Thursday, 1 January 2015

null-set or four-squares

Æon Magazine features a really inviting and illuminating essay from earlier this Summer on how Eastern thought, Buddhism in particular, which can come across to Western-thinkers as hopelessly mystical and too pliable for admitting contradictions, while saying nothing about inherent truths in any system, prevision—in a sense—and converge in the logical constructs of mathematics, modern set-theories which have applications in computing and high-level physics.

Again—I suppose that the inherent truth behind these disciplines, which appear rigourous and legitmate to the experts that create them, is not something unredoubtable in itself, like claiming that one of the two superficially different modes of philosophy is more enlightened than the other, plus religion and worldly informatics do not necessarily have the same aims. While Aristotle, championed by the Romans and the Church and became the influential standard for scientific investigation, insisted that everything was black and white—everything either was or was not—another, third option was not given, terium non datur, as the Romans called it. Around the same time, Buddha and his disciples were considering a fourth, with the option of a fifth up to the thirty-second degree, option in the range of possibilities by subjecting all question to what’s called catuṣkoṭi, a sort of four corners of being, wherein something is either true and only true, false and only false, partially both or neither true nor false. Concepts like this come across as infuriating often in Western contexts, though many thinkers have touched on this set of logical operators before and they appear contractually in programming and in the maths that allow it. Though on the surface the states of catuṣkoṭi might sound a little like the conjunctions of AND, OR, NOT and XOR, to really start seeing the states as non-contradictory, one can start to think of them in terms of relationship and functions.
The article illustrates this range of connexions through parentage and siblings: mother of is functional since any son or daughter has just one, whereas son of or sister of is relative since there could be any number of permutations, dependent on the family or none at all. This article and discussion is certainly something to step away from and reflect on—rather than reading in one sitting, but it is without a doubt fascinating that mathematicians and logicians came to restore to the same quiver of paradigms as Eastern philosophies, without being some closeted mystic or Buddha-apologist. The fifth option, which could explode into all sorts of other dimensions, is what’s called the ineffable (a pretty neat sounding word): when those paradoxes and fundamental contradictions are handed down to us, seemingly only for the sake of confusion, a kōan—the sound of one hand clapping, we have to admit that it’s an experience too big to get our heads around and thus unspeakable. Presented with this possibilities—that there are things in the cosmos which we cannot articulate or even perceive, certainly seems very real and probably comprises an infinitely bigger part of reality, it seems however that we are just pushing back contradiction by a few powers, which may be significant in itself, by knowing of something that we can’t hope to address or not knowing about it at all.