Is it possible to prove that something doesn't exist?

Question

people can prove things that exist by some experiments or other types of researches but can you actually prove something that it doesnt exists?

Answer 1

Although it may be possible to prove non-existence in special situations, such as showing that a container does not contain certain items, one cannot generally prove universal or absolute non-existence.



However, that shouldn't be justification for saying that something is true because you can't deny it. For example, someone may say "prove there are no purple cows". But just because it's nearly impossible to prove the non-existence of purple cows, that doesn't mean there *are* purple cows.



This fallacy could be used to then prove the existence of ghosts, the tooth fairy, unicorns, etc.

Answer 2

Yes.



You can perform an exhaustive search of everywhere the thing could be.

For example: Loch Ness has been scanned with sonar. They found nothing bigger than lost golf balls.



You can also think of something that would have to be true (or have to be false) if the thing existed, and test for that.

For example: the Michelson–Morley experiment disproved the existence of luminiferous aether.



Or if the claim is ridiculously unlikely a priori, then refuting any original reason TO believe it should be sufficient to dismiss it.

For example: the author of Scientology has admitted that he made the whole thing up. That's all the proof you need to stop believing that volcanoes are filled with ancient frozen aliens.

Answer 3

"Existence" technically refers to beings and facts in the world. You can prove that a fact did not happen if you set up an observation before it. As to past facts you assess the amount and quality of the pro and contra evidence and apply an statiscal baysian analysis which will yield its degree of probability which is sometimes close enough to zero for you to conclude for its inexistence. Finally, something can be proven inexistent because of its incompatibility with the laws of physics, e.g. a perpetual mechanical clock because friction slowly deprives the system of the inicial energy to keep it going according to the second law of thermodynamics.

As to rules, correlations, mathematical concepts you would better speak of their "reality" or "veracity" rather than "existence". Because they describe abstract ideas or relationships between existent being but are not things that are out there in the world in the sense they can be witnessed by our senses or aparatuses. Logical and mathematical assertions can ordinarily be proven false by hypothezing that they are true and then deducing contradictory conclusions from the hypothesis. But that is not so straight-forward because we may have difficulties translating them in a foolproof formal language. Read Gödel's theorem and you will find out not only that formal systems cannot be completed described by a formal language but you will also notice that the very theorem uses self-referential tools that sound fishy. Scientifical laws can be falsified by setting an experiment and observing a single contradictory result. But they cannot ever be proven definitely true: you would have to prove that no falsifying instance has and will never have occured and run the experiment forever. Again, the degree of evidence may lead to such a high probability of correctness as to allow us an almost certainty.

Answer 4

I would have to say yes, through logical and mathematical arguments, through philosophical arguments... but not through empirical science for reasons already clearly explained.



Mathematicians do it all the time. You can prove the non-existence of a largest prime number, for example. That is just one special and famous case of proofs of non-existence using logical arguments.



This sort of reasoning - proof by contradiction, and other forms of proof - can extend to any facet of existence, any claim, if one can create a model to which this sort of reasoning can be applied.



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Just because one cannot disprove the existence of something does not mean it exists. I agree with that statement. But just because one cannot prove the existence of something does not mean it doesnt exist, either. The universal generalization of the claim that something doesnt exist is no less fallacious than claiming something does exist without the proof, and vice versa. Fact is, in many cases its absurd to even discuss the topic because it is outside of the realm of rationality. Any claim, whatever it may be, demands proof. Believing anything, anything whatsoever, without a rigorous proof of it, is nothing short of faith. And there is nothing wrong with faith. Faith is the foundation of everything. The axioms of reason. The postulates of geometry and of arithmetic. The very principles of empirical science itself cannot be proven. All are taken on faith. The only real issue - the only real problem - is when someone is unwilling or incapable of acknowledging their faith and the inherent limitations of what they think they know. For example, I will probably get many down thumbs for this answer largely because some people find it offensive to their preconceptions of the world, whatever side of the fence they sit on. Close-minded bigotry is what stunts intellectual progress in any field.

Answer 5

By definition, evidence can not be presented for something that doesn't exist. However, the best evidence that something doesn't exist is that there is no evidence of its existence.

Answer 6

usually its done using proof by contradiction

basically assuming the it does exists and show by existing it will lead to a logical contradiction(something like 1=2 or odd=even)

Answer 7

It can be, and has been, proved with finality that there are no integers x, y, z, n > 2 with xⁿ + yⁿ = zⁿ

Answer 8

Sure! It is easy to prove that there is no rational number whose square is 2

Answer 9

Depends on what the thing is.

Answer 10

very easy

Answer 11

baa