this post was submitted on 03 Apr 2025
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If you subscribe to classical logic (i.e., propositonal or first order logic) this is not true. Proof by contradiction is one of the more common classical logic inference rules that lets you prove negated statements and more specifically can be used to prove nonexistence statements in the first order case. People go so far as to call the proof by contradiction rule "not-introduction" because it allows you to prove negated things.
Here's a wiki page that also disagrees and talks more specifically about this "principle": source (note the seven separate sources on various logicians/philosophers rejecting this "principle" as well).
If you're talking about some other system of logic or some particular existential claim (e.g. existence of god or something else), then I've got not clue. But this is definitely not a rule of classical logic.
When people colloquially say "you cannot prove a negative" they are usually referring to the fact that absence of evidence can not be used to deduce non-existence of some phenomena ("a negative"), whereas the factual discovery of a phenomena can be used to deduce that the phenomena exists ("a positive").
They are therefore not referring to formal negation but rather making a point about deductive vs. inductive reasoning and the asymmetry of these two related questions (existence vs. nonexistence).
There is a bit of nuance to add here in that practically speaking you can't really "discover a fact" by direct observation. But again this is a colloquialism as most laypeople will accept what is directly observable under their noses as factual rather than a noisy data point of one.
I think you are assuming a level of competence from people that I don't have faith people actually have. People absolutely can and do take "you cannot prove a negative" as a real logical rule in the literal negation sense. This isn't colloquialism. This is people misunderstanding what the phrase means.
I have definitely had conversations with idiots that have taken this phrase to mean that you just literally cannot logically prove negated statements. Whether folks like you get that that is not what the phrase refers to is irrelevant to why I'm pointing out the distinction.
Sure I can agree with that.
However, I think that is sort of a special case that's easy to resolve. It only comes up when they are already in the business of learning logical proofs & will likely be looking to learn from someone or a textbook who will most likely clear that up for them...
Chances are that person already has a baseline level of competency in logical thinking, or, if they don't, they soon will learn and are open to it. They've at least additionally already mastered the colloquial meaning of the phrase and are simply a bit overzealous with it's use (which should be reigned in as you aptly point out).
On the other hand, when people don't understand "you can't prove a negative" in social situations unrelated to formal logic, it's generally observed they are up to their eyeballs in conspiracy thinking and are so lost in magical thinking that they've abandoned even informal rule of thumb levels of logic.
Those are truly sad situations with deep (inter)personal, social, and political consequences, especially if they go on to harm others based on their misunderstandings.
Ironically it seems we both have less faith in the competence of others, albeit in different ways lol
Fair points. The latter case is basically where my concern is.
Conversations like this is why Lemmy feels so much more refreshing than Reddit, so thank you for that... I hadn't realized how desperately I've missed the old internet