Clearly, the problem with my understanding lies in the wording of the question being weird and unclear.
Well that would be the point
, but it's also just to make it impossible to answer. If you answer 25%, the chance is actually 50%. If you answer 50%, the chance is actually 25%. If you (in my version) answer 0%, the chance is 25% and you're still wrong. In the C) 60% version, if you answer 0% you're right because none of the answers are 0%.
what's interesting is that you can't get it right, so one could argue that 0% is right
. what this means is that there's a sentence that's true, but can't be asserted. the amazing consequence is that language cannot prove all of its true statements. one thing this means is that language is not (and cannot be) a perfect mirror of the world.
in other words, language cannot correspond to reality the way, say, code corresponds to the behavior of a computer. it's as if you had a syntax and semantics that
1) allowed you to form 5 commands, each with a unique result,
2) but the whole system had 6 possible results,
3) none of which correspond to any of the 5 commands, nor any combination of them,
4) but nonetheless all can be achieved on this "computer" (or turing machine, or whatever).
godel's incompleteness theorems (that sufficiently strong formal languages, for example arithmetic
or even the most basic forms of classical logic, either can express truths that cannot be proven, or they can prove things that are in fact false) and the liar's paradox are interesting when you think about philosophy of language, but they're a real mind @#%^ if you bring the idea of turing machines / computers. if syntax and logic can invade the physical world in the form of programming, what about self-referentiality?
at least i think it's interesting. not interesting enough to study (i only care about language; i don't care about computers or metaphysics), but interesting.
oh, the reason i was going to respond: you should take a logic class (2 actually, since classical logic = should be required education for everyone, and intermediate logic--stuff like 2nd order logic, constructing formal languages via inductive definitions and proving sh*t about the natural numbers, godel's incompleteness theorem--gets to the meat).
it's especially interesting if you're interested in programming. you'll see why us logicians are so weirded out by programming... to me, programming always seems backward... instead of explaining, i'll just say that it should give you insight and trail off. Edited, Aug 5th 2012 2:20am by milich