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3 ideas
16308 | Set theory was liberated early from types, and recent truth-theories are exploring type-free [Halbach] |
Full Idea: While set theory was liberated much earlier from type restrictions, interest in type-free theories of truth only developed more recently. | |
From: Volker Halbach (Axiomatic Theories of Truth [2011], 4) | |
A reaction: Tarski's theory of truth involves types (or hierarchies). |
21558 | 'Predicative' norms are those which define a class [Russell] |
Full Idea: Norms (containing one variable) which do not define classes I propose to call 'non-predicative'; those which do define classes I shall call 'predicative'. | |
From: Bertrand Russell (Difficulties of Transfinite Numbers and Types [1905], p.141) |
21559 | We need rules for deciding which norms are predicative (unless none of them are) [Russell] |
Full Idea: We need rules for deciding what norms are predicative and what are not, unless we adopt the view (which has much to recommend it) that no norms are predicative. ...[146] A predative propositional function is one which determines a class. | |
From: Bertrand Russell (Difficulties of Transfinite Numbers and Types [1905], p.141) | |
A reaction: He is referring to his 'no class' theory, which he favoured at that time. |