Neofregeanism and structuralism are among the most promising recent approaches to the philosophy of mathematics. Yet both have serious costs. We develop a view, structuralist neologicism , which retains each’s central advantages while avoiding their more serious costs. e key to our approach is explicating the reference of numerical terms, introduced by Hume’s principle, in terms of arbitrary reference. is allows us to treat Hume’s principle as an implicit denition serving to determine all (known) properties of the numbers (achieving a key neofregean advantage), while preserving the key structuralist advantage that which objects play the number role doesn’t matter.
Philosophy of Mathematics Seminar Convenors: Dr James Stud, Dr Daniel Isaacson, and Prof Volker Halbach