On a Certain Conception of Philosophy of Mathematics

Abstract

The article takes up the problem of the possibility and usefulness of philosophy of mathematics for grounding mathematics itself. It shows that neither taking the formal attitude of mathematical logic nor the theory of its foundations are sufficient to explain the status of mathematics and putting it in its proper place in the whole of culture. A certain comprehensive conception of philosophy of mathematics is proposed here which takes into consideration the peculiarity of mathematics in epistemological-methodological and ontological respect. The conception is rooted on the one hand in the properly understood philosophy of science and on the other hand in such an approach to methodological problems which demands philosophical complement.

The conception presented here originates from the accepted pluralism of types of knowledge and from the maximalistically understood philosophy of the classical type. It turns out that such a philosophy offers a chance of taking up philosophical problems connected also with mathematics in order to fully present the uniqueness and peculiarity of both mathematical cognition and mathematics approached from the objective side.