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Single Idea 13370

[filed under theme 5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / c. Berry's paradox ]

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]

The 4 ideas with the same theme [problem with defining a number with maximum words]:

18125 Berry's Paradox considers the meaning of 'The least number not named by this name' [Bostock]
13484 Berry's Paradox: we succeed in referring to a number, with a term which says we can't do that [Hart,WD]
9638 Berry's Paradox finds a contradiction in the naming of huge numbers [Brown,JR]
13370 'x is a natural number definable in less than 19 words' leads to contradiction [Priest,G]