ABSTRACT
This chapter provides a brief description of John Stuart Mill's philosophy of mathematics. It explains why Mill's view cannot account for contemporary mathematics or even the mathematics of his own day. The chapter also explains what Mill should have said about mathematics, given his background philosophical commitments. It concerns Mill's view of arithmetic, but it also describes about the view of geometry. Mill is committed to a certain view of the semantics of the language of arithmetic. In particular, he is committed to the idea that the sentences of arithmetic are about physical objects. Mill could have endorsed in connection with mathematics that would have been consistent with both: his background philosophical commitments; and the actual facts about mathematical practice. Mill should have endorsed mathematical fictionalism. If he had done this, he could have hung onto views like naturalism, anti-platonism, empiricism and so on while providing a much more satisfying and plausible theory of mathematics.
