What does the phrase “you can’t prove a negative” actually mean?
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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
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