How do you calculate a probability when you have no idea of the number of possibilities?
I found a rock on Earth that was not alive, therefore the probability is that Earth contains no life.
Seriously?
A man’s wife was found strangled. The man was in town that day.
Therefore the probability is that the man strangled his wife.
You’re just speaking gibberish now.
Answer this question;
Here’s what you need to do to go beyond gibberish-zone:
What you’re doing is you’re saying “The things Flannel Jesus is saying imply these things, and these things are ridiculous.”
That’s fine, that’s a great argument.
What you’re not doing is showing how what I say implies those things. You’re being very sloppy with your wording and so it’s very, very difficult to see how these ridiculous things I supposedly believe are derived from the things I’ve said.
So, what you need to do to go beyond the gibberish-zone is take something that I’ve explicitly said and derive the things you’re saying it implies.
No. What I am doing is asking questions that you are ignoring.
You’re asking irrelevant questions that don’t have anything to do with what I’ve said. I’ve never said anything about calculating probabilities when you don’t know the number of possibilities (whatever that means – that’s the kind of sloppy language I’m talking about). I’ve said that it’s a mathematically proven fact that when there’s a possibility of finding evidence for claim H, and you don’t find the evidence, that’s evidence against claim H. I’ve also explicitly explained that it’s not necessarily strong evidence, something which you don’t seem to have taken to heart yet.
All I’m saying is mathematically provable and proven. I’ve linked to resources that talk about the proofs.
All you two are saying is a whole bunch of sloppily worded defenses of an old cliche that you once heard some smart guy say (I heard a smart person say it once too, and believed it for a while, but smart people sometimes say the darndest things).
Still ignoring the question so as to accuse me. 
The question isn’t even specific enough to answer. Number of possibilities of what? It doesn’t make sense the way you phrased it.
One of the things you two guys are not getting (especially Tralix, given his last post) is that probabilities are ABOUT UNKNOWNS. That’s what they’re for. They’re useful when you DON’T have all of the information. If you had all of the information, what the hell use would a probability be? If I know that there’s life on Mars, it doesn’t make sense to talk about the probability of life on Mars, or even evidence of life on Mars.
But you guys are talking about it as if you have to know everything to talk about probabilities. You totally miss the entire point of probabilities. They’re actually to deal with the unknowns. That’s what they’re there for.
Strictly speaking, the fact that I saw a raven that was black is evidence that all swans are white - I saw something not white, and true to my hypothesis, it wasn’t a swan. It’s just evidence of miniscule significance, given how many things there are which aren’t swans.
Your example is not germane to the OP in particular, because Mars is a planet that has been searched quite heavily for signs of life, and even for signs of the possibilities of life. But I appreciate that you’re addressing FJ rather than the OP here.
The probability is as high as for anyone of whom you could say they were in town. That seems uncontroversial, if that’s the only evidence you allow. Allowing other evidence, a spouse is almost always a high-probability murderer or accomplice.
This is true. However, it’s also worth mentioning that classical probability (of the Bayes, Poisson, Gauss type) is about known unknowns, and don’t take account for the stickier problem of unknown unknowns. Modern statistics is learning to adapt to that, but it’s always going to be tricky.
We don’t use human senses to look at distant planets, that’s impossible.
FJ, perhaps if you think of it this way;
P(~C) = Undefined, where C = Calculation
P(H AND ~C) = P(H) * P(~C) = Undefined.
You can’t calculate a probability without counting the unknowns. As far as the Mars issue, you have the concerns of the probability of totally undetectable life (U), detectable life (D), difficult to detect life (DD), and effort put forth to detect life (E).
P(U) == 0, there is no possibility of totally undetectable life due to the definition of existence requiring affect.
P(DD|E) > 0, the probability of difficult to detect life even with effort put forth is greater than zero.
Perhaps it’ll help if you think about it this way:
Prior to any rovers landing on mars, there were 4 possibilities:
Detectible life exists on mars. (D)
Undetectable life exists on mars. (U)
Both of the above statements are true. (D&U)
No life exists on mars. (~D&~U)
Now, it doesn’t matter which probabilities you give to them all. As long as they’re all mathematically consistent, it doesn’t matter a single bit.
Once you find out that the entire category (or at least nearly the entire category) of detectible life has been pretty much falsified, you’ve eliminated at least some amount of the probability of there being life on mars. You certainly still have remaining the entire probability of U, but D is completely wiped out.
I can explain some potential priors you could have that wiping out D completely shouldn’t change your posterior probabilities, and it should be fairly clear why those priors are untenable:
If you assumed that p(D) was 0 prior to the trip, you could get away with not lowering your posterior probabilities.
Now, in this case we’re dealing with a person who’s arguing that there still remains a possibility of undetectable life. So, p(U) > 0 but p(D) = 0? Why in the world would the probability of undetectable life be greater than the probability of detectable life? (Reminder: this is before the trips, these probabilities are being considered) It’s a strange prior to say the least. And besides, it’s been argued that probabilities of 0 are nonexistent (as well as 1).
I had another one, but upon review, nope, 1 is the only one.
So, the only way to get away with not taking the absence of evidence as evidence of absence is to have the frankly strange and truly mathematically incoherent belief that undetectable life on mars was possible while simultaneously believing that detectable life wasn’t.
No matter what your prior probabilities were, as long as they were mathematically sensible (eg p(B&U) cannot be greater than p(B) or p(U)), the math says that the probability of life is lowered.
Now, let me get back to what I said above: the idea that when an entire category of possibility is wiped out, the probability has to be lowered. I think it’s fairly clear to see why this is the case. Let’s say we’re playing some strange dice-betting game. Before I roll the dice, you bet that the number will be 4 or above. I roll the dice, but hide the results from you (as per the rules of this strange game). You ask me “Is it a 5?” and I tell you “No.” What would you give the probability that the dice was 4 or above afterward? The only reasonable option is to lower it (assuming, I suppose, that the rules of the game dictate I must answer you, and I must answer honestly, but we can assume that). I’ve wiped out an entire sub-category of the category “4 or above”. As long as that category had p > 0, you MUST lower, to some degree, the probability of the category that it was a subcategory of.
[edit] With the inapplicable exception being times when the category that the subcategory is a subcategory of (lol) has a probability of 1 (or near-1, if we’re being sloppy). Like for example, when I roll the dice, the statement “It landed on a number” has a probability near 1, and a subcategory of that is “It landed on 5”, so when I say that it didn’t land on five, this is a rare (and inapplicable in relation to Mars) exception in which you don’t have to lower the probability of the higher category.
“Detectable life exists on mars” is a subcategory of the statement “life exists on mars”. The first is pretty much eliminated. The second must be lowered.
I would only add, if our methods of detection have exhausted all possible forms of life then insert . So really Detectable life on mars has another sub category: currently undetectable life exists on mars, which means the first is eliminated over time but the other sub category is not and so the second cannot always be lowered until both are eliminated, because future knowledge well may produce a 100% chance of life existing which would then render all your previous chances as paradoxical. It’s not that they don’t go down as a trend, it’s that they must decrease each time or even any time when all information is not present, that is what is in question.
Well, that was poorly worded.
Yes, “Currently detectable life exists on mars” is a subcategory of “life exists on mars,” so if the first is proven false (or incredibly unlikely), the higher category, as per the argument above, must have a lowered probability. Everything still stands in my argument, I just had to change the name of the subcategory. Thank you for that pedantic correction.
Yeah words is hard.
It’s not pedantic at all, it renders your equation potentially false in any particular iteration, you claim that probability will always decrease as more evidence is presented but if that evidence only shows life as we know it then we have no idea that that life which we don’t know can or can’t exist, then it does not decrease the probability, and it can not until we have information that informs us of those types of life. You can’t claim that based on all detectable life on mars is equal to currently detectable life on mars. It’s hardly pedantic if it renders what you say false? So we can clear it up by saying all potential life is only and always on a downward trail if we specify what life is in all circumstances. Frankly I doubt we can integrate such a thing into a logical or mathematical equation but we can at least make it clear outside of application so it is theoretically true without doubt.
It doesn’t matter if what you said was almost correct, it only matters in maths or logic that proofs come from the lack of exceptions.
Jesus christ you really don’t get it.
The probability of a statement will always INCREASE as more evidence for it is presented. I don’t know where you got this from.
You’re not even remotely understanding the arguments here. Please, please stop posting until you’ve read this and understand it. I can’t take you seriously when you’re saying things like quoted above.
And it didn’t render what I said false, all I had to do was change a category name from “detectible life” to “currently detectable life” and leave pretty much every other word in place in the post, and it all still stands. Currently detectable life exists on mars is a subcategory of life exists on mars. The first has been pretty much eliminated, so the second must be lowered. See my post above to understand the argument for why, when a subcategory is eliminated as a possibility, the probability of the category it was a part of must be lowered.
Well that was meant to be as more evidence that life does not exist is presented. So it makes sense. Ie absence of evidence is not evidence of absence, or I think more properly is not always so, because of variables that are still unknown. I don’t see what is wrong with saying at any particular point where the equation contains uncertain values for the parameters it is not certain that possibilities of life will decrease as more evidence of lack is presented. It’s hardly a controversial opinion.
The examples they give in that link are of course limited to Earthly concerns where all the information is available, we don’t know what the parameters of life are, whether it can exist in conditions that defy current understanding so if bayes theorem were to be applied you cannot get a definitive result without all cases being modeled within correct parameters. Bayes theorem will however show a gradually trend that chances of life decrease as more information is made available in a case of the unknown, but it can only be applied accurately to equations that contain certainties of probability parameters in statistics. If you have breast cancer the chance of a false positive is always correct, the chance of a correct diagnosis is always the same, assuming of course that later on they don’t find that there are breast cancers that are completely undetectable by modern medicine.
The language you use is so sloppy and muddled, I can’t help but believe that you’re just way over your head in this topic.
That’s what probabilities are FOR. You’re still not understanding this. Probabilities ARE uncertain values for parameters.
That’s an oxymoron.
I don’t even know what that means.
Anyway, that you’re talking about breast cancer tells me you probably didn’t read beyond the first few paragraphs.
When Columbus went to America, he had no evidence for the existence of America and yet America existed. So, as far as Columbus was concerned, or, in Columbus’ frame of reference, absence of evidence was not evidence of absence. Therefore absence of evidence is not completely and utterly ALWAYS evidence of absence. In other words, be aware of context. Something that is true in one context, or frame of reference, may not be true in another.
On another level, I think you rather glorify mathematics. You are granting it omniscience. There is more to existence than mathematics is able to talk about. One has to remember that mathematics is just a language and has no special status over other languages. It is just a very extreme language, one which is all syntax and, therefore, true to the complementarity relationship between syntax and semantics which holds for languages (the more syntax, the less semantics, and vice versa), is virtually meaningless. This means that maths has its own territory, its own domain of applicability which is largely unique to itself, but equally it cannot cover the domains of the meaningful languages such as English.
Languages are just tools, tools for communicating and thinking, and one should be wary of according them a status beyond that of tool. Maths is useful but as with any tool, it should be used with discretion. Your own mind is your best tool. Consider, for example, a sculptor chiseling a block of stone. If one arranged for a machine to chisel out a statue, it would do so mindlessly. If a person chisels out a statue, they quickly become aware of the feel of the stone, they detect when the stone is denser or lighter, detect flaws, and are able to make aesthetic judgments which will accommodate such random effects. A similar process occurs when a person uses languages.
Just musing here, but in light of what you say, I wonder about the status of zero and infinity. We have no, I think, evidence for their existence, and yet all mathematics is founded upon, among other things, the postulates that zero and infinity do exist. However, by the rule “absence of evidence is always evidence of absence” then zero and infinity do not exist. Bit of a paradox. Maths is built on a paradox. That must imply things about mathematics, and not good things such as give one confidence in the subject.
Something else which occurs to me is Gödel’s Theorem. If you recall it goes like this: there exists in mathematics truths which cannot be proved. On the face of it, there are therefore all sorts of mathematical truths just sort of floating in the ether and it is purely happenchance that one might stumble upon one of them. Maybe some of them will just always float out there undetected. How does one detect a mathematical truth? – tricky stuff mathematics. Gödel got to his wonderful theorem by getting mathematics to talk about itself……the mind boggles……….what more convolutions, permutations and the like might not lead to what more boggling theories.