And no, I'm not saying you have to recognize that anything is possible. There are things we know are impossible because we can observe how certain things work in the natural world. For instance, we know it's impossible to live (or at least live more than a few seconds) without your head. If someone said "Decapitate me and I will pick up my head, screw it back on and walk out the door." we can very well prove him wrong.
Actually, you are wrong in this argument. It is possible to prove that
a particular individual cannot live without their head (albeit it would require their decapitation to prove it); but it is not possible to prove that, for every person who ever has existed, or ever will exist, that it would be impossible for them to live without their head (unless you were to find some way to decapitate every person who ever has or will live). We make this
assumption based on observations of how things work, and extend the information we've thus far compiled.
To take your argument...
prove to me that it is
impossible for any person who has ever lived, in the history of the world, to have lived with their head cut off. You
cannot prove it. Therefore, by your own argument, you must consider it at least a possibility that a person
can live with their head cut off.
In short -- the
only logical conclusion from your initial argument is that one
must consider everything to be possible...it is impossible to discount
anything as impossible, or non-existent.
ETA: It should be noted that while I consider it a reasonable belief that it is impossible to literally be dead for three days, and then come back to life, there are hundreds of millions of people in this world who believe it has happened at least twice (Lazarus and Jesus). For such people, believing that a person could have their heads cut off and still live would not be a terribly great leap of faith...so go ahead,
prove to those people that its impossible. The best you can do is prove that
they can't live with their heads cut off.
Another ETA: It is possible to disprove
individual claims (ie. I claim that I can live without my head); but impossible to disprove
universal claims (ie. it is impossible for
anyone to live without their head).