Godel's Theorem Diagrams

Illustrates the mathematical principles involved in finite and infinite proofs.

Godel's Proof fails for a lack of comparison to a mechanical or electrical device which is dependant upon the transmission of energy to function properly and arrive at a distinction between "TRUE" and "FALSE" at the conclusion of the proof. Just as a finite voltage cannot be extended through an infinitely long circuit, or a mechanical drive cannot power a mechanism on the other side of an infinite number of moving parts, energy being reduced by resistance or friction respectively, Godel's Proof requires a traverse of an infinite Abyss.

As the number of steps (N) introduced in a finite proof increases, the distinction between true and false becomes increasingly more difficult to discern, or at least the confidence placed in the entire assemblage begins to diminish. An infinite "proof" then requires that each step follow perfectly from those preceding it, rendering it increasing likely that a tactical or strategic mistake has been made. This is the case in Godel's Proof, though it may not be immediately apparent. Godel's Proof involves a "twist" at the end, turning "#### = G" into "####' = ~G". As this step has not proceeded logically from any previous step, I argue that it introduces a value of N=oo (infinity). As the diagram above attempts to illustrate, that makes for a situation in which "true" and "false" are instrumentally, observationally, and therefore "logically" equivalent. Note that the same would be true for Cantor's Diagonal Slash, but more successfully, as a proof of a finite number of numbers in a given interval would be possible in a finite proof, but fails to materialize in a finite number of steps.