Abstract

The initial goal of the present paper is to reveal a mistake committed by Hintikka in a recent paper on the foundations of mathematics. His claim that independence-friendly logic is the real logic of mathematics is supported in that article by an argument relying on uniformity concepts taken from real analysis. I show that the central point of his argument is a simple logical mistake. Second and more generally, I conclude, based on the previous remarks and on another standard fact of IFL, that first-order logic can adequately express uniformity concepts in real analysis, whereas IFL cannot. This not only radically contradicts Hintikka’s particular claim in that article, but also undermines his whole enterprise of founding mathematics on his logic system