Single Idea 18003

[catalogued under 6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory]

Full Idea

Russell argues that in a statement of the form 'x is a u' (and correspondingly, 'x is a not-u'), 'x must be of different types', and hence that ''x is an x' must in general be meaningless'.

Gist of Idea

In 'x is a u', x and u must be of different types, so 'x is an x' is generally meaningless

Source

report of Bertrand Russell (The Principles of Mathematics [1903], App B:524) by Ofra Magidor - Category Mistakes 1.2

Book Reference

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


A Reaction

" 'Word' is a word " comes to mind, but this would be the sort of ascent to a metalanguage (to distinguish the types) which Tarski exploited. It is the simple point that a classification can't be the same as a member of the classification.

Related Idea

Idea 18002 As well as a truth value, propositions have a range of significance for their variables [Russell]