Dogman
11th September 2016, 12:08 PM
See it on these forums everyday...!
;D
https://en.wikipedia.org/wiki/Liar_paradox
This statement is false. (A)
If (A) is true, then "This statement is false" is true. Therefore (A) must be false. The hypothesis that (A) is true leads to the conclusion that (A) is false, a contradiction.
If (A) is false, then "This statement is false" is false. Therefore (A) must be true. The hypothesis that (A) is false leads to the conclusion that (A) is true, another contradiction. Either way, (A) is both true and false, which is a paradox.
However, 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".[6] (https://en.wikipedia.org/wiki/Liar_paradox#cite_note-Andrew_Irvine_1992-6) This response to the paradox is, in effect, the rejection of the claim that every statement has to be either true or false, also known as the principle of bivalence (https://en.wikipedia.org/wiki/Principle_of_bivalence), a concept related to the law of the excluded middle (https://en.wikipedia.org/wiki/Law_of_the_excluded_middle).
8447
;D
https://en.wikipedia.org/wiki/Liar_paradox
This statement is false. (A)
If (A) is true, then "This statement is false" is true. Therefore (A) must be false. The hypothesis that (A) is true leads to the conclusion that (A) is false, a contradiction.
If (A) is false, then "This statement is false" is false. Therefore (A) must be true. The hypothesis that (A) is false leads to the conclusion that (A) is true, another contradiction. Either way, (A) is both true and false, which is a paradox.
However, 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".[6] (https://en.wikipedia.org/wiki/Liar_paradox#cite_note-Andrew_Irvine_1992-6) This response to the paradox is, in effect, the rejection of the claim that every statement has to be either true or false, also known as the principle of bivalence (https://en.wikipedia.org/wiki/Principle_of_bivalence), a concept related to the law of the excluded middle (https://en.wikipedia.org/wiki/Law_of_the_excluded_middle).
8447