On Tue, Aug 20, 2013 at 5:43 PM, Shane Mage <[email protected]> wrote:
> > On Aug 20, 2013, at 1:43 PM, Chuck Grimes wrote: > > ... These can be modeled on the liar's > paradox which leads to a contradiction in the formation of definitions. > > Example. This statement is false. (A)\ > > > But---what statement does "this statement" refer to? If some prior > statement, no problem or paradox. > There are ways to recreate the Liar's paradox without self-referential statements (e.g. with a number of sentences that refer to each other). > If the statement is "this statement is false" then we must say " 'this > statement is false' is false." Again, no paradox because the contradiction > in Aristotelian logic is between false and not-false, and not-false in no > way implies true: a statement may be performative, emotional, or > meaningless and as such neither true nor false. > Not false indeed equals true unless you reject the "excluded middle" principle, which very substantially cripples logic and prevents you from doing all kinds of interesting and useful stuff with it. As Chuck says, I am not sure it is productive to re-litigate a hundred years of analytic philosophy on PEN-L. Can we just accept that these paradoxes hint at some fundamental limits to what can and cannot be precisely expressed in formal languages and we should therefore be appropriately cautious about making absolute truth-claims about anything? (Yeah, yeah I know, if you go too far down that road you end up with the crazier versions of post-modernism. As I said, appropriate caution is required..) -raghu.
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