[FOM] Wittgenstein Inspired Skepticism

Timothy Y. Chow tchow at alum.mit.edu
Tue Feb 28 15:58:31 EST 2017

Thomas Klimpel wrote:

> But the official retreat is (or at least has been for a long time) ZFC, 
> no? In addition to the consistency line of defence related to Turing 
> machines, also the von Neumann cumulative hierarchy justification can be 
> evoked. And the "primacy" of first order logic might be evoked too, 
> which also goes a bit beyond Turing machines.

I would instead say that ZFC is what is commonly cited when people are 
*not* in "retreat mode."  Retreat mode is triggered if someone questions 
the axiom of choice, or the reality of infinite sets, or the consistency 
of PA, or the existence of arbitrarily large integers.  Then the typical 
response is, "Fine, be a skeptic if you must, but at least we all agree 
that these theorems follow from these axioms according to these rules of 


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