Physical Geometry and Fundamental Metaphysics

Proceedings of the Aristotelian Society 111 (1pt1):135-159 (2011)
Abstract
I explore some ways in which one might base an account of the fundamental metaphysics of geometry on the mathematical theory of Linear Structures recently developed by Tim Maudlin (2010). Having considered some of the challenges facing this approach, Idevelop an alternative approach, according to which the fundamental ontology includes concrete entities structurally isomorphic to functions from space-time points to real numbers
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References found in this work BETA
Frank Arntenius & Cian Dorr (2012). Calculus as Geometry. In Frank Arntzenius (ed.), Space, Time and Stuff. Oxford University Press.
Cian Dorr (2004). Non-Symmetric Relations. Oxford Studies in Metaphysics 1:155-92.
Cian Dorr (2010). Of Numbers and Electrons. Proceedings of the Aristotelian Society 110 (2pt2):133-181.
Hartry Field (1984). Can We Dispense with Space-Time? PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1984:33 - 90.

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