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Full Idea
Berry: if we take 'x is a natural number definable in less than 19 words', we can generate a number which is and is not one of these numbers.
Gist of Idea
'x is a natural number definable in less than 19 words' leads to contradiction
Source
Graham Priest (The Structure of Paradoxes of Self-Reference [1994], §3)
Book Ref
-: 'Mind' [-], p.29
A Reaction
[not enough space to spell this one out in full]
| 13366 | The least ordinal greater than the set of all ordinals is both one of them and not one of them [Priest,G] |
| 13367 | The next set up in the hierarchy of sets seems to be both a member and not a member of it [Priest,G] |
| 13368 | The 'least indefinable ordinal' is defined by that very phrase [Priest,G] |
| 13370 | 'x is a natural number definable in less than 19 words' leads to contradiction [Priest,G] |
| 13369 | By diagonalization we can define a real number that isn't in the definable set of reals [Priest,G] |
| 13371 | If you know that a sentence is not one of the known sentences, you know its truth [Priest,G] |
| 13372 | There are Liar Pairs, and Liar Chains, which fit the same pattern as the basic Liar [Priest,G] |
| 13373 | Typically, paradoxes are dealt with by dividing them into two groups, but the division is wrong [Priest,G] |