Journal Article

Prolegomenon To Any Future Neo‐Logicist Set Theory: Abstraction And Indefinite Extensibility

Stewart Shapiro

in The British Journal for the Philosophy of Science

Published on behalf of British Society for the Philosophy of Science

Volume 54, issue 1, pages 59-91
Published in print March 2003 | ISSN: 0007-0882
Published online March 2003 | e-ISSN: 1464-3537 | DOI: http://dx.doi.org/10.1093/bjps/54.1.59
Prolegomenon To Any Future Neo‐Logicist Set Theory: Abstraction And Indefinite Extensibility

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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(PxQx)]] 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 Zermelo–Fraenkel set theory. The primary interpretation is where ‘BAD’ is Dummett's ‘indefinitely extensible’.

1 Background: what and why?

2 Framework

3 GOOD candidates, indefinite extensibility

4 The framework of (RV) alone, or almost alone

5 The axioms

6 Brief closing

Journal Article.  0 words. 

Subjects: Philosophy of Science ; Science and Mathematics

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