Absence of evidence vs. evidence of absence

If you’ve discussed the existence of God, you’ve most likely come across the phrase “absence of evidence is not evidence of absence” or “Absence of evidence is evidence of absence.” The truth is that both of these statements are incorrect.

The correct principle is something like the following:

The absence of evidence is not necessarily evidence of absence.

Many times an absence of evidence is evidence of absence. For instance, if I walk into my bedroom and don’t see a gorilla, that’s a good reason to think that there isn’t a gorilla in my room. However, many times absence of evidence is NOT evidence of absence. For example, if I look at my hand and don’t see germs, that is not a good reason to think no germs are on my hand.

So, how do we decide in each case whether we should conclude that something doesn’t exist based on the lack of evidence? The key is to ask, “If X were present, would I expect to see it?”. Obviously, I wouldn’t expect to see an atom with the naked eye, but I would expect to see a giraffe in my apartment.

For clarification purposes, I am not saying that one can/should believe something if there isn’t evidence of absence. Even if we don’t have evidence to the contrary for some claim, that doesn’t mean it’s rational to just believe the claim is true. We should ask whether there is is a good reason to think the claim is true.

2 thoughts on “Absence of evidence vs. evidence of absence

  1. Formal proof that absence of evidence is evidence of absence in Bayesian probability theory: oyhus.no/AbsenceOfEvidence.html

    We can try to reconcile this with your germ example in several ways. Here are a couple:
    1) Not seeing germs is evidence against germ theory, but is outweighed by the evidence that supports germ theory.
    2) The AoE⇒EoA principle really means that X cannot be evidence for Y unless ¬X is evidence against Y. Germ theory does not claim seeing germs with the naked eye as evidence for it, so the negation is not evidence against.

    I think your explanation is closer to #2. Alternatively, you could reject the use of Bayesian probabilistic reasoning for epistemology, which I would not recommend.

  2. Absence of evidence is evidence of absence all the time if you accept the likelihood principle, which is related to Bayes’ theorem. The only time it’s not is when P(E|H) = 0.

    Say E is evidence for H1 over H2 if P(E|H1) > P(E|H2).
    So suppose it’s true that E is evidence for H1 over H2 then it’s true that:
    P(E|H1) > P(E|H2)
    P(E|H1) + P(¬E|H1) = 1 and P(E|H2) + P(¬E|H2) = 1
    1 – P(¬E|H1) > 1 – P(¬E|H2)
    P(¬E|H2) > P(¬E|H1)
    The last line says absence of evidence is evidence for H2 over H1. To sum up, E is evidence for H2 over H1 iff ¬E is evidence for H2 over H1.

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