Thinking in a Coordinate-Free Way about Relations

Dialectica 68 (2):263-282 (2014)
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Abstract

How we talk about relations has a great influence on how we think about relations. By saying that Spain defeated the Netherlands we obviously say something entirely different from saying that the Netherlands defeated Spain. This makes many of us think that in the underlying relation itself one of the relata comes first and the other comes second. However, there are good reasons to view the order as a representational artifact. In this paper I present a new logic that allows us to think and talk about relations in a coordinate-free manner. The logic is minimalistic in the sense that it has no predicates except equality, but its expressive power is the same as that of first-order predicate logic

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Joop Leo
Utrecht University

Citations of this work

Relations.Fraser MacBride - 2016 - Stanford Encyclopedia of Philosophy.
Coordinate-free logic.Joop Leo - 2016 - Review of Symbolic Logic 9 (3):522-555.

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References found in this work

Plural Logic.Alex Oliver & Timothy Smiley - 2013 - Oxford, England: Oxford University Press UK. Edited by T. J. Smiley.
Theory of knowledge: the 1913 manuscript.Bertrand Russell - 1913/1992 - New York: Routledge. Edited by Elizabeth Ramsden Eames & Kenneth Blackwell.
Neutral relations.Kit Fine - 2000 - Philosophical Review 109 (1):1-33.
How Involved do You Want to be in a Non-symmetric Relationship?Fraser MacBride - 2014 - Australasian Journal of Philosophy 92 (1):1-16.
Neutral relations revisited.Fraser MacBride - 2007 - Dialectica 61 (1):25–56.

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