The Review of Symbolic Logic

Research Article

THE IDENTITY OF ARGUMENT-PLACES

JOOP LEOa1 c1

a1 Department of Philosophy, Utrecht University

Abstract

Argument-places play an important role in our dealing with relations. However, that does not mean that argument-places should be taken as primitive entities. It is possible to give an account of ‘real’ relations in which argument-places play no role. But if argument-places are not basic, then what can we say about their identity? Can they, for example, be reconstructed in set theory with appropriate urelements? In this article, we show that for some relations, argument-places cannot be modeled in a neutral way in V[A], the cumulative hierarchy with basic ingredients of the relation as urelements. We argue that a natural way to conceive of argument-places is to identify them with abstract, structureless points of a derivative structure exemplified by positional frames. In case the relation has symmetry, these points may be indiscernible.

(Received May 14 2008)

Correspondence:

c1 DEPARTMENT OF PHILOSOPHY UTRECHT UNIVERSITY HEIDELBERGLAAN 8, 3584 CS UTRECHT THE NETHERLANDS E-mail: joop.leo@phil.uu.nl