This sentence is false. As the explanation of the paradox goes, if the sentence is false, then it is true since it says it is false. But if it is true, then it is false since it says it is false. Hence the paradox.
If you think this is a paradox, please explain briefly how you solve the paradox, if you think you do.
Second, if you think it is not a paradox, please explain briefly why.
Finally, do you think it should be possible to prove there is in fact no paradox.
Thank you to stick to the point and refrain from personal attacks.
EB
I tried to find a sensible resolution of this paradox but all I found was not convincing at all.
The idea that the sentence doesn't refer to anything is wrong on the face of it.
The idea that it doesn't make sense is a bit better but not quite right. The sentence makes enough sense that you can see it is paradoxical. So, saying it doesn't make sense because it is paradoxical doesn't help since it makes enough sense to be felt as paradoxical.
Some Arthur Prior dude has a more interesting position. He asserts that there is nothing paradoxical about the liar paradox because, he says, all statements implicitly assert their truth. Thus, the statement "
This statement is false" is straightforwardly understood as "
This statement is true and this statement is false".
But then, "
This statement is true and this statement is false" is a formal contradiction and as such we can say that it is false. And then there is no paradox because to say that the statement "
This statement is true and this statement is false" is false is not contradictory with the fact that it is indeed false. Ergo, no paradox.
I don't buy it, at least not the way it is presented, but there seems to be something correct in that explanation.
Still, what I didn't find was an explanation of why it should be felt to be a paradox if it is not a paradox. To me, there's no doubt it sounds paradoxical.
Now, apparently, there is no simple solution in the context of mathematical logic. Why is that? Anybody knows?
Tarski apparently "diagnosed" the paradox as arising only in languages in which it is possible for one sentence to predicate truth (or falsehood) of another sentence in the same language and indeed of itself. So, his solution is to forbid that possibility in mathematical logic. Right, so, basically, he just changed the subject of the conversation and in effect admitted to not having a proper resolution.
Unless anyone can update my findings?
EB