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Having a level of proof is your knowing what it takes for you to be convinced that any given belief you may hold is wrong.  For instance, I believe in evolution.  The evidence is too overwhelming not to.  However, I do have a level of proof.  If you can produce the fossilized bones of a Jersey Cow, then I will be convinced that evolution is wrong, at least, as I have come to understand it.  On the other hand, your showing me that carbon dating can be incorrect is not good enough for me throw out all the other evidence.  Carbon dating is minor, and there are many other ways to determine how old something is.  Besides, carbon dating is fairly accurate... but only when it is used to measure what it was designed to measure.  But I digress...

Your level of proof should be incontrovertible – when you see it, there should be no doubt.  When the saucer lands on I-44 and the aliens emerge and say, “Hey, earthlings, take me to your liquor store...”  Yeah... that should be fairly convincing that we are not alone.  But showing me a blurry photograph... no.

As well, be careful of shifting the burden of proof, which is a favourite tacit of conspiracy theorists.  It is not my responsibility to prove that aliens (or anything else) do not exist.  It is your responsibility to prove that they do.  Here you should be really careful.  Your level of proof should never be a negative, because there is no way that you can prove a negative.  You cannot, for instance, prove that ghosts, or vampires, or invisible aliens do not exist.  You can only prove that they do.  Likewise, it could not be proven that there were no weapons of mass destruction in Iraq; we could only prove that there were.  And, of course, somebody could always say that just because we never found any doesn’t mean they were not there.  However, at what point do you concede that, based on all the evidence you have, it is wise to conclude that they probably were not there?  That point can be your level of proof.

That said, there are things we believe for which we have no level of proof.  I may believe my cat loves me, no matter how many times she bites me or tries to run away.  I may believe that my religion is correct, and nothing you tell me will change my faith.  And that’s fine... unless I’m trying to persuade you that my beliefs are correct.  Then I need a level of proof.  After all, how can I possibly persuade you that your god is wrong if I will not first accept the possibility that my god could be wrong, too?  How can I expect you to have a level of proof for abandoning your beliefs if I don’t have a level of proof for abandoning mine?

So here is the general rule:  If you are trying to persuade anybody of anything, you need to have a level of proof.  You need to be aware that you could be wrong.  Therefore, when you are researching, say, a topic for a research paper, you won’t just be looking for evidence that will support what you already believe.  After all, you can find evidence that will support that Elvis is alive... if you are willing to ignore the overwhelming evidence that he is quite dead, and has been since 1977.  The goal in research should never be simply to support your thesis.  It should be to prove that your thesis is truly correct.  And you can only do that if you first have a level of proof.  And if nothing will convince you that you are wrong, then you should choose another topic.