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THE IDENTITY OF ARGUMENT-PLACES

Published online by Cambridge University Press:  01 October 2008

JOOP LEO*
Affiliation:
Department of Philosophy, Utrecht University
*
*DEPARTMENT OF PHILOSOPHY UTRECHT UNIVERSITY HEIDELBERGLAAN 8, 3584 CS UTRECHT THE NETHERLANDS E-mail:joop.leo@phil.uu.nl

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.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2008

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