HUME’S PRINCIPLE, BAD COMPANY, AND THE AXIOM OF CHOICE | The Review of Symbolic Logic | Cambridge Core
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HUME’S PRINCIPLE, BAD COMPANY, AND THE AXIOM OF CHOICE - Volume 16 Issue 4
Abstract One prominent criticism of the abstractionist program is the so-called Bad Company objection. The complaint is that abstraction principles cannot in general be a legitimate way to introduce mathematical theories, since some of them are inconsistent. The most notorious example, of course, is Frege’s Basic Law V. A common response to the objection suggests that an abstraction principle can be used to legitimately introduce a mathematical theory precisely when it is stable: when it can be made true on all sufficiently large domains. In this paper, we raise a worry for this response to…
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