SYLLOGISMS AND OTHER LOGIC

With regard to Aristotle’s logic, Bertrand Russell makes an insightful comment, which boils down to why exactly we often confess to hating Aristotle, while admiring most of his peers, but also many philosophers of far lesser statures. The answer is that those philosophers whom we so admire are usually mere historical relics to us, long out of contention for the minds of modernity, whereas Aristotle and his logic are still very much in play, and still present a challenge to our modern thinking. I am tempted to compare this situation to the modern attitude toward the great Nietzsche, who has as many ardent fans as ferocious enemies, both of them on account of his super-active status in the actuality of modern thinking, and in large measure because of his alleged intellectual and spiritual ties to the philosophy of the Third Reich.

There is a difference, however. Nietzsche is a modern thinker, in many ways ahead of the curve, while the classical logic of Aristotle is no longer the cutting edge, but its awesome perennial prestige has been used to promote a certain backwardness of thinking, and has thus become a victim by association.

It is therefore imperative to repeat that, no matter what, Aristotle’s logic remains a titanic achievement of the human mind, one of the largest milestones in the history of human civilization, and any excessive criticism of him on account of the amazing longevity of his brainchild is an example of the unfair practice of guilt by association. In this regard, Russell’s argument is of special interest, when he says this:

"Aristotle’s logical writings show great ability and would have been useful to mankind, if they had appeared at a time when intellectual originality was still active. But, unfortunately, they appeared at the very end of the creative period of Greek thought, and, therefore, came to be accepted as authoritative. By the time that logical originality revived, a reign of two thousand years had made Aristotle very difficult to dethrone, and throughout modern times, practically every advance in science, logic, or philosophy, has had to be made in the teeth of the opposition from Aristotle’s disciples."

As for his evaluation of Aristotle’s logic for modern times, Russell is uncommonly harsh in his judgment: "I conclude that the Aristotelian doctrines, with which we have been concerned in this chapter, [on logic] are wholly false, with the exception of the formal theory of the syllogism which is… unimportant. Any person in the present day who wishes to learn logic will be wasting time reading Aristotle or any of his disciples."

Even if this is partly true, nevertheless, a few elements of Aristotle’s logic need to be presented here.

The cornerstone concept of Aristotelian logic is the syllogism, which is a three-part argument, consisting of a major premise, a minor premise, and the conclusion, or, in his own words, “a discourse, in which, certain things being stated, something different from these things follows of necessity from their being so.”

The most famous and original in the chronological sense syllogism is All men are mortal (major premise); Socrates is a man (minor premise); therefore Socrates is mortal (conclusion). All other types of syllogism can be reduced to this one. In developing his logic, Aristotle believed that all deductive reasoning is such that it can be reduced to the syllogism. The only task remained to set every argument in syllogistic form. (This optimistic belief in the syllogism managed to mislead all philosophers until Kant, as to the nature of mathematical reasoning. Kant understood that mathematics was not syllogistic, but concluded that it had to be governed by extra-logical principles, which in itself was a surrender of sorts to Aristotle’s authority.) As a matter of fact, not only was the syllogism inessential to deductive reasoning, the latter itself was not the exclusive mode of reasoning. Aside from deduction, there was also induction, and Aristotle recognized its importance, when he raised the question of how we arrive at the first premises from which deduction is supposed to start. Whereas the title of his work on the syllogistic logic was The Prior Analytics, induction was discussed in The Posterior Analytics. It is impossible, Aristotle admits, to go backwards through our deduction incessantly. At some point in this regression, we must arrive at a premise that cannot be deduced from a preceding syllogism, and, in this case, we are dealing with an intuitive truth, which reveals itself to our intuitive reason (nous), which is the mental faculty that knows without proof. Examples of such truths are, according to Aristotle’s mistaken impression, the basic axioms of geometry. Such self-evident truths, he believed, exist in every science…

Who said that Aristotle’s logic was not at all interesting? From this exciting discussion of” induction,” we now know how Kant got himself mixed up with those dangerous chimeras, the aprioris!