Mathematical recreation versus mathematical knowledge

Source abstract

Abstract Empiricism in the philosophy of mathematics has a chequered history. Mill de- fended a version of empiricism according to which the laws of arithmetic were highly general laws of nature. Mathematical truths such as 2+3 = 5 were thought by Mill to be empirical in that they tell us that if we were to take two logic books, say, and three ethics books, say, we’d have five philosophy books. But Mill’s somewhat naive empiricism found itself on the receiving end of a stinging attack from Frege. This attack, I might add, was considered by many to be decisive.