Philosophia Mathematica:nkv021 (2015)

Authors
Stewart Shapiro
Ohio State University
Geoffrey Hellman
University of Minnesota
Abstract
There are a number of regions-based accounts of space/time, due to Whitehead, Roeper, Menger, Tarski, the present authors, and others. They all follow the Aristotelian theme that continua are not composed of points: each region has a proper part. The purpose of this note is to show how to recapture ‘points’ in such frameworks via Scottish neo-logicist abstraction principles. The results recapitulate some Aristotelian themes. A second agenda is to provide a new arena to help decide what is at stake when adjudicating issues concerning the identity of neo-logicist abstracts — so-called ‘Caesar questions’.
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DOI 10.1093/philmat/nkv021
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References found in this work BETA

Thinking About Mathematics: The Philosophy of Mathematics.Stewart Shapiro - 2000 - Oxford, England: Oxford University Press.
The Limits of Abstraction.Kit Fine - 2002 - Oxford, England: Oxford University Press.
Structuralism and the Notion of Dependence.Øystein Linnebo - 2008 - Philosophical Quarterly 58 (230):59-79.

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Citations of this work BETA

Epistemic Modality, Mind, and Mathematics.Hasen Khudairi - 2021 - Dissertation, University of St Andrews

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