classical_hero said:
We are a cultured people here at MIA. Is it no surprise that we are the only nation never to have tasted war because we will never go down to the level of savages such as every other nation so far. Only savages will backstab people, and we are way above that.
Imagine if you will that you are back in 6 BC when it was fashionable to wear your bedclothes out for a day. A philosopher from Crete named CH is completely and utterly not at all contented with his fellow citizens and exclaims 'All Cretans are liars!'. This is an interesting statement, coming from a Cretan because:
If CH's statement is true, then he is a liar and hence his statement is false. A contradiction.
If CH's statement is false, then it would be possible to pop your sandals on and sail over to Crete to find a Cretan who sometimes tells the truth.
Because CH didn't contradict himself in the second case (when he was lying), the statement 'All Cretans are liars' coming from a Cretan implies that there is at least one Cretan who isn't a liar. Note that, 'not all apples are green' is the same as 'there exists an apple that isn't green'.
OK. So lets refine his statement a little. Suppose CH had said 'I am a liar':
If his statement is true, then he is lying and hence his statement is false. A contradiction.
If his statement is false, then he isn't a liar and sometimes tells the truth. This merely happens to be an example where he is lying. No contradiction.
So, if someone proclaims that they are a liar, it means that they sometimes tell the truth.
Now, ancient Greeks being ancient Greeks, took this one step further. Fe3333 living in 4 BC decided to say 'I am lying'. Since we have a little tradition going:
If Fe3333's statement was true, then he is lying when he says 'I am lying' and so he isn't, ie his statement is false.
If his statement is false, then he isn't lying when he tells us he is, and so his statement is true.
This is known as the Liar's Paradox. It was completely generalised in 14 AD by a Celt philosopher named Beorn who wrote;
All statements on this page are false.
... on an otherwise blank page. Beorn also owned a donkey named Kutzov which starved to death while standing in between two identical bales of hay unable to choose one over the other.