Why do people keep asserting you cannot prove a negative?

Question

This is false. It is possible to prove a negative by proving that the converse leads to contradiction.

For example:

You assert there are two integers, a and b, such that a/b is minimal in form and equals the square root of two, sqrt(2).

I say, let us assume that there are, as you say.

By definition of square root, this means (a/b)^2 = 2.

By mathematics, this means a^2/b^2 = 2.

By mathematics, this means a^2 = 2 * b^2.

By mathematics, 2 * b^2 is even. This means a^2 is even as well, and can be expressed as (2*k)^2 for some given k.

By mathematics, (2k)^2 = 2b^2.

By mathematics, 4k^2 = 2b^2.

By mathematics, 2(2k^2) = 2(b^2).

The ability to simplify contradicts your assertion that a/b was in simplest form.

As such, I have proved the negative existential: There exist no integers, a and b, such that a/b is the square root of two. I've also incidentally proven that sqrt(2) is irrational, but that's moot here.

You can prove negative existence.

Um, Councilman... nowhere at ALL did I mention the concept of negative numbers.

Alex:

Santa, by defintion, delivers all his presents in one night, on December 25th.

On December 25th, there are places where humans live that are in perpetual sunlight.

This is a contradiction. Thus, Santa does not exist.

sister steph:

The example shows that it is possible to prove that some given thing does not exist.

I proved, for example, that there is no cartisian pair of integers (a,b), where a/b is the square root of 2.

Such a pair does not exist. I proved it.

Therefore, it's possible to prove the non-existence of a properly defined concept.

Councilman:

I'm also not asserting that it's possible to prove ALL non-existences.

It's merely possible to prove SOME.

Alex:

As I said -- well defined.

If you now define santa as, "Santa delivers all his presents in one night and has a magical cloak that makes it night in his immediate presence and a clock that makes time stand still so that no one notices this moving area of supernatural night," well, yeah, that's a lot more difficult to find the critical contradiction of, and until you find it, you cannot assert proof of the negative.

Find a critical contradiction though, and you can. That's my only point.

I'm not saying all negatives can be proven, only that a well-defined negation can possibly be proven.

Phoenix:

It is not necessary to scour the whole universe.

If a well-defined theistic concept of deity leads inevitably to a contradiction, then it is false, and that concept of deity cannot exist.

dr_chino_m:

Given any random, arbitrary defintion of a deity, I couldn't.

Given a specific definition thereof, with descriptors, it becomes possible.

Answer 1

JP: True as stated and you're right it is possible to prove a negative therefore people shouldn't say that. I think the real problem is empirically proving the non-existence of an entity.

Answer 2

I get your point--but you are missing what the phrase means. It's not a formal principle but an informal statement of a basic principle of philosophy.

There are different ways of formulating it, but the idea is that some statements (e.g."God exists" or "god does not exist") cannot be proven to be either false or true based on a purely logical proof arising from empirical evidence. NOTE--you can construct such a proof-but to do it in the case of such statements you have to make at least one apriori (thus unproven) assumption--so it's then not an empirically based proof.

To take a bit simpler example: ASSERT: aliens have visited the Earth. Now, you can't prove that is a true statement (UFO believers aside)--there's simply no evidence; ccertainly none tha tis conclusive. But--you can't prove its false, either. Aliens could have visited--and been careful not to leave any evidence behind.

There is a difference between the two: in the later case wel could consceivably get proof one way or the other--by meeting said aliens and asking them. But there's no way, logically, to prove God does not exist--and unless the Divinity decides to make Him/Herself manifest, no way to prove God does exist. It's inherantly an unprovable statement.

That, BTW, does NOT mean it's a meaningless statement. There are many nontrivial questions that fall into the "not provable" category: whaat is "morally good" or "bad," "this piece of art/music/lliterature is bueautiful," etc. Such questions are important--and humans try to find answers to them. But not by means of empirically based proofs--because you can't. And ddon't make the error of thinking that because science can measure and find common features in what people find beautiful (or other such judgement) that this is "proof." It's not--it only describes some physical characteristics that (some) people find to have that quality. It says nothing about the truth/falsehood of such value judgements.

Answer 3

No.. that's proving a negative number, which has an existence.

EDIT: Okay.. I mis-read the question... but you still only proved that no INTEGERS, a and b, such that a/b is the square root of 2, which works fine for a mathematical proof.

Try applying that to a real-life situation such as: prove that you have never killed someone. Just because there is lack of evidence to say that you never actually DID kill someone doesn't mean you have or have not. Therefore it cannot be proven.

Answer 4

Crabby Blind Guy: You said "But there's no way, logically, to prove God does not exist--and unless the Divinity decides to make Him/Herself manifest"

--That's wrong. Just as in JP's Santa example, if God is defined in such a way as to be self-contradictory then he cannot exist. It's my contention that the bible defines God to be self-contradictory and contradictory to known facts in a number of ways. If there is no contradiction in the definition then you are right and he cannot be disproven.

Your ability to disprove something depends on the definition of the object in question. I can't prove aliens never visited the earth because the definition of that event doesn't contradict anything that we know of. However I can prove that any aliens have never made a self-contradictory object.

Answer 5

You can definitely prove many things do not exist. What you can't prove that does not exist are things like God or the supernatural. There isn't some inate reason, the only reason is that people are free to make infinite conditions on the existence. E.g. the being is outside of time, they are invisible, they can't be touched, you can't hear them, you can't smell them, they don't affect their surroundings. In such a case you can never prove nonexistence. But to be honest, if there are no observable consequences to it's existence, what does it mean for that thing to exist?

Answer 6

You can prove a negative. You can prove that omnipotent God does not exist quite easily. Theists just don't like the proof so they say their god is in some other dimension or some such rubbish.

If he is omni he will exist in all dimensions in all spectra, including the visible spectrum.

This is where the pantheists have the advantage.

Answer 7

I'll concede that it works in pure math.

But how does it work in practice? Such as the old "Prove Santa does not exist". How can this be done using your formula?

Edit : Sure, logically he can't exist. But what if we endow him with supernatural powers that are ill defined? And then keep changing those powers whenever you try to make a logical argument against him? Huh? Huh? XD

Edit #2:
Fair enough. But you had to know I was being facetious.

Answer 8

That's math, not the material world.

It is not possible to scour the entire universe to prove that something does not exist, and the fact that it goes outside the laws of nature doesn't seem to matter to those who propose the existence (whereas it should follow your model of contradiction).

I'm afraid must disagree with you here.

Answer 9

I'm positive that since I've personally been transformed by the Saving Grace of Jesus Christ when we met almost 17yrs ago, that with Him at my side He defeats negativity, and is willing to transform the lives of everyone who will come to Him, as well. (He's way beyond a MATH equation). You have to think with your HEART, sweetie.....unless you leave an option for a POSSIBILITY of Him existing, you'll never be able to understand for sure with just logic. You need to put logic together with Faith.....

Answer 10

Of course proofs exist in mathematics, JP.