Here's a spin on the classic "liar paradox," that I thought may be new for some of you.
Consider the following proposition X:
X = [This sentence is false]
What is the truth-value (true or false) of X?
Is it true? If that's the case... well you can see for yourself the trouble this leads to.
Any ideas on how to solve the paradox?
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6 comments:
I have seriously been thinking about this argument for about an hour and even brought in my roommates opinion. I think i have something to say about it but i can't think of how to write out my reasoning (i have never been good with words, that's why i'm the dumb guy in the back). I tried writing out a logic statement but i just confused myself.
Basically the statement of X, "This sentence is false," is actually saying that X actually represents the statement, "This statement is true" which is true because by saying that the original is false, the second is true, thus making the original true.
That may not make any sense to anyone but me, but i really did try to explain it logically.
In the opposite realm, the proposition may also be false. For example, X=(the sky is blue). The proposition X is true sometimes but it may be completely nullified during a different period of time. In the case that the sky is not blue, the proposition would be false. Maybe a conditional viewpoint isn't the best approach on this...it's a tricky one. This remeinds me of the riddle when you're in a cave with one person who always lies, and another who tells the truth and you must ask only one question to find your way out.
What a great sentence! If I claim X is false, then I am saying that the statement “this sentence is false” is false; therefore, the statement “this sentence is false” is actually true. This means that somehow, this sentence is indeed false, which means that the corrected version of the statement “this sentence is false” should really be “this sentence is true.” And from there one, the statement “this sentence is true” continues to affirm itself and we can conclude that the statement is such.
However… if I claim that X is true, then I am saying that the statement “this sentence is false” is actually true. Therefore, with the statement being true, then the statement “this sentence is false” is the opposite of the truth; therefore, the truth is the opposite which would read “this sentence is true.” And finally, we are back to the repeated conclusion of the first assumption that the truth behind the statement X is actually saying that “this sentence is true.”
I think it's a great riddle for the mind to mull over and I love things like this, but I don't (and hope no one else does) slave over it and think that it has lasting affects on the world if somehow it's solved (or even if it isn't). I hope what I just said doesn't discourage anyone from actually thinking it over (because it really is fun to try and work it out).
The equal sign in the statement provides the knowledge that this statement is bona fide. X then must equal "this sentence is false." By stating that this sentence is false, I in actuality am stating that this is a true fact. Yes it is a bona fide false statement. I, therefore, am being a truly honest person with high morals when I state that I have lied to you. It is sort of like deceiving for someone's benefit. I am lying, but it is for the greater good.
I agree with Jorge that the false statement is truly a false statement. The truth-value of the statement is that it is true that the statement is false. However, beyond that, there is no value in knowingly making that false statement. Jorge mentions that it’s like lying to someone for their own benefit. I agree. I do no find such an ethical move as valuable. It’s similar to Kant’s false promises ethical situation. Kant’s objection to this situation is that you could not will that a lie become a universal law because then you could never know truth. Likewise, one cannot will that there is truth-value in this statement because then you would not truly know when an actual true statement was true.
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