Philosophy of Mathematics Seminar (Monday - Week 2, MT24),

Abstract: “Arithmetical structuralism, roughly, is the view that arithmetic is only concerned with the structural properties of numbers. In this talk, I will challenge this view by showing that most (if not all) structuralist accounts do not regard computability-theoretic properties as structural, despite their relevance for arithmetical practice. I will discuss two ways the structuralist may respond to this problem, both of which will be shown to entail undesirable consequences for the structuralist position.”