[FOM] Paradoxicality and normal-form proofs

[wiman lucas raymond]

>In other words, bivalence demands that the sentence be either true or
>false, but there seems to be no human way of knowing which it is that
>could be derived from this sentence itself.  Assuming that 'true' is a
>predicate within the One Language, then, 'This sentence is true'
>provides a simple example of a sentence whose truth-value 
>fundamentally outstrips our ability to verify or falsify it. 

I recently saw an interview with Noam Chomsky from the early seventies.
He suggested that if the universal grammar of language were sufficiently
understood, then we would start to find problems which could not be
solved in our framework of thought.  He was specifically referring to
the question of human freedom, which, he pointed out, has been around as
long as the question of explaining the way that bodies fall.  The latter
has been very close to totally solved, and for the former, Greek
philosophers knew about as much as we do now.  This paradox problem
seems to be another (in some senses less trivial) example.

- Lucas Wiman