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2 ideas
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. |