On Thu, Dec 18, 2008 at 8:18 AM, Alex Smith <ais...@bham.ac.uk> wrote: > On Mon, 2008-12-15 at 22:32 -0500, Warrigal wrote: >> If a CFJ were called on X, it would be legal to judge FALSE on the >> CFJ, where X is defined as the following string, followed by a >> quotation mark, followed by the same string, followed by a quotation >> mark: "If a CFJ were called on X, it would be legal to judge FALSE on >> the CFJ, where X is defined as the following string, followed by a >> quotation mark, followed by the same string, followed by a quotation >> mark: " > > I believe it's a nice simple paradox, but not a game-winning one, as the > paradox arises as a result of the CFJ itself.
I CFJ on the following statement, then: If a CFJ were called on X on December 20 this year, it would be legal to judge FALSE on the CFJ, where X is defined as the following string, followed by a quotation mark, followed by the same string, followed by a quotation mark: "If a CFJ were called on X on December 20 this year, it would be legal to judge FALSE on the CFJ, where X is defined as the following string, followed by a quotation mark, followed by the same string, followed by a quotation mark: " Obviously, this CFJ does not cause an identical CFJ to be called on December 20 this year; therefore, the rule-defined action does not arise from this CFJ. Now, as for the true-and-false chain thing: The truth of a statement does not depend on anything the statement doesn't mention. The only things that can change the truth value of "The sky is blue" are changing the sky and changing what it means to be blue; the only things that can change the truth value of "This statement is false" are changing the statement and changing what it means to be false. Besides, the statement I CFJ'd on is false under the same circumstances as those under which it's true; if it were "constantly alternating between false and true with infinite frequency", it would still be false when true and vice versa; if it is "half true, half false", UNDECIDABLE is appropriate. --Warrigal
