[FOM] Godel Sentence

[Richard Grandy]

Arnon Avron writes

>Fixing Con(T) is begging the question. As I wrote in a previous message,
>I would like to know, e.g,, whether there is any ground to assume that
>something like (say) Goldbach conjecture cannot be equivalent
>to a sentence that we may take as naturally expressing Con_T. Your talk

You are asking about changing the underlying logic--if we instead ask 
about changing the axioms there is a cheap way of getting a positive 
answer.  Consider the system obtained by adding Goldbach's conjecture 
to Peano Arithmetic.  That system is consistent iff* Goldbach's 
conjecture is true.
-- 

Richard Grandy
Philosophy & Cognitive Sciences
Rice University
Houston, TX USA

*Assuming PA is consistent, but if PA is inconsistent we have larger 
questions to consider.