What does the phrase “you can’t prove a negative” actually mean?
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It means you can’t prove that something doesn’t exist.
To prove that, you’d have to have perfect knowledge of all things, which is impossible.
You can definitely make very, VERY, convincing circumstantial arguments that something doesn’t exist.
If I claim that purple unicorns exist, and you were to say they don’t because nobody has ever seen them, I can reply: Nobody has seen them YET, or people were not looking in the right places etc.
It’s a reference to the idea that it’s generally harder to prove that something didn’t happen, or doesn’t exist, or isn’t true, than proving that something did, or does, or is. Like, it’s probably true that there’s never been an Elephant in my house since it was built, but could I actually prove that definitely? It would be much easier to prove that there had been, because all that would be needed is a single photograph of the elephant incident. I can’t possibly hope to show you photographs of every room of my house on every day since it was built proving definitively that there was never an elephant in any of them
It means you can’t prove something didn’t happen. For example: Bob accuses Jane of stealing his cookie. Jane denies it, and Bob tells her to prove that she didn’t eat the cookie. She can’t prove she didn’t. She explain why it’s unlikely that she ate the cookie, but not prove it.
This can also go for proving something doesn’t exist. A very common one is “if you’re so sure God doesn’t exist, then prove it?” Well, you can show reasons why it’s unlikely God exists, but you can’t prove it absolutely.
Evidence and proof work in the positive sense. That is, it may be used to show something that *does* exists or something *did* occur. We can only prove negatives through confirmation of something that exists or something occurred that would be mutually exclusive.
For example, there is no way I can prove I wasn’t in the room when the murder occurred. But If I can provide CCTV footage I was elsewhere at the time the murder took place then it follows I could not have been in the room at the same time.
So while the phrase *we can’t prove a negative* is false, it means we can only do so by comparing them to positive statements that exclude the other possibilities. In examples where the negative is not exclusive it would be impossible to prove.
For example, the claim that dragons exist cannot be countered by any evidence they do not exist because (unless we get into the details about specific attributes of dragons) there is not a mutually exclusive position we can demonstrate. This would be an example of being *unable to prove the negative*.
Others have explained the idea behind the phrase. But this phrase is (or should be) used when another party is placing an undue burden of proof as an argument for or against something.
The unwary will fall into the trap of trying to “prove this”, while the savvier will retort with “you cannot prove a negative”. The reason, as others have pointed out, is straightforward. Proof of existence has to demonstrate ONE occurrence to satisfy the proof. Proof of non-existence requires evidence that UNDER EVERY POSSIBLE scenario, such an event cannot exist. These are wildly asymmetrical efforts.
What it’s supposed to mean is that you can’t prove something isn’t the case (as opposed to being able to prove something is the case). For example, if I say there’s an invisible elephant that follows me around everywhere and moved out of the way when you try to touch it, you can’t really prove that’s not true.
However, I don’t think it’s true that you can’t prove a negative. Or rather, it’s only true if your threshold for ‘proof’ is so absurdly high that it’s equally true that you can’t really ‘prove’ a positive. That level of skepticism can’t be satisfied. Let’s use the elephant example again. Sure, it’s technically true that you can’t prove the elephant isn’t there. But that’s because I’ve made the standard of proof unrealistically high. The elephant is invisible so you can’t see it. It doesn’t make any noise so you can’t hear it. It moves so you can’t touch it. It doesn’t leave footprints. I’m not describing anything, it’s just a thought experiment basically. And you can do the same thing to someone trying to prove something. Let’s say there is an elephant standing beside me. I say look, here’s an elephant. You say I don’t believe that’s really an elephant, I believe it’s an illusion. I tell you to reach out and touch it. You say well the illusion is so good and sophisticated that it has a tactile element as well. It’s still not real.
Point being that there’s a certain point when extreme skepticism makes it impossible to prove or disprove anything, except for logical truths. And as far as those go, proving a negative is trivially easy. That’s because negatives and positives in logic are often just inverses of each other with different quantifies. For example saying ‘it is not the case that all birds fly’ is equivalent to saying ‘some birds do not fly.’
TL;DR it’s not true that you can’t prove a negative unless it’s also true that you can’t prove anything
“There’s a double decker bus buried somewhere on the moon!”
“Err.. I don’t believe that’s true”
“Prove to me there isn’t then! I bet you can’t!”
The general idea is that you can’t provide evidence for something not existing unless you limit the properties of the existence.
For example, I can’t prove that there isn’t a random brown cow on the planet that gives chocolate milk, since even if I milk all the cows you can always just say I missed the cow that does it. On the other hand, if you point to a specific brown cow and say “that brown cow always gives chocolate milk instead of milk” then I can just prove it doesn’t by milking it.
Similarly, you can’t prove a species is extinct or god doesn’t exist or ghost don’t exist and so on.
The classic example is [Russell’s Teapot](https://en.wikipedia.org/wiki/Russell%27s_teapot):
Lets say I claim there is a teapot orbiting the sun somewhere between the Earth and Mars. Proving the negative of my claim would be to prove that there is no teapot. There is no way to scour every square inch of space between the Earth and Mars to make sure there is no teapot there. It’s impossible to prove that negative.
Even if technology somehow advances to the point we *could* scoured space so thoroughly to conclusively prove there is no teapot, it should be apparent just how little effort it takes to make a claim vs how much effort is involved in disproving it.
Russel’s Teapot was used to illustrate why the burden of proof should be on the person making a claim, not on those who don’t believe them. Remember this when someone says something like “Oh yeah? Well prove that there *isn’t* aliens!”
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