Mathematical recreation versus mathematical knowledge
| Abstract | It is often assumed that empiricism in the philosophy of mathematics was laid to rest by Frege’s stinging attack on Mill. I will argue that empiricism is alive and well and able to deal with almost everything that’s thrown at it. In particular, I will show how the brand of empiricism I subscribe to is able to give a satisfying account of mathematical knowledge. This brand of mathematical empiricism has a rather curious feature though: some parts of mathematics (e.g., analysis, modern algebra, ZFC set theory) are taken to be theories about which we have genuine mathematical knowledge, while others (e.g., set theory with large cardinal axioms) are (following Quine) treated as “mathematical recreation”. I will defend this demarcation against some recent criticisms from Mary Leng. | |||||||||
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