Is it impossible to prove the nonexistence of something?

This question sometimes arises in religious discussions, but it also arises in many other aspects. Some say that it's impossible to prove that something doesn't exist. However, this is actually false. Through logic and simple examination, the existence of something can actually be discarded as false without a shred of doubt. Consider the following statement:

"I found a square circle."

If we assume the accepted definitions of "square" and "circle," the existence of such an object is conclusively impossible. Therefore, the nonexistence of something has been proven.

This simple concept of disproof can actually be used quite easily on certain religious beliefs, but I won't get into that.

Man, "let" is a funny word.

Let's get into the religion thing, dude. I'm interested now.

Man, I've used that argument before but no one ever beleived me.

Of course it's possible to prove that a fallacious statement is fallacious. However when people say "you can't prove God doesn't exist" that includes the possibility that God is not within our universe, which obviously puts God beyond the reach of any logical wordplay.

Stating it doesn't exist creates the concept of it existing, so for something to not exist, it would have to reach a level of nothingness that is impossible to imagine. We would have to not think about it (the entire world), on all planes of existence (I believe we know of seven of them) for it to not exist. Existing is nothing more than the thought of it being.

Crap...Safeway Select cola does funny stuff to me.

Now that is just ridiculous. The concept of something and the actual physical existence of something are two totally different things.

Just because a person imagines a talking doughnut with play-doh fibulas in another galaxy, it doesn't mean that said doughnut is actually there.

But how can you REALLY know?

How do you know anything? If you haven't seen it, it's there or not. Ever been to Los Angeles? If you haven't, how do you know it's real? Or maybe you don't know about something, like a flying toaster from Uranus. How can you prove it's non-existance, without knowing for sure about it's existence?

Bloodshedder said:

But how can you REALLY know?

Having a mindset like that will drive you insane eventually...

What you're trying to use as a basis for your logic is the literal equivalent of an oxymoron. I don't see where contrasting the definitions of two words stuck together applies in the world of philosophy.

Prove jumbo shrimp don't exist.
Prove the four corners of the Earth don't exist.
Prove the color black doesn't exist.
Prove military intelligence doesn't exist(and refrain from American jokes).
And, a real toughie on this board: sarcasm.

When you try to draw logic between a concept's function and its meaning, you're doing little else than what you'll hear in college English class.

Numbermind, I have no idea who you're talking to.

insertwackynamehere said:

How do you know anything? If you haven't seen it, it's there or not. Ever been to Los Angeles? If you haven't, how do you know it's real? Or maybe you don't know about something, like a flying toaster from Uranus. How can you prove it's non-existance, without knowing for sure about it's existence?

A flying toaster from Uranus cannot be disproven because its definition is not self-negating. A cubed object that is spherical in shape CAN be disproven because its definition IS self-negating.

AndrewB said:

"I found a square circle."

If we assume the accepted definitions of "square" and "circle," the existence of such an object is conclusively impossible. Therefore, the nonexistence of something has been proven.

I *THOUGHT* I was replying to this. Which you said. But if those aren't your words, then you have my sympathies, since you either suffer from blackouts or have been h4X0r3d.

Read above. I gave an example of an object (spherical cube) that can be proven to not exist. You gave an example of a different class of object (flying toaster from Uranus) that cannot be proven to not exist. I don't see where the disagreement is.

AndrewB said:

I gave an example of an object (spherical cube) that can be proven to not exist.

I'm almost certain you could define a mathematical space with a spherical object featuring right angles. I think you should concentrate on context. In the 3D space and as far as current science knows, a spherical cube cannot exist. The real issue is not logic, it's rather predicates. You perfectly stated it in your first post, btw:

AndrewB said:

If we assume the accepted definitions of "square" and "circle,"

Accepted where, by whom, under what constrainsts? Context.

Numbermind said:

Prove jumbo shrimp don't exist.
Prove the four corners of the Earth don't exist.
Prove the color black doesn't exist.
Prove military intelligence doesn't exist(and refrain from American jokes).

None of these are the same as a square circle. "Jumbo shrimp" isn't the same thing because, although shrimp means small, that's not how it's used in this context, so the words aren't true opposites. The four corners of the earth is a saying... it's not meant to be taken literally, and indeed, there are no literal "four corners". "Color black" is simply said out of convenience, rather than saying "the lack of color resulting in black". And "military intelligence", while an amusing joke, does exist.

In comparison, assuming we're talking about two dimensions on a flat surface, a square circle cannot exist.

Yeah, you're being sarcastic, but Andrew actually had a point (mundane though it may be).

Well, even though we dispose of my argument, then what Linguica offered still applies. We can only define things we can experience inside our plane of existence-- and while it's perfectly correct to say a thing doesn't exist, it may exist on other planes that we were not meant to experience. In contrast, things we percieve(and exist through our thought) don't exist in our world.

A very simple example of this is not a square circle, but a triangle with three right angles. If we tie a string around the north pole, pull the string down to the Equator, across 90 degrees longitude, and back up to the north pole, we have made a triangle. But our limited sight(representing our experience) tells us that the corners of the triangle are each 90 degrees. If we were a primitive race who knew that a triangle's corners can only add up to 180 degrees(and did not yet know our world was round), we would view this phenomenon as a miracle, an impossibility. We can obviously tell through our advanced thinking that the sides of the triangle are wrapped around a sphere(thus botching the experiment) because we can recreate the model in our minds; at one time in history, though, this may have been seen as an enigma.

I'll give you another one: a perfect 90-degree angle will never be found in nature(and even in manmade objects). And yet it's a well-accepted notion in the world of mathematics. A perfect 90-degree angle only exists in our minds, defined by numbers-- and numbers themselves are an abstraction(but that's neither here nor there). Aristotle claimed there is a perfect concept of something(he gave the example of a chair) residing in some theoretical plane. It becomes flawed by our human thought of it, and further flawed when we attempt to realize it in physical form.

So, you are right on some level: the flawed earthly manifestation of an object is so far removed from its concept(and in the extreme case of a square circle, which we cannot "make" in real life) that one could claim its nonexistence without doubt. But where does existence begin and end? Between the tangible and intangible, which do we more likely perceive as "real"?

Numbermind said:

I'll give you another one: a perfect 90-degree angle will never be found in nature(and even in manmade objects).

If I bend something between 85 and 95 degrees, it will be at exactly 90 degrees during some infinitesimal period of time.

Numbermind said:

So, you are right on some level: the flawed earthly manifestation of an object is so far removed from its concept(and in the extreme case of a square circle, which we cannot "make" in real life) that one could claim its nonexistence without doubt. But where does existence begin and end? Between the tangible and intangible, which do we more likely perceive as "real"?

That reminds me of some of the works of M. C. Escher, particularly the one with a looping staircase that goes up infinitely.

That must be coincidence, I just saw a square circle. Looked different then I expected though.

Linguica said:

Of course it's possible to prove that a fallacious statement is fallacious. However when people say "you can't prove God doesn't exist" that includes the possibility that God is not within our universe, which obviously puts God beyond the reach of any logical wordplay.

True. The possibility to disprove something's existance depends of the frame of reference. Since the only way to prove that something does not exist is to prove that there can be no possibility that it exists, this means that you never can make such a proof if there is anything about the current domain that you don't know about. As such, talking about strict non-existance in terms of the universe (or beyond) is meaningless as of today, since mankind knows so little about it. You can definately talk about how likely it is, based on the current knowledge of the universe.

Numbermind said:
I'll give you another one: a perfect 90-degree angle will never be found in nature(and even in manmade objects).

You can't categorically dismiss that possibility. What is a perfect 90-degree angle? It is a well-defined term, and one of many angles that two lines may intersect with. That an angle between two random lines is exactly 90 degrees is very unlikely, but certainly not impossible. This fact would be hard to prove since any measurement has a maximum precision, but in theory 90 degrees is just as likely as any other angle.

Aristotle claimed there is a perfect concept of something(he gave the example of a chair) residing in some theoretical plane. It becomes flawed by our human thought of it, and further flawed when we attempt to realize it in physical form.

That's a new-ageish way of expressing it. Modern science has a theoretical plane, but it is realized by observing the world around us and making models of it, that is, an abstraction. This is always an approximation, with varying degrees of precision, depending of what you need. This kind of abstraction and generalization is necessary to predict future states of objects seen from a human perspective (and this is somewhat of a specialty of the human brain).

So, you are right on some level: the flawed earthly manifestation of an object is so far removed from its concept(and in the extreme case of a square circle, which we cannot "make" in real life) that one could claim its nonexistence without doubt. But where does existence begin and end? Between the tangible and intangible, which do we more likely perceive as "real"? [/B]

More new age crap. My guess is that there is an absolute reality out there that follows well-defined laws of nature, but the smallest interactions are so small, fast and hard to observe for a human observer that they seem to be entirely chaotic. That's 'just' a frame of reference thing. The perception of reality depends on how close you look at it. So existence does not "begin" and "end", the question is more where the perception of it begins and ends.

Grul said:

You can't categorically dismiss that possibility. What is a perfect 90-degree angle? It is a well-defined term, and one of many angles that two lines may intersect with. That an angle between two random lines is exactly 90 degrees is very unlikely, but certainly not impossible. This fact would be hard to prove since any measurement has a maximum precision, but in theory 90 degrees is just as likely as any other angle.

You are partially right. The probability that an angle is exactly 90 degrees is the same as any other angle: Zero percent. It is impossible. There are only ranges in physics, no absolute points.

AndrewB said:

Now that is just ridiculous. The concept of something and the actual physical existence of something are two totally different things.

Just because a person imagines a talking doughnut with play-doh fibulas in another galaxy, it doesn't mean that said doughnut is actually there.

Actually, imagining something creates it on the astral plane in a matter of speaking. The more you imagine it, the more concrete it becomes. Thus, not imagining it (nor imagining the thought of imagining it, and so on) destroys it or prevents it from being.

That is superstitious nonsense, and it makes no sense whatsoever.

AndrewB said:

You are partially right. The probability that an angle is exactly 90 degrees is the same as any other angle: Zero percent. It is impossible. There are only ranges in physics, no absolute points.

There are absolute points within a range.

Grul said:
My guess is that there is an absolute reality out there that follows well-defined laws of nature, but the smallest interactions are so small, fast and hard to observe for a human observer that they seem to be entirely chaotic.

You got that out of some moldy and rotting book out of the 19th century? There are no laws of nature. Those are the approximations and abstractions we make for practical purposes... the universe's functionality is pure interaction where all the parts' definitions would depend on the interaction they have with all the other parts... not that the parts can be told appart by us except by making abstractions and speculations. The dualistic conception or law and chaos is another one of those practical yet fantastic concepts we reason and play along with.

Grimm said:
Let's get into the religion thing, dude. I'm interested now.

OK:

[Bender voice]There is no god, and your human values are laughable! Ahh HA ha haaa![/Bender voice]

ravage said:

There are absolute points within a range.

Only virtual points.

myk said:

There are no laws of nature.

There are, we just don't know them yet.

myk said:
You got that out of some moldy and rotting book out of the 19th century? There are no laws of nature. Those are the approximations and abstractions we make for practical purposes...

You say that "there are no laws of nature", and yet in the following sentence you claim that the laws of nature are an approximation that we use "for practical purposes", contradicting yourself. The claim that there are no laws of nature is ridicilous since this would imply that everything is pure chaos where all interactions that are a made in the universe have a completely random result. The fact that you and I exist more than momentanely and that interactions can be predicted, at least with certain precision, rules out your claim.

I do not claim, however, that the laws of nature that man know of are the same as the actual laws of nature, since this obviously isn't the case. This seems to be the misconception you make.

the universe's functionality is pure interaction where all the parts' definitions would depend on the interaction they have with all the other parts...

And these interactions follow a pattern. "The laws of nature".

AndrewB said:

You are partially right. The probability that an angle is exactly 90 degrees is the same as any other angle: Zero percent. It is impossible. There are only ranges in physics, no absolute points.

This is a pretty interesting philosophical question. You seem to think that the actual world and the abstracted model of it are fundamentally incompatible, where they never can be exactly equal. This is not the case. Assume that you would measure an angle and let the precision of the measurement tent towards infinity. If the measurement turns out to be, for example, 90 degrees then the angle is indeed exactly 90 degrees.

Admittedly, this is an experiment of thought, since there can not be such a measurement. This still doesn't rule out the possibility that there is an angle that would pass such a measurement, even though the possibility that there is one is very close to zero.