HUME’S PRINCIPLE, BAD COMPANY, AND THE AXIOM OF CHOICE

Abstract One prominent criticism of the abstractionist program is so-called Bad Company objection. The complaint that abstraction principles cannot in general be a legitimate way to introduce mathematical theories, since some them are inconsistent. most notorious example, course, Frege’s Basic Law V. A common response objection suggests an principle can used legitimately theory precisely when it stable : made true on all sufficiently large domains. In this paper, we raise worry for We argue, perhaps surprisingly, requires very strong assumptions about range second-order quantifiers; should reject.