Perfection of Logic
November 28, 2021
This continues directly on from yesterday’s post on Schopenhauer.
Schopenhauer has argued that the procedure of reason must, in Ancient Athens, have been rendered in “abstract propositions.” And I’ve argued that just as Spinoza observes “perfection” to move from a concrete adjective, perfect, to an abstract noun, perfection, so Schopenhauer’s concrete verb, which I’m calling reasoning, becomes the abstract noun reason.
Schopenhauer continues, describing how these abstract propositions would be used:
These [propositions] would then be put at the head of the inquiry, just like those propositions jointly acknowledged and concerned with the material of the inquiry, as the fixed canon of debate, to which it would always be necessary to look back and to refer. In this way, what had hitherto been followed as if by tacit agreement or practised by instinct would be consciously recognized as law, and given formal expression.
Just as people once agreed on the concrete propositions relevant to their particular debate, in any given conversation, the abstract propositions of “reason” would be agreed to in advance. But of course these would then apply to all debates, or all those that chose to follow this convention.
Schopenhauer proceeds to list a bunch of rules of logic as examples.
Gradually, more or less perfect expressions for logical principles were found, such as the principles…”
- of contradiction,
- of sufficient reason,
- of the excluded middle,
- the dictum de omni et nullo,
- and then the special rules of syllogistic reasoning, as for example
- Ex meris particularibus aut negativis nihil sequitur
- a rationato ad rationem non valet consequentia
- and so on.
(I couldn’t find all of them.)
This did not take place instantaneously, however:
That all this came about only slowly and very laboriously, and, until Aristotle, remained very incomplete, is seen in part from the awkward and tedious way in which logical truths are brought out in many of Plato’s dialogues, and even better from what Sextus Empiricus tells us of the controversies of the Megarics concerning the easiest and simplest logical laws, and the laborious way in which they made such laws plain and intelligible (Sextus Empiricus, Adversus Mathematicos, 1. 8, p. 112 seqq.).
It’s fascinating that what eventually become the universal rules of logic had to be invented (or discovered), and that this involved individual people. This relates to Kuhn’s point about Newton’s laws, to which I alluded yesterday. What took centuries of experimentation to establish come to seem almost like tautologies that no amount of observation could refute.
Just as with Newton, Aristotelian logic took time to be perfected, but once perfected, it seems self-evident. It seems obvious to the point of tautology. This is in spite of the fact that Sextus Empiricus describes the great difficulty at articulating them.
Aristotle collected, arranged, and corrected all that had been previously discovered, and brought it to an incomparably higher state of perfection.
But what does he mean by perfection?
Yes, he might just mean “perfect” in the sense of complete. But it’s clear that perfection here also involves abstraction, and universality across previous debates. You might even call this consensus a kind of homogenization.
But did Aristotle perfect them himself? Had he no giants on whose shoulders to stand, as Newton had? Schopenhauer thinks that the period of imperfection proves that Aristotle did perfect them.
He therefore dismisses another possibility…
If we thus consider how the course of Greek culture had prepared for and led up to Aristotle’s work, we shall be little inclined to give credit to the statement of Persian authors reported to us by Sir William Jones, who was much prejudiced in their favour, namely that Callisthenes found among the Indians a finished system of logic which he sent to his uncle Aristotle (Asiatic Researches, Vol. IV, p. 163).
Wait, what? Aristotle might have gotten his logic from India? And a European philosopher says this is impossible? That sounds familiar!
I’ll come back to Callisthenes tomorrow.
I reproduce the rest of Schopenhauer’s argument just because it’s funny how bored he is by logic:
It is easy to understand that in the dreary Middle Ages the Aristotelian logic was bound to be extremely welcome to the argumentative spirit of the scholastics, which, in the absence of real knowledge, feasted only on formulas and words. It is easy to see that this logic, even in its mutilated Arabic form, would be eagerly adopted, and soon elevated to the centre of all knowledge. Although it has since sunk from its position of authority, it has nevertheless retained up to our own time the credit of a self-contained, practical, and extremely necessary science. Even in our day the Kantian philosophy, which really took its foundation-stone from logic, has awakened a fresh interest in it. In this respect, that is to say, as a means to knowing the essential nature of reason, it certainly merits such interest.