Bad company generalized

Synthese 170 (3):331 - 347 (2009)
The paper is concerned with the bad company problem as an instance of a more general difficulty in the philosophy of mathematics. The paper focuses on the prospects of stability as a necessary condition on acceptability. However, the conclusion of the paper is largely negative. As a solution to the bad company problem, stability would undermine the prospects of a neo-Fregean foundation for set theory, and, as a solution to the more general difficulty, it would impose an unreasonable constraint on mathematical practice.
Keywords Abstraction  Abstraction principles  Bad company  Extension  Frege  Stability  Structuralism
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