display all the ideas for this combination of philosophers
9 ideas
6858 | Formal logic struck me as exactly the language I wanted to think in [Williamson] |
Full Idea: As soon as I started learning formal logic, that struck me as exactly the language that I wanted to think in. | |
From: Timothy Williamson (Interview with Baggini and Stangroom [2001]) | |
A reaction: It takes all sorts… It is interesting that formal logic might be seen as having the capacity to live up to such an aspiration. I don't think the dream of an ideal formal language is dead, though it will never encompass all of reality. Poetic truth. |
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) |
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. |
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? |
18492 | Not all quantification is either objectual or substitutional [Williamson] |
Full Idea: We should not assume that all quantification is either objectual or substitutional. | |
From: Timothy Williamson (Truthmakers and Converse Barcan Formula [1999], p.262) | |
A reaction: [see Prior 1971:31-4] He talks of quantifying into sentence position. |
15136 | Substitutional quantification is metaphysical neutral, and equivalent to a disjunction of instances [Williamson] |
Full Idea: If quantification into sentence position is substitutional, then it is metaphysically neutral. A substitutionally interpreted 'existential' quantification is semantically equivalent to the disjunction (possibly infinite) of its substitution instances. | |
From: Timothy Williamson (Truthmakers and Converse Barcan Formula [1999], §2) | |
A reaction: Is it not committed to the disjunction, just as the objectual reading commits to objects? Something must make the disjunction true. Or is it too verbal to be about reality? |
15138 | Not all quantification is objectual or substitutional [Williamson] |
Full Idea: We should not assume that all quantification is objectual or substitutional. | |
From: Timothy Williamson (Truthmakers and Converse Barcan Formula [1999], §2) |
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) |
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) |