On 5/17/2017 3:27 AM, Bruno Marchal wrote:
Exactly. I might try to add some possible mathematical precision, but
I need to think a bit on this. Later. Up to now, the B of Bp & p is
interpreted by its computational rendering, but "B" is really
provability, and not computation. Up to here, that absence of
distinction works well (indeed for a very deep and subtle reason
related to Mechanism), but for the precision I want to add, I will
need to make the distinction.
Are you, and others, OK with those facts:
RA cannot prove the consistency of RA. PA cannot prove the consistency
of PA, etc.
But:
PA can prove the consistency of RA.
Now the key fact which I intend to use is that RA can prove that PA
can prove the consistency of RA. In fact RA can prove also that F can
prove the consistency of PA, and of RA.
What is F?
Despite this RA cannot be convinced that those facts prove its own
consistency (by incompleteness).
Are you going to introduce a new modal quantifier "convinced". I
already find the equivocation between B=believes, B=proves, B=computes
obfuscating.
Brent
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