{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:22:27Z","timestamp":1753888947420},"reference-count":54,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2018,12,5]],"date-time":"2018-12-05T00:00:00Z","timestamp":1543968000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["The Review of Symbolic Logic"],"published-print":{"date-parts":[[2019,3]]},"abstract":"Abstract<\/jats:title>Recent discussions on Fregean and neo-Fregean foundations for arithmetic and real analysis pay much attention to what is called either \u2018Application Constraint\u2019 ($AC$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>) or \u2018Frege Constraint\u2019 ($FC$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>), the requirement that a mathematical theory be so outlined that it immediately allows explaining for its applicability. We distinguish between two constraints, which we, respectively, denote by the latter of these two names, by showing how$AC$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>generalizes Frege\u2019s views while$FC$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>comes closer to his original conceptions. Different authors diverge on the interpretation of$FC$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>and on whether it applies to definitions of both natural and real numbers. Our aim is to trace the origins of$FC$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>and to explore how different understandings of it can be faithful to Frege\u2019s views about such definitions and to his foundational program. After rehearsing the essential elements of the relevant debate (\u00a71), we appropriately distinguish$AC$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>from$FC$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>(\u00a72). We discuss six rationales which may motivate the adoption of different instances of$AC$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>and$FC$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>(\u00a73). We turn to the possible interpretations of$FC$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>(\u00a74), and advance a Semantic$FC$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>(\u00a74.1), arguing that while it suits Frege\u2019s definition of natural numbers (4.1.1), it cannot reasonably be imposed on definitions of real numbers (\u00a74.1.2), for reasons only partly similar to those offered by Crispin Wright (\u00a74.1.3). We then rehearse a recent exchange between Bob Hale and Vadim Batitzky to shed light on Frege\u2019s conception of real numbers and magnitudes (\u00a74.2). We argue that an Architectonic version of$FC$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>is indeed faithful to Frege\u2019s definition of real numbers, and compatible with his views on natural ones. Finally, we consider how attributing different instances of$FC$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>to Frege and appreciating the role of the Architectonic$FC$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>can provide a more perspicuous understanding of his foundational program, by questioning common pictures of his logicism (\u00a75).<\/jats:p>","DOI":"10.1017\/s1755020318000278","type":"journal-article","created":{"date-parts":[[2018,12,5]],"date-time":"2018-12-05T08:37:04Z","timestamp":1543999024000},"page":"97-143","source":"Crossref","is-referenced-by-count":10,"title":["FREGE\u2019S CONSTRAINT AND THE NATURE OF FREGE\u2019S FOUNDATIONAL PROGRAM"],"prefix":"10.1017","volume":"12","author":[{"given":"MARCO","family":"PANZA","sequence":"first","affiliation":[]},{"given":"ANDREA","family":"SERENI","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2018,12,5]]},"reference":[{"key":"S1755020318000278_ref43","unstructured":"Sereni A. (manuscript). On the Philosophical Significance of Frege\u2019s Constraint."},{"key":"S1755020318000278_ref45","first-page":"317","article-title":"Frege meets dedekind: A Neologicist treatment of real analysis","volume":"4","author":"Shapiro","year":"2000","journal-title":"Notre Dame Journal of Formal Logic"},{"key":"S1755020318000278_ref21","doi-asserted-by":"publisher","DOI":"10.1093\/acprof:oso\/9780199645268.003.0017"},{"key":"S1755020318000278_ref40","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-26042-6"},{"key":"S1755020318000278_ref10","volume-title":"Die Grundgesetze der Arithmetick","volume":"I\u2013II","author":"Frege","year":"1893"},{"key":"S1755020318000278_ref38","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1515\/9783110378795.357","volume-title":"Mind, Language and Action: Proceedings of the 36th International Wittgenstein Symposium","author":"Peacocke","year":"2015"},{"key":"S1755020318000278_ref4","unstructured":"Boccuni F. & Panza M. (Manuscript). On the logicality of Frege\u2019s definition of real numbers."},{"key":"S1755020318000278_ref26","doi-asserted-by":"publisher","DOI":"10.1093\/mind\/110.440.937"},{"key":"S1755020318000278_ref28","doi-asserted-by":"publisher","DOI":"10.2307\/2184508"},{"key":"S1755020318000278_ref29","volume-title":"Foundations of Measurement","volume":"3","author":"Krantz","year":"1971"},{"key":"S1755020318000278_ref22","unstructured":"Hankel H. (1687). Theorie der Complexen Zahlensysteme [\u2026]. Theil I der Vorlesugen \u00fcber die Complexen Zahlen [\u2026] in Zwei Theilen. 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