My Math Forum The Liar paradox and Logic values

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 View Poll Results: A: A is false. B: A is false. 0 0% C: A is both true and false. 1 33.33% D: A is neither true or false. 0 0% E: A is not a valid statement. 2 66.67% F: I don't know. 0 0% Voters: 3. You may not vote on this poll

 August 30th, 2007, 05:06 AM #1 Newbie   Joined: Aug 2007 Posts: 11 Thanks: 0 The Liar paradox and Logic values Hi My oppinion is that A is both true and false... even if it does break the law of excluded middle. If the law really can have no exception then ill have to go for D i guess... I have heard about logic systems with more than two truth values. For instance A seems to not be a paradox only in infinite valued logic. Anibody heard about less than two truth valued logic? With only one truth value? Or none? What would we get in that case? At least no paradox would arise as well right?
 August 30th, 2007, 11:35 AM #2 Senior Member   Joined: Dec 2006 Posts: 1,111 Thanks: 0 I would contend that the statement is meaningless, since the statement makes a statement about the truth or falsity of itself, thus making it an infinite loop. In other words, there is no answer, and the statement is invalid.
 September 1st, 2007, 05:10 AM #3 Newbie   Joined: Aug 2007 Posts: 11 Thanks: 0 Thanks for the reply. I do know that in formal logic it is not a valid statement... The recursive definition does not include A as a well formed formula. But do you think it is still not valid in intuitive logic? What about in english? You still dismiss it? What about different valued logics? Do you have anything on that? And people, please don't be shy, VOTE, I mean, it's just a click and I can't really make any conclusions on 2 votes out of 20 views.
September 23rd, 2007, 10:02 AM   #4
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Quote:
 Originally Posted by Infinity I would contend that the statement is meaningless, since the statement makes a statement about the truth or falsity of itself, thus making it an infinite loop. In other words, there is no answer, and the statement is invalid.
You seem to be saying "there is no answer", but nevertheless selecting answer E.

September 23rd, 2007, 12:12 PM   #5
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Quote:
 And people, please don't be shy, VOTE, I mean, it's just a click and I can't really make any conclusions on 2 votes out of 20 views.
Voting will not decide the truth or falsity of a statement. Just because a lot of people used to think that the earth was flat, didn't mean that the earth was flat. If you can decide truth by voting, then if 51% of a group of people voted that pi was a rational number, then pi would be a rational number, which is not exactly the way things really work.

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