Wittgenstein's critical Philosophy of Mathematical Practice

Abstract On the one hand, I show that the later Wittgenstein's practice‐based approach to meaning, including the idea that the meaningfulness of mathematics ultimately is rooted in the everyday ‘applications’ it emerged from, as well as his insistence on the variability in and contingency of mathematical and mathematics‐like practices, foreshadows more recent work in Philosophy of Mathematical Practice (PMP), although Wittgenstein's approach was more radically practice‐based than what is prevalent in present‐day PMP. On the other hand, I also show that Wittgenstein's work on mathematics is driven by a pervasive critical attitude towards some key characteristics (monism, foundationalism and exceptionalism) of mainstream philosophical discourse about mathematics (then and now), which is mostly absent from present‐day PMP, and I argue that this aspect of Wittgenstein's work on mathematics could inspire present‐day practitioners of PMP to rethink the identity of their discipline.