Combining Philosophers

Ideas for Hermarchus, Rayo,A/Uzquiasno,G and Donald Davidson

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6 ideas

5. Theory of Logic / E. Structures of Logic / 1. Logical Form
There is a huge range of sentences of which we do not know the logical form [Davidson]
     Full Idea: We do not know the logical form of sentences about counterfactuals, probabilities, causal relations, belief, perception, intention, purposeful action, imperatives, optatives, or interrogatives, or the role of adverbs, adjectives or mass terms.
     From: Donald Davidson (Truth and Meaning [1967], p.35)
     A reaction: [compressed] This is the famous 'Davidson programme', where teams of philosophers work out the logical forms for this lot, thus unravelling the logic of the world. If they are beavering away, some sort of overview should have emerged by now...
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
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.
We could have unrestricted quantification without having an all-inclusive domain [Rayo/Uzquiano]
     Full Idea: The possibility of unrestricted quantification does not immediately presuppose the existence of an all-inclusive domain. One could deny an all-inclusive domain but grant that some quantifications are sometimes unrestricted.
     From: Rayo,A/Uzquiasno,G (Introduction to 'Absolute Generality' [2006], 1.1)
     A reaction: Thus you can quantify over anything you like, but only from what is available. Eat what you like (in this restaurant).
Absolute generality is impossible, if there are indefinitely extensible concepts like sets and ordinals [Rayo/Uzquiano]
     Full Idea: There are doubts about whether absolute generality is possible, if there are certain concepts which are indefinitely extensible, lacking definite extensions, and yielding an ever more inclusive hierarchy. Sets and ordinals are paradigm cases.
     From: Rayo,A/Uzquiasno,G (Introduction to 'Absolute Generality' [2006], 1.2.1)
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
Perhaps second-order quantifications cover concepts of objects, rather than plain objects [Rayo/Uzquiano]
     Full Idea: If one thought of second-order quantification as quantification over first-level Fregean concepts [note: one under which only objects fall], talk of domains might be regimented as talk of first-level concepts, which are not objects.
     From: Rayo,A/Uzquiasno,G (Introduction to 'Absolute Generality' [2006], 1.2.2)
     A reaction: That is (I take it), don't quantify over objects, but quantify over concepts, but only those under which known objects fall. One might thus achieve naïve comprehension without paradoxes. Sound like fun.
5. Theory of Logic / I. Semantics of Logic / 4. Satisfaction
'Satisfaction' is a generalised form of reference [Davidson]
     Full Idea: We can think of 'satisfaction' as a generalised form of reference.
     From: Donald Davidson (Truth and Predication [2005], 2)
     A reaction: Just the sort of simple point we novices need from the great minds, to help us see what is going on. One day someone is going to explain Tarski's account of truth in plain English, but probably not in my lifetime.