I will ask the question first and then explain. QUESTION: FPA can prove its own consistency in the Godelian sense. But can it really prove its consistency? FPA is a multi-sorte …

Consider second-order Peano Arithmetic Z2, i.e. the two-sorted first-order theory with induction and comprehension. Remove the assumption about the totality of the successor relat …

Hilbert's program is popularly understood as an attempt to justify infinitary mathematics with a finitary consistency proof. Godel's Second Theorem is usually considered as showin …

Does there exist a set theory T-which has not yet been proved to be inconsistent-and in which one can prove the existence of (1) the empty set (2) sets that are singletons and (3) …

Ultrafinitism is (I believe) a philosophy of mathematics that is not only constructive, but does not admit the existence of arbitrarily large natural numbers. According to wikiped …

According to constructivism a mathematical object to prove that it exists". There are several formulas to calculate pi, such as: so I take it pi exists according to constructiv …

At the end of the paper Division by three by Peter G. Doyle and John H. Conway, the authors say: Not that we believe there really are any such things as infinite sets, or that the …

I remember attending a lecture given by an ultrafinitist who denied that curves are a set of points, he would only say that any particular point may or not be on the curve. Similar …

Nelson's predicative arithmetic (survey article) is a very weak system of arithmetic extending Robinson's $Q$ (Wikipedia). We can have natural number objects in a topos, or even …

Possible Duplicate: Is there any formal foundation to ultrafinitism? Very recently I have come across the skeptic opinions of a school of mathematicians(ultrafinitist) ove …

Before I ask my question, let me give you a mini-preamble: in 2006, during an animated discussion on feasibility, ultrafinitism, and what else on FOM, I introduced (informally, and …