Combining Philosophers

Ideas for Donald Davidson, Stewart Shapiro and Metrodorus (Chi)

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4 ideas

5. Theory of Logic / G. Quantification / 2. Domain of Quantification

18914	Davidson controversially proposed to quantify over events [Davidson, by Engelbretsen]
	Full Idea: An alternative, and still controversial, extension of first-order logic is due to Donald Davidson, who allows for quantification over events.
	From: report of Donald Davidson (The Individuation of Events [1969]) by George Engelbretsen - Trees, Terms and Truth 3
	A reaction: I'm suddenly thinking this is quite an attractive proposal. We need to quantify over facts, or states of affairs, or events, or some such thing, to talk about the world properly. Objects, predicates and sets/parts is too sparse. I like facts.

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

13674	We might reduce ontology by using truth of sentences and terms, instead of using objects satisfying models [Shapiro]
	Full Idea: The main role of substitutional semantics is to reduce ontology. As an alternative to model-theoretic semantics for formal languages, the idea is to replace the 'satisfaction' relation of formulas (by objects) with the 'truth' of sentences (using terms).
	From: Stewart Shapiro (Foundations without Foundationalism [1991], 9.1.4)
	A reaction: I find this very appealing, and Ruth Barcan Marcus is the person to look at. My intuition is that logic should have no ontology at all, as it is just about how inference works, not about how things are. Shapiro offers a compromise.

5. Theory of Logic / G. Quantification / 5. Second-Order Quantification

10290	Second-order variables also range over properties, sets, relations or functions [Shapiro]
	Full Idea: Second-order variables can range over properties, sets, or relations on the items in the domain-of-discourse, or over functions from the domain itself.
	From: Stewart Shapiro (Higher-Order Logic [2001], 2.1)

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

10268	Maybe plural quantifiers should be understood in terms of classes or sets [Shapiro]
	Full Idea: Maybe plural quantifiers should themselves be understood in terms of classes (or sets).
	From: Stewart Shapiro (Philosophy of Mathematics [1997], 7.4)
	A reaction: [Shapiro credits Resnik for this criticism]