Combining Texts

Ideas for 'Nietzsche and Philosophy', 'The Evolution of Logic' and 'On the Syllogism IV'

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3 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'.