Whence the idea that proof of nonexistence is impossible?

Factual Questions
21

Don’t most cases of being asked to prove a negative involve checking an impossibly high or even infinite number of instances where the positive might occur/have occurred?

Example: “There is at least one human with 18 toes. If you don’t agree, prove otherwise.”
The proof of the negative would involve travelling to every single groups of humans including the most isolated Amazonian tribes and looking at their feet. And revisiting them all in short order to check on new births. Obviously impossible.
The proof of the original assertion OTOH can be easy. Just produce one 18-toed person.

Another example: “Prove that you never have committed murder”.
Which would require providing alibis for the whole of one’s life.

22

It’s not that “proof of nonexistence is impossible”, nor is it (as is even more commonly misstated) that “you cannot prove a negative” – it is that you cannot prove a universal negative.

23

It’s not a misquote; you can check the source of the OP quote here, where Q.E.D. plainly says,

It sounds to me like an assertion that proof of nonexistence is impossible, but you might interpret it differently. While not the most common way of expressing the central thesis of your linked thread’s OP, it is a viewpoint that I have seen often enough on this board. If Q.E.D.'s statement evolved out of the idea that “you cannot prove a universal negative”, then we have discovered the origin of the disputed quote, thus answering the general question.

24

What definition of “existence” are you using here? As far as I am concerned “leaving recognizable evidence” is a condition of existence. There is no difference between a creature that does not influence the universe in any way and a nonexistent creature.

First of all, a spiritual being that interferes with the thought processes of human beings is testable.

Second, all “proofs” essentially boil down to probabilities. You may claim to “know” which country you live in, but only by rejecting an infinite number of far-fetched scenarios where your aren’t really where you think you are. (“Random quantum fluctuations moved you to a planet 5000 light years from earth five minutes ago, to a room identical to the one you left”.)

If the evidence supporting some “spiritual being” is as lacking as the proof of this spontaneous 5000 light year journey, then you are as justified in saying that you know it doesn’t exist as you are in saying that you know which country you’re in. (More justified actually, since current physics predict random quantum fluctuations, while there is no sound basis for belief in a spiritual being.)

Can you give me an example of something that can be proven (or disproved)?

(When you factor in the possible influence of Martian mind control rays?)

25

The IPU is a spoof of religion. It cannot both emit light of a certain wavelength AND be invisible. This is just as certain as any mathematical proof.

Such “facts” may be proven on a different “level” than other “facts”, but they’re not proven in the absolute sense.

Say your pal Euclid tells you “there does not exist a largest prime number”. Is this proof? Of course not.

So you study Euclid’s theorem for yourself. You understand it perfectly. Is this proof? Of course not. Maybe alien mind control rays are tricking you into believing that you understand it…

So you send it to every mathematician in the world. They all confirm that Euclid is right. Is this proof? Of course not. Maybe they all decided to lie to you on a whim…

No matter what you present as “proof” I can come up with some far-fetched scenario where the “proven” fact is false. Even if my imagination fails, and I can’t think of anything, that doesn’t prove that no such scenario exists. (Absence of evidence… :stuck_out_tongue: )

26

In order to prove that “there are no big green Martians in the universe” all you have to do is examine the entire universe and find something other than a big green Martian everywhere.

Proving a universal negative may be a little tricky, but it’s not impossible.

27

This thread might be headed for GD due to posts like yours. There we’ll follow in the grand tradition of threads like Mathematics: Invented or Discovered; I think therefore I am; and What does the Incompleteness Theorem imply?.

A philosophy major friend of mine once made a statement that relates tangentially to your objections about certainty in knowledge. I’m paraphrasing, but here it is:

You provide scenarios in which a mathematical proof has been accepted without adequate justification, and in so doing you appeal to a shared standard of logic. I can admit the possibility of your far-fetched explanations only if we share a common standard of logic. Our ability to discuss this topic points to the existence of a common standard of logic, which may be the result of cultural indoctrination, formal education, or even alien mind-control rays. But its existence is not in doubt, no more than you would doubt your own existence if you accepted the Cartesian principle of cogito ergo sum. On such undoubtable statements did Descartes build up his philosophy. Like Descartes, we too can develop a system of facts around the undoubted principles of logic. In such a system, as you and I agree, proofs of nonexistence and universal negatives are indeed possible.

One last nit to pick, regarding the IPU. You wrote:

Perhaps the IPU could emit light of a wavelength not within the visible spectrum, but arbitrarily designated “pink” to give its human worshipers a mental image.

28

Naah.

You’d have to examine the entire universe instantaneously and even if you could do that you’ve only demonstrated that you were unable to find any big green Martians anywhere. (Maybe they have secret methods of hiding themselves from your omnipresent scrutiny). The problem is that the (in this case NOT but should be) falsifiable construct is “there are Martians”, not “you will succeed in finding Martians”. In contrast, the person with the theory that Martians exist gets to work against the falsifiable construct “there are no Martians”. All he has to do is find one. You, on the other hand, in failing to find one, haven’t accomlished anything – you’ve only failed to accomplish something. (At any given moment, neither you nor the other guy have found any Martians. The other guy has a hypothetical, if unlikely, “success story” outcome in which he finds one. You don’t. You just continue to have not found any Martians).

29

(Just “for the record”: I may appear to be arguing from both sides of the fence. On the one hand I am saying that we [probably :)] cannot know anything with complete certainty, but on the other hand I maintain that some things [like the IPU] can be “proven” or “disproved”.

My point is that in order for words like “proof” and “know” to have any meaning it has to be understood that they refer to near certainty. So while I cannot be 100% sure of the nonexistence of the IPU, I can be sure enough to claim that I know that it doesn’t exist.)

(I’m not sure if I understand what you mean.)

I can’t know with absolute certainty that we share a common standard of logic - I can only assume it.

Even if I postulate this assumed standard of logic, I still can’t arrive at absolute certainty within it. In order to rely completely on logic, I have to know with absolute certainty that my reasoning isn’t flawed.

Communication depends on a common standard of language. If “pink” doesn’t have the generally agree upon meaning, then it’s just a random collection of letters. I have to rely on what you say, not what you might be thinking.

30

Read what I wrote again. I wasn’t looking for Martians per se, I was looking for “Not-Martian”.

The statement “there are no big green Martians in the universe” is just another way of saying “everywhere in the universe there is something other than a big green Martian”. If I prove the latter I have proven the former.

(If you don’t accept that something cannot be both “Martian” and “Not-Martian” at the same time you are rejecting logic and all bets are off.)

So what you’re saying is that if I search the entire universe and the Martians are hiding in a part of the universe I didn’t search, then I won’t be able to find the Martians? This is nonsense.

How can he prove that he’s found one?

31

I’m not sure what you mean by this – in fact, it is the non-falsifiable nature of “Martians Exist” that should cause all right-thinking people to plump for the falsifiable “Martians don’t exist” – at least that way, if we are wrong, there’s a chance we’ll find out one day. Surely?

I am happy to subscribe to Staale Nordlie’s argument that we can know nothing with absolute certainty (with the possible exception of “I think, therefore I am”), that doesn’t mean that we should be dribblingly open-minded about everything, all the time.

32

Hmmmm… On one hand, scientists say that a theory cannot be proven true, only proven false (i.e. with counter examples). On the other hand, there’s this old chestnut (beloved by theists but also used by skeptics) that “you cannot prove that something does not exist.”

Seemingly inconsistent, wouldn’t you say?

I think we are talking apples and oranges here.

In fact, it is possible to prove that something does not exist. All you have to do is show that (a) the existence of such a being would be inconsistent with other phenomena that are known to exist, (b) the putative existence of the being in question is internally consistent, and/or © the being in question is defined as having certain characteristsics or attributes that can be shown to not exist.

An example of (a) is I can prove that there are no 10-ton mosquitoes swarming in the rainforests of South America simply by referencing the so-called “square-cube” law that states that, while strength is proportionate to the square of the linear dimension, mass is proportionate to the cube of the linear dimension. I don’t need to examine every square inch of the rainforests to “prove” that there are no such mosquitoes.

An example of (b) is that I can prove that there is no such thing as a supernatural being who loves all people equally, but who condems to eternal damnation all those who who have never heard his name. I don’t need to examine every corner of the universe to see if such a being exists – I simply need to point out that such a being is logically inconsistent to both “love all people equally” and simultaneously “condemn to hell those people who do not hear of me”.

An example of © is that if somebody claims there is a magical rain cloud that appears over my house every Thursday and waters my garden, I can disprove the existence of this raincloud simply by sticking rain sensors in the ground and observing that no rain fell on the person’s garden last Thursday.

Now, all this falls apart, of course, if somebody claims that a being exists who just happens to (a) be completely immaterial and therefore bound by the same physical laws that govern physical objects, (b) has no description, per se, therefore making internal inconsistency impossible, and © has no defined attributes or characteristsics that can be disproved by counter example.

So yes, in the abstract, I suppose its possible to posit the existence of a being who gives no evidence whatsoever of his existence, and then claim that it is impossible to disprove his existence. However, most people who claim to know about so-called “supernatural” beings do make active claims as to what that being is like, how he has interacted with the physical world, etc.

Rather than relying on the old “you can’t prove a negative” saw, I’d love to see people treat their religious beliefs as theories which can only be assumed true in the absence of counter evidence. Once counterevidence is produced, the belief must be acknowledged as incorrect. Instead, however, people tend to believe first, in the absence of any evidence, and then reject any counter evidence as irrelevant since '“you can’t prove a negative.”

Regards,

Barry

33

Nitpick: A pink flower in a darkened room isn’t black. It may look black, but people use color designations to refer to what something looks like under standard lighting conditions.

The IPU is invisible, and reflects no light. But if She did, it would be pink light.

34

And if she did, she would no longer be invisible…

35

Well, as long as my statements are under discussion, let me talk a little about mathematical proofs of non-existence.

Basically, it’s like you guys said: you say that object S has properties x[sub]1[/sub] through x[sub]n[/sub], and show that either these properties are contradictory, or they contradict what is already known.

Euclid’s proof that there is no largest prime relies on the second method, whereas Arrow’s theorem on the non-existence of an ideal voting system relies on the first.

36

I agree that there are some “apples versus oranges” things cropping up here.

The viewpoint I’ve been espousing is not intended to apply outside of a rather specific box, which is the conventional construction of scientific theory and research hypotheses, which in turn depends in part on subscribing to some conventions.

Convention One: You set up a theory. Your theory is a description of the universe or some tiny part thereof and how you think it works. A theory must account for some observable behavior or phenomenon, but it may contain huge parts that are not observed or in some cases may even be inherently impossible to observe.

Convention Two: You so not seek to “prove your theory”. (This is because theories generally attempt to map out more of “what is so” than can ever be directly tested). So when you are done your theory remains “unproven”, but “supported” insofar as it accurately predicts something (as you will see below).

Convention Three: You will instead seek to set up a counterhypothesis, one that, if true, would be inexplicable within the bounds of your theory. It is chosen for its utility value as something that can be easily and solidly disproven with an absolute minimum of abstract theory knitting together the empirical evidence; and for its utility value as something that, if not disproven, torpedoes your theory as a predictive tool.

Convention Four: The counterhypothesis does not attempt to explain stuff. It does not constitute an alternative theory. Instead, if not disproven within the experiment, it constitutes “the unexplained” and because it is unexplained your theory needs reworking or discarding.

Now, outside the box (and scientists and researchers don’t stay within its confines in real life either), sure, let’s say you formulate a theory (Bathtubs are inhabited by big green Martians at least once every 72 hours which explains where bathtub rings come from, the damn Martians put them there), you construct a counterhypothesis and set out to blow it to bits (if, in fact, there ain’t no Martians, you would not be able to capture them on time-lapse film if cameras are taped to the shower head, so let’s test that, and the photographs showing the Martians will blow that counterhypothesis to bits), and then your evidence fails to falsify your counterhypothesis and your theory fails to explain things (bathtub rings and/or the fact that the Martians who put them there didn’t show up on film) – so like most scientists you do what? Yeah, you continue to believe what you believed before and you decide the problem is that your experimental design wasn’t good (hmm, this time we’ll add film sensitive to longer and shorter wavelengths, maybe they are transparent to visible light!).

And obviously, with a bit of language manipulation most any thesis can be reworded such that if originally expressed as a negative (there are no Martians anywhere in the universe) it can be stated as a positive (the universe consists in its entirety of things that are not Martians).

My point is that the original “old saw” about “you can’t prove a negative” or “you can’t prove that something does not exist” is a half-understood / half-misconstrued ripoff of this tradition in research. You want a that your thesis describes the existence of a process that explains something in order that b you can formulate a counterhypothesis which would negate it, and in the negative this counterthesis would tend to say that the process (and its empirical “footprints”) does not occur, in order that c you can falsify the counterhypothesis by finding footprints, thus validating your thesis which would predict that you’d find them if you looked for them.

Within that framework, you don’t want to start out with the theory that “Joe’s thesis about Martians being the explanation for bathtub rings is wrong, there are no such Martians” because then your empirically-oriented counterhypothesis is positive (“Martians do exist and therefore leave Martian footprints in the tub or can be photographed as they create bathtub rings etc.”) and your falsification of it is – not, not conceptually, intrinsically demonstrable (“yeah I could study every tub throughout history and determine the perennial absence of Martians”) but pragmatically unprovable. It’s a convention based on the practical.

What you do instead is formulate an alternative theory that is positive (“bathtub rings are caused by human epidermis and soap scum floating on top of the bathwater long enough to stick to porcelain, and then when the water drains out the skin-&-scum layer stays put at water level”), generate your negative counterhypothesis (“If this is not so, then running the water without soap or humans but otherwise according to same schedule will still yield bathtub rings in 14 day experiments”), blow it out of the water (“See? No bathtub rings! Followup experiments show mild rings with humans but no soap and with soap but no humans and strong rings with combo of humans and soap”), and then you’ve explained the same phenomenon as the guys theorizing big green Martians.

There may or may not nevertheless be big green Martians (in or out of tubs) but what does their posited existence explain? Not tub rings, at this point. We have another explanation in place that doesn’t require them, and no evidence to support their existence.

Clearer?

37

To continue the apples and oranges critique.

People have been approaching this subject from two distinct viewpoints, the philosophical, as exemplified by Staale Nordlie that even mathematical proof is not final because one can conceive of mitigating outside factors, and what I might call the worldly, in which godzillatemple uses agreed-upon strictures of physics to discount ten-ton mosquitoes.

You might say, without being pejorative, that the philosophical argument proceeds from an assumption of meaninglessness and the world argument proceeds from an assumption of meaningfulness. Obviously, the two cannot be intertwined in a single discussion and still have that discussion make sense to both.

But there is a further subdivision of the worldly argument that has been little noted, although it was implied by AHunter3.

For that we need to move into the world of statistics. It is procedurally impossible to ask everyone in the U.S. at any given moment what they are watching on television. It is quite simple, on the other hand, to ask everyone in your house that question.

In statistics a completely sampleable audience is called a universe. And in fact there are slightly differently mathematical techniques for dealing with a universe than for dealing with a sample.

That’s how you give an answer to a question such as Achernar’s. You can look at the universe of countries on the Earth and determine that no individual country is larger than the continent of Asia. This is a worldly argument about a universe and so can be definitively stated.

It is only when a universe is not, even in theory, instantaneously sampleable or subject to the standard underlying agreed-upon worldly rules that you get into the problem of not being able to prove a negative.