TY - JOUR
T1 - Aristotelian continua
AU - Linnebo, Øystein
AU - Shapiro, Stewart
AU - Hellman, Geoffrey
PY - 2016/6/1
Y1 - 2016/6/1
N2 - In previous work, Hellman and Shapiro present a regions-based account of a one-dimensional continuum. This paper produces a more Aristotelian theory, eschewing the existence of points and the use of infinite sets or pluralities. We first show how to modify the original theory. There are a number of theorems (such as the existence of bisections) that have to be added as axioms. Building on some work by Linnebo, we then show how to take the 'potential' nature of the usual operations seriously, by using a modal language, and we show that the two approaches are equivalent.
AB - In previous work, Hellman and Shapiro present a regions-based account of a one-dimensional continuum. This paper produces a more Aristotelian theory, eschewing the existence of points and the use of infinite sets or pluralities. We first show how to modify the original theory. There are a number of theorems (such as the existence of bisections) that have to be added as axioms. Building on some work by Linnebo, we then show how to take the 'potential' nature of the usual operations seriously, by using a modal language, and we show that the two approaches are equivalent.
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U2 - 10.1093/philmat/nkv024
DO - 10.1093/philmat/nkv024
M3 - Article
AN - SCOPUS:84991475527
SN - 0031-8019
VL - 24
SP - 214
EP - 246
JO - Philosophia Mathematica
JF - Philosophia Mathematica
IS - 2
M1 - nkv024
ER -