Prolegomenon to any future neo-logicist set theory: Abstraction and indefinite extensibility
British Journal for the Philosophy of Science 54 (1):59--91 (2003)
| 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 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. | |||||||||
| Keywords | No keywords specified (fix it) | |||||||||
| Categories | ||||||||||
| Options |
|
|||||||||
Download options| PhilPapers Archive |
Upload a copy of this paper Check publisher's policy on self-archival Papers currently archived: 5,679 |
| External links |
 |
| Through your library | Configure |
Similar books and articlesPeter Clark (1993). Sets and Indefinitely Extensible Concepts and Classes. Aristotelian Society Supplementary Volume 67:235--249.
Laureano Luna (2012). Grim's Arguments Against Omniscience and Indefinite Extensibility. International Journal for Philosophy of Religion 72 (2):89-101.
Philip A. Ebert & Stewart Shapiro (2009). The Good, the Bad and the Ugly. Synthese 170 (3):415 - 441.
Richard L. Cartwright (1994). Speaking of Everything. Noûs 28 (1):1-20.
Stewart Shapiro & Alan Weir (2000). ‘Neo-Logicist‘ Logic is Not Epistemically Innocent. Philosophia Mathematica 8 (2):160--189.
S. Shapiro (1998). Induction and Indefinite Extensibility: The Gödel Sentence is True, but Did Someone Change the Subject? Mind 107 (427):597-624.
Roy T. Cook (2002). The State of the Economy: Neo-Logicism and Inflationt. Philosophia Mathematica 10 (1):43-66.
Roy T. Cook (2003). Aristotelian Logic, Axioms, and Abstraction. Philosophia Mathematica 11 (2):195-202.
Stewart Shapiro & Alan Weir (1999). New V, ZF and Abstractiont. Philosophia Mathematica 7 (3).
Analytics
Monthly downloads |
Added to index2009-01-28Total downloads25 ( #49,599 of 549,087 )Recent downloads (6 months)1 ( #63,317 of 549,087 )How can I increase my downloads? |
My notes
Discussion
