[FOM] From theorems of infinity to axioms of infinity

[Timothy Y. Chow]

Nik Weaver wrote:

>So if you're wedded to the language of set theory I don't object.
>Personally I feel that if one is working at this level of specificity
>then third order arithmetic is a little nicer.

The way you phrased this makes it sound like sets can be dispensed with in 
favor of pure arithmetic.  But the natural interpretation of "third-order 
arithmetic" is in terms of sets of sets of integers.

Your arguments would make more sense if you were to direct your criticism 
against ZFC in particular.  As it stands, you are making blanket 
statements against "set theory" in general that amount to shooting 
yourself in the foot.

Tim