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Argument from Ignorance

Also called argumentum ad ignorantiam, arguments of this form assume that since something has not been proven false, it is therefore true. Conversely, such an argument may assume that since something has not been proven true, it is therefore false. (This is a special case of a false dilemma, since it assumes that all propositions must either be known to be true or known to be false.) Other phrases often employed here, are "lack of proof is not proof"; "absence of evidence is not evidence of absence"; "the lack-of-knowledge inference"; and, "negative proof" or "negative evidence".

Examples
  1. "In 1950, Senator Joseph R. McCarthy responded to a doubting question about the fortieth name on a list of eighty-one case histories he claimed were of Communists working for the United States State Department by saying, 'I do not have much information on this except the general statement of the agency that there is nothing in the files to disprove his Communist connections.'" (Walton, Arguments from Ignorance, pp. 3-4.)
  2. No one has ever proved that aliens exist, therefore aliens do not exist; or, No one has ever proved that aliens do not exist, therefore aliens exist.
  3. "Of course Beethoven dictated that symphony to Rosemary Brown: in Playboy the famous authoress Elisabeth Kubler-Ross recently explained that communication with the dead is perfectly possible. Anyway, nobody has ever proved that dead composers don't manifest themselves in this way." (Eemeren, Grootendors, and Henkemans, Fundamentals of Argumentation Theory, pp. 63-4)
  4. Because we cannot conceive of any sufficient reason that a good and powerful God would allow this or that instance of suffering or evil, God does not exist.
  5. "Suppose I accuse you of cheating on an exam. 'Prove it,' you say. 'Can you prove that you didn't?' I ask — and thereby commit the fallacy of appeal to ignorance. This fallacy consists in the argument that a proposition is true because it hasn't been proven false. To put it differently, it is the argument that a proposition is true because the opposing proposition hasn't been proven true." (Walton, Arguments from Ignorance, pp. 2-3.)
Critique

Identify the proposition in question. Argue that it may be true even though we don't know whether it is or isn't.

Comment

Stephen John Wykstra has famously called William Rowe's inductive argument from evil, roughly expressed in example 2), a "Noseeum" argument.

In the Midwest we have "noseeums" — tiny flies which, while having a painful bite, are so small you "no see 'um." We also have Rowe's inductive argument for atheism. Rowe holds that the theistic God would allow suffering only if doing so serves some outweighing good. But is there some such good for every instance of suffering? Rowe thinks not. There is much suffering, he says, for which we see no such goods; and this, he argues, inductively justifies believing that for some sufferings there are no such goods. Since it gives such bite to what we cannot see, I call this a "noseeum argument" from evil. ("Rowe's Noseeum Arguments from Evil", in The Evidential Argument from Evil, p. 126.)

There are times when "negative evidence" is appropriate.

"There is, though a reasonable way of using this type of argument. In law courts, for example, the absence of proving guilt is taken as evidence of innocence. And scientists establish tests for hypotheses in order to see whether hypotheses are true. The failure of the predicted consequences to arise from the test, that is the failure to confirm, is taken as evidence against the hypothesis." (Tindale, Fallacies and Argument Appraisal, p. 118.)

Additionally, with particular relevance to William Rowe's argument above, where there is a reasonable expectation that there would be evidence, lack of evidence can appropriately play a role in inductive or abductive reasoning. For example, if I take you to the second tier of a stadium and say, I cannot see any grass mites on the field, therefore there are no grass mites; well, you wouldn't think the lack of evidence in this case persuasive. However, if I said, there is no evidence that there is ten ton tractor trailer on the field, therefore, there is no tractor trailer on the field; the absence of evidence in this case would be evidence of absence. So, in some cases, "negative evidence" is evidence. The relevant question is what one would expect to find were the proposition in question true.

On the danger of arguments from ignorance...
"The danger is that in a witch-hunt atmosphere, even a mere accusation, with no positive proof or evidence for it given, can be acted upon; the person accused can be prosecuted or punished, even if innocent of the wrongdoing cited by his accuser. Certain types of allegations are hard to refute, and because of a wave of popular hysteria, which may be generated politically by advocacy groups for certain interests or political views, absence of evidence comes to be taken as a kind of proof of the charge." (Walton, Arguments from Ignorance, p. 4.)
"This type of fallacy is one that occurs whenever proof points, not to the truth or falsity of the proposition to be proved, but merely to the fact that there is ignorance among people concerning it. The false assumptions that give rise to this fallacy are: that wehenever any person lacks information to prove a proposition, the proposition is false; or whenever any person lacks information to disprove a proposition, the proposition is true." (Shaw, The Art of Debate, pp. 117-18.)
"... when you insist on a man believing a thing because he knows nothing to the contrary. It is thus that people have been frightened by horrid pictures, drawn by priests or pretenders, of the world to come. It is thus that some would have us believe in animal magnetism, in clairvoyance, and the like, because they exhibit phenomena which we cannot explain. The legitimate conclusion in such cases is, that we should suspend our judgment, and wait for light to come from true religion, or scientific research." (McCosh, The Laws of Discursive Thought, pp. 188-89.)