[FOM] inconsistency of P

Timothy Y. Chow tchow at alum.mit.edu
Tue Oct 4 11:22:36 EDT 2011

Harvey Friedman wrote:

>I am reasonably aware of Nelson on this, but my main point is that 
>mathematicians (including Nelson, by the way) seem to regularly use - and 
>teach - facts which logically imply the consistency of at least 
>significant fragments of PA, including PRA, or single quantifier PA.  At 
>least, the former Nelson - and what about Nelson's current math teaching?

I think I indirectly answered this already in my post where I pretended to 
be Nelson (or someone with similar views), but to be explicit: When we 
teach, we play by the rules of the game that society pressures us to play.  
In my soul I am free to believe the truth.  According to the party line, 
PA is consistent, as Nelson well knows, but if you permit him to speak 
freely, he will dissent.

As an aside, lying in calculus class is something we all do in one form or 
another so I don't think Nelson can be ethically faulted for doing so.


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