TY - JOUR
T1 - Frege meets Aristotle
T2 - Points as abstracts
AU - Shapiro, Stewart
AU - Hellman, Geoffrey
N1 - Publisher Copyright:
© The Authors [2015].
PY - 2017
Y1 - 2017
N2 - 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'.
AB - 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'.
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U2 - 10.1093/philmat/nkv021
DO - 10.1093/philmat/nkv021
M3 - Article
AN - SCOPUS:85019560597
SN - 0031-8019
VL - 25
SP - 73
EP - 90
JO - Philosophia Mathematica
JF - Philosophia Mathematica
IS - 1
ER -