more from Bertrand Russell

Single Idea 18002

[catalogued under 2. Reason / F. Fallacies / 8. Category Mistake / a. Category mistakes]

Full Idea

Every proposition function …has, in addition to its range of truth, a range of significance, i.e. a range within which x must lie if φ(x) is to be a proposition at all, whether true or false. This is the first point of the theory of types.

Gist of Idea

As well as a truth value, propositions have a range of significance for their variables

Source

Bertrand Russell (The Principles of Mathematics [1903], App B:523), quoted by Ofra Magidor - Category Mistakes 1.2

Book Reference

Magidor,Ofra: 'Category Mistakes' [OUP 2013], p.8


A Reaction

Magidor quotes this as the origin of the idea of a 'category mistake'. It is the basis of the formal theory of types, but is highly influential in philosophy generally, especially as a criterion for ruling many propositions as 'meaningless'.

Related Idea

Idea 18003 In 'x is a u', x and u must be of different types, so 'x is an x' is generally meaningless [Russell, by Magidor]