Frege Meets Aristotle: Points as Abstracts

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Philosophia Mathematica, ISSN: 0031-8019, Vol: 25, Issue: 1, Page: 73-90

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Shapiro, Stewart; Hellman, Geoffrey
Oxford University Press (OUP)
Mathematics; Arts and Humanities
article description
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 (instead of Whiteheadian 'extensive abstraction'). 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'.