Prolegomenon to Any Future Neo-Logicist Set Theory: Abstraction and Indefinite Extensibility (2003)
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): [forall]P[forall]Q[Ext(P) = Ext(Q) [equiv] [(BAD(P) & BAD(Q)) [or] [forall]x(Px [equiv] 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'.
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