[FOM] inconsistency of P

[Timothy Y. Chow]

On Mon, 3 Oct 2011, Aatu Koskensilta wrote:
> When we say that (arbitrarily large) naturals don't really exist, just 
> what are we denying?

I'd say that the way to think about it is to regard mathematical 
statements as physical theories that make predictions about our physical 
experience.  To doubt that arbitrarily large naturals exist is to doubt 
that we are justified in believing that our everyday experience with 
physical quantities of small finite cardinality extrapolates in the 
"obvious" way to physical quantities with arbitrarily large finite 
cardinality.

Similarly, to doubt that there really exists a strongly inaccessible 
cardinal is to doubt (among other things) that we are justified in 
believing that nobody will ever discover a feasible contradiction in ZFC.

Tim