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Single Idea 21568

[catalogued under 6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism]

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


Bertrand Russell (The Theory of Logical Types [1910], p.237)

A Reaction

'Predicative' just means it produces a set. This is Russell's strict restriction on which functions are predicative.

Book Reference

Russell,Bertrand: 'Essays in Analysis', ed/tr. Lackey,Douglas [George Braziller 1973], p.237

Related Idea

Idea 21558 'Predicative' norms are those which define a class [Russell]