From Maximal Intersubjectivity to Objectivity: An Argument from the Development of Arithmetical Cognition

Topoi, vol. 42, pp. 271–281

Abstract

Abstract One main challenge of non-platonist philosophy of mathematics is to account for the apparent objectivity of mathematical knowledge. Cole and Feferman have proposed accounts that aim to explain objectivity through the intersubjectivity of mathematical knowledge. In this paper, focusing on arithmetic, I will argue that these accounts as such cannot explain the apparent objectivity of mathematical knowledge. However, with support from recent progress in the empirical study of the development of arithmetical cognition, a stronger argument can be provided. I will show that since the development of arithmetic is (partly) determined by biologically evolved proto-arithmetical abilities, arithmetical knowledge can be understood as maximally intersubjective. This maximal intersubjectivity, I argue, can lead to the experience of objectivity, thus providing a solution to the problem of reconciling non-platonist philosophy of mathematics with the (apparent) objectivity of mathematical knowledge.

Authors 1

1. Markus Pantsar corresponding Aachen Human Technology Center

   RWTH Aachen University · University of Helsinki

   Affiliation as printed

   Department of Philosophy, History and Art, University of Helsinki, Unioninkatu 40A, 00014, Helsinki, Finland

   Human Technology Center, RWTH Aachen University, Theaterplatz 14, 52062, Aachen, Germany