Combining Philosophers

Ideas for Anaxarchus, J. Alberto Coffa and David Lewis

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7 ideas

5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic

10816	We can use mereology to simulate quantification over relations [Lewis]
	Full Idea: We can simulate quantification over relations using megethology. Roughly, a quantifier over relations is a plural quantifier over things that encode ordered pairs by mereological means.
	From: David Lewis (Mathematics is Megethology [1993], p.18)
	A reaction: [He credits this idea to Burgess and Haven] The point is to avoid second-order logic, which quantifies over relations as ordered n-tuple sets.

5. Theory of Logic / G. Quantification / 4. Substitutional Quantification

15533	We can quantify over fictions by quantifying for real over their names [Lewis]
	Full Idea: Substitutionalists simulate quantification over fictional characters by quantifying for real over fictional names.
	From: David Lewis (Noneism or Allism? [1990], p.159)
	A reaction: I would say that a fiction is a file of conceptual information, identified by a label. The label brings baggage with it, and there is no existence in the label.

5. Theory of Logic / G. Quantification / 6. Plural Quantification

15731	Quantification sometimes commits to 'sets', but sometimes just to pluralities (or 'classes') [Lewis]
	Full Idea: I consider some apparent quantification over sets or classes of whatnots to carry genuine ontological commitment to 'sets' of them, but sometimes it is innocent plural quantification committed only to whatnots, for which I use 'class'.
	From: David Lewis (On the Plurality of Worlds [1986], 1.5 n37)
	A reaction: How do you tell whether you are committed to a set or not? Can I claim an innocent plurality each time, while you accuse me of a guilty set? Can I firmly commit to a set, to be told that I can never manage more than a plurality?

15525	Plural quantification lacks a complete axiom system [Lewis]
	Full Idea: There is an irremediable lack of a complete axiom system for plural quantification.
	From: David Lewis (Parts of Classes [1991], 4.7)

15518	I like plural quantification, but am not convinced of its connection with second-order logic [Lewis]
	Full Idea: I agree fully with Boolos on substantive questions about plural quantification, though I would make less than he does of the connection with second-order logic.
	From: David Lewis (Parts of Classes [1991], 3.2 n2)
	A reaction: Deep matters, but my inclination is to agree with Lewis, as I have never been able to see why talk of plural quantification led straight on to second-order logic. A plural is just some objects, not some higher-order entity.

5. Theory of Logic / G. Quantification / 7. Unorthodox Quantification

15534	We could quantify over impossible objects - as bundles of properties [Lewis]
	Full Idea: We can quantify over Meinongian objects by quantifying for real over property bundles (such as the bundle of roundness and squareness).
	From: David Lewis (Noneism or Allism? [1990], p.159)

5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms

14212	A consistent theory just needs one model; isomorphic versions will do too, and large domains provide those [Lewis]
	Full Idea: A consistent theory is, by definition, one satisfied by some model; an isomorphic image of a model satisfies the same theories as the original model; to provide the making of an isomorphic image of any given model, a domain need only be large enough.
	From: David Lewis (Putnam's Paradox [1984], 'Why Model')
	A reaction: This is laying out the ground for Putnam's model theory argument in favour of anti-realism. If you are chasing the one true model of reality, then formal model theory doesn't seem to offer much encouragement.