Ok then, I accept your challenge.
I'll begin with an explanation.
The paradox arises from considering the sentence as possessing a truth value (ie. being either true or false). You see, if the sentence (call it P from now on) is true, then the person saying P must be lying, making P false. Conversely, considering P as being false results in the truth being that the person saying P is telling the truth, meaning that they are actually lying, which means they're telling the truth, and so on.
In other words, whichever truth value you assign the sentence, ananlysis of it in this light produces the opposite truth value. Problem.
What does it all mean? Fucked if I know, but let's see what I can make up as I go along. What do we know about it?
- P is in English. English is a human language that, idioms aside, contains the meaning of its sentence in grammatical relations of its particles.
- P, when considered as false, turns out to be true. When considered as true, P turns out to be false, as we have just seen.
, it would appear that the problem occurs as a result of considering a sentence constructed in English to conform to logical rules. However, the problem can be restated in formal logical language without the paradox cheerfully going away.
P possesses the follwoing logical form:
sentence P:"P is false"
From this, it can be seen that I have no idea what the hell is going on. The best I can say is that considering things like this to have a truth value is what causes the problem in the first place, and so the most obvious way out of this one is simply to make sure it never comes up. Consider P as being neither true nor false.
All sorts of problems go here but I'm sleepy and Wittgenstein or someone has probably beaten me to it, so this is Pseudomancer signing off for now.