it.

Again, it could be objected that we correct each other regularly over the misuse of certain words. That would not be possible if the above were the case.

Once more, this is not relevant; when we correct one another, at least one party to that social interaction would have to understand the corrected words aright. In the above (with respect to "change") this is not so.

Some might feel that my comments rely on the word "change" having one and only one correct meaning, but this surmise would itself be incorrect. Howsoever many meanings this word has in ordinary language, no one would be able to use it in any sentence seeking to correct it/them if every one of these meanings was defective in some as yet unspecified way -- or, less radically, if the same were the case merely with respect to a more restricted sub-set of its relevant senses (i.e., those of concern to dialecticians).

Moreover, any attempt to specify what these shortcomings are cannot work either.

Consider the following 'attempt' to revise the word in question:

H3: "Change" does not mean what ordinary language would lead us to believe; it means: "development over time as a result of internal contradictions understood as real material forces acting as parts of a mediated totality."

If this is so, then H3 should be re-written as follows:

H4: "Development over time as a result of internal contradictions understood as real material forces acting as parts of a mediated totality" does not mean what ordinary language would lead us to believe; it means: "development over time as a result of internal contradictions understood as real material forces acting as parts of a mediated totality."

The replacement of the word "change" in H4 with what it allegedly means just creates an incomprehensible sentence (and the same would happen with respect to any of its cognates -- indeed, Hegelians/DM-theorists can replace the proposed 'dialectical meaning' of "change" offered above with whatever formula they deem fit, the result will not change (more irony intended)).

If it is now objected that the above example is unfair, then it behoves that objector to indicate in what way our ordinary material words for change (and what they relate to) fall short of whatever they are supposed to fall short of -- without actually using the word "change" (or one of its synonyms) anywhere in that attempt. Short of doing that, that objector's own use of this word (or one of its cognates) to express his/her objection (howsoever mild or nuanced, or 'dialectically-motivated' it is) will be subject to the very same unspecified shortcomings, and the objection itself must fail for lack of clear meaning.

In that case, however, such an objector will find him/herself in a worse predicament than the rest of us (allegedly are); this is because he/she will now be unclear, not just about our ordinary words for change, but about the application of his/her own non-standard, jargonised replacement for it, because he/she will necessarily be unclear about what it was supposed to be replacing!

That was the point of the ridiculous example given in H4.

Now it could be objected to this particular manoeuvre that it confuses use with mention; in H3 the word "change" is not being used, merely mentioned.

Fair enough; in that case consider then the following:

H3a: Change does not mean what ordinary language would lead us to believe; it means: development over time as a result of internal contradictions understood as real material forces acting as parts of a mediated totality.

If this is so, then H3a should be re-written as follows:

H4a: Development over time as a result of internal contradictions understood as real material forces acting as parts of a mediated totality does not mean what ordinary language would lead us to believe; it means: development over time as a result of internal contradictions understood as real material forces acting as parts of a mediated totality.

Once more, if the word "change" (now used, not mentioned) in H3a actually means something else (or, the processes in reality it supposedly depicts are not as we take them to be), and thus we are all currently mistaken as to its/their real meaning/import, then H3a must be meaningless too -- or, at best, it must be of indeterminate sense.

In that case, the only way that H3a can be made comprehensible is to replace the meaningless term it contains (i.e., "change") with words that we are now told constitute its 'real meaning' -- as illustrated in H4b.

The result, if anything, is worse.

It could be argued that this would mean we would not be able to correct inadequacies in the use of any word whatsoever. For example, someone might choose to say that the war in Iraq is "unfortunate". If the above were correct, no one would be able to point out that this word is wholly unsuited in such a context.

Again, this is an irrelevant objection. The word "unfortunate" in the above counter-example is not being criticised because it is inadequate in all its applications, only that it is the wrong word to use here. In this case, no one would be seeking to correct or revise its meaning, nor suggest that it was universally inadequate. Indeed, it is because of what that word already means that it is inadequate here.

This is not the case with "change". Indeed, that word is said to have unspecified universal inadequacies, which 'shortcomings' must of necessity feature in the very act of pointing this alleged fact out -- nullifying that criticism.

It could be objected that this is not in fact so with the use of "unfortunate"; someone could complain about the use of this word along the following lines: 

H5: "Unfortunate" is totally inadequate to capture the magnitude of the unmitigated disaster in Iraq.

Once more, the use of H5 would only work in this context if the above objector was appealing to the current meaning of this word, not seeking to alter it or revise it, as was the case in H3.

Again, it could be objected that the type of 'analysis' paraded in H3 and H4 could be applied to any word with equally ridiculous results. Consider, for example, this:

H6: "Recidivist" means "a second offender; a habitual criminal; often subject to extended terms of imprisonment under habitual offender statutes."

H7: "A second offender; a habitual criminal; often subject to extended terms of imprisonment under habitual offender statutes" means "a second offender; a habitual criminal; often subject to extended terms of imprisonment under habitual offender statutes."

This shows that the above comments are completely misguided; the definition of any word can be reduced to absurdity if that definition is substituted for the word in question, as was attempted in H4. Or so this objection might go.

However, H6 does not seek to re-define this word, or point out its 'real' meaning (the latter of which is supposed to be different from its accepted sense), as was the case with H3.

On the other hand, had H6 been the following, the above objection might have had a point:

H8: "Recidivist" does not mean what we ordinarily take it to mean (i.e., "a second offender; a habitual criminal; often subject to extended terms of imprisonment under habitual offender statutes."), it means "A, B and C".

Where "A, B and C" stands for the preferred replacement, or 'real meaning' of the defined term. In that case, we could legitimately conclude:

H9: "A, B and C" does not mean what we ordinarily take it to mean, it means "A, B and C".

As illustrated in H4.

It could now be objected that this would undermine the use of stipulative definitions, that is, definitions which delineate new meanings to words already in use.

Again, this worry is misplaced. Stipulative definitions do not seek to re-define the meaning of ordinary words in their entirety, merely introduce a new meaning, or extend the old. This was not the case in H3.

Once more, it could be argued that this would mean that language could not change, or that we would not be able to understand earlier uses of typographically similar words.

However, the latter half of the above worry is just a variation of the 'translation' objection fielded earlier. The reader is therefore referred back to it.

The first half of this latest objection is, though, slightly more complex. Unfortunately, in that it uses the word "change" to make its point, it can hardly be advanced by someone querying the universal applicability of that very word! Hence, until it is rephrased in a way that does not use this word (or any other related ordinary word for change), not much can be done with it.

Nevertheless, this account of the ordinary use of "change" does not rule out the evolution of language. To see this, consider the following:

H10: The word "XXX" used to mean "YYY", but now it means "ZZZ".

But, H10 is not:

H11: The word "XXX" does not mean "YYY", but now it means "ZZZ".

The account here does not deny words meant different things in the past, only that whatever they legitimately meant then has altered.

Even so, the 'dialectical theory' under review here is in fact saying something far more radical. It seems to be telling us that a specific word, "change" (and its related terms), never in the entire history of humanity captured what they would now like to tell us is the 'real meaning' of change. In fact, this is a more extreme version of H11.

In response, it could be objected that despite this, the approach adopted in this Essay still cannot account for linguistic change. "Indeed," an objector might continue, "why can't we inflict some of the present author's own medicine upon the above sentences?" Perhaps in this manner?

H12: The word "ZZZ" used to mean "YYY", but now it means "ZZZ".

Which neatly mirrors H3 and H4:

H3: "Change" does not mean what ordinary language would lead us to believe; it means: "development over time as a result of internal contradictions understood as real material forces acting as parts of a mediated totality."

H4: "Development over time as a result of internal contradictions understood as real material forces acting as parts of a mediated totality" does not mean what ordinary language would lead us to believe; it means: "development over time as a result of internal contradictions understood as real material forces acting as parts of a mediated totality."

Initially, in response to this latest criticism, it is worth pointing out that the more radical versions of H3 and H4 (i.e., H3a and H4a) were in the end the preferred alternatives, and they were chosen in order to neutralise the use/mention problem:

H3a: Change does not mean what ordinary language would lead us to believe; it means: development over time as a result of internal contradictions understood as real material forces acting as parts of a mediated totality.

H4a: Development over time as a result of internal contradictions understood as real material forces acting as parts of a mediated totality does not mean what ordinary language would lead us to believe; it means: development over time as a result of internal contradictions understood as real material forces acting as parts of a mediated totality.

This would mean that H12 is now irrelevant.

If we modify H10 accordingly, the point will become clearer:

H13: "XXX" used to mean YYY, but now it means ZZZ.

Perhaps an actual example will further help:

H14: "Lunatic" used to mean someone affected by the moon [Skeat (2005), p.351)], now it means someone who is insane.

Hence, on the view advanced here, the old word still means what it used to mean; all we have now is a modern, typographically identical token of it with a new meaning. No one is questioning that earlier meaning.

Now, if would-be critics want to revise a word in common use, all well and good; but this cannot affect the ordinary meaning of that word. Such a revision would merely relate to this new (and typographically identical) word, with its new/extended meaning. However, and on the contrary, no attempt could be made to undermine or question the use that a word already has without that revision itself descending into incoherence, as we have seen.

It could be objected once more that all this misses the point; a philosophical understanding of change (as it features in the natural and social sciences, on the lines advocated by dialecticians) seeks not to replace ordinary language, which is quite adequate in its own sphere of application. It is aimed at augmenting our comprehension of natural and social development, for political purposes. The vernacular is inadequate only when it comes to accounting for complex processes in reality; this is where Hegel's ideas can be of genuine assistance (i.e., just as soon as the rational core of his system has been separated from its mystical shell, of course).

Or so this new response might go.

However, as we will see in other Essays posted at this site, not only is the above incorrect in general (in that it is the conceptual wealth expressed in the use of ordinary language which enables the depiction and comprehension of change (in nature and society)), it is misguided in particular. This is because we are still in the dark as to what it is that dialecticians are proposing, or what they are presuming to add to our understanding of a word neither they nor anyone one else fully comprehends --, that is, if their 'theory' is correct. Once more, if our (collective) understanding of this word (or any other) is defective, then any use of that word in an attempt to correct such unspecified defects (or even vaguely hint at them) must self-destruct, too.

Of course, it could be argued that there is no such thing as a "collective understanding" of this or any other word. That complaint will be tackled head-on in Essay Twelve. Suffice it to say here that if this were the case, then dialecticians themselves would be even more in the dark as to what they were effecting to revise/criticise, since they could not now appeal to a standardised set of meanings, commonly held, that they are seeking to 'correct'/extend.

After all, Hegel himself had to appeal to the limitations of "the understanding" to motivate his own (defective) 'logic'. If there is no such thing as "the understanding", then his theory cannot loop the first Hermetic loop. As should seem obvious: in order to criticise 'commonsense'/common understanding, it is not a good idea to tell one and all there is no such thing.

Quite apart from that, we would surely be unwise to listen to dialecticians trying to extend our knowledge of 'change', nor yet to those regaling us with the 'superiority' of their 'theory', until they have succeeded in explaining clearly a single one of their theses (which, as I have shown in these Essays, they have yet to do) -- or, indeed, until they had repaired the gaping holes punched in Hegel's 'logic' elsewhere at this site (for example, here).

Howsoever limited ordinary language is -- or isn't --, when it is used properly in HM it makes sense. DM (with its obscure Hegelian jargon and radically defective 'logic') has yet to come with a parsec of this minimal goal (and that comment applies to 'systematic dialectics', too --, perhaps even more so).

In addition, but worse, dialecticians cannot actually account for change (on this, see here).

Hence, their assistance is not needed.

Quite the reverse in fact: if accepted, their 'theory' would set back the scientific study of nature and society by at least half a millennium, given its reliance on a mystical and enchanted view of natural and social development.

[Small wonder then that Dialectical Marxism is to success what George W Bush is to intellectual achievement.]

In that case, as far as competing (scientific or philosophical) theories aimed at helping us understand the world and how to change it are concerned, DM/'Materialist Dialectics' does not even make the reserve list of viable candidates.

HM, minus the Hegelian gobbledygook, though, is more than adequate.

And that is why we can be confident that not even Hegel understood this part of his own 'theory'. This is not because it is a difficult theory, nor yet because it employs special jargon that is completely incomprehensible to the untrained mind. Nor is it even because Hegel did not use H3 (or anything like it), it is because of the fact that as soon as any attempt is made (by anyone -- even a person of "genius") to correct ordinary language -- or, just as soon as the vernacular is dismissed as defective or even slightly flawed, and its terms are held to be deficient when applied beyond "certain limits", requiring that they be "surpassed", by-passed or revised -- all meaning disappears.

To repeat, it is not possible to pretend to understand an ordinary word like "change" and then claim that it is defective (whether "speculative reason" initiates such an attempt, or not). Either the objector's understanding of this word is defective -- and the ordinary term is alright as it is --, or the ordinary word is defective and no one (including that objector) actually understands it.

Again, in the latter case, there would be nothing left to modify; in the former, no one need bother.


Ordinary Language Is Not A Theory


It could still be objected to this that if ordinary language is inadequate in most scientific and technical contexts (let alone in Metaphysics), it needs reforming, supplementing or augmenting in some way.


And yet, science has managed to make significant progress over the last four hundred years without having to reform the vernacular, even if scientists have had to develop specialised and technical languages of their own. The problem (if such it may be called) only occurs when attempts are made to translate scientific concepts into ordinary terms. Since there is no scientific need to do this (although there may be several powerful ideological and economic reasons why some might want to do it, as will be argued in Essay Twelve), the alleged clash with ordinary language is completely fictional.


Of course, no one is suggesting that ordinary language can be used in highly complex theoretical areas of study, but that is no more a limitation on the vernacular than it is a defect of Das Kapital that it can't predict weekly lottery winners.


Metaphysics was originally based on the idea that there were such things as philosophical 'problems' concerning aspects of reality and human existence -- those it seems that only expert theorists were capable of solving (or even of understanding).


Keith Thomas highlighted a similar tactic among 16th century magicians:


"It would be tempting to explain the long survival of magical practices by pointing out that they helped provide many professional wizards with a respectable livelihood. The example of the legal profession is a reminder that it is always possible for a substantial social group to support itself by proffering solutions to problems which they themselves have helped to manufacture. The cunning men and wise women had an undoubted interest in upholding the prestige of magical diagnosis and may by their mere existence have helped to prolong a mode of thinking which was already obsolescent." [Thomas (1972), p.295.]


Even though Thomas finally rejects this as an adequate explanation of this phenomenon, he notes that the 'special' skill these magicians claimed to have (that is, of being able to solve problems they had in fact invented) gave them a level of prestige and social standing they would not otherwise have had.


Of course, with respect to magic, Marxists must take account of the alienated lives and beliefs of susceptible audiences -- the latter of which would have included many ordinary people.


Clearly, this is not true of Metaphysics, which was (and still is) practiced almost exclusively by rather more 'select' social groups. Hence, Thomas's reason for rejecting his own tentative explanation of the persistence of magical beliefs (i.e., that magicians provided a service which ordinary people actively sought) does not apply to Metaphysics. Moreover, his account explains neither the overwhelming influence Metaphysics has had on almost every aspect of Western thought for 2500 years (it is indeed a "ruling idea"), nor the longevity of theoretical Philosophy (with precious little to show for it after all those years --, so this pointless activity cannot be justified on economic grounds). Of course, Thomas's comments were not designed to do this.


However, one reason usually given for the prevalence/ubiquity of metaphysical beliefs is that everybody (including ordinary folk) at some time in their lives has philosophical thoughts of some sort, or asks metaphysical questions. This is supposed to show that philosophical problems enjoy universal appeal and legitimacy. Hence, the argument could go: if everyone thinks metaphysically, its existence cannot be the result of its invention by an elite group of thinkers.


Nevertheless, it is worth noting the following four points in response to this:


(1) It is important to distinguish the confused musings (on such things as the nature of space, time, 'God', 'good' and 'evil' and the nature of human existence) that most individuals indulge in from time to time from the systematic study of metaphysical questions by those who have the necessary leisure time and training to do so (i.e., professional philosophers, theorists, and rich or sponsored 'amateurs').


(2) It is not being suggested here that metaphysical beliefs were invented by the ruling-class (or their hangers-on), only that the systematic study of Metaphysics is the sole preserve of those who have (knowingly or not) consistently promoted a theoretical view of reality, and one which is (quite 'coincidentally') conducive to the interests of the powerful. [On this, see essay Twelve; a summary can be found here.]


(3) The fact that ordinary people indulge in amateurish metaphysical musing from time to time no more makes Metaphysics a legitimate pursuit than it similarly alters the nature of religious or theological discourse. Ordinary people are not somehow turned into theologians if they wonder whether there is a 'god'. If and when they do, that still fails to legitimate Theology.


The same applies to Metaphysics.


(4) The confusion endemic in both groups (that is, in professional, leisured metaphysicians and ordinary/lay amateurs) derives from one source: the misconstrual of socially-sanctioned forms of communication as if they stood for the real relations between things, or were those things themselves. [This analysis is substantiated in Essay Twelve Part One.]


However, and independently of this, only 'professional metaphysicians' have an ideological motive for projecting these social norms back onto the world as fetishised reflections of social reality in a systematic fashion. This they do because: (1) their theses mirror the world as they see it (i.e., governed by hidden forces, concepts and "essences"), and (2) it helps them legitimate class division, inequality, oppression and exploitation (historically, it is quite easy to show that this has indeed been the case with the majority of metaphysical systems), and (3) these days, it is good for the CV. [All these are spelt out in detail in Essay Twelve.]


Lay metaphysicians, on the other hand, have no class-based motivation to fetishise their own language in such a manner -- not the least because to do so would clash with the way they already employ the vernacular in their everyday interface with material reality and with other language users. [This is not to suggest that other forms of fetishisation cannot distort their ideas; far from it!]


In fact, if ordinary folk were to talk like metaphysicians in their everyday life, they would probably find themselves regarded as psychotic, or delusional.


Which reminds one of the old joke:


A: "The great questions of philosophy interest me: Who am I? What am I? Where am I?"


B: "Sounds more like amnesia to me!"


To be sure, it is the insular existence of professional metaphysicians that protects them from themselves (as it were). It is only when they have to engage in everyday practical activities alongside the rest of us that their metaphysical theories look decidedly weird, if not completely ridiculous --, even to them (as David Hume admitted):


"I dine, I play a game of backgammon, I converse, and am merry with my friends; and when after three or four hours' amusement, I would return to these speculations, they appear so cold, and strained, and ridiculous, that I cannot find in my heart to enter into them any farther.


"Here then I find myself absolutely and necessarily determin'd to live, and talk, and act like other people in the common affairs of life. But notwithstanding that my natural propensity, and the course of my animal spirits and passions reduce me to this indolent belief in the general maxims of the world, I still feel such remains of my former disposition, that I am ready to throw all my books and papers into the fire, and resolve never more to renounce the pleasures of life for the sake of reasoning and philosophy." Hume Treatise Book I Section VII.


Clearly, this is because it is in daily life where the alleged clash between philosophical musings and 'commonsense' actually occurs and really matters. When metaphysicians have to behave like 'ordinary folk' in the real world, their metaphysical fancies lose all credibility.


Naturally, this means that in ordinary surroundings this 'Emperor' looks naked even to 'true believers'.


[On this, see Cowley (1991).]


Since ordinary language has developed in an unplanned way over tens of thousands of years it can be imprecise and ambiguous, and it is manifestly 'non-scientific'. Not only that, its vocabulary is suffused with vagueness and its grammar allows for the formation of potentially misleading sentences (but these are such only to the unwary).


However, this does not mean that ordinary language is defective in any way. Far from it, ordinary language was founded on conventions and material practices our species has developed over tens of thousands of years, during which it functioned perfectly well as a means of communication. The vagaries of ordinary language enable its users to communicate effectively over a much wider area of discourse than would otherwise be the case if it were overly precise.


When required, however, precision is relatively easy to achieve; indeed, at the risk of extreme pedantry, almost any degree of accuracy is attainable. In addition, the potentially misleading grammatical forms which the vernacular contains only succeed in misleading users when they attempt to reflect on language itself (which we/they are ill-equipped to do -- why this is so will be explored in Essay Twelve), which is not so when they apply it in everyday life. In the normal course of events such potentially misleading grammatical forms do not interfere with communication, nor do they puzzle anyone.


These considerations not only account for the vibrancy of ordinary language, they shed light on the source of many of the 'paradoxes' and 'philosophical problems' created by its misuse. While ordinary language could not function without these features -- vagueness, ambiguity, metaphor, synonymy, antonymy, etc. --, they can create misunderstanding if they are not handled with due sensitivity, and, dare I say it, with no little common sense. Nevertheless, these aspects also lend to language sufficient space to enable a seemingly limitless expansion of its expressive and communicative powers -- in the Arts, for example.


However, the downside of this is that it is all too easy to misconstrue ordinary language when users try to reflect on it theoretically -- i.e., when language "goes on holiday" (to paraphrase Wittgenstein). This occurs whenever it is employed in areas that are either far removed, or insulated, from everyday material practice, or when its representational forms are confused with its communicational forms, and vice versa. As will be argued at length in Essay Twelve Part One, 'philosophical problems' arise whenever grammatical rules are misinterpreted as empirical propositions, and which thus represent substantive features of the world (DM-theorists do this in connection with the LOI, the LOC, and with the use of the word "not", for example). When language is viewed primarily as representational, its grammar fetishised, LIE is reborn.


[The development and substantiation of these allegations forms one of the main themes of Essay Twelve (summary here). Other comments connected with this will be published in the Additional Essays section at a later date. There it will be shown that representational theories of language (among other things) were invented by traditional theorists keen to argue that discourse (and particularly written language) is really a secret code (which they alone were capable of understanding) that maps-out or mirrors hidden, underlying and "essential" aspects of reality (conveniently inaccessible to the senses). This then allowed them to claim that this code (expressed in impenetrable jargon -- to keep the 'riff-raff' at bay) enabled them to re-present to themselves 'God's' thoughts, thereby providing (for their sponsors in the various ruling elites that history has inflicted on humanity) an epistemological and ontological rationalisation of the status quo (which 'justification' varied as each Mode of Production and form of the State required).


In order to do this, traditional theorists had to undermine and belittle the communitarian and communicational aspects of language (which had been its original forms, created by collective labour), and thus the vernacular. That explains why practically every single traditional Philosopher (and now DM-theorist) has either denigrated (to a greater or lesser extent) the ordinary language of the working class.]


[LIE = Linguistic Idealism.]


Now, as far as the conflict between the vernacular and philosophical or metaphysical language is concerned, and since metaphysical theories make no sense, there can be no incongruity -- that is, no more than there is a genuine clash between, say, the nonsense rhymes of Edward Lear and ordinary discourse.


Admittedly, ordinary language has changed in countless ways over the course of history. Indeed, we are now capable of forming sentences and expressing thoughts that our ancestors could not. Doubtless this process will continue. But, ordinary language remains the highest and final court of appeal for human beings in their efforts to understand anything.15 This is because the historically-conditioned conventions within which we learn and apply the vernacular express and delimit our capacity to comprehend anything whatsoever.


This claim might appear somewhat dogmatic, but it isn't. It is based on the simple observation that words like "understand", "comprehend", "know" and "grasp" are themselves ordinary language terms, and they gain whatever meaning they have from the conventions and practices governing their use at present. They do not receive this from an imaginary or ideal usage, nor do they derive it from abstractions that are accessible only to philosophers and scientists -- or even Party intellectuals. Words like these cannot themselves be challenged without any such attempt itself collapsing into incoherence -- as was illustrated above in connection with "change", and will be illustrated again elsewhere at this site.


Consequently, while scientists may quite legitimately invent new terminology to suite their needs, scientific language itself cannot confront (or reform) ordinary language without undermining itself.


Moreover, ordinary language is not a theory; it neither encapsulates a "folk ontology" nor a "folk metaphysics". It is not identical with common sense, but it is not unconnected with it. [These seemingly dogmatic claims will now be defended.]


The vernacular is not a theory since every empirical proposition in ordinary language is pairable with its negation, and so can be contradicted. No theory can have this happen to all its propositions -- or have them so semantically accommodating.


Ordinary Language Does Not 'Assume' Things are Static


This means that Rees was wrong when he asserted that:


"Ordinary language assumes that things and ideas are stable, that they are either 'this' or 'that'…." [TAR, p.45.]


Ordinary language cannot assume anything -- it is human beings who "assume" things. Clearly, they do this by means of language. Unless language had the capacity to allow for the possible truth or falsehood of the said assumptions and/or their negations, then no "assuming" could begin. This is, of course, because assumptions can be wrong as well as right.


Moreover, the rich vocabulary of ordinary language allows the "assumption" to be made that objects can and do change -- and in complex ways, too. Indeed, ordinary language enables its users to speak of countless different types of change in seemingly limitless detail. A long (but greatly shortened) list of some of the words in the vernacular that enable this was given earlier. Hence, and despite what Rees says, the sophisticated nature of ordinary language permits the formation of the following sentences that readily depict change:


H78: This protest is increasing in size as we watch.


H79: That is becoming too heavy for the children to carry.


H80: This venue is now too small for our meetings.


H81: This spider's web is beginning to disintegrate.


H82: This train is being re-painted.


H83: That light is defective; it keeps flickering.


H84: This is how to lose members rapidly: spout dialectics at them.


H85: This dispute is no longer about working conditions.


H86: This entire continent is moving closer to Asia.


H87: That is how to break an egg.


H88: This is how to change workers' minds.


H89: In an instant the pickets had re-grouped ready for the next police charge.


Many of the above sentences are somewhat stilted because they have been deliberately tailored to use the words "this" and "that" (i.e., the form of words that Rees employed to caricature the vernacular) in order to show that "things and ideas" are not "assumed" to be stable -- contrary to Rees's assertion. However, this list at least demonstrates that even using Rees's unlikely and highly restrictive phraseology, ordinary language is capable of expressing material changes that Hegel's tortuous prose could not cope with -- that is, not without re-employing terms taken from ordinary language to assist it to do just that.19


Even given this highly constrained form of language, the above list of sentences can be extended indefinitely. Of course, if the full range of devices available to ordinary speakers is called upon (H89 being just one example of such), then it would be possible to form a potentially infinite set of sentences of far greater sophistication (than anything dreamt of in Hegel's work) depicting changes of every imaginable type.


This shows that ordinary language is capable of depicting (and thus permitting the explanation of) change in the real world far better than any technical or philosophical language yet devised.


Now, this is not something that a sophisticated user of English (like John Rees) should have to have pointed out to him -- even though my having to do just that is a sad comment on the intellectual decay that dialectical thought induces in those held in its thrall.20



Ordinary Language And 'Commonsense'


'Commonsense' is often confused with ordinary language. Unfortunately, the term "commonsense" is rather vague.22 Bertrand Russell once claimed it encapsulated the "metaphysics of cavemen", but even he would have been hard-pressed to say what it was, let alone how he knew so much about it.23


If the word has any clear meaning, it appears to denote an inchoate (but changing) set of beliefs and opinions that most (all?) human beings are supposed possess (whether they are conscious of them or not). But, if this were so, it would imply that these beliefs must have been communicated telepathically from individual to individual, one generation and one community to the next, across the planet and down the centuries. How else are we to account for the alleged universality of 'commonsense'? At no point in life has a single human being ever been tutored in 'commonsense'; no one runs through the list of its canonical ideas at school, at their parents' knee or even behind the bike sheds with their friends. Nobody studies 'commonsense' at college, nor do they take tests in it or receive a diploma proving their competence.


Of course, if this is indeed so, we should perhaps stop calling it "common".


One thing is clear therefore about 'commonsense': it cannot be all that common or we would all be experts at identifying its core ideas and saying where they have come from.23a


Moreover, if 'commonsense' is encapsulated in ordinary language, it is remarkably well hidden, for, as noted above, no one seems to be able to list its main precepts. In that case, no society in history could possibly have agreed over what should be included as part of 'commonsense', and what should be left out. Hence, the idea that 'commonsense' today is the same as it was ten thousand years ago (or last week), and identical across cultures, if correct, must be one of the best kept secrets in history. If no one ever talks about it and no one knows what it includes, it is no surprise that it's a complete mystery how it is disseminated within populations, or how one generation passes 'commonsense' on to the next.


Is it in the water? Is it genetically encoded?


But if that were the case, we would all possess the same set of 'commonsense' beliefs; but we do not, apparently.


Or, rather, no one is able to say whether we do or we do not share the same set, since no one is capable of listing the 'commonsense' beliefs held by everyone -- or indeed anyone -- else. Still less is it clear how 'commonsense' beliefs may be distinguished from widely held beliefs


For example, is it a 'commonsense' belief that dogs have for legs, or a widely held belief? What about the belief that grass is green or that the sky is up? And how could one test these without biasing the result?24


Typically, the sorts of beliefs some associate with 'commonsense' include ideological, metaphysical, religious, 'folk', mystical and superstitious notions, and the like. But, this list of likely candidates varies according to who is telling the tale.


In that case, one is tempted to say that the idea that there is such a thing as 'commonsense' must be a "scientistic folk belief" itself, since it is not based on any clear evidence --, at least none that is not 'tainted' with the sorts of ideas many would include in 'commonsense', too.24b


However, since nobody appears to know which beliefs are on the favoured list, the word itself is something of a misnomer. If 'commonsense' had have lived up to its name (at least), we would all be much clearer about its content; it would after all be eminently common.


Even so, almost invariably the relationship between 'commonsense' and ordinary language is assumed to be reasonably straightforward; indeed, the latter is supposed to contain or express the former. So clear is this link imagined to be, and so universally is it held, that no one (literally no one (!) -- as far as I have been able to ascertain) questions it (even Wittgenstein made this mistake!).


But, while no competent language-user is in much doubt about his or her own language, not a soul seems to be able to say what 'commonsense' is. Even though not all of us have a mastery of speech equal to that of its most accomplished practitioners, no one (novice or adept alike) seems to know what 'commonsense' is. This is quite remarkable if the two are as intimately connected as we have been led to believe.


The case for identifying the two is no less questionable, too. As noted above, ordinary language is supposed to contain or to express 'commonsense' ideas. However, when pressed to supply details those wishing to lump the two together are often reduced to making a few vague references to things like sunrise, solid objects, colour vision, the possession of two hands, an imprecise collection of psychological or 'mental' dispositions and/or 'processes', an assortment of perceptual conundrums, a handful of proverbs and 'wise' sayings, a few vague moral, political and ideological inanities, as well as the odd superstition or two. [On this topic see, here.]


In fact, the haste to identify the two is not just unwise, it is ideologically-motivated (as will be demonstrated in Essay Twelve, summary here).


On the other hand, had more than a moment's thought been devoted to this pseudo-identity, its absurdity would have been immediately obvious: if ordinary language were identical with 'commonsense', it would be impossible to gainsay any of its alleged deliverances in the vernacular.


The plain fact is we can. And easily.


Not only are we able to deny that tables are solid, that the sky is blue, that the earth is flat, round or cucumber-shaped, that NN believes (for most p) that p, that sticks do not bend in water, that Queen Elizabeth II is sovereign in Parliament, that water falls off a duck's back, that Rome was built in a day, that an apple a day will tend to deter a doctor's visits, that φ-ing is wrong (for any conventional φ), that Capitalism is fair, that human beings are 'naturally' selfish, we can do all of these in every known language that possesses the relevant vocabulary. That, of course, is the whole point of the negative particle.25 If ordinary language were identical with 'commonsense', none of this would be possible.


To be sure, many of the beliefs entertained by our ancestors we no longer accept, but as far as the connection between 'commonsense' and the vernacular is concerned, sentences drawn from it gain their sense because of the conventions set by social practices. Although we can express our beliefs in ordinary language, the sense of a sentence does not arise from any of the beliefs we possess, nor from any we have inherited from the past. This is because beliefs themselves are dependent on language and thus on our capacity to articulate them accordingly. And we can be sure of that fact if language is social, otherwise beliefs could not be communicated, let alone formed.26


Just as social practices themselves cannot be altered individualistically (any more than the value of money can), the conventions underpinning language cannot be revised at will by any one individual or group (except perhaps at the margins).27 The conventions we have at any point in time of course change and grow in accord with the rules governing social development. They are, at basis, an expression of our "species being" and are intimately connected with our relationship with the world, with one another and with previous generations.28


Hence, just as it would it be impossible for an individual to bury, hide or incorporate a set of beliefs in ordinary language in order to form the backbone of 'commonsense', it would be equally impossible for a group to do so.


In that case, it really isn't up to a revolutionary, or party of revolutionaries (or anyone else, for that matter), to disparage such a vitally important expression of our collective (but changing) nature as human beings. Whether they do so or not is plainly up to them; the 'penalty' (if such it may be called) for attempting to do this is not always immediately obvious. However, anyone who does try to undermine the vernacular will soon find their ideas descending into incoherence (as was demonstrated above with the word "change", and will be again in other Essays posted at this site in relation to other words). In that sense, it is not a viable option to attack the vernacular, since such a strategy automatically implodes.


This means this is not an ethical issue -- but, it is a logical and political one. The latter half of that assertion will now be substantiated....


[The rest of this can be found in Essay Twelve.]



Additional Notes


15. Since the application of ordinary language underpins our understanding of anything whatsoever, it is, as noted above, the court of last appeal, which, although not democratic in one sense (we do not determine what something means by counting heads), it is in another: language is materially-grounded in the practice of the majority -- i.e., those who, through their labour, interface with material reality and one another every day. This means that certain features of ordinary language cannot be 'reformed' without ipso facto undermining our ability to comprehend anything at all. And that helps explain why traditional/metaphysical attempts to do so rapidly fall apart, and why they are fundamentally undemocratic (in the second sense, in that they are invented by a tiny minority, and are developed out of collective labour), and how in Marxism this is connected with substitutionist thinking. Cf., Wittgenstein (1974). [More on this in Essay Nine Parts One and Two.]

Moreover, many key scientific concepts have themselves been derived from ordinary language by analogical and metaphorical extension (etc.), as noted above. Indeed, even though it is possible to comprehend a scientific theory without having to translate it into the vernacular, the former cannot succeed in undermining the latter without also compromising that very attempt. [This slide into incoherence was illustrated above, and in more detail in Essay Three Part Two.]

19. Anyone who doubts this is welcome to try to express in 'Hegel-speak' what sentences H78-H89 manage to say quite easily without such 'assistance'.


20. Max Eastman's words spring to mind here:


"Hegelism (sic) is like a mental disease -- you cannot know what it is until you get it, and then you can't know because you've got it." [Eastman (1926), p.22.]


These words were, of course, written when Eastman still regarded himself as a Leninist.

[I first encountered Eastman's work after about four and a half years into this project. Some of the ideas found in the Essays posted here had been anticipated in his writings, but most had not.]

22. It needs underlining here that these comments are not aimed at the ordinary use of the term "common sense", just its philosophical deployment, highlighted in the text as "commonsense". The original meaning of the term "common sense" (i.e., that which occurs in Aristotle's work) is not relevant to the discussion in the text since the philosophical import of this term parted company with Aristotle's meaning long ago.

23. As Michael Dummett points out [in Dummett (1979), pp.390-93] there is no such thing as "the commonsense" view of the world.

23aIf 'commonsense' beliefs were culturally 'relative', each generation would possess a different, or slightly different, set of 'commonsense' beliefs -- even if there were some overlap. In that case, of course, there would be no such thing as 'commonsense'. It would still be a mystery, however, how such beliefs could be passed on if no one knew what they were.

It could be argued that this might occur at a non-conscious level, as attitudes and 'values' are passed down the generations.

Now, even if that were so (but the idea will be questioned in Essay Three Part Four), it would still be unclear exactly what was being 'passed on'. No one, researchers and subject alike, seems capable of saying (over and above the vague list mentioned earlier). This then would be the first area of scientific research where no one knew what they were talking about!

24. Again, since I do not accept the philosophical use of this term I will not try to solve this intractable problem for those who do.

24b. By that I mean that anyone attempting to show that 'commonsense' beliefs are accepted by all/most human beings would have to use evidence that was itself 'contaminated' with these allegedly 'commonsense' beliefs: for instance, that there are medium-sized objects in the world called "human beings", that there are such things as colours (so that, for example, claims that human beings believe there are colours is not itself an empty claim), just as there are edges, corners, surfaces and holes, that the words by means of which such ideas are expressed have a meaning, and so on. In short, if this evidence is to make sense to the rest of us (and, indeed, to anyone hoping to sell us this tale), those using it will have to take for granted many 'commonsense' ideas.

25. The sophisticated use to which us humans are capable of putting the negative particle, at least in English, is explored at length in Horn (1989).

26. This is a controversial claim; it will be examined in more detail in an Essay to be published at this site at a later date.

27. Unless, of course, this is done to extend language. That aside, the abrogation of linguistic rules results in the production of non-sense; naturally, both of these aims could form part of the intent of an aspiring abrogater (for creative purposes, or for effect, or whatever). However, the creative extension of language undertaken by writers and poets (etc.) still has to make some sort of sense. Think of the work of James Joyce; Joyce did not just write total gibberish, or randomly bash away at his typewriter.

Again, this does not undermine the comments made in the text above. While language does indeed develop, those responsible for helping it on its way do not do so by undermining the use of words we already have; if anything, they do so by extending language, creating novel uses for it, augmenting its vocabulary, and so on.

However, on certain aspects of the imaginative extension of language, see White (1996), and Guttenplan (2005).

28. Spelled-out more fully, this would provide some grip for the word "material" as it is used in many of these Essays. That task will be attempted when this project is finished.

The above ideas about ordinary language and common sense are developed and defended in the following: Button, et al (1995), Cowley (1991), Cook (1979, 1980), Ebersole (1967, 1979a, 1979b), Hacker (1982a, 1982b, 1987), Hanfling (1984, 1989, 2000), Ryle (1960), Macdonald (1938) and Stebbing (1958). [It has to be said that, as far as can be ascertained, all of these authors confuse ordinary language with common sense. Or, at least, they do not distinguish between them as clearly as I have done.] See also Uschanov (2002), and his longer article posted here.

I am the present reading Coates (1996), who also seems to muddle these two up. More details will be posted when I have finished that work.

The ruling-class and their hacks have always denigrated the vernacular and the common experience of ordinary folk. It is even less edifying to see Marxists (like this commentator, if he is a Marxist!) do the same thing.

More details on this topic will be given in Essay Twelve (summary here), but an excellent recent account can be found in the opening sections of Conner (2005).


As far as the propensity of the 'lower orders' to form 'superstitious' beliefs is concerned (a phrase this commentator does not use, but his intentions are reasonably clear), why we should pay any more attention to that phenomenon than we do to religious belief in general (when it grips them) is unclear. But even if it were clear, its philosophical (as opposed to its sociological, psychological or political) implications would still be in doubt. As noted above, since we can negate every single ideological, racist, and superstitious belief in the vernacular, these cannot be identical.


Ordinary Language And Ideology


Again, this is how I put things in Essay Twelve (also see here):


Admittedly, ordinary language may be used to express the most patent of falsehoods and the most regressive of doctrines, but it cannot itself be affected by "false consciousness" (and this is not the least because the notion of "false consciousness" is foreign to Marx; on that see here), or itself be "ideological".


Without doubt, everyday sentences can express all manner of backward, racist, sexist and ideologically-compromised ideas, but this is not the fault of the medium in which these are expressed, any more than it is the fault of, say, a computer if it is used to post racist bile on a web page. Ideologically-tainted ideas expressed in ordinary language result either from its misuse or from the employment of specialised terminology borrowed from religious dogma, sexist beliefs, racist theories and superstitious ideas. This is not to suggest that ordinary humans do not, or cannot, speak in such backward ways; but these are dependent on the latter being expressed in ordinary language, but are not dependent on that language itself.

It is worth pointing out at this stage that this defence of ordinary language is not being advanced dogmatically. Every user of the vernacular knows it to be true since they know that for each and every sexist, racist and ideologically-compromised sentence expressible in ordinary language there exists its negation.

This is why socialists can say such things as: "Blacks are not inferior"; "Human beings are not selfish"; "Wages are not fair", "Women are not objects", "Belief in the after-life is baseless" -- and still be understood, even by those still in thrall to such ideas, but who might take an opposite view. If ordinary language were identical with 'commonsense' -- and if it were ideological (per se), in the way that some imagine -- you just could not say such things. We all know this to be true -- certainly, socialists should know this --, because in our practical discourse we manage to deny such things every day.


In this regard, it is as ironic as it is inexcusable that there are revolutionaries who, while they are only too ready to regale us with the alleged limitations of ordinary language -- on the grounds that it reflects "commodity fetishism", "false consciousness" or "static thinking" --, are quite happy to accept (in whole or in part) impenetrably obscure ideas lifted from the work of a card-carrying, ruling-class-warrior like Hegel. Not only are his theories based on alienated thought (i.e., mystical Christianity), his AIDS was a direct result of a systematic fetishisation of language.


[AIDS = Absolute Idealism.]


This commentator also had the following to say:


"This project is inherently frustrating on so many levels, as Homer Simpson would say. On the one hand Rosa shows up the shameful ignorance of a century of Marxism-Leninism, marshalling in the process a prodigious array of sources on logic and mathematics, and also on the sciences, information that is urgently needed by her audience in view of the ignorance she contests. On the other, that so much energy should be invested to prove so little is tragic....


"Rosa occasionally acknowledges partial exceptions, but she has been so traumatized by the mountains of Trotskyist drivel she was force-fed, as well as its Stalinist counterpart, she rarely gets beyond that to see what else might be done or has been done with the dialectical tradition....


"Had Rosa not so precipitously dismissed 'academic Marxism', while copiously citing from other academics with expertise in mathematics, logic, and analytical philosophy, she would be better positioned to exploit their contributions as well as pinpoint their weaknesses. The whole history of critical theory is an excellent case in point, perhaps the best case. The Frankfurt School, their precursors, associates, and successors, all fell down on logic and mathematics. Nonetheless, they provided the tools to decipher the ideological phenomena of their time..."


The reason why so much has been 'wasted' on "so little" is that the political traditions to which this commentator refers (all dominated by Dialectical Marxism) have done considerable actual damage to our movement over the last 130 years.


In contrast, academic Marxism/'systematic dialectics' has largely been ignored in these Essays since it is politically irrelevant. Indeed, this current can damage nothing except the brains of those who still think it has anything worthwhile to offer humanity (which fact those so afflicted are not likely to appreciate for the reasons Max Eastman revealed). Well, they are welcome to their political cul de sac.


Far from being force-fed on an exclusive diet of Trotskyist and Stalinist 'drivel', I have been studying academic Marxist writings now for more than twenty-five years (indeed, at the time of writing this, the Bibliography to my thesis stretches to over 90 pages, containing references to over 3000 books and articles by academic Marxists, among others). To be sure, this brand of dialectical gobbledygook is not the 'low grade drivel' one encounters in certain Trotskyist/Stalinist works, but it is high grade drivel nonetheless --, and politically inept drivel at that (since it is written by human beings who, for all their expensive education, by and large, cannot seem to write a clear sentence to save their lives).


As I note elsewhere about this current in Marxism:


(1) Low Church Dialecticians [LCDs]: Comrades in this category cleave to the original, unvarnished truths laid down in the sacred DM-texts (written by Engels, Plekhanov, Lenin, Stalin, Trotsky, or Mao). These simple souls are highly proficient at quoting endless passages from the holy books as an answer to everything and anything, just like the faithful who bow to the East or who fill the gospel halls around the world. Their unquestioning faith is as impressive as it is un-Marxist.


They may be naive, but they are at least consistently so.


In general, LCDs are blithely ignorant of FL. Now, on its own this is no hanging matter. However this self-inflicted and woeful ignorance does not stop them pontificating about FL, or from regaling us with it alleged limitations -- charges based on ideas they unwisely copied from Hegel, the George W Bush of Logic.




Advanced Logic Class At Camp Hegel


LCDs are by-and-large active revolutionaries, committed to 'building the party'. But they have alas conspired to do the exact opposite: helping to keep it small, with countless splits and expulsions. This is a rather fitting pragmatic contradiction the dialectic has visited upon these, the least of it slaves.


Of course, they cannot see the irony in all this (even when it is pointed out to them -- I know, I have lost count of the number of times I have tried!), since they too have not taken the lens caps off.


This has meant that despite the fact that every last one of these poor schmucks strives to "build the party", few of them can boast membership roles that rise much above the risible. In fact, all we seem to have witnessed since WW2 is the creation of more and more fragmented groups -- but still no mass movement.


Has a single one of them made this connection (and this in a world where they claim everything is interconnected)?


Over and above blaming everyone and everything else for this sorry state of affairs -- are you kidding!?


The long-term lack of success enjoyed by Dialectical Marxists and the theory we are told is central to Marxism are thus the only two things in the entire universe that are not interconnected.


(2) High Church Dialecticians [HCDs]: These Marxists, on the other hand, are in general openly contemptuous of the 'sophomoric ideas' found in most of the DM-classics (even though many of them have an odd liking for Engels's first 'Law').


More often than not, they reject the idea that the dialectic operates in nature, inconsistently using Engels First 'Law' perhaps to justify this 'leap' (so that they can claim that humanity is unique), just as they are equally dismissive of these simple LCD souls for their adherence to every word in the classics.


[Anyone who knows about High Church Anglicanism will know of what I speak.] 


HCDs are mercifully above such crudities; they prefer the mother lode -- direct from Hegel, Lenin's Philosophical Notebooks and/or the writings of assorted latter day Hermeticists like Raya Dunayevskaya, CLR James, Tony Smith, Tom Sekine, Robert Albritton, Chris Arthur and Bertell Ollman -- sometimes cut perhaps with a few kilos of hardcore jargon straight from that intellectual cocaine-den, otherwise known as French Philosophy.


Or worse, that haven of intellectual heroin: the work of Heidegger.


HCDs are generally, but not exclusively, academic. Tortured prose is their forte, and a pointless existence is their punishment.


At least LCDs try to pretend that their ideas are relevant to the class struggle.


High Church dialectics, in contrast, is just good for the CV.


[And clearly, the latter sort of dialectics is not an "abomination" for that section of the bourgeoisie that administers Universities.]


Both factions, however, are well-supplied with conservative-minded comrades, happy in their own way to copy the a priori thought-forms of two-and-a-half millennia of boss-class theory, seldom pausing to give any thought to the implications of such easily won knowledge. If knowledge of the world is a priori, and based solely on armchair-inspired thought, reality must indeed be Ideal.


It is worth adding, though, that there are noted exceptions to these sweeping statements -- some academic Marxists do actively engage with the class struggle; the point is that very little of their high theory is at all relevant to that struggle.


This has meant that the baleful influence of Hegelian Hermeticism becomes important at key historical junctures (i.e., those involving defeat or major set-back), since it acts as a materialist-sounding alternative to traditional philosophical theory (even while it emulates the latter in all but name).


Dialectics (especially the HCD-strain) thus taps into thought-forms that have dominated intellectual life for 2500 years -- i.e., those that define the boundaries of 'theoretical acceptability', and thus trade only in a priori theses, and sage-like but nonetheless dogmatic pronouncements.


Hence, because of its thoroughly traditional nature, DM is able to appeal to the closet "god-builders" and dialectical mystics that revolutionary politics seems to attract -- and who, alas, appear to congregate mostly at the top of this ever-growing heap of long-term failures.


Indeed, I will continue to ignore the vast bulk of the material churned out by HCDs just so long as it remains irrelevant to the course of the class war. I suspect the Sun will cool first.


If that is regarded by this commentator as "tragic", I should care.


And I use modern Analytic Philosophy and Modern Logic since both are incomparably superior to the Hegelian gobbledygook most academic Marxists dote on. In addition, the methods they encourage (or, at least the ones that I use) deliver clear results.


Other things this commentator says have either been dealt with already at this site, or are too vague to do very much with.


Further remarks on this commentator's response to other Essays posted at this site can be found here, and here.


18. Naturally, DM-apologists will want to deny this, but apart from claiming that scientists are all "unconscious dialecticians", their evidence peters out alarmingly quickly. [This is examined in more detail in Note 20, below.]


Of course, if the claim that all scientists are "unconscious dialecticians" is to stand, then what is to stop Buddhists, for example, claiming that all scientists are "unconscious followers of The Eightfold Path"?


This is no joke; some already have! On this see, McFarlane (2003).


But, why don't we go the whole hog? Why not claim that dialecticians are "unconscious head-hunters"; there is about as much evidence to support that wild idea too.


The historical connections between FL and science are detailed throughout, for example, Losee (2001); similar links with mathematics can be found in Kneale and Kneale (1962), pp.379-742, with a brief survey in Nidditch (1998). There is a clear summary of the connection between Fregean FL and advances in mathematics in Beaney (1996), pp.269-77 and pp.1-117. However, the best introductions can be found in Weiner (1990, 1999, 2004) and in Noonan (2001); the general background is supplied by Giaquinto (2004). The relation between science and DM will examined in more detail in Essay Three Part Six, and Essay Thirteen Part Two.


For a more illuminating discussion of the way contradictions can be managed -- at least in Mathematics -- cf., Floyd (1995, 2000). For the same in science, see Harrison (1987).


19. Cf., Davis (2000), Hodges (1983), and Dyson (1997). The importance of Alonzo Church's work on the λ-Calculus can be judged by the fact that it underpins most programming languages.


Woods and Grant try to minimise all this with the following comment:


"There are two main branches of formal logic today -- propositional calculus and predicate calculus. They all proceed from axioms, which are assumed to be true 'in all possible worlds,' under all circumstances. The fundamental test remains freedom from contradiction. Anything contradictory is deemed to be 'not valid.' This has a certain application, for example, in computers, which are geared to a simple yes or no procedure. In reality, however, all such axioms are tautologies. These empty forms can be filled with almost any content. They are applied in a mechanical and external fashion to any subject. When it comes to simple linear processes, they do their work tolerably well. This is important, because a great many of the processes in nature and society do, in fact, work in this way. But when we come to more complex, contradictory, non-linear phenomena, the laws of formal logic break down. It immediately becomes evident that, far from being universal truths valid 'in all possible worlds,' they are, as Engels explained, quite limited in their application, and quickly find themselves out of their depth in a whole range of circumstances. Moreover, these are precisely the kind of circumstances which have occupied the attention of science, especially the most innovative parts of it, for most of the 20th century." [Woods and Grant (1995), p.99.]


We will have occasion to look at these wildly inaccurate claims later on, but apart from brushing modern logic under the carpet with a simple put-down, these two authors offer no examples of any technological applications of DL, even though they try vainly to 'expose' the alleged limitations of FL. It is, however, worth pointing out that these two have clearly confused logical falsehood with invalidity when they say "Anything contradictory is deemed to be 'not valid.' Validity has nothing to do with contradiction (in fact, one rule (RAA) actually depends on both).


And, anyone who thinks that, say, QM poses a threat to the LEM, would do well to read Harrison (1983, 1985), and then think again. Hence, so-called "quantum logic" poses no threat to the LEM since it has merely forced us to reconsider what we count as a scientific proposition.


[QM = Quantum Mechanics; LEM = Law of Excluded Middle.]


Of course, computers have had an incalculable affect on the world, all thanks to the Propositional Calculus.


In contrast, however, DL merely succeeds in confusing comrades (like Woods and Grant) -- which seems to be the extent of its practical import.


[Woods and Grant's other baseless claims will be picked apart in Part Three to this Essay, to be posted some time next year.]


20. Admittedly, this is a controversial claim, but only in so far as some have thought to controvert it.


As pointed out in Note 18, so divorced from reality have dialecticians become that some even claim that scientists are "unconscious dialecticians", and because of this they then imagine that the successes of science can be attributed to DL! It is worth noting that Christians claim the same for belief in God; indeed, they put the advancement of science down to divine guidance. This is one straw, it seems, that both wings of modern mysticism are keen to cling onto, for all the good it does either.


Dialecticians have been forced into this corner since, of course, few human beings have ever heard of dialectics, and (outside of the old Communist block and its satellite states) there are certainly not enough to fill a small cinema.


But, if as we are constantly being told, scientists are stuck with the rusty old concepts that FL has bequeathed them (this fable is retailed countless times in RIRE; here are a few: pp.42, 67, 69, 82, 83, 85, 86, 87, 88, 89, 91, 94, 95, 96, 97, 98, 99, 106, 107, 119, 132, 148, 152, 156, 234, 255, 354, 365, 387, 406; even John Rees joins in: TAR, pp.3-4), how was it possible for human knowledge and technique to have advanced quite so dramatically over the last 350 years? If in practice scientists actually use these 'decrepit, outmoded categories', and science has advanced as a result, does that not amount to a practical refutation of the idea that FL is inferior to DL?


Well, you would think this was a safe inference to make, but DL addles the brain so do not expect such a simple deduction from any of its victims.


[RIRE = Reason in Revolt, i.e., Woods and Grant (1995); TAR = The Algebra of Revolution, i.e., Rees (1998).]


On the other hand, is there a scrap of evidence to show that there is (or there has been) a single scientist who is (or who was) an "unconscious" dabbler in the Dialectical Black Arts? If there is, dialecticians would be well advised to keep it to themselves no longer. [The example of Mendeleyev is dealt with here.]


And what of the few genuine examples where dialectics has been used in science? If the work of Lysenko is anything to go by, we may conclude that it has not been a ringing success. It is arguable that Lysenko's theory held Soviet agriculture back for over 30 years. [On Lysenko, see Joravsky (1970), Lecourt (1977), Medvedev (1969), and Soyfer (1994).]


Of course, if and when things go wrong in non-Soviet science, dialecticians do not blame that on "unconscious dialectics"; rather they put it down to "bourgeois logic", "formal thinking" and "commonsense", etc. Which is rather odd, given the fact that all the evidence suggests that logic (both Formal and discursive) has actually helped scientists refine and test their theories, while DL has featured nowhere at all.


Small wonder then that dialecticians also believe that appearances also contradict reality; given the above, they would, wouldn't they? Now, this is, of course, an odd sort of thing for materialists to have to argue: if the material world contradicts a certain idea, ignore reality and cling to the idea! For sure, dialecticians consciously do that!


In fact, and on the contrary, all the signs are that dialecticians are pretty visible practitioners of self-delusion. So: on the one hand we are told that dialectics is and always has been central to revolutionary practice -- and that revolutionary cadres have to be, always were and still are over-flowing with conscious dialecticians --, on the other, we have witnessed little other than the constant failure of Dialectical Marxism to seize the masses, or even so much as lightly hug them.


Hence, conscious dialectics seems to be wedded to long-term failure; 'unconscious' dialectics appears to be linked to success.


But, what conclusion should we draw from the above? Perhaps this: that all revolutionaries should copy scientists and become consciously ignorant of DL. Maybe then our movement will see some success? Or would this recommendation reveal yet another failure to "understand" dialectics on my part?


Admittedly, certain 'dialectical' biologists have claimed that DL has an important part to play in the study of living systems -- for instance, the authors of DB, along with several notable members of the Communist Party from a few generations back (e.g., Haldane, Levy and Bernal). On this, see here.


Unquestionably, an appeal to organic wholes and interconnectedness makes some sort of sense both in the Life Sciences and in the study of social development. However, this admission does not mean we have to accept the entire DM-enchilada, and opt for universal Holism. [On this, see Essay Eleven Part One and Part Two.] Anyway, as is demonstrated throughout this site, the concepts found in DL and DM are far too vague or incoherent for them to play a useful role in any of the sciences. [So, no wonder they screwed-up Soviet Agriculture and Genetics.]


[DB = The Dialectical Biologist.]


Nevertheless, the authors of DB advance certain claims (which TAR quotes approvingly; e.g., p.4) that require brief comment:


[1] Levins and Lewontin maintain that something called the "Cartesian mode" [i.e., Cartesian Reductionism, CAR] has dominated post-renaissance science; unfortunately, they failed to substantiate this claim and simply left it as a bald assertion:


"The dominant mode of analysis of the physical and biological world and by extension the social world...has been Cartesian reductionism. This Cartesian mode is characterised by four ontological commitments...:


"1. There is a natural set of units or parts of which any whole system is made.


"2. These units are homogeneous within themselves, at least in so far as they affect the whole of which they are the parts.


"3. The parts are ontologically prior to the whole; that is, the parts exist in isolation and come together to make wholes. The parts have intrinsic properties, which they possess in isolation and which they lend to the whole. In the simplest case the whole is nothing but the sum of the parts; more complex cases allow for interactions of the parts to produce added properties of the whole.


"4. Causes are separate from effects, causes being the properties of subjects. and effects the properties of objects. While causes may respond to information coming from the effects.... there is no ambiguity about which is causing subject and which is caused object...." [Levins and Lewontin (1985), p.269.]


Now, these allegations are themselves couched in rather broad, general and somewhat vague terms. While it is undeniable that some philosophers and scientists adopted parts of the world-view that these two attribute to CAR, many rejected it. Indeed, since most of the theorists who allegedly adopted this mode-of-thought (if it is one) were devout Christians, they could hardly posit 'parts separate from wholes' given what they found in the book of Genesis. [On this, see below.] It is worth noting that the authors of DB cite no sources for their views (primary or secondary) -- and no wonder, that would have disconfirmed the picture they wished to paint.


Admittedly, there were different varieties of atomism that dominated early modern science, but Atomic Theory and the belief in the existence of molecules was not widely accepted by scientists until after the publication of Einstein's work on Brownian motion approximately 100 years ago. [Cf., the remarks on this topic in Miller (1987), pp.470-82; a detailed history can be found in Nye (1972).] Also, worthy of note is the fact that classical Atomic Theory (propounded by Dalton) had to be rejected before these newer innovations could make the required inroads. [Cf., Laudan (1981).]


There is an illuminating discussion of the development of these ideas in Toulmin and Goodfield (1962), pp.193-305. See also Mason (1962), Brock (1992), Pullman (1998), and Pyle (1997).


DB's authors also ignore the fact that many scientists and philosophers (these two roles were not really distinguished before the middle of the 19th century) up until about 100 years ago often depicted the unity of the world in theological terms. Many of the pioneers of modern science (and Philosophy) openly accepted Hermetic, Rosicrucian, Alchemical, Occult, Kabbalist, Neo-Pythagorean and NeoPlatonic ideas about man and nature. On this see: Copenhaver (1990, 1998), Debus (1956, 1977, 1978, 1987, 1991), De León-Jones (1997), Dobbs (2002), Easlea (1980), Faivre (1994, 1995, 2000), Harkness (1999), Henry (1986), Hughes (1992), Katz (2005), Linden (2003), McGuire (1967, 1968), McGuire and Rattansi (1966), Newman and Grafton (2001), Newman and Principe (2005), Pagel (1986), Principe (1998), Ross (1983, 1998), Shumaker (1972), Vickers (1984), Webster (1976, 1982), and Yates (1991, 2001). See also here.


And, the impact on Western science of Christianity is undeniable; a particularly illuminating account can be found in Hooykaas (1973). The book on this is of course Webster (1976).


In fact, it is arguable that DM represents a return to an earlier enchanted view of nature. Given the fact that dialectics originated in the theories of prominent Natürphilosophers (i.e., Schelling and Hegel), who themselves derived their ideas from Hermetic Mystics (for example, Plotinus, Proclus, Porphyry, Iamblichus, Pseudo-Dionysius, (and the shadowy figure, Hermes Trismegistus), John Scotus Eriugena, Meister Eckhart, Raymond Lull, Nicholas of Cusa, Giovanni Pico Della Mirandola, Marsilio Ficino, Giordano Bruno, Paracelsus, Valentin Weigel, Jacob Böhme, Emanuel Swedenborg, and Friedrich Christoph Oetinger), this is not the least bit surprising. [Details can be found in Essay Fourteen Part One (summary here). A few sources are cited below.]


Finally, DB omits any mention of the strong Organicist and Holistic tradition in modern science (represented most notably in the works of people like Herder, Goethe, Schelling and Oken). Emerging out of the aforementioned Hermetic and NeoPlatonist philosophies of the Renaissance, this strand of thought underpinned Natürphilosophie, just as it inspired Vitalist and Romantic views of nature. As is clear, this view of the world dominated the thought of those caught up in the Romantic Movement, and from whom Hegel derived many of his own ideas. This alone casts doubt on DB's simplistic picture of the development of science since Descartes. Post-Renaissance scientific thought therefore has been both Atomist and Organicist.


However, of much more interest are the common metaphysical threads that run through most of theoretical science and all of traditional Philosophy -- ones that bathe DM itself in a rather more compromising light --, certainly more than the authors of DB imagine. [A political context will be given to this phenomenon in later Essays (notably Nine Part One, and Essays Twelve and Fourteen, summaries here and here).]


On the Hermetic influences on Hegel, see J. White (1996), pp.36-43, and Magee (2001); one chapter of the latter is posted here. On Goethe, see Bortoft (1996), Naydler (1996) and Tantillo (2002). Cf., also, Collingwood (1960) and Lovejoy (1964). On the Natürphilosophy of thinkers like Böhme, Schelling, Oken, Kielmeyer and Goethe, see Benz (1983), Mason (1962), pp.349-62, Richards (2002) and Tuveson (1982). On Oersted's influence on Engels, cf., Graham (1971), and Williams (1980). See also, Brown (1977), Harrington (1996), Horn (1997) and Weeks (1993). There is an excellent summary of some of the above, and their influence on Hegel, in Beiser (2005), pp.80-109; see also Heidelberger (1998).


To be fair, Rees does go on to argue that a holistic view of nature on its own is insufficient to distinguish DM from other superficially similar systems of thought. [However, on this, see here.] Nevertheless, the examples he gives of other holistic belief systems were pointedly taken from religious/mystical views of the world: for example, TAR refers us to Roman Catholic and Taoist doctrines. [Rees (1998), p.6.] Moreover, he failed to mention the important Organicist tradition in post-Renaissance science, nor did he alert the reader to its influence on Schelling and Hegel (and hence on Engels). Admittedly, not all the advocates of these systems believed that change was caused by contradictions, but many thought that things were ruled by dialectically-connected opposites, and the like; on this, see Essay Fourteen (summary here).


Even so, it is also clear that DB's authors have themselves adopted a mildly revisionist view of Engels's work in this regard; in fact, they go so far as to say that "much of what he wrote about [the physical world] seems quaint" [DB, p.279]. True, DB's authors interpret contradictions as opposing forces [DB, p.280], but in Essay Eight Part Two, it will become clear how unwise a move that was. Nonetheless, in their characterization of CAR, DB's authors pointedly failed to argue that the absence of an appeal to "contradictions" (to account for change) was one of its weaknesses. Perhaps this was an oversight, but it does ruin the neat picture Rees tries to paint.


(2) DB counterposes DL to CAR, as a superior method, at least in the Life Sciences -- but by implication throughout the whole of science. However, as we will see in other Essays posted here, DL introduces into epistemology its own far more pernicious virus: HEX.


[HEX = Hegelian Expansionism.]


Small wonder then that the vast majority of scientists (outside of the old Stalinist block, and/or their 'fellow travellers') have completely ignored DL, if they have ever heard of it. [On Soviet science itself, see Graham (1971, 1987, 1993) and Joravsky (1961), Krementsov (1997), Pollock (2006), and Vucinich (1980, 2001).]


Nevertheless, Rees refers his readers to several other theorists who have tried to find some sort of a scientific role for DL. [TAR, p.120; note 60.] Such attempts to squeeze science into such an ill-fitting dialectical corset will be considered in detail in Essay Three Part Six and Essay Thirteen Part Two. [On David Bohm, however, see Essay Seven.]


21. In fact, Trotsky might have had in mind here the way that certain systems of classical modern logic (for example, that found in Principia Mathematica) employ non-logical principles in an attempt to provide a logical foundation for Mathematics. In the case of Principia, for instance, the so-called "Axiom of Infinity" and the "Axiom of Reducibility" might match Trotsky's description. On the other hand, in view of the additional fact that Trotsky seems to have been totally ignorant of MFL, this is highly unlikely. More likely he was merely repeating hear-say. [However, he might have got this idea from Jean Van Heijenoort.]


Nevertheless, this criticism (if this is what Trotsky meant) only applies to foundational work in one branch of MFL, that which is connected with the so-called "Logicist" program. Whatever the limitations and failings of Principia (in particular), or of Logicism (in general), amount to they do not necessarily affect other systems of MFL. On this, cf., Bostock (1997), Hunter (1996) and Kneale and Kneale (1962), pp.435-742. On the failings of Logicism (at least, Frege's version of it), see Noonan (2001).


In fact, it may soon prove possible to solve the paradox that supposedly unravelled Frege's program (i.e., Russell's Paradox). Should this come about, it would not mean that Logicism is once more a viable option -- even if it is not susceptible to the limitations some think are suggested by Gödel's Theorem, as many still believe --, but it would mean that one reason why certain DM-theorists reject it will have been removed.


Recently, much work has gone into this area following upon Crispin Wright's attempt to reconstruct Frege's system (in Wright (1983)). On this, see the excellent review article in McBride (2003); see also the discussion articles by Ian Rumfitt, William Demopoulos and Gideon Rosen in Philosophical Books 44, July 2003, and the reply to these by Crispin Wright and Bob Hale, in the same issue: Rumfitt (2003), Demopoulos (2003), Rosen (2003), Hale and Wright (2003). See also, Boolos (1998), Burgess and Rosen (1997), Demopoulos (1997), Dummett (1981a, 1981b, 1991, 1993, 1998a, 1998b), Hale (1987), Hale and Wright (2001), Schirn (1998), Slater (2000), Teichmann (1992), Wright (1992, 1998a, 1998b).  Cf., also the special edition of Dialectica 59, 2, 2005, which is entirely devoted to this aspect of Frege's work.


However, the most profound criticisms of Principia (and of Logicism in general) were advanced by Wittgenstein. The best discussion of this topic can be found in Marion (1998). See also: Shanker (1987) -- and in general, Hintikka (1996). See also Floyd (forthcoming, 1 and 2). See also here.


22. Modern-day dialecticians also find it almost impossible to avoid making derogatory remarks about FL. Here is what comrades Woods and Grant had to say:


"It is necessary to acquire a concrete understanding of the object as an integral system, not as isolated fragments; with all its necessary interconnections, not torn out of context, like a butterfly pinned to a collector's board; in its life and movement, not as something lifeless and static. Such an approach is in open conflict with the so-called 'laws' of formal logic, the most absolute expression of dogmatic thought ever conceived, representing a kind of mental rigor mortis. But nature lives and breathes, and stubbornly resists the embraces of formalistic thinking. 'A' is not equal to 'A.' Subatomic particles are and are not. Linear processes end in chaos. The whole is greater than the sum of its parts. Quantity changes into quality. Evolution itself is not a gradual process, but interrupted by sudden leaps and catastrophes. What can we do about it? Facts are stubborn things." [Woods and Grant (1995), pp.82-83.]


"The subject and the predicate of the conclusion each occur in one of the premises, together with a third term (the middle) that is found in both premises, but not in the conclusion. The predicate of the conclusion is the major term; the premise in which it is contained is the major premise; the subject of the conclusion is the minor term; and the premise in which it is contained is the minor premise. For example,


a) All men are mortal. (Major premise)

b) Caesar is a man. (Minor premise)

c) Therefore, Caesar is mortal. (Conclusion).


"This is called an affirmative categorical statement. It gives the impression of being a logical chain of argument, in which each stage is derived inexorably from the previous one. But actually, this is not the case, because 'Caesar' is already included in 'all men.' Kant, like Hegel, regarded the syllogism (that 'tedious doctrine,' as he called it) with contempt. For him, it was 'nothing more than an artifice' in which the conclusions were already surreptitiously introduced into the premises to give a false appearance of reasoning." [Ibid., p.86. Quotation marks altered to conform to the conventions adopted here.]


However, the example these two give of a syllogism is not one that Aristotle would have recognised. [This is in fact a very common error; you will find it repeated in many a bad logic text, and in the writings of those who have not studied Aristotle too carefully.]


Aristotle would have denied it was a legitimate syllogism in view of the fact that it has a particular middle premiss which is not governed by a what we would now call a quantifier expression (e.g., "Some", "All", "Every", and "No"), but concerns a named individual.


And as far as Kant's comment is concerned (and this is an almost universal error), there are many valid arguments where the conclusion is not "contained" in the premisses. One such was given here.


Woods and Grant's book is full of errors like this, just as it is replete with snide remarks about FL -- a subject about which they seem to know as much as they do about the whereabouts of Lord Lucan. [On this, see Note 23.]


23. Thesis, Antithesis, Synthesis Debunked


Practically every book and/or article I have consulted on DM has included an egregious attempt to define the so-called 'three laws' of FL. Why dialecticians imagine there are only three such laws is something of a mystery, anyway -- but it may have something to do with the mystical nature of the number three itself, which resurfaces in what some ill-informed dialecticians think is Hegel's method: "Thesis, Antithesis, Synthesis".


Indeed, here is what Hegel expert Terry Pinkard had to say about this (in an interview):


"Britannica: One of the things most associated with Hegel's thought is the thesis/antithesis/synthesis scheme, the process by which reality unfolds and history progresses. But you claim this never appears in Hegel's work.


"Pinkard: This myth was started by Heinrich Moritz Chalybäus. It appears in a history he wrote of recent German philosophy (published in the 1840s), in which he said, roughly, that Fichte's philosophy followed the model of thesis/antithesis/synthesis, but Hegel went further and cosmologized that notion, extending it to the entire universe. The book was widely read (apparently the young Marx was one of its readers), and the idea stuck. It's still touted in a lot of short encyclopedia entries about Hegel. Like many little encapsulations of thought, it has the virtue of being easy to understand and easy to summarize. It's just not very helpful in understanding Hegel's thought. It has also contributed to the lack of appreciation of Hegel in Anglophone philosophy. It's not too hard to point out all the places where it doesn't apply, dismiss it as a kind of dialectical trick, and then just go on to conclude that Hegel isn't worth reading at all." [Interview here.]


Add to that these detailed comments:


"Some say Hegel used the method of: thesis-antithesis-synthesis, and others deny this. Who is correct?

"The most vexing and devastating Hegel legend is that everything is thought in 'thesis, antithesis, and synthesis.' [...] The actual texts of Hegel not only occasionally deviate from 'thesis, antithesis, and synthesis,' but show nothing of the sort. 'Dialectic' does not for Hegel mean 'thesis, antithesis, and synthesis.' Dialectic means that any 'ism' -- which has a polar opposite, or is a special viewpoint leaving 'the rest' to itself -- must be criticized by the logic of philosophical thought, whose problem is reality as such, the 'World-itself.'

"Hermann Glockner's reliable Hegel Lexikon (4 volumes, Stuttgart, 1935) does not list the Fichtean terms 'thesis, antithesis, synthesis' together. In all the twenty volumes of Hegel's 'complete works' he does not use this 'triad' once; nor does it occur in the eight volumes of Hegel texts, published for the first time in the twentieth Century. He refers to 'thesis, antithesis, and synthesis' in the Preface of the Phenomenology of Mind, where he considers the possibility of this 'triplicity' as a method or logic of philosophy. According to the Hegel-legend one would expect Hegel to recommend this 'triplicity.' But, after saying that it was derived from Kant, he calls it a 'lifeless schema,' 'mere shadow' and concludes: 'The trick of wisdom of that sort is as quickly acquired as it is easy to practice. Its repetition, when once it is familiar, becomes as boring as the repetition of any bit of sleigh-of-hand once we see through it. The instrument for producing this monotonous formalism is no more difficult to handle than the palette of a painter, on which lie only two colours....' (Preface, Werke, II, 48-49).

"In the student notes, edited and published as History of Philosophy, Hegel mentions in the Kant chapter, the 'spiritless scheme of the triplicity of thesis, antithesis, and synthesis' (geistloses Schema) by which the rhythm and movement of philosophic knowledge is artificially pre-scribed (vorgezeichnet).

"In the first important book about Hegel by his student, intimate friend and first biographer, Karl Rosenkranz (Hegels Leben, 1844), 'thesis, antithesis, synthesis' are conspicuous by their absence. It seems Hegel was quite successful in hiding his alleged 'method' from one of his best students.

"The very important new Hegel literature of this century has altogether abandoned the legend. Theodor Haering's Hegels Wollen und Werk (2 vol., Teubner, 1929 and 1938) makes a careful study of Hegel's terminology and language and finds not a trace of 'thesis, antithesis, synthesis.' In the second volume there are a few lines (pp.118, 126) in which he repeats what Hegel in the above quotation had said himself, i.e., that this 'conventional slogan' is particularly unfortunate because it impedes the understanding of Hegelian texts. As long as readers think that they have to find 'thesis, antithesis, synthesis' in Hegel they must find him obscure -- but what is obscure is not Hegel but their coloured glasses. Iwan Iljin's Hegel's Philosophie als kontemplative Gotteslehre (Bern, 1946) dismisses the 'thesis, antithesis, synthesis' legend in the Preface as a childish game (Spielerei), which does not even reach the front-porch of Hegel's philosophy.

"Other significant works, like Hermann Glockner, Hegel (2 vols., Stuttgart, 1929), Theodor Steinbüchel, Das Grundproblem der Hegelschen Philosophie (Bonn, 1933), and Theodor Litt, Hegel: Eine Kritische Erneuerung (Heidelberg, 1953), Emerich Coreth, S.J., Das Dialektische Sein in Hegels Logik (Wien, 1952), and many others have simply disregarded the legend. In my own monographs on Hegel über Offenbarung, Kirche und Philosophie (Munich, 1939) and Hegel über Sittlichkeit und Geschichte (Reinhardt, 1940), I never found any 'thesis, antithesis, synthesis.' Richard Kroner, in his introduction to the English edition of selections from Hegel's Early Theological Writings, puts it mildly when he says: 'This new Logic is of necessity as dialectical as the movement of thinking itself.... But it is by no means the mere application of a monotonous trick that could be learned and repeated. It is not the mere imposition of an ever recurring pattern. It may appear so in the mind of some historians who catalogue the living trend of thought, but in reality it is ever changing, ever growing development; Hegel is nowhere pedantic in pressing concepts into a ready-made mold (sic). The theme of thesis, anti-thesis, and synthesis, like the motif of a musical composition, has many modulations and modifications. It is never "applied"; it is itself only a poor and not even helpful abstraction of what is really going on in Hegel's Logic.'

"Well, shall we keep this 'poor and not helpful abstraction' in our attic because 'some historians' have used it as their rocking-horse? We rather agree with the conclusion of Johannes Flügge: 'Dialectic is not the scheme of thesis, antithesis, and synthesis imputed to Hegel.'

"In an essay by Nicolai Hartmann on Aristoteles und Hegel, I find the following additional confirmation of all the other witnesses to the misinterpretation of Hegel's dialectic: 'It is a basically perverse opinion (grundverkehrte Ansicht) which sees the essence of dialectic in the triad of thesis, antithesis, and synthesis.' The legend was spread by Karl Marx whose interpretation of Hegel is distorted. It is Marxism superimposed on Hegel. Thesis, antithesis, synthesis, Marx says in Das Elend der Philosophie, is Hegel's purely logical formula for the movement of pure reason, and the whole system is engendered by this dialectical movement of thesis, antithesis, synthesis of all categories. This pure reason, he continues, is Mr. Hegel's own reason, and history becomes the history of his own philosophy, whereas in reality, thesis, antithesis, synthesis are the categories of economic movements. (Summary of Chapter II, Paragraph 1.) The few passages in Marx's writings that resemble philosophy are not his own. He practices the communistic habit of expropriation without compensation. Knowing this in general, I was also convinced that there must be a source for this 'thesis, antithesis, and synthesis,' and I finally discovered it.

"In the winter of 1835-36, a group of Kantians in Dresden called on Heinrich Moritz Chalybäus, professor of philosophy at the University of Kiel, to lecture to them on the new philosophical movement after Kant. They were older, professional men who in their youth had been Kantians, and now wanted an orientation in a development which they distrusted; but they also wanted a confirmation of their own Kantianism. Professor Chalybäus did just those two things. His lectures appeared in 1837 under the title Historische Entwicklung der speculativen Philosophie von Kant bis Hegel, Zu näherer Verständigung des wissenschaftlichen Publikums mit der neuesten Schule. The book was very popular and appeared in three editions. In my copy of the third edition of 1843, Professor Chalybäus says (p. 354): 'This is the first trilogy: the unity of Being, Nothing and Becoming...we have in this first methodical thesis, antithesis, and example or schema for all that follows.' This was for Chalybäus a brilliant hunch which he had not used previously and did not pursue afterwards in any way at all. But Karl Marx was at that time a student at the university of Berlin and a member of the Hegel Club where the famous book was discussed. He took the hunch and spread into a deadly, abstract machinery. Other left Hegelians, such as Arnold Ruge, Ludwig Feuerbach, Max Stirner, use 'thesis, antithesis, synthesis' just as little as Hegel.

"{Quote from the article of Gustav E. Mueller: The Hegel Legend of 'Thesis-Antithesis-Synthesis', in 'Journal of the History of Ideas', Volume XIX, June 1958, Number 3, Page 411. The article is still as valid today as it was in 1958.}" [This can be found here. Quotation marks have been altered to conform to the conventions adopted here; US spelling also altered to conform to UK English. The full article is Mueller (1958).]


This suggests that Marx and all subsequent Marxists who use this 'schema' are not reliable interpreters of Hegel. If so, then, according to Lenin, that must mean that Marx could not have understood Das Kapital!

"It is impossible to understand Marx's Capital, and especially its first chapter, without having thoroughly studied and understood the whole of Hegel's Logic. Consequently, half a century later none of the Marxists understood Marx!!" [Lenin (1961), p.180. Emphases added.]


Naturally, all this suggests that understanding Hegel (even if that were possible) is not integral to Marxism, or we would be faced with the ridiculous conclusion that Marx did not understand the central text of Marxism!

Let's see the dialecticians try to wriggle out of that one...



Dialectical Inanities


Nevertheless, to return to the DM-fable that there are just three principles underlying FL; in fact, there are countless principles underpinning MFL --, as many as there are authors prepared to set them up. As we will see, this fable is not even true of AFL!


[FL = Formal Logic; MFL = Modern Formal Logic; AFL = Aristotelian Formal Logic; LOC = Law of Non-contradiction";  LOI = Law of Identity; LEM = Law of Excluded Middle.]


Dialecticians who pontificate on this topic seldom (if ever) substantiate their innovative attempts to re-write the history and foundations of FL with quotations from, or citations to, a single logic text. In fact, their weak efforts to come to grips with FL -- which, in my experience, is a far more challenging subject than, say, advanced Group Theory --, bear an uncanny resemblance to the lame attempts Creationists make to summarise Evolutionary Theory (in their literature or posted on their websites).


Piss-poor caricatures like this will only ever impress the ignorant, which seems to be the aim. Anyone who knows any MFL will see them for what they are. Those who do not will be led astray accordingly.


This is the only explanation I can come up with to account for the fact that otherwise seemingly intelligent comrades (who are quite knowledgeable in science, economics, history, current affairs, etc. etc.) regularly produce descriptions of FL that are not only demonstrably incorrect, they are not even coherent in their own terms, as will be demonstrated presently. [I examine the reasons for this in Essay Nine Parts One and Two.]


It is to be hoped that long exposure to DL has not completely destroyed the critical faculties of such comrades -- although in what follows it will become painfully clear that the case for the defence is considerably weakened with the publication of each new book on dialectics.


Below, I reproduce just a few of the crass things dialecticians have said about AFL (and FL in general), most of which are highly repetitive, anyway. It is hoped that having read through what follows, the conclusion that dialecticians simply copy these allegations off one another without bothering to check will also have occurred to the reader, and not just the writer.


Apologies are therefore due once again to such hardy souls for my having to inflict yet more of this sorry material on them -- but they can spare a thought for the present author who has had to read through this stuff, and much more, over and over again, in order to try to make some sort of sense of it.


Recall, too, that the quotations reproduced here are only a tiny fraction of those that could have been included.


A particularly egregious example of this type of confusion can be found in Novack's book on DL:


"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.


"This conclusion is made explicit in the second law of formal logic: the law of contradiction. The law of contradiction states: A is not non-A. This is no more than the negative formulation of the positive assertion expressed in the first law of formal logic. If A is A, it follows, according to formal thinking that A cannot be non-A. Thus the second law of formal logic, the law of contradiction forms the essential supplement to the first law.


"Some examples: a man cannot be inhuman; a democracy cannot be undemocratic; a wageworker cannot be a non-wageworker.


"The law of contradiction signifies the exclusion of difference from the essence of things and of thought about things. If A is necessarily always identical with itself, it cannot be different from itself. Difference and identity are, according to these two rules of formal logic, completely different, utterly disconnected, mutually exclusive characteristics of both things and thoughts.


"This mutually exclusive quality of things is expressly taken note of in the third law of formal logic. This is the law of the excluded middle. According to this law, everything is and must be either one of two mutually exclusive things. If A equals A, it cannot equal non-A. A cannot be part of two opposing classes at one and the same time. Wherever two opposing statements or states of affairs confront each other, both cannot be true or false. A is either B or it is not B. The correctness of one judgement invariably implies the incorrectness of its contrary, and vice versa." [Novack (1971), pp.20-21.]


The LOI will be discussed in detail in Essay Six, but the reader will note that Novack -- except in one instance (discussed below) -- nowhere attempts to substantiate these wild assertions with a reference to a single FL-text. To be sure, he paraphrases Aristotle from time to time, but it is quite clear that he has mastered little of what he mis-read.


Let us be clear then what Aristotle himself said:


"So it must be possible to deny whatever anyone has affirmed. Thus it is clear that for every affirmation there is an opposite negation, and for every negation an opposite affirmation. Let us call an affirmation and a negation which are opposite a contradiction. I speak of statements as opposite when they affirm and deny the same thing of the same thing -- not homonymously, together with all other such conditions that we add to counter the troublesome objections of sophists....


"I call an affirmation and a negation contradictory opposites when what one signifies universally the other signifies not universally, e.g. every man is white -- not every man is white, no man is white -- some man is white. But I call the universal affirmation and the universal negation contrary opposites, e.g. every man is just -- no man is just. So these cannot be true together, but their opposites may both be true with respect to the same thing, e.g. not every man is white -- some man is white.


"Of contradictory statements about a universal taken universally it is necessary for one or the other to be true or false; similarly if they are about particulars, e.g. Socrates is white -- Socrates is not white. But if they are about a universal not taken universally it is not always the case  that one is true and the other false. For it is true to say at the same time that a man is white and that a man is not white, or that a man is noble and that a man is not noble.... This might seem absurd at first sight, because 'a man is not white' looks as if it signifies also at the same time that no man is white; this, however, does not signify the same, nor does it necessarily hold at the same time." [Aristotle (1984b), pp.27-28. Emphasis added.]


In the above passage, Aristotle was alluding to an early version of his famous "Square of Opposition":



Figure Two


On this see here and here. [The first is Parsons (2004), the second is anonymous.]


Readers will, I hope, note the sophistication apparent in Aristotle's first attempts to say clearly how he intends to use certain words, just as they will note how little the musings of comrade Novack correspond with them. In fact, Aristotle says the opposite of what Novack attributes to (him and) FL.


Moreover, I can find no reference to the LOI in Aristotle's work. On this see here.


Since this Essay was originally posted, however, the above reference has been edited; the one I linked to earlier can be found here.


The original Wikipedia article asserted that no occurrence of the law of identity could be found in anyone's work prior to that of St Thomas Aquinas in the 13th century.


The editorial change does not alter much (it just loses that useful fact), but it does locate a use of identity in Aristotle (but as far as I can see, Aristotle neither uses that word, nor that 'Law'). And even then, Aristotle does not connect identity with his logic.


Anyway that article quotes Aristotle as follows:


"Now 'why a thing is itself' is doubtless a meaningless inquiry; for the fact or the existence of the thing must already be evident (e.g. that the moon is eclipsed) but the fact that a thing is itself is the single formula and the single cause to all such questions as why the man is man, or the musical musical, unless one were to say that each thing is inseparable from itself; and its being one just meant this. This, however, is common to all things and is a short and easy way with the question)." [Aristotle (1984e), p.1643; Book VII, Part 17. I have used a more modern translation than seems to have been used by the author of the Wikipedia article. This is available here; scroll down to Part 17. This is clearly the source the author of the said article used.]


So, far from basing his logic on this notion, Aristotle seems quite dismissive of it.


However, there is another site on the Internet that does trace the history of this 'Law' (and not to Aristotle), but since it is run by an overt fascist, I will not cite it. [A Google search will find it -- if you can stomach the rest of the material on that site!]


Now it may be that Novack consulted a particularly poor Logic text (and, alas, there are many of those) -- or none at all, and just made things up. But if he did either of these, he wisely kept that shameful secret to himself. [Un fact, as we will see in Essay Twelve, Novack was relying largely on Hegel (and possibly on a few other traditional 19th Century logicians, who made similar mistakes).


[Readers are encouraged to read the rest of De Interpretatione; the above gives just a hint of the sophistication Aristotle attempted to bring to the subject all those years ago, something Hegel either did not appreciate, or tried to undo. DM-fans have thus merely compounded this serious step backwards (in an age when logic is far better understood).]


Now, as far as specifics are concerned, it turns out that Aristotle says the opposite of what Novack attributes to FL:


"...For example, the negation of 'to be a man' is 'not to be a man', not 'to be a not-man', and the negation of 'to be a white man' is 'not to be a white man', not 'to be a not-white man'....


"...For it is possible for the same thing to be and not to be: such statements are not contradictories of one another...." [Ibid., p.34. Emphases added.]


Here, it is pretty clear that Aristotle would not have accepted Novack's use of "non-A" as the contradictory of "A", for instance.


The failure to notice the difference between predicate negation and predicate-term negation has clearly confused dialecticians like Novack (and this error is almost universal among DM-theorists). But, this is something Aristotle understood two millennia ago! [On this, see here.]


Naturally, logic has moved on considerably since Aristotle's day, as have mathematics and science in general. No one (that is, other than traditionalists and confused dialecticians) would be happy with his characterisation of contradictions (etc.) today. However, it is quite apparent from what Novack and the other DL-fans quoted below say that they are significantly less logically advanced than Aristotle was 2400 years ago! It is equally clear that Novack did not consult Aristotle's writings before he simply made up the above comments, just as it is apparent that the same can be said for the other comrades quoted below.


To be sure, Aristotle makes many mistakes; for example, he often confuses propositions with what he calls "terms" (e.g., almost all the way through Prior Analytics), and he criss-crosses between talk about talk and talk about things, running both together at times, but he does at least try to be scrupulously careful. He was, after all, starting almost from scratch. Anyone who reads Aristotle (and who does not rely on comrades like Novack to put them off) will soon see why Marx thought so highly of him.


However, Novack does at least try to make a weak attempt to support what he says in the following with a direct reference to Aristotle (his only one, as far as I can determine):


"Let me cite an interesting example of this kind of thinking from Aristotle's writings. In his Posterior Analytics (Book 1; ch.33, p.158 -- this is in fact pp.146-47 in the edition I have used; RL), Aristotle says that a man cannot simultaneously apprehend first, that man is essentially animal, i.e., cannot be other than animal -- and second, that man is not essentially animal, that is, may assume that he is other than animal. That is to say, a man is essentially a man and can never be thought of as not being a man." [Novack (1971), p.21.]


Now, if we check what Aristotle actually says, we see things are not quite as Novack would have us believe (which is perhaps why Novack chose to paraphrase, but not to quote the passage in question):


"Similarly there is both knowledge and opinion of the same thing. For the one is of animal in such a way that it cannot not be an animal, and the other in such a way that it can be -- e.g. if the one is just what is man, and the other of man but not of just what is man. For it is the same because man is the same, but the manner is not the same.


"It is also evident that it is not possible to opine and to understand the same thing at the same time. For one would at the same time hold the belief that the same thing can be otherwise and cannot be otherwise, which is not possible. For in different men it is possible for there to be each of these attitudes with regard to the same thing, as has been said; but in the same man it is not possible even in this way; for he will at the same time hold a belief, e.g. that a man is just what is an animal (for this is what it was for it not to be possible for something not to be an animal), and that a man is not just what is an animal (for let that be what it is for it to be possible)." [Aristotle (1984d), pp.146-47. Bold emphases added.]


Admittedly, this passage is not the clearest that has ever been committed to paper, but it nowhere mentions "essence", and although it contains allusions to the LOC, it is couched in such terms as to make Novack's 'paraphrase' prejudicial, if not misleading, to say the least. The bold emphases bring this out. Hence, Aristotle's position is far more complex than Novack will allow, but he is happy to misrepresent it nonetheless.


Finally, on Novack: Aristotle says that "It is also evident that it is not possible to opine and to understand the same thing at the same time....", and with reference to Novack, at least, I think we can agree with Aristotle on that. Indeed, just like other DM-fans, Novack shows that not only has he not grasped the basics of FL, but he is nonetheless happy to pontificate about it.


Nevertheless, a measure of the sophistication modern logicians attempt to bring to the subject can be judged from the content of even introductory books on the Philosophy of Logic. For example: one that takes a very 'Oxford' view is Wolfram (1989); a different slant can be found in Haack (1979). Dialecticians like to call the attention to detail shown in such books "pedantry", but it is clear that their own 'relaxed attitude' to what is a very difficult topic allows them to indulge in some easy, but eminently sloppy 'thought'.


[Bertrand Russell once said: "Most people would rather die than think, in fact they do." He did not have dialecticians in mind, but he should have.]


More challenging material can be found in, say, Goble (2001), Jacquette (2002, 2006), Quine (1970) and Shapiro (2005).


As we will see in Essay Six, the LOI does not preclude change; however, in Essays Five and Eight it will be shown that it is dialecticians themselves who cannot account for motion or change. [As far as Aristotle and change are concerned, see here.]


Equally, if not more wide of the mark are comrades Woods and Grant:


"According to formal logic, the whole is equal to the sum of its parts....


"Let us examine the matter more closely. The basic laws of formal logic are:


1) The law of identity ('A' = 'A').


2) The law of contradiction ('A' does not equal 'not-A').


3) The law of the excluded middle ('A' does not equal 'B')....


"The law of contradiction merely restates the law of identity in a negative form. The same is true of the law of the excluded middle. All we have is a repetition of the first line in different ways. The whole thing stands or falls on the basis of the law of identity ('A' = 'A'). At first sight this is incontrovertible, and, indeed, the source of all rational thought. It is the Holy of Holies of Logic, and not to be called into question. Yet called into question it was, and by one of the greatest minds of all time....


"Similarly with the law of the excluded middle, which asserts that it is necessary either to assert or deny, that a thing must be either black or white, either alive or dead, either 'A' or 'B'. It cannot be both at the same time. For normal everyday purposes, we can take this to be true. Indeed, without such assumptions, clear and consistent thought would be impossible. Moreover, what appear to be insignificant errors in theory sooner or later make themselves felt in practice, often with disastrous results. In the same way, a hairline crack in the wing of a jumbo jet may seem insignificant, and, indeed, at low speeds may pass unnoticed. At very high speeds, however, this tiny error can provoke a catastrophe. In Anti-Dühring, Engels explains the deficiencies of the so-called law of the excluded middle:


"'To the metaphysician,' wrote Engels, 'things and their mental images, ideas, are isolated, to be considered one after the other and apart from each other, fixed, rigid objects of investigation given once for all. He thinks in absolutely unmediated antitheses. 'His communication is "yea, yea; nay, nay"; for "whatsoever is more than these cometh of evil." 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.'" [Woods and Grant (1995), pp.57, 91-93. Quotation marks have been altered to conform to the conventions adopted here.]


[We will have occasion to note later that Engels was not afraid to draw his own hard and fast antitheses, but that will have to pass for now. And what these two comrades have to say about the LOI will be dealt with in detail in Essay Six.]


I have made several comments about the sophomoric errors in Woods and Grant's book here, and at the end of this note, but for present purposes it is worth pointing out that these two comrades referenced no logic texts as a basis for these 'definitions'. To be sure, here and there they used a few ideas lifted from two introductory works (i.e., those written many years ago by Luce, and Cohen and Nagel), but they failed to reveal from which lamentably poor logic book they dredged these prize specimens:


"1) The law of identity ('A' = 'A').


 2) The law of contradiction ('A' does not equal 'not-A').


 3) The law of the excluded middle ('A' does not equal 'B')...." [Ibid.]


Quite what the LOC has to do with whether "A" can or cannot equal "not-A", Woods and Grant failed to say. As we will also find was the case with Hegel, these two have confused the LOC (which is about the truth-functional relation between a proposition and its negation, it is not about objects like "A", still less is it about "equality") with the LOI stated negatively. This is discussed in detail in Essay Eight Part Three.


[On the LOC in general, see Horn (2006). Unfortunately, Professor Horn alleges, without textual proof, that the LEM and the LOC are foundational axioms for Aristotle's logic --, and so was the LOI! I have e-mailed him about this (January 2009).]


Readers will note, too, that Aristotle, for example, can only be made to say such inane things if what he actually says (reproduced above) is ignored, and his words are altered so that they say the opposite of what he intended. In this case, clearly, "Aristotle does not equal Aristotle", according to Woods and Grant.


Indeed, while they are happy to tell us that according to FL "the whole is equal to the sum of its parts", what Aristotle in fact said was this:


"In the case of all things which have several parts and in which the totality is not, as it were, a mere heap, but the whole is something beside the parts...." [Aristotle (1984e), p.1650. I have used the on-line version, here.]


This is hardly an "equal to".


Moreover, their characterisation of the LEM is laughable. What, it may be wondered, has "A is not equal to B" got to do with whether of proposition "p", "either p is true or p is false" (or in some versions "p v ¬p" -- "¬" being the sign for negation)? Do these two honestly believe that an intellect of the stature of Aristotle believed that their version of the LEM was one of his foundational principles? [Indeed, the long quotation from De Interpretatione given above explicitly contradicts what these two assert.] Or, that there are any other logicians (who are not still in the "care of the community") who would accept this caricature of the LEM? No wonder they failed to provide a reference for their fictional 'version' of it.


But there is worse to come:


"Even the simplest judgement, as Hegel points out, contains a contradiction. 'Caesar is a man,' 'Fido is a dog,' 'the tree is green,' all state that the particular is the universal. Such sentences seem simple, but in fact are not. This is a closed book for formal logic, which remains determined to banish all contradictions not only from nature and society, but from thought and language itself. Propositional calculus sets out from exactly the same basic postulates as those worked out by Aristotle in the 4th century B.C., namely the law of identity, the law of (non-) contradiction, the law of excluded middle, to which is added the law of double negation. Instead of being written with normal letters, they are expressed in symbols thus:


"a) p = p


"b) p = ~p


"c) p V = ~p (sic)


"d) ~(p ~ p) (sic)


"All this looks very nice, but makes not the slightest difference to the content of the syllogism." [Woods and Grant (1995), pp.97-98.]


This is what a)-d) translate out as:


a) p is equal to p


b) p is equal to not-p


c) p or equals not-p (sic)


d) not both p not-p (sic)


a) and b) would be syntactically viable if "p" were an object, but it isn't. [If "p" were an object, it could not be used to say anything. This is precisely the mistake Hegel made, which error dialecticians have simply copied; more on that here.]


c) and d) are just gibberish.


Clearly, these two comrades did not copy these prize examples of syntactical confusion from a logic text written anywhere on this planet -- which could mean that they simply made them up. At any rate, this shows that they made no serious effort to comprehend much of what they constantly derided. [Witness the way that they have confused the Propositional Calculus with Aristotelian Syllogistic. The former was invented by the Stoics (and then largely forgotten until the middle of the 19th century); Aristotle knew nothing of it, as far as we know.]


Of course, the comment these two make about the contradictions allegedly implicit in simple predicative propositions is itself based on a novel piece of grammar (also lifted from Hegel, who borrowed it from Medieval Roman Catholic Logicians). "Caesar is a man" (W1) does not say the particular is the universal, and can only be made to do so by imposing on it a grammatical theory that these two comrades failed to justify. [Indeed, it cannot be justified; on that see Essay Three Part One (summary here).] And even if W1 could be construed in this way, Woods and Grant failed to say why this would be a contradiction, as opposed to being a simple falsehood, or simply plain unvarnished nonsense.


Just who they are seeking to influence by these blatant fibs is clear enough (i.e., those presumably as ignorant of FL as they are), but the fact that they link Marx's great name and reputation to this rubbish is something for which they should hang their heads in shame. [The fact that they probably won't do this says it all.]


[The lack of any connection between the LOC and the alleged negation of the LOI is discussed here.]


Not to be outdone in this respect, other comrades have vied to be crowned 'The Worst Expositor of Traditional Logic' in modern history. Here is Plekhanov's impressive bid:


"The 'fundamental laws of thinking' are considered to be three in number: 1) The law of identity; 2) the law of contradiction, and 3) the law of the excluded middle.


"The law of identity...states that 'A is A' or 'A = A'.


"The law of contradiction... -- 'A is not A' -- is merely a negative form of the first law.


"According to the law of the excluded middle...two opposing judgements that are mutually exclusive cannot both be wrong. Indeed, 'A is either B or non-B'. The truth of either of these two judgements necessarily means the falseness of the other, and vice versa. There is not, neither can there be, any middle." [Plekhanov (1908), pp.89-90. Italics in the original.]


And how does Plekhanov counter the garbled ideas he attributes to FL?


"Let us examine the matter from another angle.


"The motion of matter lies at the root of all natural phenomena. But what is motion? Here we have what seems to be a contradiction. If you are asked whether a body that is in motion is located at a particular place at a particular moment, you will be unable, however hard you try, to give an answer using [the above rules].... A moving body is at a particular place, and at the same time it is not there." [Ibid., p.90. Italics in the original.]


As we will see in Essay Five, this move was unwise (no irony intended). The contradiction Plekhanov alleges is no contradiction.


But his own formulation of the LOC is fraught with problems: "A is not A" is merely the alleged negation of his own ill-defined version of the LOI! He would be hard-pressed to find a logician not the worse for drink or drugs who would recognise it (not the least, once more, because it confuses (a là Hegel) objects with propositions). Small wonder then that Plekhanov does not refer his readers to a single logic text to substantiate what he says. [To be sure, Plekhanov does reference Überweg's Logic, but not in support of this 'definition' of the LOC. We will see later that Hegel was himself the source of this odd idea: that the negation of the LOI yields the LOC.]


Moreover, it is equally clear that Plekhanov confused the LEM with Aristotle's  definition of a contrary (see above), and then later with a semi-classical version of the LOC (that is, one that confuses propositions with "judgements"). As to whether there can be any 'middle' "judgements": clearly there can, since someone can judge in error. But whether the LEM allows for these will depend on the examples chosen, and on how one characterises a proposition. On this see Geach (1972c).


[Readers should once again compare Aristotle's careful wording with the sloppy use of language offered up by comrade Plekhanov.]


For the UK-SWP, this is how John Molyneux manages to get things wrong:


"Dialectics is the logic of change....


"To understand the significance of this compare it with what is know as 'formal logic' (originally developed by Aristotle and usually thought of as the rules of sound thinking). The basic idea of formal logic is that something either is the case or is not the case, but that it can't be both at the same time. For example, the cat is on the mat or it is not on the mat.


"For many purposes formal logic is useful and necessary. But as soon as you take movement and change into account, it ceases to be adequate. A cat moving goes through a moment when it is in the process of passing onto the mat or in the process of passing off it -- when it is both on and off the mat. Dialectics is in advance of formal logic because it enables us to grasp this contradiction." [Molyneux (1987), pp.49-50.]


Precisely how DL manages to help anyone "grasp" this spurious contradiction Molyneux merely left his readers to guess. But, what is there especially difficult about a cat being partially on or off a mat? Clearly, if the said cat falls asleep half on, half off the said mat we would still have the same 'contradiction', but no motion. Hence, this 'contradiction' has nothing to do with the ambulatory habits of furry mammals.


However, as we shall see in Essay Five, DL cannot even account for the motion of domestic pets, mat or no mat; Diamat or no Diamat. And as far as their capacity to "grasp" such 'contradictions' is concerned -- as seems plain -- dialecticians are content merely to label such ambiguous states of affairs "contradictions", and move on. Exactly how this helps anyone "grasp" anything is left entirely mysterious. In what way does it help us comprehend motion to be told it is contradictory? [But, don't complain -- or you risk being accused of "not understanding" dialectics.]


And does Molyneux really think that logicians/scientists (of the calibre of, say, Aristotle) failed to spot that things change? Indeed, Aristotle himself noted this much:


"...A able to receive contraries. For example, an individual man -- one and the same -- becomes pale at one time and dark at another, and hot and cold, and bad and good.


"...Suppose, for example, that the statement that somebody is sitting is true; after he has got up this same statement will be false. Similarly with beliefs.... However, even if we were to grant this, there is still a difference in the way contraries are received. For in the case of substances it is by themselves changing that they are able to receive contraries. For what has become cold instead of hot, or dark instead of pale, or good instead of bad, has changed (has altered); similarly in other case too it is by itself undergoing change that each thing is able to receive contraries.... [I]t is because the actual thing changes that the contrary comes to belong to them...." [Aristotle (1984f), p.7. Italics in the original; bold emphases added.]


Admittedly, the above work of Molyneux's is an introductory text; when he raised this point with me in private correspondence, he recommended that I should concentrate on the DM-classics, and ignore the writings of relatively minor figures like himself. As should now seem plain, the situation there is no better, and in some cases it is far worse.


However, the above passage at least scotches the myth that Aristotle's logic could not accommodate change. [See also Aristotle (1984f), pp.23-24, where he analyses six different types of change; this passage be found here, but scroll down to Part 14.]


Unfortunately, Molyneux has repeated these serious misconceptions at his blog:


"This matters because the dominant mode of thinking, based on the logic developed by Aristotle, is not founded on the principle of universal change, rather it deals with fixed states or 'things'. Its basic axioms are that A = A (a thing is equal to itself) and A does not = non-A (a thing is not equal to something other than itself), from which are derived sequences of sound reasoning known as syllogisms." [The Marxist Dialectic.]


Molyneux failed to show how a single syllogism follows from these illusory principles. ["A thing is not equal to something other than itself"?!? What the dickens does that mean? And wtf has it got to do with FL?]


As this Essay has shown, this paragraph contains about as many errors as it does words. I have posted a suitable reply here.


He also argues as follows:


"This formal logic was, and is, all well and good and very necessary for practical human affairs but it is limited -- it excludes change. Dialectical logic moves beyond formal logic by starting not with 'things' but with processes, processes of coming into being and passing out of being. The moment processes of change are fed into the equation it becomes necessary to deal with contradiction. If state A (e.g. day) changes into state B (night) it passes through a phase of A not being A or being both A and B (twilight)." [The Marxist Dialectic.]

But, twilight looks pretty much like a "state" (certainly as much a one as night and day are). Even so, it can't be a unity of twilight and not-twilight, so (if the DM-theory of change is to be believed) it cannot change! And, of course, if day is no longer day, but is twilight, then the above "A" (day) is not in fact "A and not A", it is "C" (twilight) --, hence it is not "A and B" either.


To be sure, it might be possible to get around this by defining twilight as a combination of both day and night, but that would make Molyneux's assertions stipulatively true, and would thus have been imposed on nature.


But, as we will see in Essay Seven, none of this makes sense even in DM-terms; night does not struggle against day to produce twilight, so how this alleged 'contradiction' makes anything change is a mystery. And if this alleged contradiction does not/cannot cause change, how is it a 'dialectical contradiction'?


On the other hand, what is the 'internal opposite' of day that makes it change into night? Molyneux failed to say, and it is not difficult to see why -- day has no 'internal opposite'. Its alleged opposite is night, but that is manifestly external. So, unless we believe that the future can change the present (arguing that the fact that night is hours away allows it to 'back-cause' day to change into night!), Molyneux's own example cannot be an instance of dialectical change, either!


Now, Aristotle certainly believed that during change something must remain the same (but precisely what that "something" was is subject to controversy among Aristotle scholars) -- for example, in Aristotle (1984e), p.1595. But, he also claimed that:


"...since it is impossible that contradictories should be at the same time true of the same thing, obviously contraries also cannot belong at the same time to the same thing.... If, then, it is impossible to affirm and deny truly at the same time, it is also impossible that contraries should belong to a subject at the same time, unless both belong to it in particular relations, or one in particular relation and one without qualification." [Aristotle (1984e), p.1597.]


Here Aristotle allows contrary predicates to belong to a subject providing they attach to it "in particular relations"; presumably this means they could belong to parts of that subject separately (when say a poker is cold at one end, hot at another, or when a man is half wet, half dry, for example). Nevertheless, it is clear from this, as it is from Aristotle's other writings, that he continually switches back and forth without warning between talk about talk and talk about things. In doing this, he ends up in no little confusion, which is, of course, one of the reasons modern logicians have had to re-think the whole subject from the floor up. But, having said that, as confused as he was, Aristotle is a model of clarity compared to dialecticians. [On this, see here.]


Next we turn to the 'definitions' advanced by comrade Mandel:


"Dialectics, or the logic of motion, is distinct from formal or static logic. Formal logic is based on three fundamental laws:


"(a) The law of identity: A is equal to A; a thing is always equal to itself.


"(b) The law of contradiction: A is different from non-A; A can never equal non-A.


"(c) The law of exclusion: either A, or non-A; nothing can be neither A nor non-A.


"A moment's reflection will allow us to conclude that formal logic is characterised by the thought processes which consist of putting motion, change, into parenthesis. All the laws enumerated above are true, so long as we abstract from motion. A will remain A so long as it does not change. A is different from non-A so long as it is not transformed into its opposite. A and non-A exclude each other so long as there is no movement which combines A and non-A, etc. These laws are obviously insufficient if we consider the transformation of the chrysalid (sic) into the butterfly, the passage of the adolescent into the adult, the movement of life into death, the birth of a new species or a new social order, the combination of two cells into a new one, etc." [Mandel (1979), pp.160-61. Italics in the original.]


Once more, we are not told from which slag heap these 'gems' had been rescued (but notice how similar they are to the 'definitions' we met earlier). To be sure, a rigidly orthodox comrade like Mandel would rightly feel peeved if an opponent of Marxism simply made stuff up like this. Apparently, though, it's OK if 'scientific socialists' indulge in a little fabrication themselves.


[Detailed criticism of the above claims has been confined to Essays Five and Seven.]


From earlier times, this is what we find in David Hayden-Guest's book on DM:


"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 cannot 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. Italics in the original.]


More repetition, precious little substantiation. [Notice once again the confused idea that the LEM is about things, and not propositions.]


And now this from comrade Thalheimer, whose intent was clearly to show that whatever Trotskyists (like Mandel and Novack) could misconstrue, he could garble better:


"The science of the laws of thought, formal logic, reached its highest point with Aristotle....


"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 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...." [Thalheimer (1936), pp.88-89. Italics in the original.]


To his credit, Thalheimer manages to get by with just two misrepresentations of AFL, all the while confusing the DM-version of the LOC with the DM-version of the LEM.


This is how John Somerville summed things up (and he should have known better!):


"The Aristotelian conception of the laws basic to correct thinking may be stated as follows:


"1. Law of Identity: Each existence is identical with itself. A is A.


"2. Law of Noncontradiction: Each existence is not different from itself. A is not non-A.


"3. Law of Excluded Middle: No existence can be both itself and different from itself. Any X is either A or non-A, but not both at once." [Somerville (1967), pp.44-45. Italics in the original.]


To be fair to Somerville, he did try to qualify the second point above in a footnote on p.205, where some attempt was made to understand Aristotle (but, even then, this was only in the space of a hundred words or so). However, the fact that it was tucked away right at the end of his book, when the body of this work confuses "what is said" (which is how Aristotle puts things) with "each existence" (Somerville's odd rendition), just about says it all.


We need simply note here the fact that Somerville merely copied Hegel's amateurish attempt to equate the 'negation' of the LOI with the LOC, subjecting it to no scrutiny at all. This shows that HCDs are, just like LCDs, often as not logical incompetents. That, of course, accounts for their fondness for Hegel, a logical incompetent of exemplary stature.


Many more examples of the same wild allegations can be found on the Internet; a quick Google will reveal how widespread this dialectical weed has become. For example, here:


[Although the last author is merely paraphrasing Somerville.]


The same old myths, almost word for word!


And here is one of my favourites:


"Note that Hegel uses the word contradiction to mean the conflict between two opposing sides. (page 431, Hegel's Science of Logic) He does not mean simply a logically contradictory statement such as, "That object is a horse and a television." [Quoted from the 'Dialectics For Kids' Website.]


"That object is a horse and not a horse" might be a contradiction (it would depend on whether or not there are any hidden ambiguities buried in this sentence, as well as on the meaning of the demonstrative "that"), but "That object is a horse and a television" would only be a contradiction if this were the case: "No horse is a television", but logic cannot legislate here. It might be argued that the meaning of the word "horse" precludes it from being a television, but if that is the case "That object is a horse and a television" would contain a misuse of language, and would thus be meaningless, not contradictory.


As noted earlier, dialecticians are quite happy to pontificate about logic, but do not seem to know the first thing about it.


However, in most of the above the reader will note that the LOI is defined as "A = A", "A is equal to A" -- or even "A is A" (on this see Essay Six) --, which is said to imply that "A cannot be other than A" (which is incorrect, the LOI does not preclude change; again, on this see Essay Six). The LOC is similarly characterised as "A cannot at the same time be A and not be A" (or even "A cannot be non-A"), which is said to follow from the LOI (but with no proof that it does), whereas the LEM is depicted rather loosely as "Everything must be A or not A", or even worse, "A does not equal B". In every case, dialecticians confuse objects with propositions (among other things). Several of these confusions are dissected here.


Do dialecticians really think that a philosopher of Aristotle's stature and sophistication actually believed that, say, "Everything must be rat or "non-rat" --, or, "rat does not equal cat"? [Interpreting here the 'dialectical definition' of the LEM literally, replacing "A" with "rat", and "B" with "cat".]


If they do, we might wonder why Marx rated him so highly.


Of course, anyone familiar with Aristotle's thought (or who bothers to check!) will know he never puts things this way. Indeed, I have been unable to find a sentence remotely like any of these in his work.


Nevertheless, even if their analysis of the LOC were correct, and it was true that "A is A and at the same time non-A", it would be impossible for dialecticians even to begin to express their criticisms of their own fabricated AFL-principles. This is because it would be impossible to state the following:


B1: "A is A and at the same time non-A".


If it were indeed true that "A" is at the same time "non-A", then the first half of B1 would have to be re-written as:


B2: "Non-A is non-A".


Or, more accurately, the whole of it as:


B3: "Non-A is non-A and at the same time non-(non-A)".


That is, if each "A" in B1 is replaced with what it is supposed at the same time to be (i.e., "non-A"), B1 would 'dialectically disintegrate' into B3.


Now, this fatal result can only be denied by those who reject the DM-inspired version of the LOC (i.e., those who reject "A is at the same time non-A"), and who thus do not think that the first half of B1 is false, or both false and true, "It depends...".


Even worse still, if every "A" is also "non-A", then these would surely follow from B3:


B4: "Non-(non-A) is non-(non-A) and at the same time non-(non-(non-A))."


B5: "Non-(non-(non-A)) is non-(non-(non-A)) and at the same time non-(non-(non-(non-A)))."


And so on, as each successive "A" in B3 and B4 is replaced by the "non-A" that dialecticians insist they are. Once more, this could only be denied by those who reject standard DM-criticisms of the LOC.


[And it won't do to claim that all these "non-"s will all cancel out (an odd notion in itself; on that see here), since if they did we would have to reject the idea that each "A" was at the same time a "non-A". Thus, if each "A" were at the same time a "non-A", then, when we formed a "non-(non-A)" from a "non-A", and if this could be 'cancelled' back to an "A", the "A" in "non-A" would not longer be a "non-A", since these two "non-"s would ex hypothesi have cancelled, wiping out that "non-A"!]


As should now seem apparent, the LOC has an annoying way of hitting back in a most un-dialectical fashion when challenged. Hence, as noted above: it is impossible for dialecticians to say what they mean.


The same problems afflict other DM-inspired criticisms of principles dialecticians claim to have found (some hope!) in textbooks of FL.


In addition, DM-theorists are invariably unclear what the "A"s in these alleged FL-'laws' are supposed to stand for. Based on the above, and on other passages quoted elsewhere at this site, it is obvious that DM theorists regularly confuse these letters with one or more of the following: propositions, judgements, properties, qualities, words, objects, processes, predicates, statements, assertions, type-sentences, token-sentences, concepts, ideas, beliefs, thoughts, phrases, clauses, relations, relational expression, indexicals, places, times, names --, and now, in the case of Somerville, "existences"!


The significance of logical disorder of this magnitude lies not so much with the unmitigated confusion it creates, but with the fact that the vast majority of the DL-faithful have not even noticed it!


And that includes HCDs!


And when this is pointed out to them, they simply complain about "pedantry"!


As has already been pointed out: 2400 years ago (and despite his own confusions) Aristotle was far clearer about such things than all these 'dialectical logicians' put together.


But worse: are we really supposed to believe that this sub-Aristotelian syntactic jumble encapsulates ideas that lie at the very cutting edge of modern science?


Now, anyone tempted to respond to the above on the lines that it gets the DM-view of contradictions (etc.) wrong, and that dialectical contradictions are really this, or they are in effect that, or they are…whatever, need only reflect on the fact that according to the DM-inspired criticism of the LOC, that criticism itself must be this or that, or whatever, while at the same time being not this or that, or whatever -- if we here interpret the "A"s above as "this or that, or whatever", since, on sound dialectical-principles, these letters can be interpreted in any which way we fancy.


Now, let's see those who accuse careful logicians of "pedantry" try to squirm their way out of that one!


[In Essay Eight Part Two, we shall see that this serious difficulty afflicts, and thus neutralises, the best account there is (or, at least, the best account I have so far seen) of the nature of 'dialectical contradictions'.]


In that case, the radically imprecise nature of the DM-inspired criticism of the LOC (which sees everything as "this or that, or whatever, and not this or that, or whatever" -- where each "this or that, or whatever" is just left undefined, so it can be anything you like) must itself be "both a criticism and not a criticism" of the LOC. This must be so unless, of course, criticisms are themselves exempt from their own criticism -- and cannot thus ever aspire to become one of these wishy-washy dialectical letter "A"s.


Alas, this means that dialecticians' own criticism of the LOC must now self-destruct. So, for example, any attempt made by DL-fans to define the LOC must be "a definition and not a definition" -- if their own 'analysis' of the LOC and the LOI is invoked against any such attempt.


Hence, using "D" to stand for the DM-'definition' of the LOC (whatever that 'definition' is, and whatever it means, if we are ever told), it must be the case that "D is at the same time non-D". Clearly, that would mean that the DM-inspired criticism of the LOC undermines its own definition of it! Or, at least, it does and it doesn't.


It is at this point that even DL-fans might just begin to see how devilish their own Diabolical Logic really is.


[BAD = Buddhist Dialectics/Dialecticians; MAD = Materialist Dialectician.]


However, long experience 'debating' with comrades who think Hegel is the best thing since sliced Aristotle suggests that one should never underestimate a dialectician's capacity for ignoring anything he or she does not like. 'Debating' with those whose brains have been compromised by this Hermetic virus is like debating with Buddhists -- except the latter are at least fair. With respect to both sets of mystics (the MAD and the BAD), whatever is argued against their system simply doubles back to prove their case. The fact that BAD-ies can tell us absolutely nothing about 'Nirvana' phases them not (since it is 'Nothing'!), just as it scarcely registers with MAD-ies that they cannot say what their "Totality" is.


And it is no use pointing out to MAD-ies or BAD-ies that their belief in universal contradictions is self-contradictory, for to do so would merely be to feed this monster, and thus lend it strength.


[This is especially true of MAD-Mystics found on internet discussion boards -- a recent and virulent example of which can be found here; check out the abusive ramblings of comrade "Wangwei".]


Now, it could be objected once more that DM-theorists do not object to the use of the LOC, the LOI or the LEM in their proper field of application (as several comrades pointed out above). These principles fall short when they are applied to processes in the world, to change and movement. This hackneyed response will be tested to destruction in Essays Five, Six and Eight Parts One and Two (where consideration will be given to Engels's 'analysis' of motion, Hegel and Trotsky's attempt to criticise the LOI, and the claim that change is the result of 'internal contradictions').


In the meantime, it is worth pointing out that these DM-inspired criticisms of FL are themselves phenomenal/material objects (i.e., they have to be written in ink on a page somewhere (etc.), or propagated in the air as sound waves at some point), and as such they are surely subject to change (if everything is). In that case, they "are never equal to themselves". If so, the above DM-inspired criticisms of FL must apply to each material copy of any DM-inspired criticism of FL.


In that case, no materially-configured DM-criticism of the LOC is equal to itself, and hence each phenomenal example of a DM-criticism is at the same moment both "a criticism and not a criticism".


The rest follows as before.


The counter-argument to this (that dialecticians only need to appeal to the 'relative stability' of material objects/processes to make their point) is neutralised in Essay Six. The other counter-argument -- that this ignores Hegel's use of identity to derive the alleged fact that everything is related to, or 'reflects', its 'own other', and not merely to everything that it is 'not' --, is defused in Essays Seven and Eight Part Two.


However, in an attempt perhaps to forestall the objections posted above, James Lawler argued as follows:


"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 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.'" [Lawler (1982), p.32, quoting Hegel (1975), p.215, in the edition I have used, which seems to be different from Lawler's. Italic emphases in the original. Quotation marks altered to conform to the conventions adopted here.]


Quite how the incomprehensible passage from Hegel helps clear this up I will leave to those fluent in Martian to decide, but 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.... 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. Quotation marks altered to conform to the conventions adopted here.]


We have already had occasion to note that dialecticians are hopelessly confused about what they mean by the sub-logical symbols they use, and Lawler is, as we will see, equally all over the place here (confusing these "A"s one minute with propositions and sentences, the next with properties, predicates, 'beings', indexicals, relations and/or nominalised relational expressions, among other things). How this prevents the logical tomfoolery we saw earlier, which follows from Hegel's brilliant insight -- that "A" is identical with, but at the same time different from, "not-A" -- is somewhat unclear. Even if it were correct (i.e., that "A" = "not-A", but at the same time "A ≠ not-A" (which is a slightly shorter version of: "A" is identical with, but at the same time different from, "not-A")), we would still obtain the following pig's ear from B1 (modified):


B1b: "A = A and at the same time not-A".


However, if we begin with the more 'orthodox' version encapsulated in B1c, the situation is even worse:


B1c: "A = A and A = not-A and A ≠ not-A".


Here I am taking "A is A and at the same time A is not-A, and A is also not-not-A" to have the same 'dialectical' content as "A = A and A = not-A and A ≠ not-A". If this formula of 'genius' (i.e., "A and A = not-A and A ≠ not-A", which we are assured it is 'dialectically' equal to "A") is now substituted for each "A" in B1c (but parsed by means of brackets to make it 'easier' on the eye), we obtain this monstrosity:


B6: "(A and A = not-A and A ≠ not-A) = (A and A = not-A and A ≠ not-A) and (A and A = not-A and A ≠ not-A) = not-(A and A = not-A and A ≠ not-A) and (A and A = not-A and A ≠ not-A) ≠ not-(A and A = not-A and A ≠ not-A)".


If we now do the same for B6, we obtain this 'dialectical' beauty:


B7: "((A and A = not-A and A ≠ not-A) and (A and A = not-A and A ≠ not-A) = not-(A and A = not-A and A ≠ not-A) and (A and A = not-A and A ≠ not-A) ≠ not-(A and A = not-A and A ≠ not-A)) = ((A and A = not-A and A ≠ not-A) and (A and A = not-A and A ≠ not-A) = not-(A and A = not-A and A ≠ not-A) and (A and A = not-A and A ≠ not-A) ≠ not-(A and A = not-A and A ≠ not-A)) and ((A and A = not-A and A ≠ not-A) and (A and A = not-A and A ≠ not-A) = not-(A and A = not-A and A ≠ not-A) and (A and A = not-A and A ≠ not-A) ≠ not-(A and A = not-A and A ≠ not-A)) = not-((A and A = not-A and A ≠ not-A) and (A and A = not-A and A ≠ not-A) = not-(A and A = not-A and A ≠ not-A) and (A and A = not-A and A ≠ not-A) ≠ not-(A and A = not-A and A ≠ not-A)) and ((A and A = not-A and A ≠ not-A) and (A and A = not-A and A ≠ not-A) = not-(A and A = not-A and A ≠ not-A) and (A and A = not-A and A ≠ not-A) ≠ not-(A and A = not-A and A ≠ not-A)) ≠ not-((A and A = not-A and A ≠ not-A) and (A and A = not-A and A ≠ not-A) = not-(A and A = not-A and A ≠ not-A) and (A and A = not-A and A ≠ not-A) ≠ not-(A and A = not-A and A ≠ not-A))".


Unfortunately, my computer might not have enough memory to do B8! Hence, that is left for the reader to attempt.


And it is no good complaining that this is unfair; dialecticians' sloppy use of such ill-defined letters invites such parody.


So Lawler's 'solution' is in fact a major step backward, even when compared with the implications of the crass definitions of lesser LCD souls.


[Lawler's attempt to derive, a là Hegel, a "not-A" from an "A" will be dismembered later. It is worth pointing out again that in all of this, the distinction between "not A" (predicate negation) and "not-A" (predicate-term negation) has been ignored, since Lawler and other DM-fans seem to be unaware of it. More on this here.]


On a more general note, comrades Woods and Grant make other assertions about FL that reveal just how little they know of the subject they happily misrepresent:


"It is an astonishing fact that the basic laws of formal logic worked out by Aristotle have remained fundamentally unchanged for over two thousand years." [Woods and Grant (1995), p.89.]


This is so manifestly (and demonstrably) untrue that these two comrades have to ignore and distort the major advances that have been made in logic since the 1850s to make it 'work':

"In the 19th century, there were a number of attempts to bring logic up to date (George Boyle (sic), Ernst Schröder, Gotlob (sic) Frege, Bertrand Russell and A. N. Whitehead). But, apart from the introduction of symbols, and a certain tidying up, there is no real change here. Great claims are made, for example by the linguistic philosophers, but there are not many grounds for them...." [Ibid., p.97.]


We have already had occasion to note the errors in this passage -- for example, Woods and Grant confuse George Boole with a fictional character they name "George Boyle"; they also mis-spell Gottlob Frege's name --, but these are relatively minor issues (even though they underline how sloppy these two are when it comes to matters logical). The fact that these comrades can see no difference between the old logic of subject and predicate, and the newer logics of function and argument, quantifiers and predicates of different levels, of relations and sets, tensed functors, and so on, merely underlines their ignorance.


On the superiority of MFL, see Dummett (1981a), pp.8-33, Noonan (2001), pp.25-28, 39-43. Wittgenstein himself addressed some of the confusions and limitations of the old logic in Wittgenstein (1913). The superiority of the Fregean system is brought out admirably well in Geach (1961). Also, see Zalta (2005).


Traditional logic not only ignored complex inferences inexpressible in syllogisms, it dramatically failed to cope with relational expressions, quantifiers expressing multiple generality, internal and external negation and scope ambiguity. This was partly because of the way that quantifier expressions had been interpreted by earlier logicians, who with their slavish adherence to the traditional grammar of subject and predicate helped cripple logic for over two thousand years.


The impact of this new logic, and why it was crucially important for advances in mathematics, is outlined in Giaquinto (2004).


However, these two comrades continue:


"Using a superficial and inexact analogy with physics, the so-called 'atomic method' developed by Russell and Wittgenstein (and later repudiated by the latter) tried to divide language into its 'atoms.' The basic atom of language is supposed to be the simple sentence, out of which compound sentences are constructed. Wittgenstein dreamed of developing a 'formal language' for every science -- physics, biology, even psychology. Sentences are subjected to a 'truth test' based on the old laws of identity, contradiction and the excluded middle. In reality, the basic method remains exactly the same. The 'truth value' is a question of 'either…or,' 'yes or no,' 'true or false.' The new logic is referred to as the propositional calculus. But the fact is that this system cannot even deal with arguments formerly handled by the most basic (categorical) syllogism. The mountain has laboured, and brought forth a mouse." [Ibid., p.97.]


Again, the errors in this passage are exposed here. However, Woods and Grant nowhere reference a single passage from Wittgenstein that supports the idea that he wanted to set up "a 'formal language' for every science -- physics, biology, even psychology...", nor do they show how the new logic cannot handle syllogistic inferences, when it manifestly can. On this, for example, see Lemmon (1993), pp.168-79.


Not finished, these two continue:


"The introduction of symbols into logic does not carry us a single step further, for the very simple reason that they, in turn, must sooner or later be translated into words and concepts. They have the advantage of being a kind of shorthand, more convenient for some technical operations, computers and so on, but the content remains exactly as before. The bewildering array of mathematical symbols is accompanied by a truly Byzantine jargon, which seems deliberately designed to make logic inaccessible to ordinary mortals, just as the priest-castes of Egypt and Babylon used secret words and occult symbols to keep their knowledge to themselves. The only difference is that they actually did know things that were worth knowing, like the movements of the heavenly bodies, something which cannot be said of modern logicians." [Ibid., pp.97-98.]


On a similar basis, therefore, algebraists must have been unwise to introduce symbols into mathematics. But, how many ordinary people understand algebra? Does that mean algebra is 'elitist'? However, and more revealingly, Woods and Grant's jibe about the esoteric nature of modern logic hides, one feels, the honest fact that these two comrades found Symbolic Logic too difficult too grasp. [Exhibit A for the prosecution was presented earlier.]


To be sure, modern logic is unbelievably difficult; as I noted above, in my own study of University Mathematics and Postgraduate Logic, I found that, say, advanced Abstract Algebra (Group Theory) was far easier to follow than advanced MFL (and especially when compared with the Philosophy of Logic, surely one of the most difficult subjects yet devised by the human brain). Others may find that the reverse is true. But that no more maligns MFL than it does, say, Group Theory.


Readers will however have noted the latest snide remark about ancient priests, whose knowledge, we are told, involved certain practicalities -- unlike those supposedly displayed (or not) by modern logicians. This from comrades who sing the praises  of a logical 'theory' (DL) which has no known practical applications (other than that of thoroughly confusing its acolytes), but who endlessly snipe at one that has countless.


And as far as "Byzantine jargon" is concerned, anyone who reckons they can learn something (anything) from Hegel's Logic, as these two do, has little room to accuse others of excessive devotion to jargon. The technical terms in MFL are there for the same reason they are there in modern mathematics. No such grounds exist for excusing the countless pages of terminally-obscure jargon found in Hegel's Logic; quite the reverse, as we shall see.


Unfortunately, there is more:


"Terms such 'monadic predicates,' 'quantifiers,' 'individual variables,' and so on and so forth, are designed to give the impression that formal logic is a science to be reckoned with, since it is quite unintelligible to most people. Sad to say, the scientific value of a body of beliefs is not directly proportionate to the obscurity of its language. If that were the case, every religious mystic in history would be as great a scientist as Newton, Darwin and Einstein, all rolled into one." [Ibid., p.98.]


The new terminology employed in MFL was introduced simply because the old logic of subject and predicate failed to do justice to the sorts of inferences found in everyday life, to say nothing of the complex inferences made by mathematicians and scientists. And, the reference to religious mystics is a little rich in view of the Hermetic writings from which these two caught such a nasty dose of dialectics.


"In Moliere's comedy, Le Bourgeois Gentilhomme, M. Jourdain was surprised to be told that he had been talking prose all his life, without realising it. Modern logic merely repeats all the old categories, but throws in a few symbols and fancy-sounding terms, in order to hide the fact that absolutely nothing new is being said. Aristotle used 'monadic predicates' (expressions that attribute a property to an individual) a long time ago. No doubt, like M. Jourdain, he would have been delighted to discover that he had been using Monadic Predicates all the time, without knowing it. But it would not have made a scrap of difference to what he was actually doing. The use of new labels does not alter the contents of a jar of jam. Nor does the use of jargon enhance the validity of outworn forms of thought.


"The sad truth is that, in the 20th century formal logic has reached its limits. Every new advance of science deals it yet another blow. Despite all the formal changes, the basic laws remain the same. One thing is clear. The developments of formal logic over the past hundred years, first by propositional calculus (p.c.), then by lower predicate calculus (l.p.c.) has carried the subject to such a point of refinement that no further development is possible. We have reached the most comprehensive system of formal logic, so that any other additions will certainly not add anything new. Formal logic has said all that it has to say. If the truth were to be told, it reached this stage quite some time ago." [Ibid., pp.98-99.]


I have been unable to find the term "Monadic predicate" in Aristotle, but that does not mean he did not use monadic predicates. But so what? Ancient mathematicians used ideas and abbreviations that are analogous to the symbols employed by modern mathematicians; does that mean that modern mathematics is full of "fancy-sounding terms", and thus fit only for ignorant ridicule? Or that modern formalism is no advance over ancient mathematical terminology?


And, of course, a monadic predicate (such as "ξ is a confused dialectician") can apply to more than one individual (as in "Anyone who reads RIRE, and believes everything they read, is a confused dialectician"); so it is not true that 'monadic predicates' are expressions that "attribute a property to an individual".


The question whether or not MFL has been usurped by advances in science will be dealt with elsewhere on this site (however, see Harrison (1983, 1985), on the LEM and QM); but, as far as the allegation that MFL has reached the end of the line is concerned, only someone who knows nothing of the subject would say this. Even a cursory look along the relevant shelves in a University Library will soon reveal how the subject is continuing to blossom, as will the briefest of Google searches.


[LEM = Law of Excluded Middle; QM = Quantum Mechanics.]


In fact, this by-now-familiar 'head in the sand' attitude -- perfected by these two comrades -- is somewhat reminiscent of the stance taken toward Galileo's work by Catholic Theologians: stick to Dogma comrades (it's safe), and under no circumstances look down that telescope!


One last comment by Woods and Grant is worth noting:


"Another type of syllogism is conditional in form (if...then), for example, 'If an animal is a tiger, it is a carnivore.' This is just another way of saying the same thing as the affirmative categorical statement, i.e., all tigers are carnivores. The same in relation to the negative form -- 'If it's a fish, it's not a mammal' is just another way of saying 'No fishes are mammals.' The formal difference conceals the fact that we have not really advanced a single step." [Ibid., p.86.]


Alas, Woods and Grant seriously expose their ignorance here; a hypothetical proposition like: 'If an animal is a tiger, it is a carnivore' is not an argument of any sort, so it cannot be a syllogism.


On the other hand, if it is a conditionalised argument (i.e., an argument that has been transformed into a conditional proposition), the original argument must have had a suppressed premiss (such as "No fish is a mammal", in relation to 'If it's a fish, it's not a mammal'). Either way, these are not syllogisms.


Nevertheless, Woods and Grant have clearly missed the point of hypothetical deduction in MFL (a facility that was foreign to AFL, but present in Stoic Logic). We can surely reason from premisses whose truth-status is unknown to us (as scientists often do), in order to establish their truth-values (or as a way of ascertaining them). Indeed, it is important for us to find out if any of our beliefs are false, and we can do that by drawing out their consequences. This cannot be done with categorical reasoning -- unless the hypothetical mode is used implicitly.


Hypothetical reasoning has always been used in the sciences (on this see, for example, Losee (2001)); these days this practice tends to be linked to "thought experiments" --, but, plainly, the two are not the same. However, "thought experiments" themselves have been used by scientists for centuries to confirm or refute certain theories/hypotheses. Galileo was a past master at this, as was Einstein.


On "thought experiments", see the popular account in Cohen (2005). More scholarly analyses can be found in Brown (1986, 1993, 2002, 2005), Häggqvist (1996), Horowitz and Massey (1991), McAllister (2005), Norton (1996, 2005) and Sorensen (1992). [Brown, however, takes a Platonist view of "thought experiments", something rightly rejected by Norton, for example.] Another quick Google search will reveal dozens of articles on this topic alone.


But, we do not need to appeal to arcane aspects of the scientific method; Woods and Grant themselves engage in their own form of hypothetical 'reasoning'. They do this when they derive what they take to be false conclusions from premisses which they attribute to what they call "formal" thought. They manifestly do not hold the latter propositions true; they merely reason from their assumed truth to what they then claim are obvious falsehoods, in order to show that the original assumptions must have been false, or were of limited applicability. They could not do this with a categorical argument, where the premisses are known to be true or known to be false.


[In saying this, the reader should not think that I attribute to Woods and Grant a clear logical strategy here; few of their arguments work (and many are aimed at targets that would give the phrase "straw man" a bad name, as we have seen). But that is not the point; they certainly intended to argue hypothetically, which is.]


In practice, we see once again that dialecticians only succeed in shooting themselves in the oversized foot they have firmly lodged in their even bigger collective mouth.


Finally, it is worth noting that, Graham Priest's work aside, the best defence of the 'dialectical view' of contradictions I have encountered in the literature (i.e., that found in Lawler (1982)) will be discussed in detail in Essay Eight, Part Three.


However, anyone who wants a more accurate account of the foundations of AFL need look no further than Lear (1980).


24. This controversial claim will be substantiated in a later Essay. Cf., Note 25.


25. This idea is advanced, for example, in Engels (1954), p.258. It is discussed in detail in Essay Seven.




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