Lack of evidence is proof enough that something isn't true until that evidence comes forward. That's not to mention that claiming something doesn't exist is commonly in response to someone saying that it does.

There's no solid evidence but there's been a few people in this world (even children) who claim to have some sort of extrasensory perception or some memory of being somewhere else. I'm a tiny bit skeptical of this case but I will admit if she's not bullshitting everyone, her soul has had a terrific journey. Someone in the comment section in the video I'll post below makes a good point about Ms. Karlen: she seems to have no concern for Otto Frank; if her soul belonged to Anne in a past life, she would have been chiefly concerned with being reunited with her father while he was still alive. HOWEVER. There are probably several reasons this didn't happen, and I'm not going to split hairs over it.

No. A lack of evidence is merely a lack of proof of something's existence, not proof that it doesn't exist. I'm an atheist who is perfectly comfortable with actively believing that god doesn't exist. I think human psychology's penchant for inventing gods anywhere and everywhere regardless of how absurd it may sound is evidence enough for me that god is nonsense, but I would never go so far as to claim to know that he doesn't exist. No matter how much I believe that he doesn't exist, I can't know that he doesn't. Same with reincarnation.

The fact that so many people who claim to have past lives also seem to believe that they were someone significant in their previous life, despite the statistical improbability of that being the case, is actually more of an argument against reincarnation to me than an argument in favor of it.

We can't truly, unequivocally know anything for sure. So either we can eliminate the word "know" from the English language or we can recognize it as meaning "I believe to an extremely high degree of certainty".

I feel that the theory that these people have (the "I was someone important in my past life" thing) sort of discredit their claims. I don't know who I was. I was probably a nobody, but I know that there's something beyond my comprehension that has filled my life with a constant discomfort and longing for a time I hadn't lived in (during this particular lifetime anyway).

True. But to claim knowledge, even a negative claim that something doesn't exist, is still making a claim that something is true. And to make a claim requires proof. A lack of proof for reincarnation only proves that reincarnation hasn't been proved. Nothing more. It may be evidence for its unlikelihood, but not for its nonexistence.

And you can't claim to know something that hasn't been proved with sufficient evidence, only that you believe.

You can't prove a negative though. So you're basically arguing here that one can never know that anything is untrue.

Well, yeah. Aside from math you can't actually prove anything. That's just the nature of science and the world in general. In the strict sense of the word you can't actually "know" much of anything. You can be sure beyond a reasonable doubt, but that's not the same thing as knowing something.

And just because you can't prove a negative (at least not a vague negative like that) doesn't mean you can make a claim and not have to prove it. If you claim that reincarnation doesn't exist you have to back it up.

You just acknowledged that you can't prove a negative but you still want proof that reincarnation doesn't exist?

I'm saying that if you're making a negative claim that doesn't relieve you of your obligation to back up what you're saying. So if you're saying there is no such thing as reincarnation you have to provide evidence the same as if you're saying that it does exist.