Principia

Hello,

I am in need of help in resolving a philosophical argument over the non-existance of an entity. In particular, it is not clear whether it is possible to prove non-existence. Asserting a proof of non-existance seems to be a logical fallacy; however, in mathematics such proofs can be accomplished through 'proofs by contradictions' (e.g. all freshman math majors know how to demonstrate that there are no rational numbers that equal the square root of two).

What is the correct way of arguing non-existance?

Thanks,
SC

Francois Tremblay

You are correct. Since contradictions cannot exist, if something can be shown to be a contradiction, then it cannot exist. The infamous example of the Invisible Pink Unicorn comes to mind.

I am not sure how it is supposed to be a fallacy. If a concept does not contain contradictions, then positing a universal negative is usually unwise. However, the case of contradictions is pretty clear cut (indeed, there cannot be any fallacies if we do not recognize logic).

[ March 05, 2002: Message edited by: Franc28 ]</p>

Principia

I guess the question then is how to realize when an assertion of a negative can be proven. The typical example of an unprovable negative is the following statement: "There are no purple elephants." Of course, adding the restrictive qualifier "on this planet", or "on this continent" makes the statement more likely to be proven (or disproven)...

So the assertion "you cannot prove a negative," is not entirely true? If so, in what specific situations is it not true?

Thanks,
SC

tronvillain

Proving a negative:
1)If x, then y.
2)Not y.
3)Therefore, not x.

So, proving the nonexistence of an entity requires the existence of the entity to entail something observable which is not observed. Since determining that something is not observed can be difficult or impossible, proving a negative can be difficult or impossible.

Oh, and there's not necessarily anything contradictory about the IPU.

bd-from-kg

Scientiae:

As you note, in a few cases it’s possible to show the “nonexistence” of an entity by showing that its definition is self-contradictory. There are many arguments purporting to show that the definition of “God” (understood as a being who is omnipotent, omniscient, omnibenevolent, etc.) is self-contradictory. But for most alleged entities this is clearly impossible.

Another possible tack is to analyze what it means to say that something exists. From a logical positivist perspective, to say that something exists simply means that the hypothesis of its existence has more explanatory and predictive power than any other hypothesis. Thus, if there is no data for which the hypothesis that X exists provides the “best” explanation in this sense, then X doesn’t exist. In particular, if there is no data that cannot be explained more simply on the basis of entities that are necessary in any case to explain lots of other observations, then X does not exist.

Of course, this understanding of what it means to say that something exists is anathema to neo-Platonists. On the other hand, it is very difficult to give an adequate account of what it means to say, for example, that quarks exist on any other basis.

Finally, you can appeal to what it means to “prove” something. If the only thing that counts as a “proof” is something that produces absolute metaphysical certainty in the conclusion, there is no such thing as a “proof” of anything. Or alternatively, one might count strictly logical proofs (whose only premises are axioms of logic) as producing “absolute certainty” in a sense, in which case it is possible to prove tautologies, but nothing else. If you want to be able even to talk meaningfully about proving anything but tautologies, the requirement of absolute certainty must be abandoned. And in that case it clearly is possible to prove that certain things do not exist. For example, one can prove with reasonable certainty that there is no current King of France.

Without more information about the type of “entity” being considered it’s difficult to analyze the question much further.

By the way, it should be obvious that the assertion "you cannot prove a negative" cannot be proven. If it’s false it obviously can’t be proven, and if it’s true it can’t be proven because it asserts that it can’t be proven. So those who assert it are asserting a proposition which they admit they cannot prove. Very odd.

Jayhawker Soule

<img src="graemlins/notworthy.gif" border="0" alt="[Not Worthy]" /> ! great ! <img src="graemlins/notworthy.gif" border="0" alt="[Not Worthy]" />

John Page

May I venture that contradictions can exist, but only in the mind? An apparent contradiction results from an "internal" misrepresentation of reality.

Proof in the negative is impossible because of our subjective view of reality. That our views are subjective results in us being able to (literally) contradict each other (saying the opposite) without a test against external reality. Hence the definition of truth as a statement that is factual (i.e. an accurate statement about reality).

I'm probably re-stating above previous listings, bd-from-kg really has it down.

Scientiae:

You ask how a proof for non-existence can operate. I believe it can, provided however, that you put logical (or mathematical) bounds defining where you are looking.

[ March 05, 2002: Message edited by: John Page ]</p>

owleye

Scientiae...

1. On the use of "non-existence."

If you mean by this something along the lines of proving that some individual thing does not exist, then this is merely one feature of the issue that you are addressing. The usual issue surrounding "proving a negative" occurs when, for example, the allegedly innocent is supposed to be able to prove their innnocence. Gary Condit, for example, is supposed to be able to prove his innocence in the disappearance of Shandra Levy. Unfortunately, all protestations of innocence are taken as further evidence of his guilt.

2) On what is included under the term 'prove'.

If you include evidence that supports the existence of X, as a proof of its existence, then you can achieve a proof through a process of elimination, if there is a known context in which the only possibility of its existence is within this context. For example, I can prove that X is not in this room by obtaining evidence from observations throughout the room. If nothing is found that supports X's being in the room, I would say X is not in the room.

If everything has at least some context in which the possibility of existence can be assuredly found, then an investigation into that context which fails to find it would prove its nonexistence.

Of course, if evidence is not the sort of thing that goes into what you have in mind for proof, then I'm afraid that proving the existence of something is going to be just as difficult as proving the non-existence of it.

Fell

jpbrooks

Granted.
But doesn't this argument conflate truth with "provability"? If not, then it is still possible, according to the above argument, for the claim (that "you cannot prove a [universal] negative") to be true, but unprovable.

(I'll be back later.)

[ March 05, 2002: Message edited by: jpbrooks ]</p>

Francois Tremblay

Right, surprisingly I agree with the other answers. But it is not just that an entity may involve some other result in reality that happens to be false : but the concept ITSELF which may be contradictory. The example of a god (omnipotence, omnibenevolence, Creator) is a good example in terms of internal contradictions, because there are many.

Here is my article on the contradictions of the god-concept (I also discuss universal negatives).
<a href="http://www.objectivethought.com/articles/nogod.html" target="_blank">http://www.objectivethought.com/articles/nogod.html</a>

[ March 05, 2002: Message edited by: Franc28 ]</p>