Neo-logicism and Russell’s Logicism

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Most advocates of the so-called “neologicist” movement in the philosophy of mathematics identify themselves as “Neo-Fregeans” (e.g., Hale and Wright): presenting an updated and revised version of Frege’s form of logicism. Russell’s form of logicism is scarcely discussed in this literature, and when it is, often dismissed as not really logicism at all (in lights of its assumption of axioms of infinity, reducibiity and so on). In this paper I have three aims: firstly, to identify more clearly the primary metaontological and methodological differences between Russell’s logicism and the more recent forms; secondly, to argue that Russell’s form of logicism offers more elegant and satisfactory solutions to a variety of problems that continue to plague the neo-logicist movement (the bad company objection, the embarassment of richness objection, worries about a bloated ontology, etc.); thirdly, to argue that Neo- Russellian forms of neologicism remain viable positions for current philosophers of mathematics
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The Metaontology of Abstraction.Hale, Bob & Wright, Crispin
All Things Indefinitely Extensible.Shapiro, Stewart & Wright, Crispin

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