Re: Meyer's Argument against Gödel's Theorem



MoeBlee wrote:
jeffreykeg...@xxxxxxxxx wrote:

Gödel noticed that arithmetic cannot prove its own consistency.
This (the fact that there is something arithmetic cannot prove) is
a meta-proof that arithmetic is consistent.

No, we have: IF PA (or whatever system rich enough for a certain
amount of arithmetic) is consistent THEN PA does not prove its own
consistency.

This is indeed the content of Godel's second incompleteness theorem,
as I said in another post. But isn't some business at the end of his
paper where he writes something like "Thus, the formula is decided by meta-mathematical
means"?

That in itself is not a proof of the consistency of PA,
since in itself it does not reveal that there is a formula that PA
does not prove but only that IF PA is consistent THEN there is a
formula that PA does not prove, which is known already anyway. So a
proof of the consistency of PA must come from some other means.

--
hz
.

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