``PA is consistent'' - Was Re: [FOM] Proof "from the book"

Matt Insall montez at fidnet.com
Thu Sep 2 13:18:45 EDT 2004

Arnon Avron wrote:
<<That "if S is consistent then G is true" is provable not only in S (which
might prove false sentences), but also in PA (which proves only true

Are you saying that PA is (definitely) consistent?  If not, then I
misunderstand you, for it seems to me that only consistent theories have the
property you claim for PA above:  ``proves only true sentences''.
(Exercise:  Can a consistent theory prove a false sentence?)  If you are
claiming that PA is (known to be) consistent, then how does your proof of
the consistency of PA go?  In what theory does your proof reside?

Dr. Matt Insall
Associate Professor of Mathematics
Department of Mathematics and Statistics
University of Missouri - Rolla
Rolla MO 65409-0020

insall at umr.edu

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