21565 | Richard's puzzle uses the notion of 'definition' - but that cannot be defined [Russell] |
Full Idea: In Richard's puzzle, we use the notion of 'definition', and this, oddly enough, is not definable, and is indeed not a definite notion at all. | |
From: Bertrand Russell (On 'Insolubilia' and their solution [1906], p.209) | |
A reaction: The background for this claim is his type theory, which renders certain forms of circular reference meaningless. |
13369 | By diagonalization we can define a real number that isn't in the definable set of reals [Priest,G] |
Full Idea: Richard: φ(x) is 'x is a definable real number between 0 and 1' and ψ(x) is 'x is definable'. We can define a real by diagonalization so that it is not in x. It is and isn't in the set of reals. | |
From: Graham Priest (The Structure of Paradoxes of Self-Reference [1994], §3) | |
A reaction: [this isn't fully clear here because it is compressed] |