04 Jun 07
Originally posted by doodinthemoodI believe what the original poster was driving at was that the statement "I am lying" is undecidable. However, given Godel's original statement:
It is false. He is saying it with the intention to create a paradox, not with the intention to insincerely deceive, and thus, is not lying. He is also not telling the truth, but that isn't relevant. The point is that he is not lying.
"For any consistent formal, computably enumerable theory that proves basic arithmetical truths, an arithmetical statement that is true but not provable in the theory can be constructed. That is, any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete." (http://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems)
I'm not sure the English language and it's grammar constitute are consistent, formal, or computably enumerable enough to use this terminology.
04 Jun 07
Originally posted by JirakonStatement P = {A man walks up to you and says, "I am lying."}
A man walks up to you and says, "I am lying." Is his statement true or false?
Is P true or false?
Well, I had my brother to walk up to me and say it word by word (I had to bribe him with a fiver first) so now I'm sure it is true.
04 Jun 07
"his statement" refers to the statement made by the man, namely, "I am lying." His statement does not include the initial "a man walks up to you and says," as he did not say that.
He is saying it with the intention to create a paradox, not with the intention to insincerely deceive
How do you know what his intentions are? What if he is insane, believes he is telling the truth, and insincerely tries to deceive you? Then it would be a true statement.
There is enough information given to either prove that no matter what the man's intentions, the statement itself must be true, or that no matter what the man's intentions, the statement itself must be false. I suppose that could be a big hint 🙂