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2 ideas
23445 | Naïve set theory says any formula defines a set, and coextensive sets are identical [Linnebo] |
Full Idea: Naïve set theory is based on the principles that any formula defines a set, and that coextensive sets are identical. | |
From: Øystein Linnebo (Philosophy of Mathematics [2017], 4.2) | |
A reaction: The second principle is a standard axiom of ZFC. The first principle causes the trouble. |
13282 | Aristotle relativises the notion of wholeness to different measures [Aristotle, by Koslicki] |
Full Idea: Aristotle proposes to relativise unity and plurality, so that a single object can be both one (indivisible) and many (divisible) simultaneously, without contradiction, relative to different measures. Wholeness has degrees, with the strength of the unity. | |
From: report of Aristotle (works [c.330 BCE]) by Kathrin Koslicki - The Structure of Objects 7.2.12 | |
A reaction: [see Koslicki's account of Aristotle for details] As always, the Aristotelian approach looks by far the most promising. Simplistic mechanical accounts of how parts make wholes aren't going to work. We must include the conventional and conceptual bit. |