Posted: Sat Oct 07, 2006 3:57 am
Ight, Phil 101 teach said if we can come up with an example that defies Aristotle's Law of Non-Contradictions we get an automatic A for the class (Law states that something cannot be A and not A at the same time and with the same respect).
I did some research, and came up with this...
(from a website..please read!!...the italics are not as important in my opinion...make sure you get the last part tho)
The problem of the paradox is that it seems to show that common beliefs about truth and falsity actually lead to a contradiction. Sentences can be constructed that cannot consistently be assigned a truth value even though they are completely in accord with grammar and semantic rules. Consider the simplest version of the paradox, the sentence This statement is false. If we suppose that the statement is true, everything asserted in it must be true. However, because the statement asserts that it is itself false, it must be false. So the hypothesis that it is true leads to the contradiction that it is true and false. Yet we cannot conclude that the sentence is false for that hypothesis also leads to contradiction. If the statement is false, then what it says about itself is not true. It says that it is false, so that must not be true. Hence, it is true. Under either hypothesis, we end up concluding that the statement is both true and false. But it has to be either true or false (or so our common intuitions lead us to think), hence there seems to be a contradiction at the heart of our beliefs about truth and falsity.
However, the fact that the liar sentence can be shown to be true if it is false and false if it is true has led some to conclude that it is neither true nor false. This response to the paradox is, in effect, to reject one of our common beliefs about truth and falsity: the claim that every statement has to be one or the other. This common belief is called the Principle of Bivalence, and is related to the law of the excluded middle.
The proposal that the statement is neither true nor false has given rise to the following, strengthened version of the paradox:
This statement is not true.
If it is neither true nor false, then it is not true, which is what it says; hence it's true, etc.
This again has led some, notably Graham Priest, to posit that the statement is both true and false (see paraconsistent logic).
Nevetheless, even Priest's analysis is susceptible to the following version of the liar:
This statement is only false.
If it is true and false then it is true, which means that it is only false since that's what it says, but then it can't be true, so it is false, etc.
A. N. Prior claims that there is nothing paradoxical about the Liar paradox. His claim (which he attributes to Charles S. Peirce and John Buridan) is that every statement includes an implicit assertion of its own truth. Thus, for example, the statement "It is true that two plus two equals four" contains no more information than the statement "two plus two is four", because the phrase "it is true that..." is always implicitly there. And in the self-referential spirit of the Liar Paradox, the phrase "it is true that..." is equivalent to "this whole statement is true and ...". Thus the statement "This statement is false" is said to be equivalent to
This statement is true and this statement is false.
The latter is a simple contradiction of the form "A and not A", and hence is false. There is no paradox because the claim that this two-conjunct Liar is false does not lead to a contradiction.
(now these are my thoughts)
Go back to the "this statement is only false." How does this not defy the law?? Adding Prior's claim (as in the example) does make it false...(as pointed out in the last part of the article..) OR DOES IT? How can you add Prior's claim once but not again...It seems to me, that to consistently use Prior's claim, you would have to say:
IT IS TRUE that this statement is true and that this statement is false.
Since they agreed that the "this statement is true and this statement is false" is false, the implicit assertion of its own truth makes it both...right? It may be Bivalent, (idk, maybe not) but it seems that could be worked around..
WHAT DO YOU GUYS THINK? AM I SOUND HERE? IF NOT, ANY OTHER IDEAS HOW TO BREAK THE LAW?
I did some research, and came up with this...
(from a website..please read!!...the italics are not as important in my opinion...make sure you get the last part tho)
The problem of the paradox is that it seems to show that common beliefs about truth and falsity actually lead to a contradiction. Sentences can be constructed that cannot consistently be assigned a truth value even though they are completely in accord with grammar and semantic rules. Consider the simplest version of the paradox, the sentence This statement is false. If we suppose that the statement is true, everything asserted in it must be true. However, because the statement asserts that it is itself false, it must be false. So the hypothesis that it is true leads to the contradiction that it is true and false. Yet we cannot conclude that the sentence is false for that hypothesis also leads to contradiction. If the statement is false, then what it says about itself is not true. It says that it is false, so that must not be true. Hence, it is true. Under either hypothesis, we end up concluding that the statement is both true and false. But it has to be either true or false (or so our common intuitions lead us to think), hence there seems to be a contradiction at the heart of our beliefs about truth and falsity.
However, the fact that the liar sentence can be shown to be true if it is false and false if it is true has led some to conclude that it is neither true nor false. This response to the paradox is, in effect, to reject one of our common beliefs about truth and falsity: the claim that every statement has to be one or the other. This common belief is called the Principle of Bivalence, and is related to the law of the excluded middle.
The proposal that the statement is neither true nor false has given rise to the following, strengthened version of the paradox:
This statement is not true.
If it is neither true nor false, then it is not true, which is what it says; hence it's true, etc.
This again has led some, notably Graham Priest, to posit that the statement is both true and false (see paraconsistent logic).
Nevetheless, even Priest's analysis is susceptible to the following version of the liar:
This statement is only false.
If it is true and false then it is true, which means that it is only false since that's what it says, but then it can't be true, so it is false, etc.
A. N. Prior claims that there is nothing paradoxical about the Liar paradox. His claim (which he attributes to Charles S. Peirce and John Buridan) is that every statement includes an implicit assertion of its own truth. Thus, for example, the statement "It is true that two plus two equals four" contains no more information than the statement "two plus two is four", because the phrase "it is true that..." is always implicitly there. And in the self-referential spirit of the Liar Paradox, the phrase "it is true that..." is equivalent to "this whole statement is true and ...". Thus the statement "This statement is false" is said to be equivalent to
This statement is true and this statement is false.
The latter is a simple contradiction of the form "A and not A", and hence is false. There is no paradox because the claim that this two-conjunct Liar is false does not lead to a contradiction.
(now these are my thoughts)
Go back to the "this statement is only false." How does this not defy the law?? Adding Prior's claim (as in the example) does make it false...(as pointed out in the last part of the article..) OR DOES IT? How can you add Prior's claim once but not again...It seems to me, that to consistently use Prior's claim, you would have to say:
IT IS TRUE that this statement is true and that this statement is false.
Since they agreed that the "this statement is true and this statement is false" is false, the implicit assertion of its own truth makes it both...right? It may be Bivalent, (idk, maybe not) but it seems that could be worked around..
WHAT DO YOU GUYS THINK? AM I SOUND HERE? IF NOT, ANY OTHER IDEAS HOW TO BREAK THE LAW?