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Absence of Evidence =|= Evidence of Absence

  • Does this proposition always hold (true), or are there exceptions?
  • Is it a logical fallacy to claim: “absence of evidence is evidence of absence”?
  • How is this proposition related to the argument from ignorance fallacy? Explain.
  • Burden of proof, null hypothesis, negative proof, and “one cannot prove a negative”!

The statement “Absence of Evidence is not Evidence of Absence” seems to be correct.

The mere absence that something is present is not evidence that something is absent. Lacking evidence for (the presence of) something does not constitute evidence of the absence of that thing.

Negative Proof and the Burden of Proof (Onus Probandi):

The burden of proof is on the proposition, not the opposition! The one who makes a claim carries the burden of proof, regardless of the positive or negative content of the claim. One way in which one would attempt to shift the burden of proof is by committing the fallacy "the argument from ignorance" or "the argument from personal incredulity". Negative proof by reductio ad absurdum (reduction to absurdity), such as a proof by contradiction or proof of impossibility, are typical methods to fulfill the burden of proof for a negative claim. A proof by contradiction is a valid rule of inference called modus tollens (also proof by contraposition):

Negative Proof and the Argument from Ignorance:

The argument from ignorance: "some proposition X is true because it has not (yet) been proven false," or "some proposition is false because it has not (yet) been proven true."

To assert that "absence of evidence is evidence of absence" is a logical fallacy called the argument from ignorance.

"Something is concluded to be absent because it has not been proven to be present," or "Something is concluded to be present because it has not been proven to be absent."

Example:

Proposition G: "God exists" is accepted as true because G has not been proven false. That is, the lack of sufficient evidence capable of constituting proof of god's existence is not sufficient evidence constituting proof of the non-existence of god.

Proposition G: "God exists" is concluded to be true because its negation ~G: ("God does not exist”) has not been proven true.

Negative Proof through Negative Claims:

A negative claim is the opposite (negation) of an affirmative (positive claim). A negative claim asserts the non-existence or exclusion of something. For a positive claim, only a single example is required to demonstrate the positive claim.

Negative Proof through Negative Evidence:

Absence of evidence: ex., no careful research has been done. Evidence of absence: ex., an observation that suggests there were no dragons in my garage. The difference between absence of evidence and evidence of absence lies in whether investigation (i.e. scientific experiment) would have detected the phenomenon if it were there.

MODUS TOLLENS (relies on the contrapositive of the original implication to be equivalent to it).

Premise (1): P -> Q.

Premise (2): ~Q

{then}__

Conclusion: ~P.

(which reads...)

Premise (1) If P, then Q.

Premise (2) Not Q.

{then}

Conclusion: Not P.

Please note that ‘arguing from ignorance’ for ‘absence of evidence’ is not necessarily fallacious!

Example:

"This drug has no long-term risks, until proven otherwise."

Were such an argument to rely imprudently on the lack of research to promote its conclusion would be considered an informal fallacy (argument from ignorance).

Can even null results can count as evidence of absence, though not conclusive proof (in and of themselves)? Ex., A hypothesis may be falsified if an essential predicted observation is not found empirically.

In cases where there should be evidence if the hypothesis were true, absence of evidence can count as evidence (not proof) of absence, depending on the detection power of the experiment (including instruments), the confidence of the inference, limiting confirmation bias, etc.

Therefore, the argument from ignorance for "absence of evidence" is not necessarily an informal fallacy.

  1. Do you agree? Why or why not? Please explain!
  2. What is the relationship between the argument from ignorance and the saying "absence of evidence is not evidence of absence?
  3. What implication does the saying "absence of evidence is not evidence of absence" have on whether one cannot prove a negative (claim)?
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Let's look at modus tollens for a second. This is clear:

  • P → Q
  • ~Q
  • ~P

If P entails that Q exists, then the absence of Q entails the absence of P. However, we also have to consider the following, which is fallacy called denying the antecedent:

  • P → Q
  • ~P
  • ~Q

If P entails Q, but P doesn't exist, that doesn't say anything about the existence of Q. Q might exist independently of P, P might be one of many independent things that entail Q. The logic does not specify that Q entails P, only that P entails Q; the proposition is directional.

Unfortunately, many people do not mind their Ps and Qs. They assume a bidirectional relationship — or worse, they are confused about which is the antecedent and which the consequent — and so they make unfounded assertions.

In scientific research P is usually a theory and Q an experiential event, e.g.:

  • If theory P is correct, we can produce event Q
  • We cannot produce event Q
  • Therefore, something is wrong with theory P

This is perfect fine reasoning (though of course drastically oversimplified, since it doesn't account for methodological issues). In these cases, absence of evidence does count as evidence of absence, since the existence of the theory entails the existence of the observed outcome. But it is easy to muck up the logic, e.g.:

  • The existence of miracles would be proof of God's existence
  • Miracles do not exist
  • Therefore God does not exist

The problem with this logic is that the major premise assert that miracles entail a God. Logically we can say that if God does not exist there will be no miracles (that's proper modus tollens), but logically we have to consider the possibility that a God can exist without ever doing any noticeable miracles. God does not (from our premise) entail miracles, so the absence of miracles is not evidence of the absence of a God.

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