Argument from ignorance

An argument from ignorance, also known as argumentum ad ignorantiam or appeal to ignorance, is an informal logical fallacy that asserts a proposition to be either true or false merely because it has not been proven or disproven.^[1]

General form of the argument:

1. P has never been disproven therefore P is/(must be) true.
2. P has never been proven therefore P is/(must be) false.

Such arguments may focus on the fact that true things can never be disproven, (converse of the 1st form) or alternatively, that false things can never be proven (converse of the 2nd form) and may claim or imply that the converse of these statements are just as true and thus reconstructing the original fallacy.

Arguments that appeal to ignorance rely merely on the fact that the veracity of the proposition is not known, or undetected, to deduce a conclusion without consideration to other valid possibilities, namely:

1. While P may not have been disproven it may still be false.
2. While P may not have been proven it may still be true.

This fallacy can be, and has been, used effectively to arrive at many a wrong conclusion and is considered by some to be a special case of a false dilemma or false dichotomy in that both these fallacies fail to consider perfectly valid alternative possibilities. Such arguments may take the form:

1. If a proposition has not been disproven then it can't (possibly) be considered false and therefore must be considered true.
2. If a proposition has not been proven then it can't be considered true and therefore must be considered false.

These forms are identical to the general form and likewise ignore the fact that true things can be both true and remain unproven as can false things remain false without being disproven.

This fallacy is sometimes confused, and or combined, with logically valid Contrapositive arguments that utilize the Transposition rule of inference in classical logic to infer that If P implies Q then Not-Q also implies Not-P to exactly the same extent. For example if we assume the proposition that If it's raining outside then the streets are (or must be) getting wet, then we can also infer that if the streets are not getting wet then it is not (and must not be) raining outside. The inference that it cannot be raining outside because the streets are not getting wet is exactly as true, or perhaps exactly as untrue, as the original proposition. The statements are logically equivalent.

The phrase absence of evidence is not evidence of absence can be used as a short hand rebuttal to the second form of this fallacy but is often directed, without full consideration, at any conclusion derived from null results obtained by experiment.

In this regard Irving Marmer Copi writes:

"In some circumstances it can be safely assumed that if a certain event had occurred, evidence of it could be discovered by qualified investigators. In such circumstances it is perfectly reasonable to take the absence of proof of its occurrence as positive proof of its non-occurrence." (Introduction to Logic, Copi, 1953, Page 95)

Contraposition is a logically valid rule of infrance that allows one to create 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 if you negate all the variables and switch them back to front you will get a new proposition i.e. If Not-B then Not-A that is just as true as the one you started out with and that the 1st implies the 2nd and the 2nd implies the 1st.

Transposition is exactly the same thing except it has its own name and uses funny symbols instead of big words.

Absence of evidence is the absence, or lack of, any kind of evidence that may show, indicate, suggest, or be used to infer or deduce a fact.

Evidence of absence is evidence of any kind that shows, indicates, suggests, or can be used to infer or deduce the non-existence or non-presence of something.

Negative evidence is sometimes used as an alternative to Absence of evidence and is often meant to be synonymous with it, however, the term may also refer to evidence with a negative value, or null result equivalent to evidence of absence or it may even refer to positive evidence about something of a negative or unpleasant nature.

Null Result is a term often used in the field of science to indicate evidence of absence.

Arguments from incredulity take the form:

1. P is too incredible (or I can't imagine how P could possibly be true) therefore P must be false.
2. It's obvious that P (or I can't imagine how P could possibly be false) therefore P must be true.

These arguments are similar to arguments from ignorance in that they too ignore and do not properly eliminate the possibility that something can be both incredible and still be true, or obvious and yet still be false.

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 P were false then I would know it, in fact I do not know it, therefore P cannot be false

In practice these arguments are often fallacious and rely on the veracity of the supporting premise. For example the argument If I had just sat on a wild porcupine I would know it, in fact I do not know it, therefore I did not just sit on a wild porcupine is probably not a fallacy and depends entirely on the veracity of the leading proposition that supports it. (See Contraposition and Transposition in the Related terms section in this article)

Absence of Evidence is a condition where no valid conclusion can be inferred from the mere absence of detection, while Evidence of absence is a conclusion that relies on specific knowledge in conjunction with negative detection to deduce the absence of something.

For example by determining that a given experiment is sensitive and reliable enough to detect the presence of X, when X is present, one can exclude the possibility that X could be both present and not detected. With this possibility removed a null result condition no longer represents a mere Absence of evidence and may be considered Evidence of absence and is as reliable as the proposition that supports it. (See Contraposition & Introduction to Logic, Copi, 1953, Page 95)

Analysis:

There are 4 possible outcomes and only 2 where the results are null:

1. Not detected and X is not present.
2. Not detected and X is present. (Option eliminated by proposition)
3. Detected and X is not present. (False positive, not a case of 'null' detection)
4. Detected and X is present. (Not a case of 'null' detection).

To the extent that option 2 can be eliminated one can deduce that if X is not detected then X is not present, therefore evidence of absence.

(These examples should contain or represent missing information.)

• Statements that begin with "I can't prove it but…" are often referring to some kind absence of evidence.
• "There is no evidence of foul play here" is a direct reference to the absence of evidence.

• When the doctor says that the test results were negative, it's usually good news.
• Under "Termites" the inspector checked the box that read "no".
• The results of Michelson–Morley's experiment reported no shift at all in the interference pattern.

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

• A biopsy showing the absence of malignant cells.
• The null result found by Michelson–Morley's famous experiment represents "strong evidence" that the luminiferous aether was not present.
• You very carefully inspect the back seat of your car and lo… no tigers.
• The train schedule does not say that the train stops here at 3:00pm on a Sunday.

(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." - Then California's Attorney General Earl Warren (before a congressional hearing in San Francisco on 21 February, 1942)

• Yeah, Yeah, Michlseon-Morely, I can see people's eyes glazing over. We need better examples.
• You look in the back seat of your car and lo... no adult sized kangaroos and then use this negative/null adult sized kangaroo detection results in conjunction with the previously determined fact (or just plain old proposition) that adult sized kangaroos, if present, cannot evade a visual search in the back seat of cars to deduce a new fact that there are no adult sized Kangaroos present in the back seat of your car

• The presumption of innocence, if present, effectively removes the possibility that the accused may be both guilty and unproven, from consideration in judgment, and as such the accused is considered as innocent unless proven guilty. (See decision table below)
  1. Innocent and unproven. Judged as innocent.
  2. Innocent and proven. Judged as innocent.
  3. Guilty and Unproven. Judged as innocent. (Presumption of innocence)
  4. Guilty and Proven. Judged as Guilty. (Innocent unless/until proven guilty is a summary of this and easier to remember.)

From "Fallacies: classical and contemporary readings By Hans V. Hansen, Robert C. Pinto"

"It is generally accept that the philosopher John Locke introduced the term in his Essay Concerning Human Understanding:"

"Another way that Men ordinarily use to drive others, and force them to submit their Judgments. And receive the Opinion in debate, is to require the Adversary to admit what they alledge [sic] as a Proof, or assign a better. And this I call Argumentum ad Ignorantum" - John Locke

• Fallacies: classical and contemporary readings By Hans V. Hansen, Robert C. Pinto
• Introduction to Logic by Irving Marmer Copi.
• Essay Concerning Human Understanding Book IV - John Locke

• Argument from silence
• Indeterminacy problem
• False dilemma

• Fallacy Files article on Appeal to Ignorance
• Explanations of Basic Fallacies - Appeal to Ignorance