On 3/14/2013 7:32 PM, david petry wrote: > On Thursday, March 14, 2013 11:38:51 AM UTC-7, fom wrote: > >> More precisely, mathematical facticity relative to >> the epistemic justification of a derivational system >> is more important than mathematical actuality relative >> to dialectical argument. > > > "liberal (and even some socialist) mathematicians are often > content to work within the hegemonic Zermelo?Fraenkel framework > (which, reflecting its nineteenth-century liberal origins, > already incorporates the axiom of equality) supplemented only > by the axiom of choice" ( A. Sokal, "Transgressing the Boundaries: > Towards a Transformative Hermeneutics of Quantum Gravity") >
That is a very humorous quote from my point of view.
When I tried to publish, it was with a paper entitled "A Formal Description of Identity".
Among all of the possible statement concerning a philosophy of mathematics that you could have chosen, the one you did is exactly the negation of my philosophy.
The very objection I have to Zermelo-Fraenkel set theory is the manner in which the identity predicate is employed. I do not view the axiom of extension as foundational.