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One of the more distinctive features of Bob Hale and Crispin Wright's neologicism about arithmetic is their invocation of Frege's Constraint – roughly, the requirement that the core empirical applications for a class of numbers be " built directly into " their formal characterization.In particular, they maintain that, if adopted, Frege's Constraint adjudicates in favor of their preferred foundation – Hume's Principle – and against alternatives, such as the Dedekind-Peano axioms. First, we show that, if sound, Hale and Wright's arguments for Frege's Constraint at most establish a version on which the relevant application of the naturals is transitive counting – roughly, the counting procedure by which numerals are used to answer " how many "-questions. from Rutgers University in 1998 and held appointments at King's College London and the University of Pennsylvania before joining the OSU Philosophy Department in 2007.In recent years, philosophical theories of reasoning in general, and logical inference in particular, have been heavily influenced by a regress argument, which purports to undermine a general conception of reasoning that has widespread acceptance amongst psychologists, and cognitive scientists –what we call the intentional, rule-following account.Instead of the traditional round patty found in competing fast-food outlets, Wendy's patty was square and sized so its edges would stick out over the edge of the round bun.
Specifically, we argue that a range of received accounts of psychological processes in cognitive science have the resources to address the regress.In June 1975, the 100th Wendy's opened in Louisville, Kentucky. December 1976 saw Wendy's 500th open in Toronto, Canada.In 1977, Wendy's went national with its first network television commercial, making it the first restaurant chain with less than 1,000 units to mount a national advertising campaign.Second, we show that this version of Frege's Constraint fails to adjudicate in favor of Hume's Principle.If this is the version of Frege's Constraint that a foundation for arithmetic must respect, then Hume's Principle no more – and no less – meets the requirement than the Dedekind-Peano axioms do.
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