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Full Idea
In Russell's mature 1910 theory of types classes are defined in terms of propositional functions, and functions themselves are regimented by a ramified theory of types mitigated by the axiom of reducibility.
Gist of Idea
Classes are defined by propositional functions, and functions are typed, with an axiom of reducibility
Source
report of Bertrand Russell (The Theory of Logical Types [1910]) by Douglas Lackey - Intros to Russell's 'Essays in Analysis' p.133
Book Ref
Russell,Bertrand: 'Essays in Analysis', ed/tr. Lackey,Douglas [George Braziller 1973], p.133
Related Idea
Idea 14459 Reducibility: a family of functions is equivalent to a single type of function [Russell]
| 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] |