When is absence of evidence not evidence of absence?

Question

"Absence of evidence is not evidence of absence."

I think this statement raises some kind of epistemic problem. Like, how are we supposed to conclude the potential non-existence of something, like Santa Claus or dragons?

Answer 1

I think the distinction is that people often conflate "negative obervations" with "absence of evidence".

To take the Santa example - if you simply declared "I have no evidence that Santa exists, therefore he does not exist", then you would be arguing from an absence of evidence.

However, if you said "Santa is said to travel in a flying sleigh, and no radar returns consistent with such a vehicle have ever been observed" then this is not an absence of evidence. This is a hypothesis (namely, that Santa flies around the world in his sleigh) from which we can make a prediction (that the sleigh would be visible on radar) and then we make an observation that the predicted scenario does not arise.

This is a negative observation - it's not an absence of evidence, it's evidence that our hypothesis may be incorrect.

Of course, you could argue that the sleigh is magically hidden from radar by the pixie dust mixed into its paintwork, but at some point Occam's Razor kicks in and reminds you that the simplest explanation for a negative observation is that the thing you were expecting to see simply doesn't exist.

Answer 2

Elliot Sober offers a useful argument on this :

"Absence of evidence isn't evidence of absence" is a slogan that is popular among scientists and nonscientists alike. ...

There has been some philosophical work on the motto that doesn't use a probability framework and it provides a good way of isolating the problem I want to address. Here are two example arguments from Douglas Walton's insightful 1996 book, Arguments from Ignorance:

I do not have any evidence that it is raining here and now.

It is not raining here and now.

I do not have any evidence that there is a storm on the surface of Jupiter now. There is no storm on the surface of Jupiter now.

Though neither argument is deductively valid, it is easy to see how each can be turned into a valid argument by adding a premise. The arguments have the form:

I do not have any evidence that p is true.

p is false.

Just add the premise

(P1) If p were true, then I'd have evidence that p is true.

This further premise may be true in the case of the rain. Suppose, as in Walton's example, that I am sitting in a house with a tin roof and that I'd hear the characteristic pitter-patter if rain were falling. It is easy to imagine that the extra premise Pi is false in the case of the storm on Jupiter; suppose, instead, that

(P2)If p were true, then I'd have no evidence that p is true.

The Jupiter example is enough to show that the motto "absence of evidence isn't evidence of absence" is sometimes true and the rain example is enough to show that it is sometimes false. This is because P2 is true of some propositions in some circumstances and the same goes for P1. So let us agree that absence of evidence does not logically entail that you have evidence of absence. And let us also agree that there are situations in which absence of evidence is evidence of absence. What more is there to say about the motto than this ? (Elliott Sober, 'Absence of Evidence and Evidence of Absence', Philosophical Studies: An International Journal for Philosophy in the Analytic Tradition, Vol. 143, No. 1, Models, Methods, and Evidence: Topics in the Philosophy of Science. Proceedings of the 38th Oberlin Colloquium in Philosophy (Mar., 2009), pp. 63-90: 64.)

Sober goes on to explore cases in which P1 and P2 are both false. This produces interesting nuances but the quotation above should give you a sound basic assessment of the statement.

Answer 3

Go into your kitchen. Is there an elephant? In this case, absence of evidence is evidence of absence. You know that if there was an elephant, you would have evidence. No evidence, no elephant.

But is there a mouse? It is quite possible that there is a mouse but no evidence.

So you need to decide two things: How likely is it a priori that a statement is true? And how likely is it that there would be no evidence if the statement was true? From these two you can figure out how likely the statement is false if there is no evidence.

Answer 4

A better phrase is "absence of proof is not proof of absence". One definition of "evidence" is that E is evidence for H if seeing E justifies a Bayesian update that increases the probability assigned to H. And if all the relevant probabilities are in the open interval (0,1), then E being evidence for H under this definition means that (not E) is evidence for (not H); that is, the posterior probability of (not H) increases when one sees (not E).

However, the amount by which the posterior for (not H) increases on seeing (not E) can be arbitrarily small, even when keeping constant the amount by which the posterior for H increases on seeing E. For instance, seeing one white raven proves that there exists a white raven, but seeing one black raven is only a tiny bit of evidence that no white ravens exist.

And in many contexts, people use "evidence" to mean not merely something that increases the posterior by any amount, but something that increases the posterior by a significant amount. By this definition of "evidence", absence of evidence often isn't evidence of absence. But there certainly are cases where even by this more restrictive definition, absence of evidence is indeed evidence of absence. For instance, in poker, if someone folds in a situation where, if they had a royal flush, they could reveal it and win, that is rather strong evidence that they don't have a royal flush. If the victim of a robbery says they stabbed the robber, and a suspect doesn't have any stab wounds, that is evidence they aren't the robber.

Answer 5

If there is a real standard of proof, like observation, or constructive demonstration, it only exists when it exists, not when it would be annoying or problematic for it not to exist. Annoyances and problems, particularly paradoxes, are part of reality.

In classical logic that results in the truism that you cannot prove an assertion that is 'truly negative' in quality. You cannot know that unicorns don't exist, only that they are highly unlikely. You cannot get rid of God via any proof.

You can rule out 190-degree planar triangles, but only via proof that they would change the nature of geometry, not because you haven't found any. And then you can find geometry that has this nature: one where planes are interchanged with spheres, and it turns out to be useful to investigate those.

Maybe an example from non-classical logic, one with a slightly different epistemology, will help. This is a principle in the Intuitionist interpretation of mathematics to a much higher degree than it is in classical logic.

From the Intuitionist point of view, evidence of absence would be constructive proof that any instance would result in a contradiction with other principles.

So, we have a proof -- the 'hairy ball theorem' that a smooth vector flow on a sphere does not exist. If we found such a thing, it would necessarily destroy its own construction logically.

But there is still an absence of evidence for an actual discontinuity, given any given vector field. We cannot necessarily locate it by constructively interrogating the vector field itself. When we can't, we should not act as though it exists or does not exist.

Clearly this is not evidence for the absence of the discontinuity, because we know that the field cannot be smooth unless the system itself is inconsistent. It does in some sense exist, but not in a sense that we should take seriously, and not in a way that we can safely act upon. Because there is in fact a possibility that there is an eventual inconsistency in our accumulated reasoning.

Answer 6

Like many such statements, it's only roughly true... but only for certain types of argument.

For instance, if we have an argument like this:

If A (we have evidence) then B.
A (we have evidence).
Therefore B.

This is the classic Modus Ponens, and in this type of argument lacking evidence does not mean evidence of lack.

Consider Modus Tollens however:

If A then B (we have evidence).
Not B (we have no evidence)
Therefore not A.

In this form it is logically true that absence of evidence is in fact evidence of absence.

The question then becomes whether the Modus Tollens formulation is in fact sound for the specific subjects.

I can for instance say:

If it is raining then my car will be wet.
My car is not wet.
Therefore it is not raining.

While this looks fine, it lacks enough detail to be sound. If I check my car and find it dry because it is in my garage then that doesn't prove that it is not raining. The logic is valid but the initial premise is not sound, so the argument fails. In this case absence of evidence for rain does not constitute evidence of absence.

But how about this similar argument:

If it is raining on my car then my car will be wet.
My car is not wet.
Therefore it is not raining on my car.

Now I am fully justified in claiming that absence of evidence is in fact evidence of absence. My car is not wet, therefore it is not raining on my car. This is both valid and sound.

We may be able to make similar arguments about dragons or Santa Claus. Testing the soundness of those arguments might take some doing however. We'd need a starting premise that was much more compelling than If dragons existed then we would have unambiguous evidence of their existence.

Establishing the soundness of the initial premise is potentially impossible. In some cases you will run up against someone who simply modifies the definition of their preferred thing to avoid any possibility of a sound logical argument against it. Can't see a dragon? That's because it's invisible. And intangible. And doesn't react to any of your senses or any possible detection apparatus you can propose. Doesn't mean it doesn't exist.

Which I suspect is a large part of the reason why we generally accept that absence of evidence is not in fact evidence of absence.

Answer 7

1. An absence of something is different than an evidence of something, that's clear.
2. You imply that an evidence proves "something". Acceptable. Evidence of rain proves that the air has a high humidity.
3. But a non-evidence is not necessarily the proof of the opposite of "something". An absence of rain does not prove that the air humidity is low. Formally, you are affirming the consequent with your suggestion to prove something by not having an evidence.
4. So, you cannot "conclude the potential non-existence of something" by not having an evidence.

No relation with epistemology. Just a fallacious interpretation of a useless cliché, like:

"The cliché of an absence is not the absence of a cliché" does not mean that the presence of a cliché implies the presence a cliché of non-absence (or a non-cliché of abscence).

Answer 8

This is the Contrapositive https://en.wikipedia.org/wiki/Contraposition

In your statement "absence of evidence is not evidence of absence", we can write it formally as x -> y where

(x) = absence of evidence (y) = not evidence of absence

The truth table can be written as (!x || y) (not x or y)

Let's assume y is true (no proof of absence)

If y is true (we have no evidence of absence) then the absence of evidence doesn't matter, the answer is still true. If y is not true (we have evidence of absence) then this can only be correct if x is true (there is absence of evidence).

Answer 9

This is about burden of proof. If I say that God exists, the burden of proof is on me. The statement that there is no evidence that God does not exist is not evidence that God does not exist is not an argument for the existence of God. The burden of proof remains with me as with Russell's Teapot. For the avoidance of doubt of theists, atheism is not a belief system. It is simply the absence of belief in God. Atheists have no evidence that God does not exist nor do we believe that God does not exist. Belief is irrelevant to us. The burden of proof remains with the theist, or the believer in Santa Claus or orbiting teapots. Occam's Razor is good for cutting excess fat from confused thought.