Event Detail

The aim of this talk is to show that when we shift our focus from solving philosophical problems to solving mathematical ones, we see that an as-if interpretation of mathematics can be used to provide an account of both the practice and the applicability of mathematics. I begin first with Plato to show that much philosophical milk has been spilt owing to our conflating the method of mathematics with the method of philosophy. I then use my reading of Plato to develop what I call as-ifism, the view that, in mathematics, we treat our hypotheses as if they were true first principles and we do this with the purpose of solving mathematical problems not philosophical ones. I next extend as-ifism to modern mathematics wherein the method of mathematics becomes the axiomatic method, noting that this engenders a shift from as-if hypotheses to as-if axioms. I next distinguish as-ifism from if-thenism, and use this to develop my structural as-ifist position. I end by showing that taking a methodological as-ifist route, by placing our focus on what is needed for the practice and applicability of mathematics, we are neither committed to the unconditional consistency of our mathematical axioms nor the unconditional truth of our background meta-mathematical theory. Simply, it is methodological considerations, and not metaphysical ones, that “condition” our as if assumptions of both the consistency of our mathematical axioms and the truth of our background meta-mathematical theory.