You can't prove a negative

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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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The claim, "'''you can't prove a negative'''" (or "'''...universal negative'''") is often used as a shorthand in discussions to refer to the difficulty of gathering evidence to "prove" that something does not exist. Proving that a phenomenon is not real takes a lot more time and effort than to demonstrate that it is real. This is especially true when the definition of the phenomenon can be changed at will by its believers (see [[God]]). It is 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.
  
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".
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==Science, hypotheses and statistics==
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<!-- probably should be moved to "Hypothesis" or "Statistical hypothesis testing" (or whatever), and expanded -->
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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 a drug under study is an effective treatment), while the null hypothesis is the opposite (that the drug is ineffective).
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It is possible to "prove", by a well designed [[Wikipedia:Clinical trial|clinical trial]], that a drug has an effect. However, it is impossible to prove that the drug has no effect: the effect might simply be too small for that particular experiment to detect; a later, larger, or differently designed experiment might well find it. For this reason, scientists and statisticians refer to a failed experiment (one in which the experimental hypothesis was not supported by evidence) as one that "''failed to reject the null hypothesis''" rather than one that "''supported the null hypothesis''" (and they ''never'' claim that such a result "''proved the null hypothesis true''").
  
 
==Misuses==
 
==Misuses==
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Because it is overly broad, this phrase is often overused or misapplied.  Contrary to the claim, it can be just as easy to prove a negative as a positive.
 
Because it is overly broad, this phrase is often overused or misapplied.  Contrary to the claim, it can be just as easy to prove a negative as a positive.
  
One example of a situation where one can prove a negative is for a claim which negates a simple factual untruth.  For instance, to the extent that it is possible to "prove" that "[[Richard Dawkins]] lives in England," it is then trivial to prove that "Richard Dawkins does not live in the United States."
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One such example is proving a claim which negates a simple, factual ''un''truth.  For instance, if one can "prove" that [[Richard Dawkins]] is currently in his home in England, then obviously one has proven that Dawkins is ''not'' currently in the United States.
  
Similarly, any claim that implies a logical contradiction cannot be true, and thus you can prove that it is not true. For example: "I know a man who both is exactly six feet tall, and is not exactly six feet tall." This statement is not true for any person, and one need not be [[omniscient]] to assert that there is no such man.
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Similarly, if any claim implies a logical contradiction, it cannot be true. In the previous example, if one were to claim that Dawkins was in England and in the United States at the same time, then the claim itself would be a contradiction. As an example of a claim that implies a contradiction, consider this mathematical statement: "There are no prime numbers whose square root is a rational number." This is a "universal negative" that is relatively easy to prove using a "proof by contradiction" (see [[Wikipedia:Irrational number]]), which is a form of ''[[reductio ad absurdum]]''. See the latter article for more examples.
  
Although a claim may not directly contradict itself, it is a common practice in argumentation to show that the claim leads to an inevitable contradiction.  This technique is known as [[modus tolens]], or [[reductio ad absurdum]].
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''Reductio ad absurdum'' is a form of [[modus tollens]] argument. [[Strong atheist]]s who assert that there is no [[god]] may sometimes rely on this tactic, for instance by invoking the [[argument from evil]] to show that a god with some set of characteristics cannot exist in the known world.
 
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[[Strong atheist]]s who assert that there is no [[god]] may sometimes rely on this tactic, for instance by invoking the [[argument from evil]] to show that a god with some set of characteristics cannot exist in the known world.
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==See also==
 
==See also==
 
* [[Shifting the burden of proof]]
 
* [[Shifting the burden of proof]]
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==External link==
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* [http://www.infidels.org/library/modern/richard_carrier/theory.html Proving a Negative (1999)], by [[Richard Carrier]]
  
 
[[Category:Logical fallacies]]
 
[[Category:Logical fallacies]]

Revision as of 16:36, 31 December 2007

The claim, "you can't prove a negative" (or "...universal negative") is often used as a shorthand in discussions to refer to the difficulty of gathering evidence to "prove" that something does not exist. Proving that a phenomenon is not real takes a lot more time and effort than to demonstrate that it is real. This is especially true when the definition of the phenomenon can be changed at will by its believers (see God). It is 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.

Contents

Science, hypotheses and statistics

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 a 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 a well designed clinical trial, that a drug has an effect. However, it is impossible to prove that the drug has no effect: the effect might simply be too small for that particular experiment to detect; a later, larger, or differently designed experiment might well find it. For this reason, scientists and statisticians refer to a failed experiment (one in which the experimental hypothesis was not supported by evidence) as one that "failed to reject the null hypothesis" rather than one that "supported the null hypothesis" (and they never claim that such a result "proved the null hypothesis true").

Misuses

Because it is overly broad, this phrase is often overused or misapplied. Contrary to the claim, it can be just as easy to prove a negative as a positive.

One such example is proving a claim which negates a simple, factual untruth. For instance, if one can "prove" that Richard Dawkins is currently in his home in England, then obviously one has proven that Dawkins is not currently in the United States.

Similarly, if any claim implies a logical contradiction, it cannot be true. In the previous example, if one were to claim that Dawkins was in England and in the United States at the same time, then the claim itself would be a contradiction. As an example of a claim that implies a contradiction, consider this mathematical statement: "There are no prime numbers whose square root is a rational number." This is a "universal negative" that is relatively easy to prove using a "proof by contradiction" (see Wikipedia:Irrational number), which is a form of reductio ad absurdum. See the latter article for more examples.

Reductio ad absurdum is a form of modus tollens argument. Strong atheists who assert that there is no god may sometimes rely on this tactic, for instance by invoking the argument from evil to show that a god with some set of characteristics cannot exist in the known world.

See also

External link

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