Several years ago, I was on a date with a woman who said “I bet you’re married. Prove that you’re not.” It’s easy to prove that you’re married, because you might have a marriage certificate or wedding ring. How do you prove that you’re not, though? The lack of a wedding ring may just mean you took it off. A visit of your house, with evidence that you’re the only person living there, doesn’t eliminate suspicion that you may be separated. My tax files show that I file as an individual, but so can those who are married. There’s no such thing as a “single certificate.” I wondered how it was possible to really prove that you’re truly single, and not married.

Same thing with the accusation “You’re racist!” It’s easy to prove that someone is racist if they use derogatory language, own a Klan robe, openly discriminate, and so on. How can you prove that you aren’t racist, though? “But I have black friends” is seen by many as a cliche used by racists to disprove their beliefs.

Pretty much, what I’m asking is if there’s any way to prove a negative in the absence of data, which really wouldn’t exist anyhow, that supports that negative; that you aren’t married, aren’t racist, aren’t a spy for the Russians, and so on.

It is logically impossible to prove a negative. Even the existence of data which supports the negative position can’t help. It only takes one “positive” data point to disprove your argument; unless you have collected all of the information in existence you can never prove that point does not exist.

The best answer to your query that I can come with is: If someone really needs you to prove one of these things it’d be easier to just not to associate with her/him anymore than you must.

Three men on a train to Scotland.
They see a black sheep (side on).

One says “This proves there are black sheep in Scotland.”
Two says “No, it just proves there is at least one black sheep in Scotland.”
Three says “No, all it proves is that there is at least one sheep with one black side in Scotland.”

Well, you can disprove some things if you have some axioms to work with. If all baseball players wear hats, and I am not wearing a hat, then I am not a baseball player.

That sort of thing doesn’t come up much in real life, though, because it’s rare to find universally applicable statements. In your example, you might say “everyone who is married has a ring, i don’t, so I’m not married,” but your date would probably just contest the first statement.

Since the logical aspect has been answered, I’ll say that this is really a test, observation under stress. I’ll bet she watched you closely to see if you’d fumble. I think workinprogress’s reponse is great, would have thrown the ball right back in her court.

However, it is possible in practice to prove a negative if your scale is small enough. I can prove there are no elephants in my bedroom. I would not, however, be able to prove that there are no elephants in Panama (although I don’t think there are any).

For the more nebulous atributes listed in the OP, of course, this won’t work.

Open up your wallet, and show that you have money in it. That should be good enough.

You clearly can’t prove it. Anything you do might not be good enough for her. You’d have to invite her to do searches of marriage records for you (on her dime). No living arrangement evidence would be good enough, since you can be separated but still married.

It is of course perfectly possible to prove a negative, and it is done in math all the time. You assume the negative is true, and show that it leads to a logical contradiction, and this is not true. You actually mean that you can’t prove an existential negative. However, since the OP has lived a finite time in a finite number of places, someone wishing to put enough money into hiring detectives to interview all acquaintances can probably account for his whereabouts and living conditions to a level of detail that would be close to a proof.

I hope the OP liked this woman, because if someone had said something similar to me I would have responded with one of several comebacks that would not have helped the relationship one bit.