[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
inference."
Tim
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