> Something that's mathematically perfect fits that criteria.
No, it doesn't. A one-time pad still needs a source of randomness, and a guarantee no reuse. How certain are you that you don't have a backdoored RNG, or initialization vector reuse?
Or, for a fully general argument, how certain are you that we're not living in a computer simulation, where the Dark Lords of the Matrix can just lookup their logs to see what random values were generated for your one-time pad? Or if we go to that extreme, how can you be absolutely certain of the truth of anything - including mathematics - if said Dark Lords could be messing with our brain and memories?
Or more mundanely, how about this: a flurry of cosmic rays strike the RAM containing the message and by random chance flip the same bits that were set in the on-time pad. Tada, message decrypted.
I'm pretty damn certain none of those hypotheticals are the are even remotely worth worrying about. I may even be more than P(1 - 2^-512) certain that they are false. But it's still merely a very high, finite probability. P(0) or P(1) don't exist - you can approach them, but you can't ever reach them.
Any idea, no matter how crazy or out of place with our understanding of the universe could happen, at least in principle. Therefore if we want “never” have a meaning at all, we need to set an cutoff point where we stop caring. Obviously an appropriate value depends on the situation, but in this case I'm pretty sure that an appropriate cutoff is somewhere up of P(2^-512).
