A Calculus of Regions Respecting Both Measure and Topology

Journal of Philosophical Logic 48 (5):825-850 (2019)
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Abstract

Say that space is ‘gunky’ if every part of space has a proper part. Traditional theories of gunk, dating back to the work of Whitehead in the early part of last century, modeled space in the Boolean algebra of regular closed subsets of Euclidean space. More recently a complaint was brought against that tradition in Arntzenius and Russell : Lebesgue measure is not even finitely additive over the algebra, and there is no countably additive measure on the algebra. Arntzenius advocated modeling gunk in measure algebras instead—in particular, in the algebra of Borel subsets of Euclidean space, modulo sets of Lebesgue measure zero. But while this algebra carries a natural, countably additive measure, it has some unattractive topological features. In this paper, we show how to construct a model of gunk that has both nice rudimentary measure-theoretic and topological properties. We then show that in modeling gunk in this way we can distinguish between finite dimensions, and that nothing in lost in terms of our ability to identify points as locations in space.

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Author Profiles

Tamar Lando
Columbia University
Dana Scott
Carnegie Mellon University

Citations of this work

Mereology.Achille C. Varzi & A. J. Cotnoir - 2021 - Oxford: Oxford University Press.
Extended Simples, Unextended Complexes.Claudio Calosi - 2023 - Journal of Philosophical Logic 52 (2):643-668.
Counterparts, Determinism, and the Hole Argument.Franciszek Cudek - forthcoming - British Journal for the Philosophy of Science.
Boundary.Achille C. Varzi - 2013 - Stanford Encyclopedia of Philosophy.

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Composition as a Kind of Identity.Phillip Bricker - 2016 - Inquiry: An Interdisciplinary Journal of Philosophy 59 (3):264-294.

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