[FOM] Fwd: invitation to comment (charlie)
Timothy Y. Chow
tchow at alum.mit.edu
Mon Oct 10 18:19:20 EDT 2011
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.
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