So, you’re more right than you’d think.
The reason we say this is because from a formal logical standpoint (where we try to ground debates) it is true – you can never *really* prove that something doesn’t exist, because it’s impossible to look *absolutely everywhere* and categorically rule out it existing anywhere.
But when you look at it from a more probabilistic model, if we’ve been searching for something for a very long time and have been unable to find it, that’s at least some weak evidence that it doesn’t exist (or at least that it doesn’t exist in any sense that we can perceive, in which case it’s like it doesn’t exist).
I have ten boxes sitting on the table in front of me, and I tell you that one of them contains a valuable gold bar. You’re not entirely sure you believe me. So you open each box and look inside, and you find no gold bars. You now have firm evidence that there isn’t a gold bar.
But let’s say I have 100,000 boxes in front of me and tell you that at least one of them contains a gold bar. There’s absolutely no way you can check every single box for a gold bar. You can check 10 boxes, find no gold bars, and assume that there’s less than a 1:10 chance of any given box to contain a gold bar. You can check 1,000 boxes and assume the chance is less than 1:1,000. But short of opening every single box there’s no way for you to state with certainty that there are *no* gold bars in any of the boxes.
Most things to which your statement apply resemble the latter case (100,000 boxes) more than the former (10 boxes). It’s impossible–or at least infeasible–to examine every single possibility so there’s always a chance, however small, that there’s something there to find. That something might be wildly improbable or uncommon, but that’s not the same thing as impossible or nonexistent.
Let’s start with another aphorism: where there’s smoke, there’s fire.
The meaning there is pretty clear; if you see smoke, that’s evidence of there being fire, because nothing else causes smoke.
But, what if there’s no smoke? Does that mean there’s no fire? Well, it can mean that, but it isn’t by itself proof. Maybe it’s a clean fire, or it’s a windy day, or maybe you are looking in the wrong direction.
That’s where your expression comes in. It’s a reminder that just because you don’t have evidence of something, isn’t proof that the something isn’t there.
Where it gets tricky is that sometimes absence is evidence, but that’s because it’s linked to something else — “there is no forest fire here And I know that because if these particular treed were burning they’d made smoke” is a very different statement then “there is no fire in town because I don’t see smoke right now.”
Absense of evidence means you have no proof that something does or doesn’t exist. Evidence of absense means you have proof that something does not exist.
If I accuse you of having a secret bank account, you’ll have a hard time proving you don’t. You’ll ask why you should even have that bank account? I’ll claim to hide money. You ask where the bank statements are from that account? I’ll claim you burned them to hide the account. If we go to every bank in town and you don’t have an account with any of them, I’ll claim it’s a bank in a foreign country.
I have no proof that you do have this account, but you have no proof that you don’t have it either. My absense of evidence isn’t your evidence of absense.
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