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THE IDENTITY OF ARGUMENT-PLACES

  • JOOP LEO (a1)
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.

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*DEPARTMENT OF PHILOSOPHY UTRECHT UNIVERSITY HEIDELBERGLAAN 8, 3584 CS UTRECHT THE NETHERLANDS E-mail:joop.leo@phil.uu.nl
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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

K Fine . (1998). Cantorian abstraction: a reconstruction and defense. The Journal of Philosophy, 95, 599634.

K Fine . (2000). Neutral relations. The Philosophical Review, 109, 133.

J Leo . (2008). Modeling relations. The Journal of Philosophical Logic, 37, 353385.

C Parsons . (2004). Structuralism and metaphysics. The Philosophical Quarterly, 54, 5677.

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The Review of Symbolic Logic
  • ISSN: 1755-0203
  • EISSN: 1755-0211
  • URL: /core/journals/review-of-symbolic-logic
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