display all the ideas for this combination of texts
4 ideas
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. |
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. |
21566 | 'Propositional functions' are ambiguous until the variable is given a value [Russell] |
Full Idea: By a 'propositional function' I mean something which contains a variable x, and expresses a proposition as soon as a value is assigned to x. That is to say, it differs from a proposition solely by the fact that it is ambiguous. | |
From: Bertrand Russell (The Theory of Logical Types [1910], p.216) | |
A reaction: This is Frege's notion of a 'concept', as an assertion of a predicate which still lacks a subject. |
21567 | 'All judgements made by Epimenedes are true' needs the judgements to be of the same type [Russell] |
Full Idea: Such a proposition as 'all the judgements made by Epimenedes are true' will only be prima facie capable of truth if all his judgements are of the same order. | |
From: Bertrand Russell (The Theory of Logical Types [1910], p.227) | |
A reaction: This is an attempt to use his theory of types to solve the Liar. Tarski's invocation of a meta-language is clearly in the same territory. |