Frege meets Aristotle: Points as abstracts

Stewart Shapiro, Geoffrey Hellman

Research output: Contribution to journalArticle

3 Scopus citations

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 (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'.

Original languageEnglish (US)
Pages (from-to)73-90
Number of pages18
JournalPhilosophia Mathematica
Volume25
Issue number1
DOIs
StatePublished - Jan 1 2017

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