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

Chen, Lu (2019) Intrinsic local distances: a mixed solution to Weyl’s tile argument. [Preprint]

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Official URL: https://link.springer.com/article/10.1007%2Fs11229...

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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Item Type:

Preprint

Creators:

Creators	Email	ORCID
Chen, Lu	luc@umass.edu

Keywords:

Atomistic space; Discrete spacetime; Weyl's tile argument; Intrinsic distance; Path-dependent distance; Metric; Euclidean geometry; Non-Euclidean geometry

Subjects:

General Issues > Scientific Metaphysics
Specific Sciences > Mathematics

Depositing User:

Ms. Lu Chen

Date Deposited:

18 Jan 2020 17:47

Last Modified:

18 Jan 2020 17:47

Item ID:

16827

Official URL:

https://link.springer.com/article/10.1007%2Fs11229...