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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.
Gist of Idea
'All judgements made by Epimenedes are true' needs the judgements to be of the same type
Source
Bertrand Russell (The Theory of Logical Types [1910], p.227)
Book Ref
Russell,Bertrand: 'Essays in Analysis', ed/tr. Lackey,Douglas [George Braziller 1973], 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.
23457 | Type theory cannot identify features across levels (because such predicates break the rules) [Morris,M on Russell] |
21556 | Classes are defined by propositional functions, and functions are typed, with an axiom of reducibility [Russell, by Lackey] |
21566 | 'Propositional functions' are ambiguous until the variable is given a value [Russell] |
21567 | 'All judgements made by Epimenedes are true' needs the judgements to be of the same type [Russell] |
21568 | A one-variable function is only 'predicative' if it is one order above its arguments [Russell] |