Re: 2nd paradox in Godels incomplertenes theorem that makes it inval

On Oct 22, 4:19 pm, translogi <wilem...@xxxxxxxxxxxxxx> wrote:
(In FOL you cannot make a sentence, that asserts its own un
provability)

YES, YOU CAN.
That is exactly what Godel's first incompleteness theorem does.
And you CAN do that in first-order PA, or even in slightly weaker
systems.

Of course, "exactly" is over-reaching a little, there.
There are models of PA in which the sentence in question
arguably does NOT mean "I am not provable". But it clearly
does mean that in the STANDARD model.

Still you are slightly right in that the whole import of the
result (of G1Inc.) is that there must be other models with
non-standard (contrarian, infinitary) takes on "provability".
Even those models, however, agree that no finite proof G1
is available. They just sort of can't quite *say* that (in the
language of PA).


.

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