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Do Simple Infinitesimal Parts Solve Zeno's Paradox of Measure?

Chen, Lu (2019) Do Simple Infinitesimal Parts Solve Zeno's Paradox of Measure? [Preprint]

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Abstract

In this paper, I develop an original view of the structure of space—called infinitesimal atomism—as a reply to Zeno’s paradox of measure. According to this view, space is composed of ultimate parts with infinitesimal size, where infinitesimals are understood within the framework of Robinson’s (Non-standard analysis. North-Holland, Amsterdam, 1966) nonstandard analysis. Notably, this view satisfies a version of additivity: for every region that has a size, its size is the sum of the sizes of its disjoint parts. In particular, the size of a finite region is the sum of the sizes of its infinitesimal parts. Although this view is a coherent approach to Zeno’s paradox and is preferable to Skyrms’s (Physics, philosophy and psychoanalysis. Volume 76 of the series Boston studies in the philosophy of science, pp 223–254, 1983) infinitesimal approach, it faces both the main problem for the standard view (the problem of unmeasurable regions) and the main problem for finite atomism (Weyl’s tile argument), leaving it with no clear advantage over these familiar alternatives.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Chen, Luluc@umass.edu
Keywords: Continuum; atomistic space; Zeno's paradox of measure; infinitesimals; Weyl's tile argument; unmeasurable regions
Subjects: Specific Sciences > Mathematics
Depositing User: Ms. Lu Chen
Date Deposited: 18 Jan 2020 16:49
Last Modified: 18 Jan 2020 17:46
Item ID: 16825
Official URL: https://link.springer.com/article/10.1007/s11229-0...
DOI or Unique Handle: https://doi.org/10.1007/s11229-019-02350-2
Subjects: Specific Sciences > Mathematics
Date: 2019
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/16825

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