Frege Meets Aristotle: Points as Abstracts

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Philosophia Mathematica:nkv021 (2015)
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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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10.1093/philmat/nkv021

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Author Profiles

Stewart Shapiro
Ohio State University
Geoffrey Hellman
University of Minnesota

Citations of this work

Epistemic Modality and Hyperintensionality in Mathematics.Timothy Bowen - 2017 - Dissertation, Arché, University of St Andrews
The Metametaphysics of Neo-Fregeanism.Matti Eklund - 2020 - In Ricki Bliss & James Miller (eds.), The Routledge Handbook of Metametaphysics. New York, NY: Routledge.

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References found in this work

The limits of abstraction.Kit Fine - 2002 - New York: Oxford University Press. Edited by Matthias Schirn.
Structuralism and the notion of dependence.Øystein Linnebo - 2008 - Philosophical Quarterly 58 (230):59-79.

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