Re: Godel's comments about the "true reason" for incompleteness

Re: Mar 20, 10:55 am, "R. Srinivasan" <sradh...@xxxxxxxxxx>:

After having responded to that post, I think it would help to focus on
just, say, two of the most obviously ridiculous things in it:

Now think of the following situation. Let us add P&~P-->Q (and only
this single sentence, where P and Q are arbitrary) into the language
of PA,

Please get back after you've consulted a logic book to see that it
makes no sense to say that we add just a single sentence to a
language.

If
P&~P->Q has been translated to a formula S in the first-order language
of PA, and if PA proves S, are you denying that PA has *effectively*
proven itself consistent?

Please get back after you've consulted a book on logic to see that a
theory proving a tautology (or even just a contingency) does not
entail that the theory is consistent, and not anywhere in the
imagination of anyone but the most bitterly confused does it entail
that the theory has ""effectively" proven ITSELF consistent".

MoeBlee
.