Abstract: In recent decades, empirical issues concerning the actual contents of our mathematical talk and thought have risen to prominence within the philosophy of mathematics, and these issues cannot be adequately addressed independently of our best relevant science. Conversely, there are certain theoretical assumptions which, despite being commonly adopted by number cognition researchers, are philosophically and linguistically contentious. This chapter highlights three of these assumptions, explains why they are suspect, and highlights some important, general lessons for number cognition research these considerations suggest.
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