Mathematics and experience

Ladislav Kvasz

pp. 117-129

in: Maria C. Galavotti, Elisabeth Nemeth, Friedrich Stadler (eds), European philosophy of science, Berlin, Springer, 2014

Abstract

Mathematics was considered by the members of the Vienna Circle an a priori discipline consisting of analytic propositions. The aim of the present paper is to draw attention to the experiential dimension of mathematical knowledge. Following the interpretation of physical knowledge as knowledge constituted by the use of instruments, I am trying to interpret also mathematical knowledge as knowledge based on instrumental experience. This interpretation opens a new perspective on the place of the logicist program in philosophy of mathematics. The aim of the present paper is to argue that mathematics is based on experience and that mathematical experience is instrumental. The difference between mathematics and physics is that in the case of mathematics the instruments are not measuring devices but tools of symbolic representation. In order to distinguish the mathematical experience from the physical one (i.e. from the experimental experience), I will call the instrumental experience in mathematics as symbolic experience. In analogy with the measuring devices of physics I will interpret the tools of symbolic representation as tools constituting symbolic experience.