Prolegomenon To Any Future Neo-Logicist Set Theory: Abstraction And Indefinite Extensibility
Author: Shapiro S.
Source: British Journal for the Philosophy of Science, Volume 54, Number 1, March 2003 , pp. 59-91(33)
Publisher: Oxford University Press
Abstract:The purpose of this paper is to assess the prospects for a neo-logicist development of set theory based on a restriction of Frege's Basic Law V, which we call (RV): PQ[Ext(P) = Ext(Q) [(BAD(P) & BAD(Q)) x(Px Qx)]] BAD is taken as a primitive property of properties. We explore the features it must have for (RV) to sanction the various strong axioms of ZermeloFraenkel set theory. The primary interpretation is where BAD is Dummett's indefinitely extensible.1 Background: what and why?2 Framework3 GOOD candidates, indefinite extensibility4 The framework of (RV) alone, or almost alone5 The axioms6 Brief closing
Document Type: Research article
Publication date: 2003-03-01
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