Absence of evidence is evidence of absence

>Because -A means "it is not the case that A" which obviously does not correspond to absence.
Since event A is evidence of B, A not being the case is the absence of that evidence.

>To say that evidence is absent is to say that evidence has so far been undetected.
Obviously A is only evidence if it includes being detected. So A not occurring would include A not being detected.

>If you define absence to correspond to non-existence, any proof for the absence of evidence is the evidence of absence will have employed circular logic.
If by "non-existence" you mean A not occurring then I don't see how that's circular.

but the original phrase "absence of evidence is evidence of absence" refers to the known evidence at a given time does it not? i.e. there's an absence of evidence but then evidence could be found so that there's no longer an absence, the definition used doesn't seem to take that into account

>A not being the case is the absence of that evidence.
Is it "absence of that evidence" or "absence of evidence"?

A not ocurring is not equivalent to notA ocurring in the sense that while A did not ocurr something else (the logical negation of A) ocurred. If you have event A be, I got two tails after tossing two coins, not A mean you got either one head on either coin or two heads, that's different from I didn't toss the coin, which is abssence of A. But I know you already understand this, because you have already baited Veeky Forums multiple times, but we got some schizo folk here, so it's not that much of a strech to think you have conviced yourself.

It's true.

When people say 'Absence of Evidence is not Evidence of Absence', what they're really trying to say is 'I believe that the conditional probability of me observing evidence B in the event that theory A is true is so low that I don't gain any information by NOT seeing it.'

Information is anthropic, so probability calculations are fundamentally tied to someone's prior beliefs. I'm told that ostriches exist but don't naturally live where I live, so me not seeing them here doesn't give me evidence that they don't exist.

However, if I never heard of them before and was instead told that they live ONLY where I live, then me not seeing any ostriches WILL make it seem less probable to me that they exist since I expected to see them.

I don't see how that changes anything. It's a conditional probability, so the condition can change.

It could be either, depending on what A is. You could have A be all events satisfying the definition of evidence, or just a specific event satisfying that definition. Either way, it works.

>I don't see how that changes anything.
Because the definitions don't take it into account, making them questionable

>You could have A be all events satisfying the definition of evidence
Evidence of what?

>You could have A be all events satisfying the definition of evidence, or just a specific event satisfying that definition.
"evidence" was never actually defined in the OP

>A not ocurring is not equivalent to notA ocurring
This.

>If you have event A be, I got two tails after tossing two coins, not A mean you got either one head on either coin or two heads, that's different from I didn't toss the coin, which is abssence of A.
Not getting two tails is the absence of A. I don't see why you think only not tossing the coin is the absence of A. Explain why.

It doesn't affect the conclusion, so why would the definitions need to take that into account?

B

See Definition 1 in the OP.

>It doesn't affect the conclusion, so why would the definitions need to take that into account?
It does affect the conclusion since it means the definitions do not actually represent what they claim to represent. If I change definition 2 to "Batman, a=not A", the image does not prove "Batman is evidence of absence".

>See Definition 1 in the OP.
Did you misread the definition?

>A be a set that contains itself
Lol retard, A may be can be in some class C that has all events A that satisfy that satisfy that P(B|A)>P(A). The negeation of such a class (as it can be written in first order logic you can negate the expresion) is exactly All events that dont satisfy that, i.e. event's that go are evidence of the logical oposite event. notB, i.e. that's different from abssence taken in the meme phraze by sagan, that is the empty fucking set.
No, that's the logical negation, abssence is literally just not seeing shit, aka, not even doing the experiment. If you don't like that deffinition of "abssence" though shit, because you are disccussing another issue and being dense on purpose. The point if the fraze is that just because you haven't seen or tested some thing it doesn't mean it's proof it doesn't exist, look russels teapot.
Because you are incorrenctly appling the english languange to first order logic.

>It does affect the conclusion since it means the definitions do not actually represent what they claim to represent.
I don't see how it even affects the definitions. Conditional probability has no problem with evidence changing over time.

> If I change definition 2 to "Batman, a=not A", the image does not prove "Batman is evidence of absence".
It technically does prove that. The proof would be valid but not sound

No.

>No.
Are you sure? Definition 1 defined "evidence of B", not "evidence".

>>A be a set that contains itself
Who are you quoting?

>The negeation of such a class (as it can be written in first order logic you can negate the expresion) is exactly All events that dont satisfy that, i.e. event's that go are evidence of the logical oposite event. notB, i.e. that's different from abssence taken in the meme phraze by sagan, that is the empty fucking set.
Again, I don't see any logic here. Why do you think only not tossing the coin is the absence of A? You are incorrectly applying English to first order logic.

Evidence of B is evidence. Are you okay buddy?

>Evidence of B is evidence.
"evidence" has not defined, so I'm not sure what you're saying "evidence of B" is. Can you provide a definition for "evidence" so that we can be on the same page?

You basically proved a tautology.

There is no evidence=there is no evidence.

Hume btfo logic with his raven paradox .
And logic cant predict the future evidence. Only what is at hand.

Attached: photo_201704141831352ktp_smile_2_export1.jpg (266x266, 45K)

>"evidence" has not defined
See

Yes, that's a definition of "evidence of B". What is the definition of "evidence"?

Actually it's proving the opposite:

There is no evidence (of B) = there is evidence (against B)

>Hume btfo logic with his raven paradox .
The raven "paradox" is very logical, and basically says the same thing as "absence of evidence is evidence of absence."

Because abssence of "evidence" means not having evidence. You can have evidence for notB which is still evidence.
>but that's stupid
Again, if you don't like that wording then you are discussing a whole different issue.
en.m.wikipedia.org/wiki/Evidence_of_absence

I don't know what you mean by "evidence" then, since evidence is an event which increases the probability of some other event.

>I don't know what you mean by "evidence" then
I haven't meant anything by "evidence", which is why I've asked you to define it since you've used it repeatedly.

The issue is that these are not meaningful definitions, just linguistic tricks, i.e. any event C with probability in (0,1) can be shown to be all three (evidence, absence of evidence, and absence) since P(C|C)>P(C|not C) and C= not not C, allowing you to derive meaningless conclusions such as "absence is evidence", "evidence is absence", "absence of evidence is absence", etc. since anything which is evidence is also absence of evidence and also absence.

>Because abssence of "evidence" means not having evidence. You can have evidence for notB which is still evidence.
You can't have no evidence for B or notB if either is possible, since the absence of one is equivalent to the presence of the other. So your interpretation of the phrases is useless.

>You can't have no evidence for B or notB if either is possible
Why not?

I just did. See

Then every event except {} is evidence, and so the absence of evidence would be defined as {}.

Because of the proof in OP, which shows that the absence of evidence for B is evidence for notB.

Do you have evidence for or against the existance of a planet filled with primitive humans beyond our hubble sphere?

...

Common m8, your bait was much better, this circular reason can be detectes by even a 14 year old on /pol/.

>which shows that the absence of evidence for B is evidence for notB.
Why does that show that "You can't have no evidence for B or notB if either is possible"?

with non-zero prob.

>The issue is that these are not meaningful definitions, just linguistic tricks, i.e. any event C with probability in (0,1) can be shown to be all three (evidence, absence of evidence, and absence) since P(C|C)>P(C|not C) and C= not not C, allowing you to derive meaningless conclusions such as "absence is evidence", "evidence is absence", "absence of evidence is absence", etc. since anything which is evidence is also absence of evidence and also absence.
This.

No, if evidence is simply any conditional that updates the probability of an event, then the absence of evidence is evidence of absence, since P(absence | absence of evidence) can be calculated as long as P(evidence of absence) > 0. If P(evidence of absence) = 0 then the phrase cannot be applied. So either way, the phrase is proven.

>No, if evidence is simply any conditional that updates the probability of an event
You previously said "evidence is an event which increases the probability of some other event." Which definition do you want to use?

>If P(evidence of absence) = 0 then the phrase cannot be applied.
Right, so since the phrase cannot be applied, we do not have "absence of evidence is evidence of absence", so we must have "absence of evidence is not evidence of absence".

>Do you have evidence for or against the existance of a planet filled with primitive humans beyond our hubble sphere?
Depends on our prior beliefs. If we assume the cosmological principle, then events which occur in our Hubble volume effect the probability of events outside it.

How is it circular reasoning? Your opinion on whether the proof is connected to the phrase does not affect its conclusion.

>Why does that show that "You can't have no evidence for B or notB if either is possible"?
Because if you have no evidence for B then you have evidence for notB, and vice versa. How is this hard to get?

>How is this hard to get?
Because "having evidence" has no meaning in this context.

>You previously said "evidence is an event which increases the probability of some other event." Which definition do you want to use?
You are confusing my definition with your own. If you use my definition then the null set cannot be the absence of evidence, since not all events increase the probability of some event. If we use your definition then the absence of evidence cannot occur as the null event is impossible, which you probably realize since you felt the need to append . Nice try.

>You are confusing my definition with your own.
I don't know what definition you're referring to, I haven't provided one for "evidence", only used the ones provided in this thread.

>Right, so since the phrase cannot be applied, we do not have "absence of evidence is evidence of absence", so we must have "absence of evidence is not evidence of absence".
No, that doesn't follow. We must have that your interpretation is wrong.

>If you use my definition then the null set cannot be the absence of evidence, since not all events increase the probability of some event.
If we use your definition, then the absence of evidence are events with probability 0 or 1.

>Because "having evidence" has no meaning in this context.
I have already explained the meaning.

>No, that doesn't follow.
Since the phrase cannot be applied, we do not have "absence of evidence is evidence of absence", so we must have "absence of evidence is not evidence of absence". Or are you using a different logic system?

>I have already explained the meaning.
Which is? What does it mean to "have evidence"?

>I don't know what definition you're referring to, I haven't provided one for "evidence", only used the ones provided in this thread.
No, you claimed that evidence is every event except the null set, and that the absence of evidence is the null set with nonzero probability, which is contradictory since the null set by definition has probability zero in conditional probability.

>the null set with nonzero probability
What are you referring to?

>If we use your definition, then the absence of evidence are events with probability 0 or 1.
No. The probability of absence of evidence is 1-P(A), and P(A) =/= 0 or 1. So you're just spouting nonsense.

>The probability of absence of evidence is 1-P(A), and P(A) =/= 0 or 1.
What is A? This doesn't look well-defined.

>So you're just spouting nonsense.
If we use your definition "evidence is an event which increases the probability of some other event", then since any event A with probability not 0 or 1 increases the probability of itself, absence of evidence are events with probability 0 or 1.

>Since the phrase cannot be applied, we do not have "absence of evidence is evidence of absence", so we must have "absence of evidence is not evidence of absence".
That doesn't follow. The non-existence of "absence of evidence" under your interpretation renders both phrases inapplicable. So the only conclusion is that your interpretation is useless.

See and

Why would the null set have non-zero probability?

>The non-existence of "absence of evidence" under your interpretation
The empty set exists as an axiom, I'm not sure what you mean.

>That doesn't follow. The non-existence of "absence of evidence" under your interpretation renders both phrases inapplicable.
This is incorrect. If you don't have "absence of evidence is evidence of absence" then you have "absence of evidence is not evidence of absence" and vice versa. How is this hard to get?

>If we use your definition "evidence is an event which increases the probability of some other event", then since any event A with probability not 0 or 1 increases the probability of itself, absence of evidence are events with probability 0 or 1.
That would only apply if the phrase was being used to mean "the absence of A is evidence for the absence of A" which it never is.

Why are you asking me? You wrote it.

>That would only apply if the phrase was being used to mean "the absence of A is evidence for the absence of A" which it never is.
What part does not follow? P(A|A)>P(A|not A) whenever 0

>Why are you asking me? You wrote it.
I don't see anywhere where I wrote something as nonsensical as that, can you be more specific?

>The empty set exists as an axiom, I'm not sure what you mean.
What does mathematical existence have to do with the absence of evidence existing in reality?

>What does mathematical existence have to do with the absence of evidence existing in reality?
You claimed that the absence of evidence does not exist under my interpretation. But the empty set does exist, so I'm not sure what you're referring to.

>What part does not follow?
Where did I say a part does not follow? It follows in a context which is not applicable.

See

>Where did I say a part does not follow? It follows in a context which is not applicable.
Then what part is not applicable?

>See
Yes, there's nothing there indicating that the empty set should have non-zero probability. Can you be more specific?

>You claimed that the absence of evidence does not exist under my interpretation.
Yes, do you understand what existing in reality means?

>Then what part is not applicable?
The whole part. See

>Yes, do you understand what existing in reality means?
Yes, though it is not clear what relevance this has here.

>The whole part. See
But "the absence of A is evidence for the absence of A" follows directly from your definition of "evidence", and the definitions provided in the OP (whenever A has probability in (0,1)).

So the empty set has zero probability, meaning P(absence of evidence) = 0 under your interpretation. Thanks.

>So the empty set has zero probability, meaning P(absence of evidence) = 0 under your interpretation.
And so the absence of evidence is not evidence of absence.

>But "the absence of A is evidence for the absence of A" follows directly from your definition of "evidence", and the definitions provided in the OP (whenever A has probability in (0,1)).
So what?

See

does it follow from definition 1 that the set of evidence is the set of events increasing the probability at least one event? then by definition 3 the absence of evidence is the set of events that increase the probability of 0 events are those events with probability either 0 or 1.

>does it follow from definition 1 that the set of evidence is the set of events increasing the probability at least one event?
Set of evidence for what?

>See
I'm not sure what you're referring to, are you saying there's at least one alternative to either being evidence of absence or not being evidence of absence? That doesn't follow from the definitions. If you don't have "absence of evidence is evidence of absence" then you have "absence of evidence is not evidence of absence" and vice versa. How is this hard to get?

>Set of evidence for what?
The set of evidence, as per the definition here

>I'm not sure what you're referring to, are you saying there's at least one alternative to either being evidence of absence or not being evidence of absence?
No, I'm saying that your interpretation of evidence of absence is inapplicable.

>If you don't have "absence of evidence is evidence of absence" then you have "absence of evidence is not evidence of absence" and vice versa.
Yes, but you haven't defined "absence of evidence" and "evidence of absence" correctly.