Full Idea
In his 1903 theory of types he distinguished between individuals, ranges of individuals, ranges of ranges of individuals, and so on. Each level was a type, and it was stipulated that for 'x is a u' to be meaningful, u must be one type higher than x.
Gist of Idea
For 'x is a u' to be meaningful, u must be one range of individuals (or 'type') higher than x
Source
Bertrand Russell (The Principles of Mathematics [1903], App)
Book Reference
Russell,Bertrand: 'Essays in Analysis', ed/tr. Lackey,Douglas [George Braziller 1973], p.129
A Reaction
Russell was dissatisfied because this theory could not deal with Cantor's Paradox. Is this the first time in modern philosophy that someone has offered a criterion for whether a proposition is 'meaningful'?
Related Idea
Idea 21554 Sets always exceed terms, so all the sets must exceed all the sets [Lackey]