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A negative proof (known classically as appeal to ignorance) is a logical fallacy which takes the structure of:
- X is true because there is no proof that X is false.
If the only evidence for something's existence is a lack of evidence for it not existing, then the default position is one of skepticism and not credulity. This type of negative proof is common in proofs of God's existence or in pseudosciences where it is used to attempt to shift the burden of proof onto the skeptic rather than the proponent of the idea. The burden of proof is on the individual proposing existence, not the one questioning existence.
A common retort to a negative proof is to reference the existence of the Invisible Pink Unicorn or the Flying Spaghetti Monster as just as valid as the proposed entity of the debate. This is similar to reductio ad absurdum, that taking negative proof as legitimate means can prove practically anything, regardless of how absurd.
 When proof is presented
One important element to remember in regards to negative proof is that once positive evidence has been presented the burden shifts to the skeptic to refute the evidence presented. One cannot keep arguing from the position of "negative proof" after the presentation of evidence. This point, however, is completely lost on most creationists (such as intelligent design advocates) who shout from the rooftops that there are no transitional fossils long after they've been repeatedly shown them.
 What the fallacy isn't
A common saying in pseudologic is "You can't prove a negative." That saying is not true. An absence of something can be proved in various ways, e.g., by a reductio ad absurdum or by proving something else that is inconsistent with the presence of that something (a very useful approach known in mathematics as proof by contradiction[wp]). For example, in law, a party may have the burden of proving nonreceipt of certain correspondence and may bear that burden of proof (at least by a preponderance of the evidence) by introducing into evidence a docket record in which the correspondence would have been noted. In mathematics, there are plenty of proofs of negative propositions, such as "there is no largest prime number" or "there is no rational square root of 2". One might also note that the saying itself is a negative.
 See also
| Articles about logical fallacies|
|Affirming the consequent||Denying the antecedent||
|Fallacious argument styles|