On Wed, Aug 21, 2013 at 3:48 PM, Shane Mage <[email protected]> wrote:
> > 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. > > > The "excluded middle" says: Either A or notA. If "false" is A, then > "true" can be termed notA ONLY if statements must be either true or false. > Which is manifestly NOT the case. Frederic's birthday was not his > twenty-first, but that didn't in fact, in logic, or in law (even Pirate > law) make him "a little boy of five." > Ok, all you are saying is that natural language contains sentences that cannot be formalized into propositions that have truth values. Great, but what have you really achieved? You will now just have to accept that you cannot easily specify just what class of sentences you can exclude in this way without in essence crippling the ability of the language to express truth-claims. > The ways of paradox may be quaint, but every one of them reflects a > defective way of formulation. > There is nothing quaint about these paradoxes. You have a choice of either (a) giving up on "natural language" and restrict yourself to a stunted formal language in which logic can be used without running into these paradoxes, or (b) accepting that natural language cannot be completely formalized and reduced to logic consistently, and you need to be cautious in making truth-claims in natural language terms. -raghu.
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