Is Absence of Evidence ever Evidence of Absence?

[RJG]

No one is claiming that "absence of evidence" means absence of all possible evidence. They are obviously talking about absence of a particular kind of evidence or a particular piece of evidence.

....Again, what is being said is that absence of X is evidence for Y.

Not possible. Logically, you can't get evidence Y from the absence of evidence X. There is no logic that connects P1 (absence of evidence X) to C1 (evidence Y).

"Sneezing" (1) is the evidence of the presence of the cat.
"Not-sneezing" (2) is the evidence of the absence of the cat.

So again, where/what is the "absence-of-evidence"?

If sneezing counts as evidence then non-sneezing counts as absence of evidence.

Not so. If you have evidence that "sneezing" occurred, then you ALSO have evidence that "not-sneezing" did not occur. If you know one, then you know the other.

[-0+]

You are misinterpreting the meaning of what is being said. This is what Consul has said:

"Absence of evidence for milk is evidence for absence of milk."

Where? ...

In this sense, for example, if there is milk in your fridge, there should be perceptual evidence for it that you can obtain by opening its door and looking inside, since milk is easily visible stuff. And if you do so (thoroughly) without finding any (positive) perceptual evidence for the presence of milk, then this is (negative) perceptual evidence for the absence of milk, and you are thereby justified in believing that there is no milk in your fridge.
[...]
So the absence of evidence for a thing or fact is evidence for its absence if and only if it is perceptually accessible (directly or indirectly at least), and no perceptual evidence for it has been found—provided the search for evidence was performed non-superficially, painstakingly, i.e. with great care and attention.

In this example, "a thing or fact" is "milk in your fridge", not just "milk". Adding "in your fridge" is significant because this small domain allows enough evidence to be obtained to believe with some confidence that "there is no milk in your fridge" (without a finite domain, no evidence of absence can be obtained because the percentage of domain searched remains at zero), and including "in your fridge" in the proposition means that any evidence relating to the inside of the fridge is relevant to the proposition.

Also, this includes a big "if and only if" so instead of this being a simple "A is B", this becomes "A and C is B". If anything, it is C (accumulated evidence of perceptible things in fridge that are ~milk) that is B, not A.

What you are failing to see is that absence of evidence for one thing can be presence of evidence for a different thing.

How can absence of evidence for P (one thing) be presence of evidence for Q (a different thing)?

Yes, A (absence of evidence for P) and B (presence of evidence for Q) can both be True at the same time, but how can A ever imply B?

If P and Q are independent variables then A doesn't reveal anything about B (B may be True or False).

If Q is dependent on P (eg, Q is ~P, or some other function of P) then A reveals there is also absence of evidence for Q (B is False).

[Pattern-chaser]

...

You're responding like an Aspie here.

Oh? You mean clearly and explicitly expressing their intended meaning, without the intentionally-deceptive use of implication and deniability that usually accompanies allistic social communication? You do? Good. That's OK, then.

[Leontiskos]

As I already explained in previous posts, if there should be evidence for p if p is true, then absence of evidence amounts to evidence of absence.—…then absence of evidence for p is evidence for ~p.

Thinking about this some more, I think there are three cases and only one succeeds:

P: Proposition/Thesis
O: Observation

Case 1:

1a. P -> O
2a. ~O
3a. ∴ ~P

This is is a sound syllogism, and it based on the idea that if the thesis is true then some observation will be present (1a). But the problem is that (2a) doesn't count as absence of evidence. ~O would only count as absence of evidence if (O -> P). Since we don't know that (O -> P), ~O does not count as absence of evidence. This case fails. An example of (1a) would be, "If it rained then my car is clean." The problem is that a clean car isn't evidence of rain, so there is an absence of cleanliness but not an absence of evidence. Further, the absence of cleanliness is evidence that it did not rain.

(This is the case that we have been overlooking in the thread)


Case 2:

1b. O -> P
2b. ~O
3b. ∴ ~P

This is an invalid syllogism (negating the antecedent). In this case (2b) does count as absence of evidence, for we know from (1b) that (O -> P). The problem is that this absence of evidence does not count as evidence of absence. This case fails. An example of (1b) would be, "If there is ice in my drink, then it will be cold." Ice really is evidence of coldness, but the absence of that evidence does not mean that the drink will not be cold.


Case 3:

1c. P <-> O
2c. ~O
3c. ∴ ~P

This is a sound syllogism, and it is the only case where absence of evidence is evidence of absence. In this case (2c) does count as absence of evidence, for we know from (1c) that (O -> P). Therefore O counts as evidence and ~O counts as absence of evidence. Further, evidence of absence (~P) really does follow from absence of evidence (~O). This case succeeds. An example of (1c) would be, "There is milk in the refrigerator if and only if I can see it." Note that (1c) could also be written (O <-> P).


(To better ground evidentiary realities logical implication could be read in a probabilistic way, such that (P -> Q) could mean that P implies Q with some specified level of probabilistic certainty.)

[Leontiskos]

...The relevant difference is that Sherlock's deductive capabilities are much greater than the mediocre detective's, and thus the absence of crime-detection in Sherlock's mind constitutes a more reliable indication of the lack of crime than the absence of crime-detection in the mediocre detective's mind...

What is the non-perceptual evidence in this example?

My point is that Sherlock Holmes and the mediocre detective could examine the same physical/perceptual evidence and yet come to different conclusions or at least different levels of certitude because Sherlock's deductive capabilities far exceed the mediocre detective's. The point is that 1) The deductive capabilities are not perceptual evidence, and 2) The absence of a deduced conclusion is evidence for the falsity of that conclusion. Feel free to disagree with either of these two points.

...So long as the same qualification of "evidence" is applied to both sides of the "is" equation, does what qualifies as "evidence" make much/any difference to the topic question?

The OP was trying to define what sort of inferences are legitimate. I was pointing out that by limiting the question to perceptual experiences they were missing legitimate forms of evidence.

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It could have been more ambiguous. For instance, it may be more common for people to say something like, "There is no evidence of P". In this context 'no', may be most commonly interpreted as 'zero' (not-any, none), but 'no' can also mean 'not' or 'negative' (especially in other contexts). These meanings are logically different. Likewise, the 'a-' prefix in words like 'atheism' can mean 'not', 'without', or 'opposite to'. Using logically different meanings like these interchangeably can corrupt logic and communication. It is easy to imagine how an idea like "The evidence does not (positively) support P" (support may be negative or zero) can mutate into "There is no evidence of P" .

I agree with this.

'Absence' may be used to make it clearer that this means 'zero' rather than some other meaning of 'no'.

"Evidence of P" may be more ambiguous than "Absence of P".

"Evidence for P" suggests "positive support For P".

"Evidence of P" can be interpreted as:
(1) "Evidence that is relevant to P" (could be For or Against P)
(2) "perceptual experience of P".

I think you are on the right track. I want to say that (1) includes (2), which is why immediate perceptual experience, such as milk, trips up your dichotomy. I tried to show that (1) and (2) are essentially the same here and here. The idea is that the act of recognizing some visual experience as including milk is a mini-proposition that occurs almost instantaneously, so I think they can be collapsed. That said, I am not opposed to separating 'propositions' from 'perceptions,' it's just that the middle ground between the two will become murky.

I tried to comment on the ambiguity in this post. To go your route, we could clarify each term in the sentence, "Absence of evidence of P is evidence of absence of P." Throughout the thread I have talked about privative absence vs. simple absence. The idea is that an absence which warrants an inference about some proposition is privative, and an absence that does not warrant such an inference is simple.

My contention is that this is how we must interpret the sentence if it is to be true:

• [Absence] of [evidence of P] is [evidence of absence of P].
• [Privation] of [the sort of thing that would have counted as evidence for P's presence] is [a justified reason to believe that P is absent].

...and this assumes that the privation is the kind of privation that justifies an inference precisely about P's absence ([privation] -> [absence of P])

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You are misinterpreting the meaning of what is being said. This is what Consul has said:

"Absence of evidence for milk is evidence for absence of milk."

Where? ...

Sorry, I was just paraphrasing the basic theme of the thread.

In this example, "a thing or fact" is "milk in your fridge", not just "milk". Adding "in your fridge" is significant because this small domain allows enough evidence to be obtained to believe with some confidence that "there is no milk in your fridge" (without a finite domain, no evidence of absence can be obtained because the percentage of domain searched remains at zero), and including "in your fridge" in the proposition means that any evidence relating to the inside of the fridge is relevant to the proposition.

No, I don't think so. A few times throughout the thread it was pointed out that evidence is different from proof. What you are looking for here is proof of milk.

The foundation of certitude for the absence of milk has to do with milk and your line of sight. For example, "The absence of perceptual experience of milk is evidence for the absence of milk in my line of sight." Everything else builds on top of that, whether you want to talk about refrigerators or grocery stores or the entire Earth. In each case you are just compounding various lines of sight in order to possess more certitude. In the refrigerator you can search the whole thing relatively quickly and have perfect certitude. But a finite space does not need to be exhaustively searched in order to obtain evidence for the absence of milk. It only needs to be exhaustively searched to obtain proof of the absence of milk. With each minute that we search a finite space the probability that milk exists in the finite space diminishes.

What you are failing to see is that absence of evidence for one thing can be presence of evidence for a different thing.

How can absence of evidence for P (one thing) be presence of evidence for Q (a different thing)?

Yes, A (absence of evidence for P) and B (presence of evidence for Q) can both be True at the same time, but how can A ever imply B?

If P and Q are independent variables then A doesn't reveal anything about B (B may be True or False).

If Q is dependent on P (eg, Q is ~P, or some other function of P) then A reveals there is also absence of evidence for Q (B is False).

The point isn't that A and B are merely related, but rather that they are identical. This is even implied if you do the substitution you suggested. According to your definitions these two statements are equivalent:

• Absence of evidence for P is presence of evidence for Q.
• A = Absence of evidence for P
• B = Presence of evidence for Q
• A is B (A = B)

Here is an example:

P: "There is milk in the fridge"
Q: "There is no milk in the fridge"
Z: "I see milk in the fridge"
A: "I do not see any milk in the fridge"
B: "I do not see any milk in the fridge"

Note that Z represents presence of evidence for P, which is precisely what is absent in A (and B).

This is an example of Case 3 from this post.

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This strikes me as a red herring and an unnecessary tangent. Evidence is based on expectations...

What would be an argument for "evidence is based on expectations"?

I explained it to you in this post, which you ignored. If there are no causes that produce reliable effects, then there can be no evidence. Expectations are just how we instantiate that reliability, and we call it 'evidence'. For instance, your example about the coins in your pocket presupposes that your expectation that coins are tactile is grounded in reality.

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No one is claiming that "absence of evidence" means absence of all possible evidence. They are obviously talking about absence of a particular kind of evidence or a particular piece of evidence.

....Again, what is being said is that absence of X is evidence for Y.

Not possible. Logically, you can't get evidence Y from the absence of evidence X. There is no logic that connects P1 (absence of evidence X) to C1 (evidence Y)

This is an assertion, not an argument.

"Sneezing" (1) is the evidence of the presence of the cat.

So again, where/what is the "absence-of-evidence"?

If sneezing counts as evidence then non-sneezing counts as absence of evidence. [(s=e) -> (~s=~e)]

Not so. If you have evidence that "sneezing" occurred, then you ALSO have evidence that "not-sneezing" did not occur. If you know one, then you know the other.

Are you denying that that if sneezing counts as evidence then non-sneezing counts as absence of evidence? [(s=e) -> (~s=~e)]

Apparently you don't like the law of identity.


-Leontiskos

[RJG]

Logically, you can't get evidence Y from the absence of evidence X. There is no logic that connects P1 (absence of evidence X) to C1 (evidence Y)

This is an assertion, not an argument.

Your claim that non-evidence X yields evidence Y is purely nonsensical [~e=e is not logically possible].

Argument:
P1. Non-evidence (of any kind) is NOT evidence (of any kind), plain and simple. [~e=~e]
C1. Therefore, the non-evidence of X can never be the evidence of Y.

"Sneezing" (1) is the evidence of the presence of the cat.
"Not-sneezing" (2) is the evidence of the absence of the cat.

So again, where/what is the "absence-of-evidence"?

If sneezing counts as evidence then non-sneezing counts as absence of evidence. [(s=e) -> (~s=~e)]

Not so. If you have evidence that "sneezing" occurred, then you ALSO have evidence that "not-sneezing" did not occur. If you know one, then you know the other.

Are you denying that that if sneezing counts as evidence then non-sneezing counts as absence of evidence? [(s=e) -> (~s=~e)]

Yes, I'm denying this faulty reasoning! Both sneezing (s) and non-sneezing (~s) are evidence! (neither is not-evidence!). Again, if you know X, then you know ~X. If you sneeze, then the cat is nearby. If you don't sneeze, then the cat is not-nearby. "Sneezing" and "not-sneezing" are both evidence (of the presence and absence of the cat).

Law of identity: X=~(~X);
If X is present, then ~X is absent
If X is absent, then ~X is present.
If you have evidence for the presence of X, then you ALSO have evidence for the absence of ~X.

[Terrapin Station]

This strikes me as a red herring and an unnecessary tangent. Evidence is based on expectations...

What would be an argument for "evidence is based on expectations"?

I explained it to you in this post, which you ignored.

Right. I ignored the rest of the post except for what I quoted. I'm not about to indulge the ridiculous logorrhea that people have on boards like this. I don't want to tell people how much they can type, but I'm not about to read hundreds of words on what either are or need to be (because of issues), say, 10-15 different topics. So you can type as much as you like, but I'm not going to read any arbitrary amount that you want to type. It's up to you whether you care if I bother reading everything you type or not.

Re the idea of the rest of that post being an argument for evidence being based on expectations, just to start with the first thing that would need to be discussed, re "Evidence is itself a consequence of the relation between a cause and the effects which that cause reliably produces. When we say that X is evidence of Y we are saying that X is an effect characteristically produced by Y":

(a) I don't agree with the claim(s) in quotation marks there, and
(b) I wouldn't say that the claim(s) in quotation marks do anything with respect to an argument for "evidence is based on expectations."

And I'm not going to tackle more than one issue at a time. I want to settle issues, not compound them while not settling them.

[Leontiskos]

Right. I ignored the rest of the post except for what I quoted.

Yes, I've noticed that you don't read posts carefully, and sometimes not at all. Therefore you should expect a lot of re-quoting from me. This is a philosophy forum, not a place for instant messaging.

If there are no causes that produce reliable effects, then there can be no evidence. Expectations are just how we instantiate that reliability, and we call it 'evidence'. For instance, your example about the coins in your pocket presupposes that your expectation that coins are tactile is grounded in reality.

(So at this point you could either concede that your coin analogy presupposes that expectation, or prove me wrong by showing how the coin analogy functions without any expectations.)

[-0+]

Case 3:

1c. P <-> O
2c. ~O
3c. ∴ ~P

This is a sound syllogism, and it is the only case where absence of evidence is evidence of absence. In this case (2c) does count as absence of evidence, for we know from (1c) that (O -> P). Therefore O counts as evidence and ~O counts as absence of evidence. Further, evidence of absence (~P) really does follow from absence of evidence (~O). This case succeeds. An example of (1c) would be, "There is milk in the refrigerator if and only if I can see it." Note that (1c) could also be written (O <-> P).

??
There can be milk in the fridge without having the ability to see it. How does this qualify as an example of "if and only if" (especially "only if")?

[-0+]

My point is that Sherlock Holmes and the mediocre detective could examine the same physical/perceptual evidence and yet come to different conclusions or at least different levels of certitude because Sherlock's deductive capabilities far exceed the mediocre detective's. The point is that 1) The deductive capabilities are not perceptual evidence,

There are numerous levels of difference they could have after examining the same scene. They will normally have different perceptual evidence due to differences in the way they examine the scene.

If they are AI detectives and only one of them examines the scene and uploads raw sensory data to the other, they could interpret this data differently and recognise/perceive things differently.

If they have the same higher-level data of what is perceived (by one of them) to be present at the scene, the data they select as being relevant to the proposition could differ if they have different knowledge of correlations between things. Perception of anything that is understood to have some correlation with anything referred to in the proposition may be considered to be relevant. Correlations are normally based on statistical data (historical perceptual evidence).

If they have the same relevant perceptual data, they could weigh this up differently. It is not uncommon for judges and jurors who are exposed to the same evidence in court to reach different conclusions. All sorts of things may come into play that lead to different conclusions. These things could ultimately be based on perceptual evidence or on other things like wishful thinking.

A distinction may need to be drawn between (perceptual) evidence and judgement?

and 2) The absence of a deduced conclusion is evidence for the falsity of that conclusion.

?? The absence of any deduced conclusion or the absence of a particular deduced conclusion? What is the reasoning behind this point?

The OP was trying to define what sort of inferences are legitimate. I was pointing out that by limiting the question to perceptual experiences they were missing legitimate forms of evidence.

The more inclusive "evidence" becomes, the easier it may be for something to qualify as "evidence of absence", but the harder it becomes for something to qualify as "absence of evidence" (and vice versa the more exclusive "evidence" becomes). If deduction (a process) or any non-perceptual evidence is included as "evidence", it needs to be included both ways for an argument to be consistent.

[Pattern-chaser]

The absence of a deduced conclusion is evidence for the falsity of that conclusion.

I think the absence of a deduced conclusion is evidence for the uncertainty of that conclusion, as deduction is the only bulletproof form of logical reasoning. To declare an uncertain conclusion "false" may be going a bit too far, don't you think?

[Terrapin Station]

Right. I ignored the rest of the post except for what I quoted.

Yes, I've noticed that you don't read posts carefully, and sometimes not at all. Therefore you should expect a lot of re-quoting from me. This is a philosophy forum, not a place for instant messaging.

Again, I am NOT indulging the logorrhea that people have on boards like this. People write horrible, rambling, unclear posts that poorly broach tons of issues. If they'd learn to write better, I'd read and respond to longer posts. But I'm not about to indulge horrible writing.

[Terrapin Station]

And then if you write something longer in reply, questions/points etc. are ignored, regardless of how long the response is.

I've no interest in that. People need to learn how to communicate better.

[-0+]

In this example, "a thing or fact" is "milk in your fridge", not just "milk". Adding "in your fridge" is significant because this small domain allows enough evidence to be obtained to believe with some confidence that "there is no milk in your fridge" (without a finite domain, no evidence of absence can be obtained because the percentage of domain searched remains at zero), and including "in your fridge" in the proposition means that any evidence relating to the inside of the fridge is relevant to the proposition.

No, I don't think so. A few times throughout the thread it was pointed out that evidence is different from proof. What you are looking for here is proof of milk.

This has nothing to do with looking for proof, just evidence of absence. (OP may be looking for high threshold of evidence to justify belief in absence (of milk in fridge) but, as noted previously, evidence doesn't have be conclusive to count as evidence.)

The foundation of certitude for the absence of milk has to do with milk and your line of sight. For example, "The absence of perceptual experience of milk is evidence for the absence of milk in my line of sight." Everything else builds on top of that, whether you want to talk about refrigerators or grocery stores or the entire Earth. In each case you are just compounding various lines of sight in order to possess more certitude.

Yes, these are all finite domains.

In the refrigerator you can search the whole thing relatively quickly and have perfect certitude.

"Relatively quickly" depends on the minimum size of what is being searched for (milk) relative to the size of the domain (fridge), and "perfect certitude" requires perfect ability to detect milk if it is present.

If "milk" is defined as a container of milk that is at least one pint/litre/gallon in volume, then this is relatively easy to detect, and this specifies the minimum size of what is being searched for: a relatively large proportion of the volume inside the fridge, requiring relatively low resolution of scanning inside fridge to have confidence that milk is absent from fridge. Without this qualification, the minimum volume of milk is a much smaller proportion of the volume of the fridge requiring much higher resolution of scanning and more time to search exhaustively. A minuscule volume of milk may also be very difficult to detect (especially if this is inside something else that is inside the fridge).

But a finite space does not need to be exhaustively searched in order to obtain evidence for the absence of milk. It only needs to be exhaustively searched to obtain proof of the absence of milk. With each minute that we search a finite space the probability that milk exists in the finite space diminishes.

Yes, but in order to have any evidence of absence of milk in any domain, there generally* needs to be evidence of something in the domain that is non-milk, this thing needs to occupy some space in the domain that cannot also be occupied by milk, and this occupied space needs to be a nonzero proportion of the space inside the domain. This requires the domain to be finite. If the domain is infinite then any space perceived to be occupied by non-milk is zero proportion of the domain space so this has no effect on probability that milk exists.

How can there be evidence of absence of milk without scoping this to a finite domain (eg, a fridge) that milk is absent from?

Looking for evidence of absence of milk in fridge is as much about what is inside the fridge as it is about milk. Any evidence of what is inside the fridge may be relevant. Any evidence of milk outside the fridge may also be relevant (especially if it is known there is only one container of milk in the kitchen).

*Even evidence of non-milk outside the fridge may be relevant if there is a correlation between this and presence of milk in the fridge. This can be an exception to the "generally*" comment above.

In any case, it appears that evidence of absence of milk in D requires presence of evidence of presence of something somewhere that is relevant to presence of X in D, and absence of evidence of milk in D doesn't imply this.

[-0+]

[...]
"Evidence of P" can be interpreted as:
(1) "Evidence that is relevant to P" (could be For or Against P)
(2) "perceptual experience of P".

I think you are on the right track. I want to say that (1) includes (2), which is why immediate perceptual experience, such as milk, trips up your dichotomy.

Yes, (1) includes (2) but (2) doesn't include all of (1). (1) can include perceptual experience of many other perceptible things that are relevant to its proposition. (1) could also potentially include non-perceptual evidence if this is permitted. (2) only includes perceptual experience of its perceptible thing. The datatype of parameter P differs: it is a proposition in (1) and a perceptible thing in (2).

That said, I am not opposed to separating 'propositions' from 'perceptions,' it's just that the middle ground between the two will become murky.

A proposition and a perceptible thing are semantically quite distinct. A proposition can be True or False. A perceptible thing is an object that can be included in a proposition.

It may not seem that there is much difference between perceptible "milk" in (2) and proposition "milk is present" in (1). But their complements are very different.

The complement of proposition "milk is present" is proposition "milk is absent". If perceptible "milk" is the set of of all perceptible things that qualify as milk, then perceptible "~milk" is the set of all perceptible things that don't qualify as milk (eg: beer implies ~milk; ~milk doesn't imply beer; ~beer doesn't imply milk; ~milk doesn't imply "milk is absent".)

Attempting to use different datatypes like these interchangeably is likely to cause problems.

To go your route, we could clarify each term in the sentence, "Absence of evidence of P is evidence of absence of P."

Expanding this to make "presence" explicit where this is implicit:
"Absence of evidence of presence of P is presence of evidence of absence of P"

Previously, this was expressed semi-semantically as:

Absent(Evidence(Present(X))) is Present(Evidence(Absent(X)))
- where X is something perceptible in a domain (eg, "milk in fridge")

Both sides of "is" look balanced with consistent datatypes for each function and the only differences are that Absent() and Present() are in reverse positions.

Absent(P) is another way of expressing "P is Absent". Likewise for Present(P). These are propositional, and parameter P is perceptual.

How to interpret "Evidence" in this example?

2 separate functions can be defined to better distinguish each interpretation of Evidence:
(1) R-Evidence(proposition) is "Evidence" relevant to the proposition
(2) P-Evidence(perceptible,domain) is "perceptual experience" of perceptible in domain

As "Evidence" is a function of propositional expressions in both cases, this suggests it is R-Evidence.

Is there a way to interpret this as P-Evidence?

The main phrase of interest may be "evidence of absence of P": Is there any evidence of absence of P? Absence is not perceptible so this appears to
rule out interpreting this particular "evidence" as P-Evidence. R-Evidence is needed to obtain evidence of absence.

However, "X" can be expanded into "P-Evidence(Y,D)", where Y is perceptible thing (eg "milk") and D is domain (eg, fridge), and the central "is" can be turned into function "Is-Equivalent(A,B)", resulting in:

Is-Equivalent(
Absent(R-Evidence(Present(P-Evidence(Y,D)))),
Present(R-Evidence(Absent(P-Evidence(Y,D))))
)

This may be semantically more complete. However, this doesn't help the Is-Equivalent expression to be True.

Basically this boils down to:
A: Absent(Evidence(P))
B: Present(Evidence(Q))
C: Is-Equivalent(A,B)

A and B can both be True, but A doesn't imply B, so C is not True.

Alternative semantic interpretations are welcome.