Journal of Philosophical Logic 49 (5):981-1004 (2020)

Authors
Lu Chen
Koc University
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 nonstandard analysis. This view, I argue, provides a novel reply to the inconsistency arguments proposed by Arntzenius and Russell, 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 finite additivity.
Keywords Continua  Gunk  Infinitesimal  Nonstandard analysis  Region-based topology  Measure theory  Inconsistent Argument  Nonstandard measure theory
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DOI 10.1007/s10992-020-09544-x
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References found in this work BETA

Mereology.Achille C. Varzi - 2016 - Stanford Encyclopedia of Philosophy.
Non-Standard Analysis.Abraham Robinson - 1961 - North-Holland Publishing Co..
What Price Spacetime Substantivalism? The Hole Story.John Earman & John Norton - 1987 - British Journal for the Philosophy of Science 38 (4):515-525.

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Sorites On What Matters.Theron Pummer - 2022 - In Jeff McMahan, Timothy Campbell, Ketan Ramakrishnan & Jimmy Goodrich (eds.), Ethics and Existence: The Legacy of Derek Parfit. Oxford: Oxford University Press. pp. 498–523.

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