Frege’s Constraint and the Nature of Frege’s Foundational Program (original) (raw)
2018, The Review of Symbolic Logic
Recent discussions on Fregean and neo-Fregean foundations for arithmetic and real analysis pay much attention to what is called either ‘Application Constraint’ ($AC$) or ‘Frege Constraint’ ($FC$), 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 ACACAC generalizes Frege’s views while FCFCFC comes closer to his original conceptions. Different authors diverge on the interpretation of FCFCFC and on whether it applies to definitions of both natural and real numbers. Our aim is to trace the origins of FCFCFC and to explore how different understandings of it can be faithful to Frege’s views about such definitions and to his foundational program. After rehearsing the essential elements of the relevant debate (§1), we appropriately distinguish ACACAC from FCFCFC (§2). We discuss six rationales which may motivate the...
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