[FOM] n-th order ZFC

[Roger Bishop Jones]

On Wednesday 13 Jul 2011 11:33, Robert Black wrote:
> 
> .. the fact that you can believe arithmetical
> truths without *thinking that* you are thereby committed
> to the existence of numbers hardly (yet) shows that you
> can believe arithmetical truths without thereby *being*
> committed to the existence of numbers.

Believing A and B is compatible with A entailing not B (and 
therefore my final throwaway line was irrelevant).

However, I reject the idea that belief in any mathematical 
proposition "commits" one to any metaphysical proposition
(and with it Quine's entire position on criteria of 
ontological commitment).

This is a natural consequence of being a logicist in the 
sense of one who holds that mathematical propositions are 
best understood under a semantics which renders them 
analytic.

Roger Jones