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Logical and Spiritual REFLECTIONS

Book 3. In Defense of Aristotle’s Laws of Thought

Chapter 5. Misrepresentation of Aristotle

Aristotle’s three laws of thought are often misrepresented, in the service of some doctrine or other. Often, nowadays, the motive is a desire to defend Buddhist antinomies; some decades ago, the motive might have been to defend Marxist contradictions; before that, maybe Hegelian ones. Usually, the proposed reading of Aristotle is unfair to him, a misrepresentation of his evident intentions.

During the late Middle Ages in Europe, the authority of Aristotelian philosophy was unmatched. The reason for this was that before that period many of the works of Aristotle (384-322 BCE) had been mostly lost to Christian Europe; when they were rediscovered, the superiority in many respects of the knowledge they contained was such that his influence became great[1]. But, as a result of that overwhelming belief in everything Aristotelian, scientists of the Renaissance period and after often had to struggle hard to overcome what had become an academic bias.

It could be argued, paradoxically, that Aristotle’s influence on the Christian European mind was one of the factors that led to the intellectual Renaissance; nevertheless, just as students must rebel from teachers to some extent to innovate and advance, an anti-Aristotelian reaction had to occur. Many historians thus regard Aristotelianism as the impetus of the Renaissance and thus of modern science.

Note moreover, Aristotle himself was no rigid ideologue; his approach was open-minded and adaptive, what we now call ‘scientific’. Although many of his material opinions[2] have turned out to be false, they were quite reasonable for his period of history – and for the Middle Ages. Had he still been around in the modern era, he would no doubt have adjusted his views.

Opposition to Aristotelianism, ranged over the special sciences, more philosophical issues and logical aspects, in no particular order. With regard to his logical work, the greater emphasis Francis Bacon put on induction was indeed a marked improvement; whereas, attempts in the late 19th and early 20th centuries to supersede Aristotle’s formal logic with more systematic deductive approaches seem (to me at least) rather pretentious. The attempts, lately, to belittle or do away with Aristotle’s laws of thought fall in the same category (again, in my opinion).

In many cases, criticisms of Aristotle’s thought were and are of course justified. But in many cases, too, the critics were and are just (I suspect) seeking a shortcut to academic notoriety, taking an easy ride on the ongoing wave (in some quarters) of ‘Aristotle bashing’. It is very easy to be critical regarding someone who cannot answer back; I daresay, if that genius were still around, they would not dare.

A case in point (taken at random) is the following presentation, drawn from an Internet site[3]. I quote:

The three laws of “formal logic” which Aristotle set down in his Posterior Analytics are as follows: (1) Law of Identity: Each existence is identical with itself; (2) Law of Non-contradiction: Each existence is not different from itself; (3) Law of Excluded Middle: No existence can be both itself and different from itself.

Of course, nowhere in the Posterior Analytics, or anywhere else in Aristotle’s known writings, are such inane formulations of his laws of thought to be found. Anyone who has read Aristotle knows this is not his language or terminology, nor his thought or intent. He does not speak of “existences” and is not concerned with whether or not they are “identical with” or “different from” themselves.

These statements are, admittedly, not presented as verbatim quotations; but they are not, either, declared to be mere readings or interpretations; they are made to seem like loyal paraphrases. But they are not a fair statement of what Aristotelian logic is about. It is not about tautology or the lack of it, not even in an ontological sense.

In Aristotle’s Posterior Analytics, we find the following statements of the law of non-contradiction: “it is impossible to affirm and deny simultaneously the same predicate of the same subject”, and of the law of the excluded middle: “every predicate can be either truly affirmed or truly denied of every subject”.[4]

But the above author seems rather to base his formulations on common statements of the laws of thought, like “A is A”, “A cannot be not-A” and “Either A or not-A”[5]. Such statements, however, are not meant as comprehensive expressions, but as shorthand formulas; they are more like titles, stand-ins for fuller statements that comprise all that can be said about these laws. The simplest way to read them is as follows:

  1. Something that is evidently A must be admitted to be A.
  2. Something admitted to be A cannot also be claimed not to be A (i.e. no thing can be claimed both to be A and not to be A).
  3. And no thing can be claimed neither to be A nor not to be A.

In this primary reading, note well, the term “A” is everywhere a predicate, as Aristotle presents it, rather than a subject, as it may seem. In all three cases, the tacit subject of the proposition is “some thing”, an individual thing under consideration, i.e. any apparent object of cognition. Moreover, all three propositions are primarily logical or epistemological statements, rather than ontological ones. They tell us how to behave in our discourse or cognition.

In a second phase, we can give “A” the role of subject that it superficially has in the expressions “A is A” and “A cannot be not-A”, and “Either A or not-A”. Such perspective suggests a more ontological reading of these laws, namely that every existent has a particular identity, i.e. ‘a nature’, whatever that happen to be.

Each thing is something specific (say “A”), not just anything whatsoever (“both A and not A”), nor nothing at all (“neither A nor not A”). It includes some distinguishable aspects and excludes others: it is not infinitely elastic in appearance. It neither includes nor excludes everything. It cannot include things incompatible with it (“contradictions” of it). Its negation may replace it, but nothing in between (no “middle”) can replace both it and its negation.

Note this: the law of the excluded middle could, in analogy to the law of non-contradiction, equally well be called the law of non-neutrality. These laws respectively tell us that there is no common ground and no neutral ground between A and not-A. They ontologically together firmly separate A and not-A, allowing of no wishy-washy togetherness or further possibility. They do not however epistemologically exclude that we might (occasionally, though not invariably) come across contradiction or uncertainty in our thinking.

Even such interpretations ought not, in any event, be treated as the whole of the meaning of the laws of thought, but more modestly as a beginning of explication[6]. They make clear, anyway, that these laws are not about equation or non-equation of things or symbols with themselves, as the already mentioned author’s formulations misleadingly suggest.

Additionally, the wording he proposes for the law of the excluded middle “No existence can be both itself and different from itself” – is formally wrong. This could be construed as a statement of the law of non-contradiction, perhaps, but the law of the excluded middle would (using the same sort of language) have to be stated as “No existence can be neither itself nor different from itself”.[7]

Clearly, Aristotle’s concern was whether the ideas we form about the world are compatible with experiential data and with each other. That is, one might say, an interest in the intersection between appearance and belief, or seeming reality and alleged knowledge. The two components of consistency with experience and other ideas correspond roughly to the tasks of inductive and deductive logic, respectively.

Elsewhere on the same website[8], the said author apparently advocates, in lieu of his pseudo-Aristotelian laws, something called “materialist dialectics,which “holds that the basic rules of correct thinking should reflect a universe not in which the static and changeless is at the core but in which change is at the core.” He goes on to propose three questionable alternative “laws”, which place change at the center of things.

Thus, the above quoted debatable presentation of the laws of thought is used to convey the idea that Aristotle had a static view of existence, and to propose instead a more dynamic alternative set of laws. It is tendentious rewriting of history.[9]

In truth, Aristotle is throughout his work very much concerned with dynamic becoming as well as with static being. His laws of thought are precisely intended to help the intellect cope with variety and change, and remain lucid and poised in the midst of the cacophony of sense-impressions and ideas.

Consider, for instance the following statement drawn from his Metaphysics[10]:

For a principle which every one must have who understands anything that is, is not a hypothesis; and that which every one must know who knows anything, he must already have when he comes to a special study. Evidently then such a principle is the most certain of all; which principle this is, let us proceed to say. It is, that the same attribute cannot at the same time belong and not belong to the same subject and in the same respect.

With characteristic intellectual accuracy, Aristotle expresses the law of non-contradiction by saying that nothing (i.e. no subject of a true proposition) can both be and not-be the same thing (i.e. have and not have the same predicate) in the same respect at the same time.

These last words are crucial to his statement, yet often ignored by dishonest critics such as the above quoted. By these words, Aristotle implied that something may well be subject to both a predicate and its negation – in different respects at the same time, or in the same respect at different times, or in different respects at different times.[11]

He is not ignoring that a given thing may have a variety of aspects at once, or that it may change in various ways over time. He is simply reminding us that in a given location and time of its being, a thing cannot contradict itself. His intent is therefore clearly not an attempt to deny the existence of variety and change, but to affirm the consistency that things nevertheless display at any given place and time.

Evidently, the earlier quoted attempted reformulation of the laws of thought as “Each existence is identical with itself; not different from itself; and can[not] be both itself and different from itself” is not only an inaccurate rendition of Aristotle, but an extremely superficial one[12].

Aristotle should be given the credit, respect and gratitude due him for a timeless and irreplaceable achievement.

[1] The rediscovery occurred mostly by way of translation into Latin (from Arabic, sometimes via Hebrew) of Greek classical texts in the libraries of Moslem Spain. These included works by Aristotle on physics, metaphysics and ethics. Aristotle’s thought was also made known to the West indirectly through commentators like Avicenna (Persia, 11th century) and Averroes (Muslim Spain, 12th century). His influence reached its peak perhaps with the writings of Thomas Aquinas (Italy, 13th century).

[2] For example, his cosmological views, which led to the Ptolemaic model that Copernicus and Galileo had to overcome.

[3] History and Theory of Psychology Course, by Paul F. Ballantyne, Ph.D. “Aristotelian and Dialectical Logic”, in posted May 2003 at http://www.comnet.ca/~pballan//section1(210).htm. (I was recently pointed to this website by a Buddhist correspondent arguing against Aristotelian logic; that is how I came across it.)

[4] Both these statements are there (in Book 11) referred to as laws, and the latter is specifically called the law of the excluded middle. Translation by G. R. G. Mure. See http://graduate.gradsch.uga.edu/archive/Aristotle/Posterior_Analytics_(analytic).txt.

[5] Or at least the first two; for the third law he misconceives altogether. See further on.

[6] Many more issues arise in them, such as: what do we mean by predicating “A” of something? What is the relation between a label like “A” and what it intends? At what stage may we consider “A” the exclusive label of that thing? Further: so far, the laws have been expressed in terms of an individual thing; but what about their application to kinds of things? Clearly, these laws of thought are pregnant with the whole philosophical enterprise!

[7] Such a glaring formal misstatement of the law discussed tells us much about the critic’s logical awareness, or lack of it! When I advised him by e-mail of this formal error, his response was at first flippant, then he made a small show of open-mindedness, but finally he made no effort to correct his statement.

(N.B. I have just recently looked again at his website and found out that he now seems to his credit to have corrected this and other errors.)

[8] In http://www.comnet.ca/~pballan/logic2.htm. He there quotes statements like “What Aristotle sees as the most basic characteristic of existence is static self-identity” by J. Somerville, p. 45 in “The Nature of Reality: Dialectical Materialism”, in The Philosophy of Marxism: An Exposition. (Minneapolis: Marxist Educational Press, 1967/1983).

[9] For an understanding of the logic of change in formal terms, see in my works: Future Logic, chapter 17, and Volition and Allied Causal Concepts, chapter 14. See also, Buddhist Illogic, chapter 6.

[10] Book 4, Part 3. (Translated by W. D. Ross.) Posted in the Internet Classics website at http://classics.mit.edu/Aristotle/metaphysics.4.iv.html

[11] Grass can be green and yellow, but not in exactly the same places and times of its existence. Grass can mean what the cows eat or what the hippies smoke, but these two same words do not refer to the same things. If such differences of perspective are impulsively or dogmatically ignored – well, that does not prove that contradictions exist. To affirm contradiction is to lack depth.

[12] Due no doubt to the influence of dimwitted modern symbolic logic, which makes every effort to reduce and limit these complex laws to their simplest possible expression, thus concealing most of their philosophical riches and depth. Why do they wish to so simplify? In order to fit logic into their simplistic “formal languages”, designed by people (like Gottlob Frege) with hopelessly bureaucratic minds, who think that standardizing thought processes makes them more “scientific”. But science is not a deductive, Cartesian enterprise; it is an inductive, evolutionary process. They claim to go above common ‘intuition’; but actually, all they do is permanently impose their own insights, and thereby inhibit future insights in the field. Development of the science of logic depends on alertness and flexibility, rather than on institutionalization and rigidity.

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