The paradox of the mathematical discipline: an analysis from formalist materialism

Abstract

This paper formulates and presents attempts to resolve a paradox in the philosophy of mathematics. This paradox is present in the approaches of a wide range of positions, including formalist materialism. This position, eloquently typified by Gustavo Bueno, adheres to the idea that mathematics is a positive science like any other.

Here, the traditional label of «formal science» completely revalorises its meaning. Mathematical activity is carried out by flesh-and-blood subjects, who operate with material symbols rather than purely abstract ideas. Moreover, they have a cultural origin: it is a consequence of a specific historical course, of particular social mechanisms, and of certain forms of instruction and dissemination of knowledge. Mathematics does not naturally proliferate in all human communities.

And yet, truth in mathematics is universal. How is this possible? How can a cultural product be universally true? This is the so-called paradox of the cultural origin of mathematics.