or didn’t exist somewhere at some time. (edit: or even that he thought of it at some time without documenting it.)
It sounds like this is at least related to the criterion of falsifiability.
I think what you’re really looking at is the difference between deductive and inductive reasoning. Deductive reasoning is the use of general principles to draw individual conclusion; the famous:
Socrates is a man
All men are mortal
therefore, Socrates is mortal.
Inductive reasoning is the use of individual cases to draw general conclusions.
Socrates is a man. Socrates is mortal.
Plato is a man. Plato is mortal.
Aristotle is a man. Aristotle is mortal.
Therefore, all men are mortal.
Obviously, it’s possible to be more certain with deduction than induction, but as a general tool, induction is more useful than deduction.
You’ve got it backwards. This technique works when the conclusion is ABSURD, not accurate. That’s why it’s called reductio ad absurdum (“reduced to the absurd”).
Moreover, even if we were to grant your objection, the point remains that proving a negative does NOT require “knowing the answer to all the potential positives.”
If that’s what people meant, then they shouldn’t be saying “You can’t prove a negative.”
Frankly, I think that the people in question are simply parroting a convenient adage without bothering to consider whether its logic holds water.
Kind of like what **Revenant Threshold **said. The problem has nothing to do with negatives, really, and has everything to do with the fact that you can never achieve certainty outside of math and logic (where, as Hales points out, you can quite easily prove negatives).
As has been pointed out, you can never prove with absolute certainty that a negative is true; but you can establish such strong evidence in favor of a negative that you would be a fool to disbelieve it. See: unicorns, the current existence of
But the exact same problem exists with any positive statement: you can’t establish any positive statement with certainty either. (At least not any interesting ones.) Our evidence for (say) the theory of evolution, or the theory of gravity, or the existence of my grandmother is pretty overwhelming, but it’s at least possible it’s all a hoax perpetrated by an alien super-race, or whatever. That is to say, the chance of being wrong is about the same as the chance of our being wrong about the non-existence of unicorns. Which is to say: you can prove a negative to about the same degree that you can prove a positive, at least if we are talking about empirical claims.
As pointed out, no, it doesn’t. There might, conceivably, be some evidence for the positive. Someone might have recorded his utterances somewhere where he talks about elephants of various fluorescent colors, or what have you.
Proving the negative in such a case, however, is impossible because you’d essentially have to show what all of his thoughts were at all times and show that the negative claim is, in fact, not among them.
It is all about proving certain negatives. And the dodge that you can’t have 100% certain epistemological proof for some positive claims is a non sequitor. We’re not talking about standards of ultimate proof, but of the barest possible levels of inquiry. “All humans we have ever known of are mortal.” is a positive claim easily falsified by showing one immortal we have known of. “Some humans through history are actually not mortal.” is an impossible negative claim to falsify as you’d have to know every single human’s date of death from the first human being to the present. Maybe the Highlander is hiding in New Jersey somewhere.
“Bob got a DWI” is possible to prove, as all you have to do is show the police report. “Bob has never driven drunk” is impossible to prove, as you’d have to be able to show hard proof of each and every single time Bob drove and what his BAC was.
Now, sure, some positives can be impossible to prove too. But when we talk about the (rhetorical) fallacy of proving a negative, the vast majority of the time we’re talking about someone who:
-has shifted the burden of proof
-cannot prove their own positive claim
-has thus shifted the burden of proof to those who disagree and has demanded that they prove a negative claim
-and that negative claim requires a standard of proof that is impossible
-upon admission that it cannot be done (due to being physically impossible), the person declares that their positive claim stands as written.
I disagree. The evidence for the negative statement “There are no unicorns” is as strong as the evidence for the positive statement “Bob got a DWI”. So if the latter is proved, then the former is too. So it’s false that you cannot prove a negative; it is merely true that you cannot prove some negatives–namely, those negatives where it is (say) physically impossible to gather the required evidence (such as evidence that Bob never drove drunk, or that Socrates never thought of a purple elephant).
But there are positives that it is impossible to prove, and for precisely the same reason. “There are 1*10^15 grains of sand on this beach” or “Such-and-such star has a mass of precisely n grams” or “Socrates thought about the Mediterranean sea at 12:03 pm on such-and-such a day.”
So I deny that there is a real structural disanalogy between negatives and positives. It may be easier to generate impossible-to-prove negatives, but that’s just because they may tend to impose more wide-ranging search requirements on one. It doesn’t mean that there is some principled reason why negatives cannot be proved and positives can.
“You know oxygen was first discovered in 1774.”
“That can’t be true. William Shakespeare mentioned oxygen in one of his plays.”
“No, he didn’t. Shakespeare never wrote anything about oxygen.”
“You’re wrong. And you can’t prove a negative.”
“Sure I can. I’ll just load all of Shakespeare’s plays off Gutenberg. Now I’ll run them all through a word search program with the keyword oxygen. And look, zero hits. There, I’ve just proved Shakespeare never mentioned oxygen in any of his plays.”
I don’t think that’s true. “Bob got a DWI” seems like a trivial thing to prove. You look through the court records, and if you find Bob’s conviction for DWI, you’ve just proved it. “There are no unicorns” is much harder to prove inductively. The more accurate statement is “No unicorns have been found.”
No, it most certainly isn’t. We do not have perfect knowledge of every square inch of the planet. You could have made the same argument that there are no coelocanths. There is a significant distinction between assuming something to be true, and actually being able to prove it. And that’s why I mentioned the burden of proof, because the burden of proof is on the person who makes a claim that unicorns exist and the null hypothesis is that they do not. But it’s the null hypothesis, not the null theory, after all.
And as I said, some negatives can be proved, like “there is nothing in this box.” But “nowhere on earth is there a unicorn” cannot be proven. It’s a very, very safe assumption, but it is not proof. It’s the same reason why debates about faith often end up with some theists shifting the burden of proof and demanding that you disprove God.
I also just said that there are some positives you cannot prove, so restating that some negatives can be proven and not all positives can, doesn’t disagree with my argument.
That’s the point.
As I just elaborated on, the difference is in the use of the rhetorical fallacy of proving a negative, whereby someone shifts the burden of proof to a claim that virtually impossible to prove and so on and so forth.
P.S. Nemo, yes, if the burden of proof is shifted to a narrow enough claim of course it could be falsified. But if the claim was “Shakespeare did discover Oxygen, but he didn’t think it was very important and never wrote it down or told anybody” then we can argue that it’s extremely unlikely and that we have no reason to falsify the null hypothesis, but we cannot prove that he definitely did not do such a thing. We can, however, prove the contents of his plays.
Yes, but this is logic, which exists on an ideal plane. In theory, a negative claim could be tested even if practical realities would make such a test too difficult to perform. A claim that “Bigfoots are not real” could, in theory, be tested by searching every spot on the planet Earth. During the course of this search you would find every item on the planet. And if none of those items was a bigfoot then you would have proven that bigfoots don’t exist.
Even if it was some claim like “Bigfoots never existed” and you were prevented from examining the evidence by the impossibility of traveling back in time, the logic itself would still be valid.
Fair enough. That’s why I was careful to state that it was a rhetorical fallacy as it’s most often used.
But I do see your point. Most people when they say “You can’t prove a negative” don’t mean it in the formal sense. They mean “It’s too difficult to collect the evidence that would prove a negative for anyone to actually do so” and I agree that’s often true.
You can equally infer from that, “Therefore, all mortal beings are men.”
Apologies, perhaps a poor word choice on my part. The absurd conclusion certainly has to be obviously wrong, or contradictory, which is what makes it wrong. But it has to be a conclusion that follows from some part of the premise even as it rejects another part of it. It has to be an accurate absurdity in that it must be a correctly determined piece of nonsense. And that’s where the problem lies, because you can’t guarantee the correctness of that determinative process.
It does, because without knowing them, we can’t compare them to the negative to know that they aren’t contradictory or otherwise supplantitive.
The problem with this technique is that sometimes one person’s absurdity is another person’s quantum physics. Absurd things can be true.
True. Yet another problem.
It seems like we are selectively choosing what is easy and hard to prove.
“Bob has never gotten a DWI” can be proven even though it is negative. Run a NCIS check or request criminal histories from all 50 states.
Similarly “Bob always drives drunk” is impossible to prove, though it is an affirmative statement. You would need evidence of each and every time that Bob drove, and have a corresponding BAC test above .08.
No, we’re not. Some positives are impossible prove, as are some negatives. When someone talks about the rhetorical fallacy of proving a negative, they’re generally talking about the impossibility of providing negative proof once the burden of proof has been shifted fallaciously from a positive claim that hasn’t been proven.
That was the point. That some negatives can be impossible to prove and are used as part of the fallacy of shifting the burden of proof, while other negatives are easy to prove and/or unlikely to be used for burden-shifting.
Simply, the way that debates are often structured means that it’s much less likely that anybody would fallaciously shift the burden of proof from a negative to a positive that’s impossible to prove.