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Single Idea 13484

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

Full Idea

Berry's Paradox: by the least number principle 'the least number denoted by no description of fewer than 79 letters' exists, but we just referred to it using a description of 77 letters.

Gist of Idea

Berry's Paradox: we succeed in referring to a number, with a term which says we can't do that

Source

William D. Hart (The Evolution of Logic [2010], 3)

Book Ref

Hart,W.D.: 'The Evolution of Logic' [CUP 2010], p.63

A Reaction

I struggle with this. If I refer to 'an object to which no human being could possibly refer', have I just referred to something? Graham Priest likes this sort of idea.

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]