I'm not sure you're responding to the same point by the GP. GP claims some truths cannot be proven. You took one claim that could be proven ( https://en.wikipedia.org/wiki/Gentzen%27s_consistency_proof ) and tried to proclaim its truth without referring to the proof.
Even the GP's claim is problematic. The Gödel's theorems don't prove that some truths cannot be proven. It only proves either ZF is inconsistent, or some truths in it cannot be proven.
Ironically GP's implicit assumption that ZF is indeed consistent mirrors your response in which you claim Peanno is consistent... :D
That said, if you somehow proved that "some truths cannot be proven within a fixed formal axiom system (that is sufficiently powerful)", and then you also take into account the Church-Turing thesis, i.e. that Turing machines can fully model our thoughts, then the proof of the claim about "some truths cannot be proven" is more or less complete.
Of course you can always posit the existence of some "unknown unknowns" that are outside of our wildest imaginations and thus invalidating whatever we thought we have known. But that's outside of our current ability to reason.
I could go on and talk about what I understand about divine inspiration and knowledge, but I suppose those topics are a bit too speculative for the crowd here...
> I could go on and talk about what I understand about divine inspiration and knowledge, but I suppose those topics are a bit too speculative for the crowd here...
Even the GP's claim is problematic. The Gödel's theorems don't prove that some truths cannot be proven. It only proves either ZF is inconsistent, or some truths in it cannot be proven.
Ironically GP's implicit assumption that ZF is indeed consistent mirrors your response in which you claim Peanno is consistent... :D
That said, if you somehow proved that "some truths cannot be proven within a fixed formal axiom system (that is sufficiently powerful)", and then you also take into account the Church-Turing thesis, i.e. that Turing machines can fully model our thoughts, then the proof of the claim about "some truths cannot be proven" is more or less complete.
Of course you can always posit the existence of some "unknown unknowns" that are outside of our wildest imaginations and thus invalidating whatever we thought we have known. But that's outside of our current ability to reason.
I could go on and talk about what I understand about divine inspiration and knowledge, but I suppose those topics are a bit too speculative for the crowd here...