Wittgenstein and Stenlund on Mathematical Symbolism

Abstract

In recent work, Sören Stenlund (2015) contextualizes Wittgenstein’s philosophy of mathematics as aligned with the tradition of symbolic mathematics. In the early modern era, mathematicians began using purely formal methods disconnected from any obvious empirical applications, transforming their subject into a symbolic discipline. With this, Stenlund argues, they were freeing themselves of ancient ontological presuppositions and discovering the ultimately autonomous nature of mathematical symbolism, which eventually formed the basis for Wittgenstein’s thinking. A crucial premise of Wittgenstein’s philosophy of mathematics, on this view, is that the development of mathematical concepts is independent of any ontological implications and occurs in principle without normative connections to empirical applicability. This paper critically examines this narrative and arrives at the conclusion that Stenlund’s view of mathematical progress is in stark contrast to the later Wittgenstein’s writing, which emphasizes links between symbolisms and their applications.