THE ROLE OF INTUITION IN THE THEORY OF MATHEMATICAL KNOWLEDGE: PHILIP KITCHER'S PERSPECTIVE

Abstract

One of the subjects of study of the philosophy of mathematics has to do with how we access the knowledge of the objects of mathematics, being so abstract objects. In this article, we will show that this form of "access" is intuition, understood as a dynamic process that requires the experience of mathematicians, whose effects will be seen in the concrete world. Starting from the dilemma exposed by Benacerraf, we will review how intuition is a possible solution and how it has always played a leading role in the epistemology of mathematics. Finally, we will review the role of Kitcher's ideas versus the theory of mathematical knowledge and the role of intuition.