[FOM] From theorems of infinity to axioms of infinity
Timothy Y. Chow
tchow at alum.mit.edu
Fri Mar 22 20:11:11 EDT 2013
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.
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