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Ideas for 'Truth and the Past', 'Comments on a Certain Broadsheet' and 'The Evolution of Logic'

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4 ideas

5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / c. Berry's paradox
13484 Berry's Paradox: we succeed in referring to a number, with a term which says we can't do that [Hart,WD]
     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.
     From: William D. Hart (The Evolution of Logic [2010], 3)
     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.
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / c. Burali-Forti's paradox
13482 The Burali-Forti paradox is a crisis for Cantor's ordinals [Hart,WD]
     Full Idea: The Burali-Forti Paradox was a crisis for Cantor's theory of ordinal numbers.
     From: William D. Hart (The Evolution of Logic [2010], 3)
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
13507 The machinery used to solve the Liar can be rejigged to produce a new Liar [Hart,WD]
     Full Idea: In effect, the machinery introduced to solve the liar can always be rejigged to yield another version the liar.
     From: William D. Hart (The Evolution of Logic [2010], 4)
     A reaction: [He cites Hans Herzberger 1980-81] The machinery is Tarski's device of only talking about sentences of a language by using a 'metalanguage'.
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / b. The Heap paradox ('Sorites')
8194 Surely there is no exact single grain that brings a heap into existence [Dummett]
     Full Idea: There is surely no number n such that "n grains of sand do not make a heap, although n+1 grains of sand do" is true.
     From: Michael Dummett (Truth and the Past [2001], 4)
     A reaction: It might be argued that there is such a number, but no human being is capable of determing it. Might God know the value of n? On the whole Dummett's view seems the most plausible.