GOD, TRINITY, INFINITY

Moving on from all things are numbers to how Pythagoras and his disciples have addressed the mystery of God, we should not be surprised that numbers are playing an essential role here, too. In Bertrand Russell’s words, The combination of mathematics and theology… began with Pythagoras. The whole conception of the eternal world, revealed to the intellect, but not to the senses, is derived from him. (On the other hand, this conception, rather paradoxically, is not limited to the intellect. As Russell himself observes, “personal religion is derived from ecstasy [the irrational element!], theology, from mathematics; and both are found in Pythagoras.”) But for him, Christians would not have thought of Jesus Christ as the Word; but for him, theologians would not have sought logical proofs of God and immortality. (Even though Russell traces the idiocy of proving God’s existence to Pythagoras, my quarrel is not with him, but with the later theologians who should have known better.)

Returning to Aristotle, he writes in Physics that the Pythagoreans “both hold that the infinite is being, and divide it.” The most interesting thing about this, is that the most difficult intellectual problem of Christian theology, namely, God’s Oneness and Infinity, the latter ostensibly indivisible, and directly corresponding to One, rather than to Many, becomes divisible into a triad, that is the Trinity, without any objection from Christian philosophy whatsoever; but by the same token such a conclusion was reached by Pythagoras well before the Christian theological challenge so that he cannot possibly be suspected of some secret Christian agenda. Neither, of course, can be Aristotle. Yet another excerpt in the same vein comes here from his De coelo, and it happens to be even more explicit in this connection: “As the Pythagoreans say, all things are defined by threes; for end and middle and beginning constitute the number of the All, and also the number of the Triad.”

The key point that I wish to be making here is that by placing number above infinity, the Pythagoreans did not really solve the mystery of the Deity, but only came up with a superior concept of the number, turning it into a substitute for God. Their most significant failing, however, is that their concept of the Deity is devoid of the ethical component, and in an important quote elsewhere they allow evil to partake of infinity, which is a fatal flaw of their construct, in my opinion.

Dividing the Infinite downgrades the Infinite, and raises the power of numbers to a status above Divinity, thus, in these numbers, the Pythagoreans have actually found their substitute for God. As for the power of the Triad, the so obvious association with the mystery of the Trinity, which I mentioned earlier, does leap to mind, but this association would be wrong and superficial, from my personal point of view. My idea of the Trinity has always meant the three Manifestations of One God, which has nothing to do with the right or left of presumably the middle; the beginning, the middle, and the end. But what strikes me as very clever is the unity of space and time, hidden in the concept of the Pythagorean Triad, yet the said Triad somehow fails to reach beyond these Kantian Undinge, and, therefore, the Infinite has to be free of these limitations and non-divisible by mere definition. As I said before, in this entry, the said Triad would make sense only as “God,” who thus controls the Universe--- by arranging it into “before, now, and after,” on the one hand, and into “the beginning, the middle and the end,” on the other. But this simplistic arrangement is all riddled with holes, as Aristotle rightly observes in the following passage:

“Since there are some who say that there is a ‘right’ and ‘left’ of the heavens, as, for instance, those called Pythagoreans-- for such is their doctrine,-- we must investigate whether it is as they say. Wherefore one of the Pythagoreans might be surprised in that they say that there are only these two first principles, the right and the left, and they pass over four of them as not having the least validity; for, there is no less difference up and down, and front and back than there is right and left in all creatures.

And now, to bring this entry to an end, here is another passage from Aristotle’s Metaphysics ii.9:300a15:

“The same holds true for those who construct the heavens out of numbers; for some construct nature out of numbers, as do certain of the Pythagoreans.”

Previously I observed that the Pythagoreans ascribe divinity to numbers in a manner that makes numbers a substitute for God. In this last passage, numbers are, in fact, acting as God: The heavens being constructed out of numbers can easily read as numbers creating the heavens. Which now renders self-evident my final reference for the reader to my earlier entry …And God Was Number in the Philosophy section.