Acquiring mathematical concepts: The viability of hypothesis testing. (19th November 2019) - Buijsman, Stefan
Abstract : Can concepts be acquired by testing hypotheses about these concepts? Fodor famously argued that this is not possible. Testing the correct hypothesis would require already possessing the concept. I argue that this does not generally hold for mathematical concepts. I discuss specific, empirically motivated, hypotheses for number concepts that can be tested without needing to possess the relevant number concepts. I also argue that one can test hypotheses about the identity conditions of other mathematical concepts, and then fix the application conditions based on those hypotheses—under the assumption that the neo‐logicist view on abstraction principles is correct.