Thursday, January 20, 2005

Euclid's Fifth

Axiom 5 (Cf. Euclid's Fifth-- Postulate, Symphony, or Amendment): For every universe of discourse, and every paradigm not in that universe of discourse, there exists (a) none (b) at most one (c) one and only one (d) at least one (e) more than one (f) a countably infinite cardinality (g) an uncountably infinite cardinality of universes of discourse coincident with that paradigm, and parallel to the first universe of discourse.

The Commentary on Axiom 5: Choose one, (a) through (h), like picking up off the ground one acorn out of thousands. In the first analysis your choice is free, but to be informed by it is to be bound, and to be bound by it is to be informed. You are what you geometrize, but in the final analysis the geometry, like the joke, is on you. Plato: ho theos geometrizei. Mighty oaks from little acorns. The oak, like the joke, is on you. Aristotle: Entelechy! (Humpty Dumpty: "Impenetrability!") So in the final analysis (but only in the final analysis) you cannot plead the Fifth.



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