Elucidations Episode 82: Robert May discusses Frege and the problem of identity
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Apr 13, 2016 In this engaging discussion, Robert May, a Distinguished Professor of Philosophy and Linguistics at UC Davis, delves into Frege's groundbreaking ideas on identity. He unpacks how Frege seeks to reduce arithmetic to logic, exploring the intricate relationship between statements like 'A equals A' versus 'A equals B.' The conversation highlights Frege's distinctions between sense and reference, and how individual cognitive processes shape our understanding of truth. May emphasizes the overarching significance of identity in philosophy, touching upon its implications across logic, language, and metaphysics.
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Frege's Logicism and the Problem of Identity
- Frege aimed to reduce arithmetic to logic, arguing that mathematical equality is a form of object identity.
- This raised a problem: if 2 + 3 = 5 is an object identity, how does it differ from the trivial 5 = 5?
Frege's Puzzle: A Cognitive Issue
- Frege argued that 2 + 3 = 5 and 5 = 5 have different content; the former shows 5 as a sum.
- He reframed the problem as a cognitive one: how do we recognize this difference in content?
Sense and Reference
- Frege distinguishes between sense (mode of presentation) and reference (object referred to).
- 2 + 3 and 5 have the same reference (5) but different senses, explaining the non-triviality of 2 + 3 = 5.