Tralix…no.
No, absence of evidence is evidence of absence. That’s the way it works.
It is a LAW that P(H) is the weighted average of P(H|E) and P(H|~E), (E being Evidence). If E makes H more likely, then necessarily, mathematically, it must be the case that notE makes H less likely. You can’t have your cake and eat it too. You can’t have E be evidence for H but refuse to have notE be evidence against.
FJ…no.
No, absence of evidence is not evidence of absence. That’s the way it works.
In that explanation you are making the all too common and egocentric mistake of presuming that ALL evidence has been seen, your “E”. That formula is ONLY valid when E represent ALL possible evidence, not merely the evidence at hand.
The lack of evidence at hand, is NOT evidence that there is no evidence that is NOT at hand.
You cannot accurately calculate any probability until you weigh ALL possibilities.
It is simple statistics analysis.
You are proposing that because you couldn’t find the coin under the lamp post, the coin no longer exists period.
Some of the argument involves something that is unknown and hence cannot be rendered by maths or logic precisely, hence we cannot say that something is more or less likely because we don’t have sufficient knowledge, ie there is a gap in our evidence, logic cannot deal with an unknown quantity at least not absolutely. And you can’t render any equation in maths with unknowns which will lead to an exact outcome, if likewise you are dealing with an unknown. Hence probability and hence there is no way that a precise outcome can be determined in your equation with gaps in the systems knowledge, there is no reduction or increase of the likelihood if the facts involved have unknowns.
Or in mathematical terms, “You can’t resolve simultaneous equations that have more variables than knowns”.
And you can’t calculate a probability from it either.
Well I wish I had said that it would of saved time, but yes. 
Hello Every One !!!
Come on, this is just nit-picky. So yes, maybe there’s some infinitesimal probability that some other life-form that we can’t see guidelines on Mars. So maybe the rocks are really present and all referring to with each other, we would never and could never know as their language and worldview.However, in my post I was also considering personal mind-set. It is well known and well documented that individuals are definitely able of rejecting from their interest.
E is any potential piece of evidence. Not all. You’re being presumptuous. I thought you were just lecturing me on not doing that…
Don’t make up stuff just because you’re wrong, to try to make yourself look right.
I think the mistake you two are making is not differentiating between weak and strong evidence. When you see the word ‘evidence’ you don’t think “raise probability of H by some amount,” you think “proof of H”.
When I say absence of evidence is evidence of absence, I certainly am not saying it’s CONCLUSIVE evidence, or even very strong evidence. But it is, necessarily, mathematically, evidence. P(H) is the average of P(H|E) and P(H|~E) (E being ANY SINGLE potential piece of evidence), and so if P(H|E) is higher than P(H)…you know how averages work, right?..P(H|~E) MUST be lower.
Given that half of the time Tom rolls the die he gets a 2 (for unknown reasons) and also that half the time Sue rolls the die she gets a 3, upon seeing that the rolled die is 3 without seeing who rolled it, what is the probability that Sue rolled it?
I didn’t realize we were playing math puzzle games.
If you don’t understand the symbols, I can link you to something that will explain it more thoroughly than I did. If you don’t understand why P(H) must be the weighted average between P(H|E) and P(H|~E), we can work that out too. Just let me know which part you’re having a problem understanding.
Oh, I well understand the entirety of your thinking on the issue.
Play the game and you might come to understand mine.
No, the game isn’t relevant. If you have 3 values (A, B and C) and you know that one of the values (B) is the average of the other 2 (A and C), and furthermore you know that one of those is higher than the average (C), then the remaining value (A) MUST be lower than the average. No game of yours is going to be a counterexample.
B, in this case, is P(life on mars).
C, in this case, is P(life on mars | having found evidence of life on mars)
A, in this case, is P(life on mars | NOT having found evidence of life on mars)
So, if you had an idea of the probability of life on Mars prior to any trips to Mars, and then they did the trips and found no evidence, a rational response would be to lower your confidence in the existence of life on Mars.
Keep in mind, what I’m saying is not a prescription of HOW MUCH you should lower it. Maybe before the trips, you thought the probability was 90%, so after the trips, maybe it could be even 89% (if you have some very strange priors). Hell, 90% is probably just rounding anyway, so maybe after the trips the probability rounds to 90% again (again, must have very strange priors). I’m not saying it’s STRONG evidence, I’m saying something really quite innocuous, and something that’s mathematically proven – and really indisputable, regardless of your trite cliches.
Yeah but the point is, no matter how often you search mars for life, there’s always the possibility that your parameters of what life is are wrong, and that you hence could not detect them, which means that actually the probability of life over time does not necessarily decrease the less evidence you find, it remains the same, how much it decreases then becomes if it should at all, given an infinite amount of time with all the wrong parameters you are never going to find life even if it exists and the probability is 1:1.
Unknowns, they are annoying.
facepalm
please go learn about Bayesian probabilities. I’ll link you to some material if you like.
I have to agree that the probability of life on Mars is extremely low.
Those who proclaim that the unknown is too vast to be calculated are missing a very relevant point.
Did a google search for Absence of Evidence Bayes. Here are the first few results:
Pretty much exactly what I said
That is still not true.
What you have said is that if I don’t look but rather keep the only little tiny bit of evidence that I have, I am more probably correct in my conclusion.
Your assumption is that evidence has been seriously sought and not found.
In that case, your statement is true. But it isn’t because the “lack of evidence” requires a higher probability, but rather that the lack of finding after seeking yields a higher probability that what was being sought wasn’t there to be found.
The absence of seeking evidence is evidence of seeking absence.
I don’t think I said that. Could you quote where I said that?
In this part;
No probability can be ascertained by a single bit of evidence if no contrary evidence has been sought.
The statement above says that even the tiniest bit of evidence yields a higher probability than no evidence.
As right as that seems to you, it is totally misleading because in the absence of seeking evidence, NOTHING can be predicted because you have equal chance of finding contrary evidence that you never sought. You must be able to falsify a conclusion in order to maintain any claim of it being valid.
In effect, if I pray for $10 and get it, the evidence is that my prayers get answered. So you are saying that it is a higher probability that my prayers get answered than the evidence offered by me not praying at all (the absence of evidence).
Or I could say that a fairy placed a book on my desk and the evidence is that a book is on my desk. You are saying that I have a higher probability of being right about the fairy than if I didn’t look on my desk to even see if there was a book on it (the absence of evidence).
There has to be a seeking of contrary evidence involved, else nothing matters and any speculation is as valid as any other.
If you find “evidence of no life” but never looked for evidence of life, you have merely fooled yourself.
I don’t mean this to be rude, but the point your making is, I think, being obscured by sloppy language.
I’m not sure I’m understanding you here, but as far as I can tell, this is actually tautologically correct. Yes, H will have a higher probability if you see even the tiniest bit of evidence than if you see no evidence. That’s what evidence is. It raises the probability of the thing that it’s evidence for. That’s true for tiny evidence and large evidence. I don’t understand what’s disagreeable about that.