"You Can't Prove a Negative"
From SkepticWiki
The claim "you can't prove a negative" is often used as a shorthand in discussions to refer to the difficulty of gathering experimental evidence to "prove" that something does not exist. Proving that a phenomenon isn't real takes a lot more time and effort than it takes to demonstrate it. This is especially true when the definition of the phenomenon can be changed at will by its believers. Its very difficult to prove the general non-existence of a phenomenon, and this difficulty is used by believers of many kinds of phenomena to give the appearance of credibility to their beliefs.
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[edit] Discussion
[edit] Illustration
In general, statements of the form "X exists" are (if true), easy to prove. One simply shows an example of X as a proof. For example, I can prove a claim that "White swans exist" by exhibiting a normal (European) swan. I can similarly prove that "black swans exist" by exhibiting an Australian one.
On the other hand, it is in theory impossible to prove beyond question that "No green swans exist" (or more generally any statement of the form "No X exists"). I can show cages and cages full of five thousand swans, all of which are white and black, but what about the five thousand and first? In order to prove that no green swans exist, I would need to produce and examine every swan in existence, including swans on unexplored Pacific islands and even unknown planets in distant galaxies.
Sir Karl Popper discussed this problem under the name of "Falsifiability," the property of a theory to be able to be disproven (which of course, is not the same as it being disproven). Under his theories, "science" can only address issues which are falsifiable. A key characteristic of many pseudosciences are that they make claims that cannot be disproven or even critically examined in the sense defined above.
[edit] Problems
As stated, the rule "You can't prove a negative" is demonstrably false. For many phenomena, the existence of the phenomenon would have some consequences that are themselves falsifiable. You can easily prove that there is no dragon in your refrigerator. (A dragon, or any dragon-sized creature, would provably not fit into a box the size of your refrigerator. More generally, you could simply look in the refrigerator -- do you see a dragon? Do you see any place large enough that a dragon could hide? Ergo, no dragon!) With some cleverness, you could easily prove that there are no leaking pipes in your house. While far more difficult (and probably impractical), you could even prove that there are no weapons of mass destruction in Iraq.
One might observe too, that the designation of statements as "negative" is arbitrary. The "negative" claim that "no swans are green" is equivalent to the "positive" claim that "all swans are non-green."
The claim of "You can’t prove a negative" is generally intended to argue that:
- There ought to be no expectation that general laws can be proven, and the inability to prove a general rule does not disprove that rule.
[edit] Negative Statements and Distribution
In Aristotelian logic statements are divided into 4 categories, most often referred to as "A", "E", "I", and "O". The first two are universal statements, of the positive and the negative, and the latter two are particular, of the positive and negative. For a brief understanding of the 4 different types of statements, study the difference between these statements:
A: All gods have fuzzy beards. E: No gods have fuzzy beards. I: Some gods have fuzzy beards. O: Some gods do not have fuzzy beards.
In regards to the argument "You can't prove a negative", this is almost always referring to the E statement, better known as the universal negative. Distribution refers to whether articles are exhausted in the expression. For example, in an A statement the subject (first time) is distributed because all of that term is covered in the statement. Here are the distributions for the 4 statements:
A: Subject E: Subject and Predicate I: Predicate O: None
As you can see, the universal negative E statement is particular difficult because here we are making definite claims about 2 terms. In other types of statements the non-distributed term can be considered to act as an anchor to make the statement work.
Alas there is still a way to prove universal negatives. When claiming that something does not exist, the subject with be "that would is in existence" and the predicate with be the object of criticism, such as "unicorns," or "lochness monsters." If the predicate is self-contradictory then the universal negative statement must be true. For example, the statement "there are no married bachelors" has to be true because "married bachelors" is a self-contradiction. Similarly arguments for strong atheism follow a similar method. The claim will be "there are no god(s)" which can be proven to be true if god(s) are shown to contradict themselves. This is done by listing characteristics of god(s) and then showing why they are logically invalid. One of these characteristics in attacked in the Problem of Omnipotence whereby the strong atheist will show that an omnipotent being is restricted from using his omnipotence against himself, and therefore isn't actually omnipotent. With omnipotence proven to be self-contradictory, the strong atheist can claim that any god which requires omnipotence is itself self-contradictory and therefore not part of the realm of that which exists.
A major problem with this avenue of argument for the strong atheist is that god in the most general sense is never actually defined, so even if they are able to take away some self-contradictory characteristics of god, there still leaves open the possibility of a god (or gods) which are not self-contradictory, such as a god that is the most powerful in the universe, but not all powerful (in the case of the Problem of Omnipotence). These new, logically possible, gods might be defined as demigods by some, but the lack of a clear univeral definition of god(s) prevents the strong atheist from putting this debate to rest.
[edit] In Science
Science, of course, cannot prove general laws in a mathematical sense, since doing so would require an observation of an infinite number of facts. The claim that “You can’t prove a negative” may apply to scientific laws, as in,
- You can’t prove that some mechanical interaction does not conserve energy.
This, unfortunately is true. It is impossible to observe every possible mechanical interaction, and evaluate each one for conservation of energy.
General observations involving a finite number of facts may be proven, however. It is not true that “You can’t prove that no major planet has a hyperbolic orbit”. You can prove this quite easily by observing that:
- Mercury orbits in an ellipse,
- Venus orbits in an ellipse,
- …
- Pluto orbits in an ellipse.
This proof, however, is subject to the assumption that all major planets are known; the 2004 discovery of Sedna and the 2005 discovery of "2003 UB313" suggests that if "major planets" can be redefined, one cannot prove it. (Consider: how would you disprove the statement "No undiscovered major planet has a hyperbolic orbit"?)
Much scientific practice has developed to address this issue. In particular, the field of statistics distinguishes between the so-called experimental hypothesis and the null hypothesis. The experimental hypothesis is usually the statement that the scientist would like to investigate the truth of (for example, that the drug under study is an effective treatment), while the null hypothesis is the opposite (that the drug is ineffective). It is possible to prove, by gathering a clinical group together, that the drug has an effect -- but it is impossible to prove that the drug has no effect; it might happen that the drug has an effect, but one too small for that particular experiment to notice (and that a later, larger, or differently run experiment might find it). For this reason, scientists and statisticians refer to a failed experiment as one that "failed to reject the null hypothesis" -- one where all the evidence available was negative, but the null hypothesis is still not "proven."
[edit] The Zammit Challenge
Beginning in 1964, James Randi offered a prize for demonstration of any paranormal claim. Such a demonstration, would of course, prove the existence of paranormal phenomena in general.
Apparently as a response to James Randi’s paranormal challenge, various paranormal advocates began offering rewards for proof that paranormal phenomena do not exist. One notorious example is the one million dollars offered by lawyer Victor Zammit for the proof that there is no afterlife.[1]
On its face, it may seem that these were simply the inverse of the Randi Challenge. But the Zammit challenge, and others like it, were greeted by cries of “You can’t prove a negative” from the skeptical community. In fact The Randi Challenge essentially demands the demonstration of a single fact, whereas the paranormal challenges, would require something like proof of a general law. In particular, the Zammit challenge specifically requires a "rebuttal" of all the (so-called) evidence he has amassed regarding the afterlife. Furthermore, the 'the level of proof required to rebut the evidence will be the Cartesian test, "beyond any doubt". This means that there has to be absolutely no doubt at all in the minds of the Committee that the 'evidence' has been rebutted." (Zammit)
From the above discussion, it should be clear that this challenge is unwinnable. The applicant is required to examine every cited instance of evidence and conclusively demonstrate that no paranormal explanation (including those not yet offered) is true. If the paranormal exists, then it should be at least possible to meet the Randi challenge. The Zammit challenge is unattainable in any case. So, we may then regard it as worthless for demonstrating anything. It is, of course, fallacious to assume that if the Zammit challenge is not met, then the paranormal must exist. Likewise, failure to meet the Randi Challenge is also no proof that the paranormal does not exist, but such failure constitutes better evidence of the non-existence of paranormal phenomena.
[edit] In Law
In criminal law, the maxim of “You can’t prove a negative” is reflected in the “presumption of innocence”. That is, arguments of the form
- You can’t prove that the defendant didn’t commit the crime.
are inadmissible.
Since it is perfectly possible to not-commit a crime and at the same time, have no evidence of that non-commission, the lack of proof does not imply anything.
Often, of course, one can prove that a defendant didn’t commit a crime, which again demonstrates that “You can’t prove a negative” is of limited value.
[edit] Other cases
It has been claimed that the United Nations demanded that Saddam Hussein prove the non-existence of weapons of mass-destruction under his control. This may be historically inaccurate, but had such a demand been made, it would have required evidence that every square inch of Iraq did not contain WMD.
In mathematics it is often possible to prove something, even on an infinite set. While it cannot be done by perfect induction, the structured nature of mathematics often makes such questions isomorphic to a finite set. For example
- You can’t prove that there are no positive integer solutions to an + bn = cn for n > 2.
turned out to be incorrect; such a thing could be proven.
