Understanding in mathematics. From classics to non-classics and post-non-classics. Article two

Abstract

The article deals with the issue of understanding in the classical, non-classical and post-non-classical traditions and their realization in understanding of mathematics. The understanding of mathematics is considered on the example of the works of L. Wittgenstein and J. Deleuze. For the nonclassical author Wittgenstein, mathematics is a rule-based activity akin to the language game. Deleuze did not write directly about mathematics, but we can take his idea of the autonomy of discourse, its independence from the subject. Senses appear by themselves in the play of other senses. It happens not through intuition and not through the game of the subject, but through the interaction of the senses themselves. Mathematics has its own plane of immanence: mathematical discourse. A comparison is made between the ideas of Deleuze and those of the fictionalist H. Field: it is shown that Field could as well speak about the discourse. However, the question of the ontological status of logic (as opposed to mathematics) remains open. It is impossible to solve it in the non-classical theories of understanding. The Wigner’s question about the effectiveness of mathematics in the natural sciences also remains open.