Realism on Thin Ice: An Argument from Mathematical Practice

(Logic/Philosophy of Mathematics, Englisch)

n Maddy (2011), Penelope Maddy introduces two methodologically equivalent but philosophically distinct positions which presumably respect set-theoretic practice; termed Thin Realism and Arealism, the former has a realist bent and the latter an anti-realist one. Since both positions agree on the level of method, Maddy concludes that for her idealized naturalistic inquirer, who practices an austere version of naturalism dubbed Second Philosophy, there is no substantive difference between the two positions. I argue that Thin Realism loses its tenability when extended beyond set-theoretic practice and toward broader mathematical practice. Additionally, I submit that the issues presented for Thin Realism are not issues for Arealism. Central to my argument is the observation that mathematicians approach problems in everyday practice from multiple foundational vantage points. Moreover, I consider various foundational goals proposed in Maddy (2017) and demonstrate that none of them force a whole-hearted endorsement of one foundation over another.

From here, the problem for Thin Realism is presented in the form of a dilemma. The first horn is that if the Thin Realist accepts ontological pluralism, then this is at odds with the putative unity of mathematical practice. Thus, she is charged with showing how engaging in mathematical practice from different foundational approaches does not lead to what Quine terms a change of subject. The second horn is that if she rejects ontological pluralism, then she must do so by appeal to some epistemological faculty other than the methods of working mathematicians. However, this takes the Thin Realist beyond her epistemological standards. In turn, this presents a naturalistic way to undermine Maddy's conclusion that Thin Realism and Arealism are two equally admissible ways of describing the underlying constraints of mathematical practice for the Second Philosopher.

Chair: Leon Commandeur

Zeit: 10:40-11:10, 09. September 2022 (Freitag)

Ort: SR 1.006

Anmerkung: (Online Talk)

Jared Ifland

(Florida State University, United States)

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