I had a guy recently tell me this statement was false and I couldn't help but disagree. Thoughts?

Maybe it's not evidence since it's something that's not there. But it should be considered as such if work has been done to search for evidence where it might be found.

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Sometimes absence of evidence is evidence of absence, and sometimes it isn't. You have to ask yourself if the specific test starts with the expectation of something being there if the claim is true. If that's the case, then the absence can be evidence against the claim. Typically, the more specific a claim, the stronger evidence that absence can become. But if their claim is something broad like 'some sort of (undefined) god exists', then it gets tougher since we are left with something so broad and generic that we don't know what to expect. So if we don't even know what to look for, not finding anything doesn't really help with coming to a conclusion much. However, if the claim is that Moses led the Israelites through the dessert for years, then there are certain things we'd expect to find if this was true. Since this evidence does not exist, it suggests that the events described simply never happened.

Hope that helps.

"An absence of evidence is evidence of absence."

The statement really is false. The concepts are not equivalent. 

'Absence of evidence' refers to the inconclusive. For example, there is no evidence that life exists on Mars, but one cannot conclude as a result that no life exists on Mars.

'Evidence of absence' refers to the conclusive. For example, you search a closet, find that it is empty, and conclude there are no shoes in the closet.

The difference is mainly about the level of certainty involved in the search for evidence. You may under some circumstances conclude that you would find what you're looking for if it was there, and you don't find it, you may conclude that it is not there. 

The book God: The Failed Hypothesis concludes based on 'evidence of absence' that a personal God (as opposed to a deistic God) does not exist.

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