Combining Philosophers

Ideas for Diogenes Laertius, John M. Cooper and Peter van Inwagen

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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
Mereology is 'nihilistic' (just atoms) or 'universal' (no restrictions on what is 'whole') [Inwagen, by Varzi]
     Full Idea: Van Ingwagen writes of 'mereological nihilism' (that only mereological atoms exist) and of 'mereological universalism' (adhering to the principle of Unrestricted Composition).
     From: report of Peter van Inwagen (Material Beings [1990], p.72-) by Achille Varzi - Mereology 4.3
     A reaction: They both look mereologically nihilistic to me, in comparison with an account that builds on 'natural' wholes and their parts. You can only be 'unrestricted' if you view the 'wholes' in your vast ontology as pretty meaningless (as Lewis does, Idea 10660).