Sunday, 26 December 2021

Kant's antinomies precede Gödel's incompleteness theorem by exactly 150 years, and are perhaps more profound and less widely understood. In knowing that you don't know you might take a step back in dogma but you also take a step forward in intellectual hubris, so that the idea of a method, a universal method presents itself. Such a method may never be fully carried through but it appears to contain the potentiality to resolve all questions. To show that the method itself, in its strongest and most developed form will inevitably founder on certain fundamental questions which it is incapable of resolving either way, is an immense step beyond this hubristic faith. Unlike Gödel, Kant's incompleteness proof does not invoke phantoms of self-reference. This makes it more thorough, but historically it left the door open for various spectres of self-reference in German idealism to appear to bridge the unbridgeable gap revealed by Kant. Perhaps computational theories of consciousness purport to do as much for Gödel.

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