[duaneb]

Depending on what you're observing, it's only statistical probability you actually observed anything. There is no such thing as an inductive proof; there is no way you can prove anything exists to another person.

I suggest Hume and the writings of the logical positivists. This will wipe the idea of being able to "prove" with science or observation right out of your brain. No matter how much information you have, you don't have enough to predict the future. If our planet collides with some huge energy burst, all the people who said "I know for a fact that the earth will still be moving around the sun at the approximately same rate and mass" will have been PROVEN false. But there is no such trick to prove anything about tomorrow.

[awptimus]

Other people don't factor into this. Proving to them is not necessary. Once an event occurs, it occurred. Your knowledge of what that event or the total state of that event might be uncertain, but the event's occurrence is no longer probabilistic.

[duaneb]

Yea, but you are probably talking about a completely different event than the other person, or whatever happened in your memory, or maybe just a past version of yourself. The world is not naturally quantized into discrete events, causes, and effects, and it is in this disagreement over simple assumptions that "this event happened" that cause people to disagree about "certain" things. Look at how utterly useless witness testimony can be, no matter how hard they swear up and down, if the memory is suspect at all.

So, if you want to lie to yourself, I guess you could "prove" something to yourself. But you know you can't trust your observations for about a billion different reasons.

Why is this important? Because you can always know if a bridge has failed, but you never know if it's not going to fail. Never. No matter how certain you are, unless you can form a deductive proof showing that the structure will NEVER fail (which I suspect is impossible for a computer, let alone a human), you will always have doubt. If you don't recognize the doubt, you are lying to yourself.

Furthermore, once you realize how.... loosely science binds together, you realize that the "laws" we think we "know" are broadly accurate but fall to pieces in the details.

So no, proving a negative is not possible. It's not a proof unless you can show the state of the universe, which is again impossible without consensus, which is itself probabilistic and flawed. If you are 100% certain that an event has happened in any way that you could deductively prove something, that gamma ray burst could easily mess with your plans.

A non-deterministic universe is one of increasing, but always <100%, certainty.