Liczba, wielkość, miara

Abstract

In this article, I tackle the problem of the ontological status of mathematics. I dispute the positions of two schools of thought; namely, the Platonists (for example, Roger Penrose, who places the subject of mathematics in his Platonian world of mathematical ideas), and the constructionists (such as John Stewart, for whom the whole mathematics consists of abstractions). Mathematics – in my view – consists in a search for the Aristotelian form in reality, which explains its unique and the otherwise unbelievable effectiveness in describing the world. This latter quality cannot be explained on the basis of the two positions I criticize.