51–59 of 59 posts
Earlier quoted context omitted.
But there's only a 50% chance that the person asking that will have balls.
I would speculate that of the people to ask annoying trick questions, the vast majority of them are smug males.
Appears to be a clever case of the first incompleteness theorum.
While the usual analogy for the first theorem is drawn to the liar's paradox ("This is a false statement."), it's important to remember that it is only an analogy. The first theorem states, in layman's terms, that we can construct a valid mathematical statement which is complete and utter nonsense. (Much like "This is a false statement." is neither true nor false, but nonsensical.)
The second incompleteness theorem simply states (again, in layman's terms) that the consistency (where we say something is consistent if it contains no contradictions) of certain systems cannot be shown from the rules of the system itself. (Or alternatively and more correctly, if you're able to show the consistency of these systems using their own rules, then they're inconsistent.)
That said, please remember that these are mathematical theorems and as such their "applications" to other areas such as metaphysics, even by their creator, are not rigorous or necessarily meaningful. They live where they belong: in the depths of mathematical logic, in the heart of mathematics.
I refuse to play silly mind games which make me feel incompetent.
However, the question merely states IF you choose, not that you have to.
Therefore, I am entirely correct by answering either A or D.
Thus it is not unanswerable and is incorrect in stating so.
A more distilled version: Which of the following is the answer to this question? A) B B) A
answering the question at random is not the same as answering the question posed - so the fact that the two answers are not equal shouldn't be a problem. right?
edit: i hate paradoxes, i'm pretty certain i'm wrong, but i can't put my finger on precisely why. :)
Earlier quoted context omitted.
Is "The above question has no solution", which is choice C, not a Godel sentence?
No. Godel's incompleteness theorems say nothing about non-arithmetical or non-mathematical statements nor do they apply in contexts where no formal system exists. Some sort of paradox, sure, but Godel doesn't apply. Truth is not a mathematical concept, and determining the "truth" or "falsehood" of a sentence has nothing to do with Godel's incompleteness theorems.