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2 ideas
10073 | There cannot be a set theory which is complete [Smith,P] |
Full Idea: By Gödel's First Incompleteness Theorem, there cannot be a negation-complete set theory. | |
From: Peter Smith (Intro to Gödel's Theorems [2007], 01.3) | |
A reaction: This means that we can never prove all the truths of a system of set theory. |
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. |