At the end of “The A-Unicornist Replies. But is scientism still in the picture?” I point out that Mike D’s claim that philosophy is dependent on science stumbles, among other things, on the fact that the nature of scientific enquiry is defined philosophically:
Jones says “science is defined as p.” P is a philosophical assertion about the nature of science. If Mike is correct then the truth of p will be determined at least in part by the deliverances of science. But this is viciously circular since “the deliverances of science” is already determined by whether or not one accepts p and thus the truth of p cannot be decided by the deliverances of science.
This prompted Joseph Palazzo to accuse me of failing to understand Kurt Gödel’s incompleteness theorems. He writes:
Hmmm, your last paragraph — the argument against Jones in which you are using Bertrand’s self-referential proposition — is an indication that you don’t understand Godel’s incomplete theory, an error which I have also pointed out to you in another thread.
Joseph seems to think Gödel’s incompleteness theorems are a pair of magic genies that can be called upon every time a person encounters self-referential incoherence or vicious circularity. However, things don’t work like that. Yes, every axiomatic system needs a starting point of unproved axioms. But that doesn’t mean a person can cry “Gödel, save me!” every time they make a self-contradictory assertion. Unless Joseph wants Christians to cry “Gödel!” every time somebody challenges the coherence of the Trinity or raises the Euthyphro.