Labyrinth of Continua

Philosophia Mathematica 26 (1):1-39 (2018)
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Abstract

This is a survey of the concept of continuity. Efforts to explicate continuity have produced a plurality of philosophical conceptions of continuity that have provably distinct expressions within contemporary mathematics. I claim that there is a divide between the conceptions that treat the whole continuum as prior to its parts, and those conceptions that treat the parts of the continuum as prior to the whole. Along this divide, a tension emerges between those conceptions that favor philosophical idealizations of continuity and those that are more readily available for mathematico-scientific use.

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Patrick Reeder
Kenyon College

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References found in this work

On what grounds what.Jonathan Schaffer - 2009 - In Ryan Wasserman, David Manley & David Chalmers (eds.), Metametaphysics: New Essays on the Foundations of Ontology. Oxford, England: Oxford University Press. pp. 347-383.
Guide to Ground.Kit Fine - 2012 - In Fabrice Correia & Benjamin Schnieder (eds.), Metaphysical grounding: understanding the structure of reality. Cambridge: Cambridge University Press. pp. 37--80.
Metaphysical Dependence: Grounding and Reduction.Gideon Rosen - 2010 - In Bob Hale & Aviv Hoffmann (eds.), Modality: metaphysics, logic, and epistemology. qnew York: Oxford University Press. pp. 109-135.
Parts: a study in ontology.Peter M. Simons - 1987 - New York: Oxford University Press.

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