Limits - Part 1

The Philosopher wrote in his Metaphysics that a particular branch of the Pythagorean school, adapting the original teaching of Pythagoras, taught that the first principles of the cosmos were ten, divided into the following table of opposites:

limited–unlimited
odd–even
one–many
right–left
male–female
rest–motion,
straight–curve
light–darkness
good–evil
square–oblong

Now I've already written about straight lines and curved, and a little about females, but this list will give up a few more mysteries before the ancient body is entirely exhumed. It ought to give you pause. First of all, is each column related, or are they in reality unorganized pairs of independent principles? From what we know elsewhere of Pythagorean thought, the latter proposition, unmodified, is out of the question. The square, the odd, and the one are all related, in fact, by the construction of number using the gnomon, or carpenter's square. It's a fair bet that the other seven principles in the table are likewise related. If they are related, is there a primary principle that governs the others, along the lines of the possibility that the forming of a "more perfect Union" is the governing principle within the Preamble to the U.S. Constitution? If so, are the rest of the principles ranked? Our modern eye will pick out two immediately, male-female and good-evil, as being important. We might think that the good-evil pair is the most important of the lot, and governs the rest - that is to say, we might interpret the table to mean that there is something good about light, and evil about darkness. But perhaps the Pythagoreans didn't think in this hierarchy at all. Perhaps they thought there was something oblong about evil, and something odd about male.

For some reason, growing up with my algebra, I always thought that even numbers were stronger, more 'male' if you will, than odd numbers. I didn't like negative numbers a bit - my homework was always in a war, and we won if the total was positive by the end of the lesson. But the even still was better. I think I liked the strength of the number two, in which all the other even numbers shared. But reflecting back after many years, it's obvious that if strength is conceived as independence, the strongest are the prime numbers, and the odd numbers share in the primes most fully (although the number two, the principle female number, also shares in the primes).

If the Pythagoreans were to have proposed a hierarchy, almost certainly the governing principle would have been not that of good and evil, but that of the one and the many. The study of ethics, questions of good and evil, was a specialized investigation of the principles of action in rational animals. Important for humans, yes, but what does Jupiter care? But as far as we can judge, the Pythagoreans avoided the question of a governing principle by claiming that the principle of being was nothing more than precisely the opposition of each to the other. As for Modern Philosophers, after disagreeing for centuries about the problems raised by particulars, universals, and their unwashed cousins, they came to the conclusion that the question was insoluble, though these days they're not so sure. The Philosophers might find that this old table relieves them of a great deal of labour (though this argument from leisure would not appeal to Immanuel Kant), if only they were to consider the relationship of the One with the Straight, the Odd, and most importantly, the Limit.