The Epistemological Subject(s) of Mathematics

In B. Sriraman (ed.), Handbook of the History and Philosophy of Mathematical Practice. Switzerland: Springer Nature. pp. 1-27 (2023)
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Abstract

Paying attention to the inner workings of mathematicians has led to a proliferation of new themes in the philosophy of mathematics. Several of these have to do with epistemology. Philosophers of mathematical practice, however, have not (yet) systematically engaged with general (analytic) epistemology. To be sure, there are some exceptions, but they are few and far between. In this chapter, I offer an explanation of why this might be the case and show how the situation could be remedied. I contend that it is only by conceiving the knowing subject(s) as embodied, fallible, and embedded in a specific context (along the lines of what has been done within social and feminist epistemology) that we can pursue an epistemology of mathematics sensitive to actual mathematical practice. I further suggest that this reconception of the knowing subject(s) does not force us to abandon the traditional framework of epistemology in which knowledge requires justified true belief. It does, however, lead to a fallible conception of mathematical justification that, among other things, makes Gettier cases possible. This shows that topics considered to be far removed from the interests of philosophers of mathematical practice might reveal to be relevant to them.

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Silvia De Toffoli
University School of Advanced Studies IUSS Pavia

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References found in this work

Knowledge and its limits.Timothy Williamson - 2000 - New York: Oxford University Press.
The Structure of Scientific Revolutions.Thomas S. Kuhn - 1962 - Chicago, IL: University of Chicago Press. Edited by Ian Hacking.
Famine, Affluence, and Morality.Peter Singer - 1972 - Oxford University Press USA.
Famine, affluence, and morality.Peter Singer - 1972 - Philosophy and Public Affairs 1 (3):229-243.
What is Justified Belief?Alvin I. Goldman - 1979 - In George Pappas (ed.), Justification and Knowledge. Boston: D. Reidel. pp. 1-25.

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