display all the ideas for this combination of texts
7 ideas
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) |
8078 | Modus ponens is one of five inference rules identified by the Stoics [Chrysippus, by Devlin] |
Full Idea: Modus ponens is just one of the five different inference rules identified by the Stoics. | |
From: report of Chrysippus (fragments/reports [c.240 BCE]) by Keith Devlin - Goodbye Descartes Ch.2 | |
A reaction: Modus ponens strikes me as being more like a definition of implication than a 'rule'. Implication is what gets you from one truth to another. All the implications of a truth must also be true. |
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? |
6023 | Every proposition is either true or false [Chrysippus, by Cicero] |
Full Idea: We hold fast to the position, defended by Chrysippus, that every proposition is either true or false. | |
From: report of Chrysippus (fragments/reports [c.240 BCE]) by M. Tullius Cicero - On Fate ('De fato') 38 | |
A reaction: I am intrigued to know exactly how you defend this claim. It may depend what you mean by a proposition. A badly expressed proposition may have indeterminate truth, quite apart from the vague, the undecidable etc. |
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) |