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Single Idea 18130

[filed under theme 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility ]

Full Idea

Russell's Axiom of Reducibility states that to any propositional function of any order in a given level, there corresponds another which is of the lowest possible order in the level. There corresponds what he calls a 'predicative' function of that level.

Gist of Idea

Axiom of Reducibility: there is always a function of the lowest possible order in a given level

Source

report of Bertrand Russell (Substitutional Classes and Relations [1906]) by David Bostock - Philosophy of Mathematics 8.2

Book Ref

Bostock,David: 'Philosophy of Mathematics: An Introduction' [Wiley-Blackwell 2009], p.238

The 4 ideas from 'Substitutional Classes and Relations'

18130 Axiom of Reducibility: there is always a function of the lowest possible order in a given level [Russell, by Bostock]
21560 Any linguistic expression may lack meaning when taken out of context [Russell]
21561 'The number one is bald' or 'the number one is fond of cream cheese' are meaningless [Russell]
21562 There is no complexity without relations, so no propositions, and no truth [Russell]