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Infinitesimal Gunk

Chen, Lu (2019) Infinitesimal Gunk. [Preprint]

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Abstract

In this paper, I advance an original view of the structure of space called Infinitesimal Gunk. This view says that every region of space can be further divided and some regions have infinitesimal size, where �infinitesimals are understood in the framework of Robinson's (1966) nonstandard analysis. This view, I argue, provides a novel reply to the inconsistency arguments proposed by Arntzenius (2008) and Russell (2008), which have troubled a more familiar gunky approach. Moreover, it has important advantages over the alternative views these authors suggested. Unlike Arntzenius's proposal, it does not introduce regions with no interior. It also has a much richer measure theory than Russell's proposal and does not retreat to mere fi�nite additivity.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Chen, Luluc@umass.edu
Keywords: Continua; Gunky space; Infinitesimals; Nonstandard analysis; Region-based topology; Measure theory; Nonstandard measure theory; Hyperfinite additivity
Subjects: Specific Sciences > Mathematics
Depositing User: Ms. Lu Chen
Date Deposited: 18 Jan 2020 16:50
Last Modified: 18 Jan 2020 17:46
Item ID: 16826
DOI or Unique Handle: https://doi.org/10.1007/s10992-020-09544-x
Subjects: Specific Sciences > Mathematics
Date: 2019
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/16826

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