Can you not prove that Antec did not produce the Sonata case a billion years ago?
sort of trivial example, but to be pedantic, you still can't, all one could say is that we haven't dug one up yet.
i was referring more to (still rather well-defined) things like attempting to prove your own past intents, and proving your own actions did not have a negative effect on someone else's income/credibility etc which is obviously impossible.
a much simpler and still well-bounded problem would be to prove that the entire universe did not
come into existence precisely 12 minutes ago.
No, I don't think that it is likely that Earth is the only place where intelligent life exists. But I do not think that we have been visited by any intelligent extraterrestrials. The distances between solar systems is just too great for that to be likely.
i'd agree that "we" have probably not been visited - it's nearly impossible for intelligent life to not exist elsewhere, but the timing would have to be... well, i wouldn't be an atheist if we managed to find any civilization at a similar level to our own. time began what, 6 billion years ago? people have been around for a hundred thousand or so, 200 years ago we were just cavemen with steam, nice clothes and gunpowder, and in a thousand years (if not 100) only cockroaches and fish will be living here. so the chance of encountering anything we can even comprehend gets cut down by a factor of 100 million or so on top of the chance of simply finding intelligent life or life finding us.
having said that, remember the distance alone isn't a huge problem - initially, manned moon landings were supposed to be one-way missions too. once we're capable of getting moving anywhere near c, time dilation will allow us to travel thousands of light years within the span of a career for anyone on board. not sure if any human would be able to cope with still being young when their daughter's grandchildren are centuries in the ground, and of course noone on Earth would ever know what came of it, but the option is still there, especially in the context of a mass exodus or similar. the bigger problems are things like navigation, colliding with anything big enough to be visible when you're moving that fast, surviving when even background radiation gets blueshifted into x-rays etc etc