I actually believe it's primarily a third reason the author didn't mention: (3) not understanding what a "proof" is and what it means to "prove" something. Of c

I actually believe it's primarily a third reason the author didn't mention: (3) not understanding what a "proof" is and what it means to "prove" something. Of course it ties into the 2nd reason in that many people aren't motivated to learn what a proof actually is. The "impossible to absolutely prove" phrase has a misuse of "prove". A proof is absolute. A proof is either valid or invalid judged solely on whether it follows the rules of the predicate calculus (or the rules of some other proof-framework you're using which is likely using the predicate calculus or an extension behind the scenes anyway). A proof's conclusions are "true" if and only if they are true. ( http://yudkowsky.net/rational/the-simple-truth http://yudkowsky.net/rational/the-simple-truth ) It is true (so far as we know, we might be wrong in the end) that we can't be absolutely certain that something is false, but it's the same case for being absolutely certain that something is true. (Here "absolutely certain" means "no admittance to even the possibility of being incorrect".) This is more generally identified as the problem of induction, but it's more of a law than a problem. One can guess from the name it has to do with inductive arguments that rely on guessing+evidence rather than deductive proofs that rely on accepting premises (which may be true or false) and a proof framework like the predicate calculus. Edit: Have a Feynman video on UFOs. :) http://www.youtube.com/watch?v=wLaRXYai19A http://www.youtube.com/watch?v=wLaRXYai19A When he says "I can't prove it's impossible", the interpretation you should take is "I can't produce a set of premises we can all agree with that leads to a deductive proof that UFOs are impossible."