Sunday, April 23, 2017

Contemporary math and Buddist catuskoti

Another one from the archive.

Here is Graham Priest's study of contemporary mathematical logic as applied to the catuskoti. One of my comments on it is here, following:

Priest discusses relations and functions regarding truth values. The Aristotelian principles against contradiction, i.e., the excluded middle and non-contradiction, rely on the function of truth values. Priest's solution around this is to make them relation values. But when it comes to Buddhist emptiness he seems to mix and match functions and relations. On one hand emptiness is based on relations, since nothing has an inherent existence but is conditioned by its relations to other things. But on the other hand it is also based on a function because the previous relations apply only to conventional reality; ultimate reality per this other Priest article posit is as "pure form" (11), itself a preconditional function for conventional reality.
I.e., the relation between the truth values of relations and functions is itself a function. Which is of course Gorampa's assertion in an actual ultimate versus a nominal ultimate, where this function is metaphysical. Whereas Tsongkapa's assertion is that the relation between the truth values of relations and functions is itself a mutual relation, i.e., these two truths about emptiness themselves require that their interaction be relational. Emptiness in this case is not a metaphysical actual ultimate in opposition to conventional reality. The paradox is that this relation is also a function in that this is an ultimate(um) on the nature of existence, so it is both and neither a function and/or relation in the Aristotelian sense.

And as I stated earlier in the thread, this whole mess is clarified by differance, which is itself a transcendental precondition for, or function of, relational and conventional existence. Yet it is not metaphysical in the sense of being transcendent of said conventional existence, itself also dependently arisen from said existence and thus also a relational truth value. All very twisted and folded.

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