{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,15]],"date-time":"2025-11-15T17:18:40Z","timestamp":1763227120536},"reference-count":52,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2022,4,8]],"date-time":"2022-04-08T00:00:00Z","timestamp":1649376000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["The Review of Symbolic Logic"],"published-print":{"date-parts":[[2023,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>One prominent criticism of the abstractionist program is the so-called <jats:italic>Bad Company<\/jats:italic> 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\u2019s 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 <jats:italic>stable<\/jats:italic>: when it can be made true on all sufficiently large domains. In this paper, we raise a worry for this response to the Bad Company objection. We argue, perhaps surprisingly, that it requires very strong assumptions about the range of the second-order quantifiers; assumptions that the abstractionist should reject.<\/jats:p>","DOI":"10.1017\/s1755020322000144","type":"journal-article","created":{"date-parts":[[2022,4,8]],"date-time":"2022-04-08T08:31:10Z","timestamp":1649406670000},"page":"1158-1176","update-policy":"http:\/\/dx.doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":2,"title":["HUME\u2019S PRINCIPLE, BAD COMPANY, AND THE AXIOM OF CHOICE"],"prefix":"10.1017","volume":"16","author":[{"given":"SAM","family":"ROBERTS","sequence":"first","affiliation":[]},{"given":"STEWART","family":"SHAPIRO","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2022,4,8]]},"reference":[{"key":"S1755020322000144_r23","doi-asserted-by":"publisher","DOI":"10.1007\/BF00627774"},{"key":"S1755020322000144_r29","doi-asserted-by":"publisher","DOI":"10.1093\/acprof:oso\/9780199273669.001.0001"},{"key":"S1755020322000144_r8","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1093\/oso\/9780198236542.003.0015","volume-title":"The Philosophy of Mathematics Today","author":"Dummett","year":"1998"},{"key":"S1755020322000144_r31","first-page":"294","article-title":"Les math\u00e9matiques et la logique","volume":"14","author":"Poincar\u00e9","year":"1906","journal-title":"Revue de M\u00e9taphysique et de Morale"},{"key":"S1755020322000144_r4","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1093\/oso\/9780198239208.003.0009","volume-title":"Language, Thought, and Logic","author":"Boolos","year":"1997"},{"key":"S1755020322000144_r35","unstructured":"[35] Roberts, S. 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