Chapter 7 - Conventionalism and Inter-subjectivity

Summary

In Chapter 7, I focus on the ‘conventionalist threat’ against the account presented in this book. I present Warren’s conventionalist account of mathematics and discuss Wittgenstein’s philosophy of mathematics and its debated conventionalism. I identify strict conventionalism according to which mathematical truths are fundamentally arbitrary as the main threat against the present account. I then show that, due to arithmetic’s foundations in the evolutionarily developed proto-arithmetical abilities, my account survives the conventionalist threat. Arithmetical knowledge, under the present understanding, is maximally inter-subjective, which is enough to deal with the threat of arbitrariness. I then discuss the nature of mathematical conventions further, pointing out their importance without succumbing to the view that arithmetic is fundamentally based only on conventions.