Combining Texts

Ideas for 'fragments/reports', 'Letters to De Vries' and 'Vagueness'

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5 ideas

5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
21611 Formal semantics defines validity as truth preserved in every model [Williamson]
     Full Idea: An aim of formal semantics is to define in mathematical terms a set of models such that an argument is valid if and only if it preserves truth in every model in the set, for that will provide us with a precise standard of validity.
     From: Timothy Williamson (Vagueness [1994], 5.3)
5. Theory of Logic / D. Assumptions for Logic / 1. Bivalence
21606 'Bivalence' is the meta-linguistic principle that 'A' in the object language is true or false [Williamson]
     Full Idea: The meta-logical law of excluded middle is the meta-linguistic principle that any statement 'A' in the object language is either truth or false; it is now known as the principle of 'bivalence'.
     From: Timothy Williamson (Vagueness [1994], 5.2)
     A reaction: [He cites Henryk Mehlberg 1958] See also Idea 21605. Without this way of distinguishing bivalence from excluded middle, most discussions of them strikes me as shockingly lacking in clarity. Personally I would cut the normativity from this one.
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
21605 Excluded Middle is 'A or not A' in the object language [Williamson]
     Full Idea: The logical law of excluded middle (now the standard one) is the schema 'A or not A' in the object-language.
     From: Timothy Williamson (Vagueness [1994], 5.2)
     A reaction: [He cites Henryk Mehlberg 1958] See Idea 21606. The only sensible way to keep Excluded Middle and Bivalence distinct. I would say: (meta-) only T and F are available, and (object) each proposition must have one of them. Are they both normative?
5. Theory of Logic / H. Proof Systems / 4. Natural Deduction
21612 Or-elimination is 'Argument by Cases'; it shows how to derive C from 'A or B' [Williamson]
     Full Idea: Argument by Cases (or or-elimination) is the standard way of using disjunctive premises. If one can argue from A and some premises to C, and from B and some premises to C, one can argue from 'A or B' and the combined premises to C.
     From: Timothy Williamson (Vagueness [1994], 5.3)
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / b. The Heap paradox ('Sorites')
21599 A sorites stops when it collides with an opposite sorites [Williamson]
     Full Idea: A sorites paradox is stopped when it collides with a sorites paradox going in the opposite direction. That account will not strike a logician as solving the sorites paradox.
     From: Timothy Williamson (Vagueness [1994], 3.3)