Argument from ignorance

The very lack of evidence is thus treated as evidence; the absence of smoke proves that the fire is very carefully hidden. The argument from ignorance (or argumentum ad ignorantiam and negative proof) is a logical fallacy that claims the truth of a premise is based on the fact that it has not (yet) been proven false or that a premise is false because it has not (yet) been proven true. This is often phrased as "absence of evidence is not evidence of absence".

This can be seen as somewhat related to cherry-picking: Someone will point out something in particular about anything topical which is not easy to immediately explain. A viewer with no experience nor expertise on the subject matter might be unable to come up with an explanation or to identify the artifact/phenomenon. The individual then abuses this to claim that the unexplained artifact or phenomenon is evidence of a particular theory. The lack of a counterargument for the theory does not mean the theory is necessarily correct — that is the fallacy the individual is guilty of.

If the only evidence for something's existence is a lack of evidence for it not existing, then the default position is one of mild skepticism and not credulity. The reason for this is that one is making an extraordinary claim by asserting its existence, and extraordinary claims require extraordinary evidence. This type of negative proof is common because it is used as an 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.

Form

 * X is true because there is no proof that X is false.

Or


 * You do not know what X is. Therefore we do.

Incomplete information
This argument is not always the same as negative proof: if there is relevant information missing, an accurate judgement may not be possible. Some people were found to treat missing information as a positive, as a negative, or as "average". A critical thinker needs to analyse the evidence to determine what relevant information is missing, and whether what is missing is significant, or may be at risk of confirmation bias. When key information is missing, normally the result should be lower confidence in judgement and less extreme judgement. Kardes and Posavac found individuals who know more about a subject were found to be more sensitive to recognizing omissions, and developed better and more appropriate judgements.

Variations
Another form that this fallacy can take is the form that of an argument from incredulity (also known as argument from personal belief or argument from personal conviction), which is that one's personal incredulity or credulity towards a premise is a logical reason for acceptance or rejection. This incredulity can stem from ignorance (defined as a lack of knowledge and experience) or from willful ignorance (defined as a flat-out refusal to gain the knowledge). The concept of irreducible complexity is based entirely around this idea of personal incredulity.

Examples
For example, if you accuse a person of a wrongdoing, it is up to you to prove it. It is an argument from ignorance to suggest someone is guilty because they can't prove their innocence. For example, "Andrew can't prove he didn't eat the last jellybean, therefore he must have eaten it".

Almost all the claims from the anti-science movement revolve around some form of personal incredulity or argument from ignorance.

Proponents of the anti-science movement will usually pick some aspect of a currently accepted scientific theory and argue that it must be wrong because they do not believe it explains some aspect of the natural world. Common examples of this are such claims as "you can't prove global warming is caused by humans", "I don't see how evolution could increase the complexity of an organism", "material properties of the brain cannot presently explicitly explain consciousness so it must be caused by non-materialist processes", or "I don't know how this alternative medicine works, but it does".

The significance of missing information is often represented in scientific publications using the confidence interval (CI). A confidence interval of 0.6 to 1.6 means a wide range of effects, from a 40% reduction to a 60% increase. When the Department of Health and Human Services dropped its recommendation of regular flossing, it cited a Cochrane Review that reported only "very unreliable" evidence of the benefits of flossing because there were no adequate controlled trials. The New York Times ran the headline "Feeling Guilty About Flossing? Maybe There's No Need". The lack of confirmatory evidence was wrongly taken as evidence against flossing, but people with a different confirmation bias may make the opposite interpretation.

Retort
Ignorance is ignorance; no right to believe anything can be derived from it. In other matters no sensible person will behave so irresponsibly or rest content with such feeble grounds for his opinions and for the line he takes. A common retort to a negative proof is to propose a query about the existence of another thing that has no proof as valid. This is similar to reductio ad absurdum, that taking negative proof as legitimate means that one can prove practically anything, regardless of how absurd.

A religious apologist using the argument from ignorance would state something like, "the existence of God is true because there is no proof that the existence of God is false". But a counter-apologist can use that same "argument" to state, "the nonexistence of God is true because there is no proof that the nonexistence of God is false". This immediately demonstrates how absurd the argument from ignorance is by turning the tables on those who use this "argument" fallacy, like some religious apologists.

It is possible to show formally that absence of evidence is, in fact, evidence of absence, though weaker than actual counter-evidence. In probability theory, if $$P(H|E) > P(H)$$ (observing event E makes hypothesis H more likely), then, necessarily, $$P(H|\neg E) < P(H)$$ (failure to observe event E makes hypothesis H less likely).

Let H be the hypothesis and E the evidence, and assume $$P(H|E) > P(H)$$. By the and since $$P(E) + P(\neg E) = 1$$,

$$P(H) = P(H|E)P(E) + P(H|\neg E)P(\neg E) = P(H|E)P(E) + P(H|\neg E)(1 - P(E)) > P(H)P(E) + P(H|\neg E)(1 - P(E))$$

Therefore,

$$P(H)(1 - P(E)) > P(H|\neg E)(1 - P(E))$$

and dividing by $$1 - P(E)$$, which is positive,

$$P(H) > P(H|\neg E)$$

QED.

Therefore:


 * If a series of well-timed sabotages throughout the country would be evidence for a network of spies infiltrating it, then if no sabotages occur, that, by itself, is evidence of no such network existing (as opposed to evidence of the spies existing but biding their time).
 * If observable divine miracles would be evidence for God's existence, then lack of observable divine miracles is, by itself, evidence against it.

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 valid 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. Confirmation bias, anyone?

Negative evidence
A common saying in pseudologic is "You can't prove a negative." This is, as the hatnote up top says, simply not true. This is clearly not true because any statement can be rewritten into the negation of its negation. Any provable statement can be written as a negative. For example, "X is true" can be rewritten as "X is not false", a negative statement! If "X is true" can be proven true, then you have also proven a negative statement "X is not false".

Karl Popper applied the concept of falsifiability to judge what is unscientific, using the example of Russell's teapot. Popper stated that what is unfalsifiable is unscientific, and it is pseudoscience to declare an unfalsifiable theory to be true.