[dardner]

Professor Casey,

You must forgive me, after spending sometime looking for, I have not been able to find the relevant document to which I am about to refer.

Frequently in religious debates I hear the phrase; Absence of evidence is not evidence of absence. This seems obviously true. The advent of DNA testing or the appearance of the Coelacanth bears this out.

Some months ago I encountered someone claiming that (I think a she) had formed a logical proof that absence of evidence is in fact evidence of absence. For what it’s worth I believe she said it was a probabilistic logic proof but I’m not sure that matters in this case. She provided a link to where the whole thing was expressed formally in logical symbols and of course it was all Greek to me.

What troubles me here and why I don’t think Probabilistic form means all that much is because, well, isn’t the statement, Absence of evidence is evidence of absence, analytically true? In this sense definitional. Wouldn’t assigning a probability to this necessarily be 0 and in this case be irrelevant?

I know this is difficult to answer without actually seeing her proof but do you have any idea how his could have been verified without making the error I believe she did, in this case logical valid but false?

Cheers’

[gerard.casey]

The question you raise is located not in the pure empyrean region of formal logic but in the much messier and obscure region of informal logic.

Take the phrase: “Absence of evidence is not evidence of absence”

Is this necessarily true?

I don’t think so. It depends on what it is that one is seeking evidence of and in what context. Let’s take a few examples.

If you were to claim that there is an elephant in my dining room I would (carefully) check this claim out. My dining room is finite and relatively small, and there is nowhere an elephant, even a baby elephant, could hide. I look all around and I see no elephant. There is a complete absence of evidence for the presence of an elephant. I would conclude, and I think my conclusion would be reasonable, that the absence of evidence for the presence of an elephant is conclusive evidence of an elephant’s absence.

Now, replace the elephant in our example with a postulated subatomic particle. So far, our finite range of experiments has disclosed no evidence for its existence. Can we conclude, therefore, that it does not exist? I think not. The more we look without finding anything, the more we are inclined to believe it not to exist but it is always possible that it is, as it were, just around the corner.

I would like to see the logical proof to which you refer. I suspect it may be the application of some form of Bayesianism with which, I have to confess, I’m not really au fait. If you do find it, post the link.

Best wishes,

Gerard Casey

[dardner]

Professor Casey,

I can’t be sure of the exact example but adding Bayesian to my search I am certain this is what was being discussed. My gripe here is, as I think you pointed out, not with formal logic or even the validity of Bayesianism.

Strictly speaking, comparing the sentences ‘absence of evidence is evidence of absence’ and ‘absence of evidence is not evidence of absence’ it would seem to me the former is true and the latter is false. I have not encountered any instance of this being left as a simple semantic argument.

I don’t take the ‘is not’ phrase as necessarily true compared to the ‘is’ phrase. Rather, I take it to be obviously true in regards to the intent of the person saying it. I think your elephant example gets to the heart of the difference. That being proof and evidence. An elephant not being in a specified place and time is proof of an elephant not being in a specified place and time. If I say an elephant was in a specified place at some prior time and we observed elephant footprints and feces that doesn’t prove an elephant was there but it is certainly evidence of an elephant. This, I think, is the problem with the celestial teapot argument. I don’t need to observe the teapot to think it exists but I do need some evidence. Perhaps a celestial tea spill.

I hope that clarifies where I am coming from. It seems that the ‘is’ sentence is not adequate to disprove the ‘is not’ sentence because they are not saying the same things. What’s more troubling, if I am understanding this Bayesian thing correctly, it is saying the longer something goes without evidence the less likely it will be true. I don’t see how one could get there from absence of evidence is evidence of absence. How can any probability, greater than zero, be assigned when you have already concluded that there is no evidence?

I think there is another angle that I am overlooking but this is making my head hurt, I hope reading this doesn’t have the same effect on you.

[gerard.casey]

Reading your second last paragraph, you seem to say that the propositions ’Absence of evidence is evidence of absence’ and ‘Absence of evidence is not evidence of absence’ are not opposed to each other because ‘they are not saying the same things.’

If we plotted them on the Square of Opposition, a lot would depend on whether we took them to be universal propositions or particular propositions. If we took them to be universal, then they would be contraries, and contraries cannot both be true. However, if we took them to be particular, then they would be subcontraries, and subcontraries cannot both be false but may both be true.

Perhaps the addition of a temporal adverb might clarify matters. So

‘Absence of evidence is evidence of absence’ would become
‘Absence of evidence is [sometimes] evidence of absence
as in the case of my elephant in the room example.

‘Absence of evidence is not evidence of absence’ would become
‘Absence of evidence is not [always] evidence of absence
as in the case of my subatomic particle example.

*****

You write: ‘If I am understanding this Bayesian thing correctly, it is saying the longer something goes without evidence the less likely it will be true. I don’t see how one could get there from absence of evidence is evidence of absence.’

Once again, I believe material [as distinct from formal] factors come into play here. Everything depends on the would-be obviousness of what it is that one seeks evidence of in relation to the relative finitude of the search area.

*****

[dardner]

Professor Casey,

Great points I think you have made this much clearer for me and maybe I can refine what I am getting at.

Doesn’t plotting these statements out in the square of opposition take for granted that the propositions are in opposition? If they are, great, but my contention is that the two sentences are not speaking to each other.

If absence of evidence is evidence of absence then there is evidence.
If absence of evidence is not evidence of absence then there is no evidence.
Absence of evidence can not be both evidence and no evidence.
Therefore, absence of evidence in premiss 1 is not the same as absence of evidence in premiss 2.

If the meaning of absence of evidence in premiss 1 is used in 2 then premiss 2 is self-contradictory and vice versa.
—-
If absence of evidence is sometimes evidence of absence and absence of evidence is not always evidence of absence then absence of evidence is contingent on evidence of absence?
—-
Doesn’t making them particular support my idea that absence of evidence is given in two different ways?

Is my thinking that the ‘not’, in this case, is leading to a difference in definition and not denying something of ‘absence of evidence’ in the ‘is’ statement incorrect?

I am having trouble coming up with a set of sentences analogous to these. I’m led to believe that there is either something strange in the sentences themselves or, I fear, I have made a thorough demonstration of my stupidity. Or both!

Thanks in advance for your input. This discussion has inspired me to go back through the logic course and pay better attention this time.

Best Wishes

[gerard.casey]

Proposition 1: Absence of evidence is evidence of absence

Subject: Absence of evidence—S
Predicate: evidence of absence—P
Copula: affirmative, either universal, particular or singular
Giving us either SAP, SIP or SA’P

Proposition 2: Absence of evidence is not evidence of absence

Subject: Absence of evidence—S
Predicate: evidence of absence—P
Copula: negative, either universal, particular or singular
Giving us either SEP, SOP or SO’P

The most plausible interpretation of these propositions is as universals and that’s how I’ll take them from now on. If they are taken particularly then it is possible for both to be true simultaneously. If, for example, the propositions ‘students are intelligent’ and ‘students are not intelligent’ are taken universally, then both propositions cannot be simultaneously true; if taken particularly, both can be simultaneously true.

Both of our propositions have exactly the same subject and exactly the same predicate and so are comparable and so can be plotted on the Square of Opposition. They differ in quality—one is affirmative and the other is negative.
We than have SAP vs SEP

Let’s take your second paragraph and amend it slightly[material within []]

If absence of evidence is evidence of absence then there is evidence [of absence].
If absence of evidence is not evidence of absence then there is no evidence [of absence].
Absence of evidence can not be both evidence [of absence] and no[t] evidence [of absence].

True

Therefore, absence of evidence in premiss 1 is not the same as absence of evidence in premiss 2.

Yes, they have different properties, as given by the predicate in their respective propositions but just as a term, ‘absence of evidence’ signifies exactly the same thing.

If the meaning of absence of evidence in premiss 1 [as given by the attachment of the predicate] is used in 2 then premiss 2 is self-contradictory and vice versa.

Well, yes, for this would be to assert SAP and SEP simultaneously.

I hope this helps a little.

Best wishes,

Gerard Casey

[chemacailletbois]

Forgive me for resurrecting a LONG dead horse.

But I think I can “win” :] this discussion in one sentence.

Absence of evidence is ALWAYS evidence of absence, and it is sometimes PROOF of absence.

When people say “Absence of evidence is NOT evidence of absence,” I suspect what they really mean is “absence of evidence is not PROOF of absence.” Which is still not necessarily true, as in the elephant example.

[gerard.casey]

Dear Chema,

Six years later! I’m impressed that someone would be determined to go through this old thread to take up the topic again.

I’ve looked over the previous posts and I’m not sure that I can add anything new or illuminating to what I’ve said already.

It may well be that I don’t fully appreciate the point of your post. If that is so (and it is very likely to be so!), if you wanted to summarise the point at issue for me, you could email me directly at gerardcasey68@icloud.com and we can continue the conversation there.

Best wishes,

Gerard Casey

[chemacailletbois]

I was just summarizing what I thought was the salient point of the discussion. And also gently poking fun at how complicated it got above when it seems like it can be worded quite simply. Did I miss anything important?

[gerard.casey]

Dear Chema,

I have a sinking feeling that I’ve lost my grip on whatever was the point of the thread! But let me try to say what I think is the case without, I hope, making matters more complicated than they already are, and thus providing you with another, well-justified, occasion for gently poking some fun at my effort!

If I understand you correctly, you make two claims:

absence of evidence is always evidence of absence; and
absence of evidence is sometimes proof of absence.

You then go on to say that when people say, “absence of evidence is not evidence of absence” (i.e. when they deny no. 1) what they are really doing is to assert “absence of evidence is not proof of absence” ( i.e. they deny no. 2).

Having kicked the ideas around in my head for a few minutes, I am inclined to think that you have a point. If there is no evidence for the existence of phenomenon or event X, then that, just by itself, constitutes some evidence for the non-existence of X, though not necessarily conclusive evidence. (Perhaps we haven’t looked hard enough, or we’ve looked in the wrong places.) However, in certain situations (e.g. the question is whether or not there’s an elephant in the room, and the room is sufficiently small and we’re not talking about some species of microscopic elephant!), then the absence of evidence for the presence of an elephant (e.g. you can’t see it; there’s nowhere for it to hide, etc. etc.) is not only some evidence of the elephant’s absence but conclusive evidence; in your words, proof.

Thank you for clarifying matters.

With every good wish,

Gerard Casey

[Author]

Posts