It is often said that it's impossible to prove a negative existential. It is said that it's a logical fallacy of the following form: "X is true because there is no proof that X is false." But why is that a fallacy?

You cannot prove or disprove an existential negative because absence of evidence is not evidence of absence; ie if you cannot see colour, this is not evidence that colour does not exist

You can play around with the idea a bit. e.g. if everything that exists just depends on our ability to "sense" it, then in that context, everything that exists [or can exist] is real and change is an illusion. In that sense, all illusion is reality. OW, if by not being able to able to see colour, you cannot prove the non-existence of colour, then not being able to sense anything is not a reliable indicator of its absence and de facto, that thing which is beyond your capability to sense, exists. You can hence use absence of evidence to prove that something that is not visible, exists. The study of ontology deals with these questions: * What is existence? * Is existence a property? * Which entities are fundamental? * How do the properties of an object relate to the object itself? * What features are the essential, as opposed to merely accidental, attributes of a given object? * What is a physical object? * Can one give an account of what it means to say that a physical object exists? * What constitutes the identity of an object? * When does an object go out of existence, as opposed to merely changing? * Why does anything exist rather than nothing? (This overlaps with questions in cosmology.) http://en.wikipedia.org/wiki/Ontology edit:. Excuse me, just saw this is in Physics and Math. I thought it was in Philosophy! Moderator please delete all irrelevant posts. Thanks

Because the state of an assertion is not binary: true or false. It can be true, false, or uncertain. If there is no proof that X is false, that is not evidence that X is true. It is evidence that X is uncertain. Like many fallacies, this one is disguised in grammar. The two statements There is no proof that X is false, and, There is proof that X is not false, look almost identical. But they are not identical.

X doesn't HAVE to be true because there is no proof that X is false. But since we don't know if X is false or true then X is undetermined. It is not impossible to prove that something doesn't exist at a certain place, but it is impossible to prove that it doesn't exist AT ALL. Who knows, there might be infinite universes or different realities - to prove that something doesn't exist at all, you would have to search everything. Of course, a proof of something not existing is theoretically possible - if you are God

Can somebody provide several examples of negatives which cannot be proven? I am not sure what is meant by the following: Five or six different specific examples might give me a clue relating to the meaning of the above. Consider the following. There are well known analytical methods for solving quadratic, cubic, & 4th degree polynomials. It has been proven that there is no analytical solution of higher order polynomials. It can be proven that there are no integers such than P / Q = SqRoot(2). Would either of the above be a proof of a negative. If not, why not?

While that is the title of this thread, it is not really the subject of the thread. The OP makes two statements: Dinosaur just gave examples of proofs of a negative existential. That is completely different. This is just a false dilemma. Lack of proof that X is false is just that -- lack of proof that X is false. If you want to prove that X is true, either prove that X is true or prove that "X is false" is false.

Take for example the existence of life after death (also called the afterlife) or the existence of God. We don't even understand what life and consciousness is. I do believe that science will eventually be able to answer that question, but not any time soon. To deny something exists simply because there is no evidence of it, is at times, simplistic. A better way of thinking is to realize that there are so many things we just don't know. That, to me, is better than being fed answers presented as fact, but end up being BS. Ideas have to be proven right just as much as they have to be proven wrong and until someone can present proof that life after death or a God do not exist, we simply don't know. To say something doesn't exist just because our limited senses can't detect them is naive. In a few hundred years, future societies will be looking at our scientific views like we looked at our ancestors who thought the universe revolved around them, that the world was flat and other views we find ridiculous today. Scientific naturalism has its limits. The scientific point of view simply doesn't have many answers now, and many of its answers will no doubt be proven wrong in the future.

It depends on what the question is. When attempting to understand the working of nature, there is no competition with science.

The following type of argument is often given too much credence. Since Isaac Newton, science has seldom found that previous theories were not accurate descriptions of reality if one takes into accdount the information available at the time. For example, NASA still uses Newtonian gravitational equations for most of our space program activities. Neither Relativity nor quantum theory showed that Newton's equations were incorrect. It only showed that they were not applicable to some extreme situations which could not be investigated prior to the late 19th century. Modern scientists do not sneer at Newon's equations & future scientists will not sneer at our science.

If there is no proof that X is false, we can only say that “X may be true”. Or, if you want to sound confident, you can say “given our present knowledge, it is likely that X is true”. There is always the possibility that evidence against the truth of X may one day turn up and render X false – so be confident at your own risk. The case of black swans provides a classic example of this sort of fallacious reasoning. Before the Europeans discovered Australia, European philosophers were in a position to argue that “all swans are white because there is no proof that they are black (or any other non-white colour)”. That all changed when black swans were discovered in Australia.

Hopefully this won't set the tone for the whole discussion. Anyway, an honest atheist should admit that there is no way to prove the statement ``God doesn't exist'' empirically. Science can only put limits on the definitions of ``God'' and ``existence''. If this is how you see science, then you should think about it some more. The scientific method gives us a way to understand and classify the world around us. Such understanding and classification is a priori limited by our senses, and technology. When the scientific method is followed, a consistent ``answer'' is never proven wrong, it is always improved. ====Edit====== It has just occurred to me that ``existence'' means very different things to mathematicians and to physicists. Math is a consistent set of logical rules, so the existence or non-existence of things are dictated by logic. So, in Dinosaur's example, one defines the set of integers, the set of rational numbers, and the set of irrational numbers. Then existence is as simple as checking the definition: [tex]\sqrt{2}[/tex] is irrational, no irrational number can be rational, and all rationals can be expressed as ratios of integers. Therefore, there exists no integers P and Q such that [tex]P/Q=\sqrt{2}[/tex]. Existence, in this case, is a question of applying consistently the definitions.

A bit more on ``existence''. How do we know dark matter exists? (This is a question for physicists, and not for mathematicians.) We know, for example, that spiral galaxies don't behave the way that they should. There seems to be problems with the way their arms rotate, and the number of visible stars that we can see in them---in short, to get the right rotational velocities, either there is more matter which we don't see, or gravity is somehow different. As to the question of modifying gravity, we know from observation that any modification to gravity must look like cold, non-interacting particles---this is a relatively recent discovery. Now, either we have cold, non-interacting particles (dark matter), or we have to modify general relativity to look like it contains just the right amount of cold, non-interacting particles. Often people invoke ``Occam's Razor'', which would suggest the simpler of the two. This is a matter of taste, and Occam's Razor is more of a loose guideline, like ``Always double down with 11'' or something. But the fact remains, current technological limitations mean that we can't differentiate between the two hypotheses.

In principle, yes, you can prove a negative. I can prove that a pink unicorn of height 6 feet and length 10 feet weighing 500 lbs does not exist in a specific point in space relative to my living room just by observing the space. But in practice, it's impossible to do this everywhere.

So logical, and still religious. Now about the original question: Several times it is possible to prove a negative, when we can simply check of the truthiness of the negative statement: " There are no blue balls in that black box" Well, after opening the box we can verify the negative statement's truthfulness...