Argument from ignorance

Often seen in anecdotal evidence, superstitions, correlation-causation fallacies, and experiments with small sample size

• "I took a placebo pill and now my symptoms are completely gone. The placebo cured my symptoms."
• "I wore red socks and we won the baseball game. My red socks helped win the game."
• "When ice cream sales increase, so do murders, therefore more ice cream causes more murders". (These events correlate due to the common element of high temperatures. High temperatures, not ice cream sales, leads to more murders).[5]

These examples contain or represent missing information.

• Statements that begin with "I can't prove it but ..." are often referring to some kind of absence of evidence.
• "There is no evidence of foul play here" is a direct reference to the absence of evidence.
• "There is no evidence of aliens, and therefore, aliens do not exist" appeals to an absence of evidence.
• "A recent study said there is no strong evidence that shows flossing reduces cavities or gum disease." The NIH dental health expert indicated that large-scale, long-term clinical trials are expensive and challenging to perform, and that patients would still likely benefit from flossing.[6][7]

These examples have the potential for "false negative" results.

• When the doctor says that the test results were negative (a month later the test is positive).
• Under "Termites" the inspector checked the box that read "no" (a week later termites are discovered).
• A patient uses an antibiotic for only one day and stops because they feel it isn't working. (Had they used it for 7 days the drug would have worked).

These examples contain definite evidence that can be used to show, indicate, suggest, infer or deduce the non-existence or non-presence of something.

• One very carefully inspects the back seat of one's car and finds no adult-sized kangaroos.
• The police did not find a gun in the suspect's clothing.
• The elderly patient did not have any teeth in his mouth.

(Draws a conclusion based on lack of knowledge or evidence without accounting for all possibilities)

• "I take the view that this lack (of enemy subversive activity in the west coast) is the most ominous sign in our whole situation. It convinces me more than perhaps any other factor that the sabotage we are to get, the Fifth Column activities are to get, are timed just like Pearl Harbor ... I believe we are just being lulled into a false sense of security." – Earl Warren, then California's Attorney General (before a congressional hearing in San Francisco on 21 February 1942).
• This example clearly states what appeal to ignorance is: "Although we have proven that the moon is not made of spare ribs, we have not proven that its core cannot be filled with them; therefore, the moon’s core is filled with spare ribs."[8]
• Carl Sagan explains in his book The Demon-Haunted World:

Appeal to ignorance: the claim that whatever has not been proven false must be true, and vice versa. (e.g., There is no compelling evidence that UFOs are not visiting the Earth; therefore, UFOs exist, and there is intelligent life elsewhere in the Universe. Or: There may be seventy kazillion other worlds, but not one is known to have the moral advancement of the Earth, so we're still central to the Universe.) This impatience with ambiguity can be criticized in the phrase: absence of evidence is not evidence of absence.[9]

Contraposition is a logically valid rule of inference that allows the creation of a new proposition from the negation and reordering of an existing one. The method applies to any proposition of the type If A then B and says that negating all the variables and switching them back to front leads to a new proposition i.e. If Not-B then Not-A that is just as true as the original one and that the first implies the second and the second implies the first.

Transposition is exactly the same thing as Contraposition, described in a different language.

Null result is a term often used in science to indicate evidence of absence. A search for water on the ground may yield a null result (the ground is dry); therefore, it probably did not rain.

Arguments from self-knowing take the form:

1. If P were true then I would know it; in fact I do not know it; therefore P cannot be true.
2. If Q were false then I would know it; in fact I do not know it; therefore Q cannot be false.

In practice these arguments are often unsound and rely on the truth of the supporting premise. For example, the claim that If I had just sat on a wild porcupine then I would know it is probably not fallacious and depends entirely on the truth of the first premise (the ability to know it).