Review of Symbolic Logic 1 (3):335-354 (2008)

Joop Leo
Utrecht University
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 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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DOI 10.1017/s1755020308080222
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References found in this work BETA

Philosophy of Mathematics: Structure and Ontology.Stewart Shapiro - 1997 - Oxford, England: Oxford University Press.
The Limits of Abstraction.Kit Fine - 2002 - Oxford, England: Oxford University Press.
Philosophy of Mathematics: Structure and Ontology.Stewart Shapiro - 2000 - Philosophical Quarterly 50 (198):120-123.
Neutral Relations.Kit Fine - 2000 - Philosophical Review 109 (1):1-33.
Structuralism and Metaphysics.Charles Parsons - 2004 - Philosophical Quarterly 54 (214):56--77.

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Citations of this work BETA

Relations.Fraser MacBride - 2016 - Stanford Encyclopedia of Philosophy.
Modeling Occurrences of Objects in Relations.Joop Leo - 2010 - Review of Symbolic Logic 3 (1):145-174.
Relational Complexes.Joop Leo - 2013 - Journal of Philosophical Logic 42 (2):357-390.
A Tractarian Universe.Albert Visser - 2012 - Journal of Philosophical Logic 41 (3):519-545.

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