[FOM] Fwd: invitation to comment (charlie)

[Timothy Y. Chow]

Charlie Silver wrote:
>  To me, the question of whether numbers exist is really a question about 
>  whether abstract entities exist (unless you can arrive at a principled 
>  way to separate some abstract entities from others).

There's a distinction here between whether individual numbers such as 12 
and 15 exist, and whether an infinite totality of numbers exists.  I agree 
that if one doubts whether the number "12" exists then one must equally 
doubt whether the symbol "=" exists.  If one doubts that an infinite 
totality of numbers exists then one must also doubt that an infinite 
totality of proofs or formulas exists.

It doesn't follow, however, that doubting the existence of an infinite 
totality of proofs or formulas forces one to doubt the existence of finite 
collections of them, or of rules of inference that are tacitly understood 
to apply only if certain feasibility conditions are met.

Tim