Combining Texts

Ideas for 'Parmenides', 'Physics' 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
Are a part and whole one or many? Either way, what is the cause? [Aristotle]
     Full Idea: There is a difficulty about part and whole, ...whether the part and the whole are one or more than one, and in what way they can be one or many, and, if they are more than one, in what way they are more than one.
     From: Aristotle (Physics [c.337 BCE], 185b11), quoted by Kathrin Koslicki - The Structure of Objects 6.3
     A reaction: He only states the problem here, but doesn't pursue it. I take the real question of mereology to be what makes a many into a one. I don't see a problem with a many being simultaneously a one.