Philosophy of Mathematics Seminar (Monday - Week 4, HT25)

Abstract: I argue Frege had an unappreciated line of argument against using Hume's Principle as a foundational logical axioms, the starting point of the neo-Fregean logicist programme. The line of argument comes from Frege's letters to David Hilbert. I use this connection to level Frege's objections against Hilbert to Hale and Wright and ultimately give a new explanation of the Caesar problem. I conclude that Frege has all along given us, if not the numbers, at least the key diagnostic objection for why Hale and Wright are unable to establish both platonism and logicism.