IF logic and the fundamentals of mathematics

Abstract

The aim of this paper is to scrutinize Hintikkas's affirmation wich claims that true elemental logic is not classical logic, but IF logic. Thus, the framework in which the relation between logics and mathematics is ordinarily thought is completely inadequate. In order to achieve this goal, we expose the functions or characteristics that a logic must have, and secondly, we present the constitutive ideas of the IF logic. Further ahead we demonstrate some of the mathematical properties of the IF logic and analyze the complexities which result from the negation in this system. At the end, we offer some reasons to contextualize and to question the conclusions which Hintikka obtains from his proposal for a philosophy of mathematics.