Intrinsic local distances: a mixed solution to Weyl’s tile argument

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Abstract

Weyl's tile argument purports to show that there are no natural distance functions in atomistic space that approximate Euclidean geometry. I advance a response to this argument that relies on a new account of distance in atomistic space, called "the mixed account," according to which local distances are primitive and other distances are derived from them. Under this account, atomistic space can approximate Euclidean space (and continuous space in general) very well. To motivate this account as a genuine solution to Weyl's tile argument, I argue that this account is no less natural than the standard account of distance in continuous space. I also argue that the mixed account has distinctive advantages over Forrest's (1995) account in response to Weyl's tile argument, which can be considered as a restricted version of the mixed account.

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Author's Profile

Lu Chen
Koc University

Citations of this work

Why the Weyl Tile Argument is Wrong.Lu Chen - forthcoming - British Journal for the Philosophy of Science.

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References found in this work

The metaphysics within physics.Tim Maudlin - 2007 - New York: Oxford University Press.
Philosophy of Mathematics and Natural Science.Hermann Weyl - 1949 - Princeton, N.J.: Princeton University Press. Edited by Olaf Helmer-Hirschberg & Frank Wilczek.
Philosophical Papers, Volume II.David Lewis - 1986 - New York, US: Oxford University Press.
The Metaphysics within Physics.[author unknown] - 2007 - Tijdschrift Voor Filosofie 69 (3):610-611.
The Fabric of Space: Intrinsic vs. Extrinsic Distance Relations.Phillip Bricker - 1993 - Midwest Studies in Philosophy 18 (1):271-294.

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