Wittgenstein and Stenlund on Mathematical Symbolism

Martin Gullvåg Sætre

doi:10.15845/nwr.v12.3642

Authors

Martin Gullvåg Sætre University of Bergen

DOI:

https://doi.org/10.15845/nwr.v12.3642

Keywords:

Wittgenstein, symbolic mathematics, ontological mathematics, symbolism, mathematical symbolism, mathematical progress

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.

Author Biography

Martin Gullvåg Sætre, University of Bergen

Martin Gullvåg Sætre completed his PhD at the University of Bergen in December 2023, where he was a member of the project Mathematics with a Human Face: Set Theory within a Naturalized Wittgensteinian Framework. His dissertation, Wittgenstein on the Anthropological Grounds of Mathematics, explored the later Wittgenstein’s writings and lectures on mathematics, positioning them within Wittgenstein’s anthropologically oriented philosophy.

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