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):
For AllPFor AllQ[Ext(P) = Ext(Q) equivalent to [(BAD(P) BAD(Q)) boolean OR For Allx(Px equivalent to 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'.
| Original language | English |
|---|---|
| Pages (from-to) | 59-91 |
| Number of pages | 33 |
| Journal | British Journal for the Philosophy of Science |
| Volume | 54 |
| Publication status | Published - Mar 2003 |