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Full Idea
We will define a function of one variable as 'predicative' when it is of the next order above that of its arguments, i.e. of the lowest order compatible with its having an argument.
Gist of Idea
A one-variable function is only 'predicative' if it is one order above its arguments
Source
Bertrand Russell (The Theory of Logical Types [1910], p.237)
Book Ref
Russell,Bertrand: 'Essays in Analysis', ed/tr. Lackey,Douglas [George Braziller 1973], p.237
A Reaction
'Predicative' just means it produces a set. This is Russell's strict restriction on which functions are predicative.
Related Idea
Idea 21558 'Predicative' norms are those which define a class [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] |