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"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?

63

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.

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    I think this is morally right, but unfortunately there is no clear separation between "negative evidence" and absence of evidence. It is usually said that absence of evidence is evidence of absence if the presence should be expected to produce evidence, if true. However, this does not work for idle unfalsifiable speculations, like Santa. One can always say that Santa is magical, and is not supposed to register on radars, or that the sleigh is metaphorical. In such cases the issue is burden of proof, not negative evidence. – Conifold Feb 5 at 20:38
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    Better evidence of Santa's absence would be something more like the computation of the fuel requirements of travelling that fast, and the limited quantity of fuel in the world. To make the lack of observations into a contradiction, one would need to prove we have adequate coverage that an object moving that fast would be observed. But the fact it is moving that fast, and all our radar and sonar are designed for things moving slower might be the very reason it would not be observed. – jobermark Feb 5 at 21:44
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    @probably_someone, it's probably because they have escaped the Matrix. – elliot svensson Feb 6 at 16:43
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    @elliotsvensson But seriously, a lot of conspiracy theorists, young-Earth creationists, and flat-earther types explicitly reject Occam's Razor. Arguments based on it simply fail to be convincing for them, and there doesn't appear to be a good way to demonstrate to them that Occam's Razor is a good rule of thumb. – probably_someone Feb 6 at 16:45
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    @probably_someone, it's a good heuristic, but it's not the only heuristic. I have been led to believe that plausibility, explanatory scope, and explanatory power have seats at the table together with Occam's razor, though I acknowledge that some folks dispute that. – elliot svensson Feb 6 at 16:47
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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.

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    I do not have evidence that it is raining here and now , does it mean that I have evidence that it is not raining here and now, and my evidence is that I do not have evidence that it is raining here and now? Can the absence of evidence sometimes be itself the evidence of the opposite? Thank you – SmootQ Feb 5 at 10:19
  • The problem here, is that I can assert that the fact that I don't have evidence that it is raining here and now, does not contribute to the evidence that the opposite is the case, and the evidence for the opposite is the fact that I do not see rain and that the world is dry here and now. – SmootQ Feb 5 at 10:21
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    Hi ! I can't see that 'I do not have (any) evidence that it is raining here and now' means 'I have evidence that it is not raining here and now'. I can't see that Sober intends this. Any answer is a target for any number of arrows - I appreciate that and it's just as it should be. I was only trying to put the OP in square 1 of an analysis and appraisal of the slogan. – Geoffrey Thomas Feb 5 at 10:29
  • So, I misunderstood the answer, thank you Geoffrey +1 ! – SmootQ Feb 5 at 11:59
  • @SmootQ. It happens to us all ;)- You are a really welcome new presence on PSE. I already look out your answers and comments. High quality. Best - Geoffrey – Geoffrey Thomas Feb 5 at 12:08
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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.

  • A robot or a baby wouldn't be able to gauge how likely a statement is to be true, though. Does that mean the reasoning is flawed? – elliot svensson Feb 6 at 16:10
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    @elliotsvensson If the reasoning is flawed, I guess that means you have no way of knowing that there isn't an elephant in your kitchen. – immibis Feb 6 at 22:28
  • But what ratio should we assign the prior probability of an elephant in my suburban California kitchen? 1 in a billion? 1 in a trillion? It's impossible to be sure! – elliot svensson Feb 6 at 22:30
  • I'm playing Devil's advocate: there's no difficulty in assigning such probabilities because they get "canceled out" when you divide by other probabilities that you also assign. I don't have to know "0.0000343 % of the time", I just have to know that "A is one in a trillion, but B is one in five trillion, for Pete's sake". – elliot svensson Feb 7 at 0:13
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    This is wrong. It's pure math. An Elephant is by definition a certain size, and visible. It takes up space. A kitchen only has so much space, and one can determine that the volume of space visible to you, which has no elephant, is complete proof that no elephant exist in the kitchen. Assuming of course you are talking about a real elephant. A mouse however takes up significantly less space, and you can not determine with a quick glance, if a mouse may occupy any of the small spaces that you have no visual of. If it was in a shoe box, you'd have proof, like with the elephant in the kitchen. – KjetilNordin Feb 7 at 11:30
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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.

  • combine with answer with the one @gnasher gave and you have a complete statement. Bayes is indeed the mathematical answer to the probability question. – Tom Feb 7 at 12:48
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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.

0

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).

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    I wonder if the "is" would not be better symbolized as "<=>", if and only if. Welcome to Philosophy! – Frank Hubeny Feb 7 at 19:19
  • That would be a good distinction, thanks for the suggestion. I suppose this is a specification OP would need to define, it's hard to interpret thy question as asked. The accepted answer from anaximander suggest that "x therefore y" which would match the contrapositive definition. The truth table for "if and only if" would cause the statement "there is no evidence of absense" to be true only if we had a positive statement "there is absence of evidence" which is confusing too. It seems to make more sense if we change the sentence to only use positive statements. – Zakk Diaz Feb 7 at 21:50
  • Instead maybe it should be accurate to ask "is absence of evidence proof of evidence of absense" – Zakk Diaz Feb 7 at 21:51
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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.

0

Probably the issue is deeper than what has been addressed. The expression raises a problem related with the usage of the concepts in our mind.

For every possible idea, even the idea of absence of existence ("absence of evidence"), we create a mental concept.

A hole in the ground is something that does not exist, but nevertheless, we create the concept, and we can use the concept. You can say "watch that hole in the ground", and what are you watching? Not the hole! It is impossible to actually see a hole. As much, you can see the darkness caused by the hole, or the borders of the hole, but not the hole itself. A hole is invisible.

It is absolutely natural, however, to use ideas about absence. The number zero expresses absence, and we use it multiple times a day. The infinite does not exist, but we know what absence it expresses. "Being single" expresses the idea of lack of a person. And so on. Can you feel nothing? No. What you can do is to not feel something. In final terms, interacting with nothing is physically impossible, but in our mind it is possible, since absent stuff is always represented by existing stuff.

Formally, I would say that this problem expresses the Immanuel Kant's noumenal and phenomenal nature of reality and our perception, respectively. We can see something that we know represents a hole; that is the phenomenal representation that we get of the world. On the contrary, we don't have access to the noumenal nature of the universe. It is impossible for us to interact with the real nature that lies beneath the objects of our perception. Interaction (physical or mental) requires of objects; though it is impossible to interact with something that is not an object.

We represent the possibility of interacting with a manifestation that is not an object as the fact of not interacting with an object. That is enough for our survival.

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