Charles Parsons Mathematical Thought and Its Objects

This is the second, revised, version of a section-by-section discussion of Charles Parsons’s eagerly awaited Mathematical Thought and Its Objects (CUP, 2008: pp. xx + 378)1 – though not every section gets the same level of attention. For convenience, the divisions here correspond to the chapter/section divisions of the book. Parsons himself says that his book has been a very long time in the writing. Its chapters extensively “draw on”, “incorporate material from”, “overlap considerably with”, or “are expanded versions of” papers published over the last twenty-five or so years. So what we are reading is a multi-layered text with different passages added at different times.2 This does make for a pretty bumpy read, with the to-and-fro of argument not always ideally well signalled. The prose style can make for hard going too. Consequently, I sometimes am not too confident that I am reading Parsons aright. But let’s dive in . . .