Combining Texts

Ideas for 'works', 'The Periodic Table' and 'Existence,Ontological Commitment and Fictions'

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2 ideas

4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
What in the real world could ground the distinction between the sets {A,{A,B}} and {B,{A,B}}? [Inwagen]
     Full Idea: Nothing in the world of nominalistically acceptable things could ground or explain the non-identity of the set {A,{A,B}} with the set {B,{A,B}}.
     From: Peter van Inwagen (Existence,Ontological Commitment and Fictions [2003], p.154)
     A reaction: [He cites Goodman for this thought] Van Inwagen is offering this to show that the existence of sets is abstract, whereas Goodman was denying the existence of sets altogether. I'm with Goodman. Nice example.
4. Formal Logic / G. Formal Mereology / 1. Mereology
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.