Calculating the probability of the conclusion based on the probability of the premises

Watching the clouds cannot refute and therefore does not confirm, but how is that related?

A. I don't know of an argument whose two premises are dependent on each other from a probabilistic point of view. Can you give an example? In any case, in an argument about God, this is certainly not the case.
B. Why do we need to include the chance that it is true even though one of the premises is false? As far as I'm concerned, without proof of God, this is a heavenly teapot that I don't give a chance to.
C. And suppose that there is indeed an independent chance that there is a God even without the argument, and suppose that I give 60% confidence in the premises, who said that the chance independent of the argument completes the product of probabilities to over 50%?
D. Regarding the crow paradox, as Shishi said, it seems to me that we should distinguish between a case that happened to be in our hands that could have two properties, x or y, one of which would refute the argument and the other not, in which case it does indeed strengthen the general law.
But when we did not have the opportunity to obtain a proof that had the potential to refute the general law, even its reversal did not strengthen the general law, since it cannot be said that it “stood the test of refutation, and was not refuted”, it did not stand the test of refutation at all.

A. For example – 1. All people are mortal. 2. Socrates is a man. The plausibility of both assumptions depends on the existence of people in some sense (assumption 1 can exist in a vacuum but that is not the intention when it is assumed – we do not use the word people to indicate something unknown about which anything can exist because then the predicate is arbitrary and the whole assumption is meaningless).
B. He wrote to you in principle. You can also give a chance to other proofs or give a chance to a celestial teapot (if you give a chance to the fact that the universe is not complex, then perhaps it is reasonable to also give a chance to the existence of a celestial teapot).
C. Again, he answered you in principle. If you think that the chance that both assumptions hold is 36% and that the chance that God exists regardless is 2%, then you alone know what the overall chance is in your opinion, what do you have to ask here?

By the way, you seem to assume that what matters is whether the chance is above or below 50%. That's not necessarily justified.

In fact, what I wrote about the crow paradox is not true. Testing clouds cannot disprove the claim, but testing colored things (=not black) can. What is true is that this is a very large and diverse group that is difficult to test. After all, if I tested one crow, I will not adopt the claim for all crows. Even if I test all crows within a radius of 200 m from my house. In order to be convinced that all crows are black, I need to test a large number of crows with enough conditions that I believe are likely to have an effect. So it is true that it is also possible to do this for the group of colored things (and the fact is that if I test the whole thing, I will prove the claim), but there it requires much more, and therefore even testing one or a few individuals is completely marginal (much more marginal than testing a crow, which is also completely marginal).

Everything has already been answered here. I will only add that I am in agreement with Yishai's last excuse. This is indeed the explanation for the crow paradox. Finding a white cloud does indeed confirm the thesis that all crows are black, but because of the large number of cases, the confirmation is minimal. Therefore, of course, Hampel was wrong in his attack on induction.
The conclusion is that logical equivalence does not mean confirmatory equivalence. And in this, it is similar to what was discussed with Didan. Dahana, in a valid argument there is equivalence between the premises and the conclusion (in fact, it is a deduction, not an equivalence, but we will leave that aside). And yet I have shown that the plausibility of the premises is not equivalent to the plausibility of the conclusion. And carefully.

Just another comment on Yishai's mistake. Of course, examining clouds can refute the claim that anything that is not black is not a crow. If we examine this white object in the sky and discover that it is not a cloud but a crow, the thesis has been refuted. The examination in question is of course not an examination of the color of the clouds (given that it is a cloud and I examine its color) but an examination of the nature of white objects (given that it is white and I examine whether it is a crow). And that's it.

So from now on, when I come to examine a logical argument, do I have to make sure that I agree with its (independent) premises by more than 70%? For some reason, the Rabbi did not mention this in the notebooks when he told the reader to form a position after reading them. It seems to me that this is a point that almost no one pays attention to, and it causes many people to form a wrong position regarding the existence of God (Rach”el), and also on other issues. And should I now start examining my entire worldview anew?
And regarding the ravens and clouds, I did not understand why a black raven strengthens the general law more than a white cloud.

Yosef, how did you arrive at a claim that is the opposite of what I wrote? On the contrary, I wrote that there is no corroborative equivalence.
Regarding crows, I explained that it is a function of the number of relevant objects. The claim that all crows are black speaks about all crows. It is said that there are a hundred thousand of them in the world. If you examine one of them, you are corroborated to a certain extent. The claim that everything that is not black is not a crow speaks about all non-black objects. There are many, many billions of such. If you examine one, you are corroborated to a very small extent.

I just understood the conclusion.
But regarding the question itself, I didn't understand.
Assuming that in an argument about God, the premises are independent (which is the case for the answer), and assuming that this is the only argument in the world in favor of the existence of God, then it is apparently clear that I have to check to what extent the premises are reasonable in my opinion, what is wrong with that? God is a heavenly teapot without this proof. Even if there is 1% a priori for his existence, it will not close the gap in a situation where confidence in the premises is less than 70%.

Not true
When you have 50% certainty that it is true how can you say it is a teapot? You can put 50-50 on the rest for example

Regarding my mistake, it is what I wrote when I corrected myself: “Checking clouds is not helpful, but checking colored things is helpful,” and it is explained in the second response at the end, and so it is understandable to anyone who pays attention to my words and comments.

He says that assuming the premises of the proof are not true, and then there is no 50% certainty, then the chance of God's existence is 1%. If there are two premises and he asserts that each is 60% true, then he is very far from 50%.

I don't understand. If they are definitely not true? Then clearly there is no point in proving. But if each one has a chance of over 50% then clearly we have already gone beyond the teapot boundary.

I meant that before the proof, God is like a teapot, so even if I include the a priori chance (without proof) of his existence, it usually won't bring the argument's probability above fifty percent.
After the argument, it's clear that God is no longer a teapot, but can I even be called a believer if my belief is less than 50%? Besides, if I had to bet on whether there is a God or not, I would choose the no option, because the chance gave me less than fifty percent.

You are wrong in your calculation. If both assumptions are reasonable in your opinion, then the probability that God also exists is higher than 50%. Get rid of teapots, and make a calculation that beyond the probability of the assumptions, all other possibilities are equally weighted.
Suppose that the proof of his existence is based on two assumptions, each 60%. Now we will divide into two possibilities:
1. Without proof, there is a 50% chance that he exists (because there is no indication and it is not a teapot).
2. With proof, he certainly exists.
The chance that there is proof is 36%. If this is true - there is a God in 36%.
The chance that there is no proof is 64%. If this is true - there is a God in 32%.
Therefore, the total chance that there is a God is: 68%.
I am beginning to remember the jokes of Euler and others. Of course, no such calculation should be taken seriously. He just came to show that in general the conclusion is not weaker than its premises but even stronger than each of them.
There is a God. Proverbs.
There is a God!!! (This is a joyful exclamation of course). 🙂

The whole calculation is understandable, but why do you claim that without proof there is a 50% chance that God exists? How is that different from a teapot?

I explained. When there is no information, all possibilities are equally likely. The teapot argument says that there is no reason to assume that there is a God, and therefore even in the absence of information, one should take a chance of 0. But in our case, this is not true, because if there is 50% proof, then even without the proof, it is impossible to say that this is a case of teapot. Note that the teapot argument always refers to what the situation is beyond what is before us.

I swear to God that I can't understand this.
How does the existence of an argument affect the a priori probability (the probability without the argument)?
For example, if we had a game in which I only win if two coins I toss land on heads, the chance of winning is of course 25%, so it's not worth it for me to bet.
According to the rabbi, since there is a chance of winning (25%), then even a priori there is a chance that heads will come up twice, and therefore my chance of winning is more than 25%, and I really don't understand this.
For example, if a person comes to me and claims that he saw a celestial teapot, then there is a 50% chance that he is telling the truth (I have no information about his level of credibility), and since I have a 50% chance that he is right (and there is a teapot anyway), then there is also a 50% a priori chance of the existence of such a teapot, and so it turns out that there is a 75% chance that there is indeed a teapot.

I swear to God that I will try one more time, and if not – then no.
The entire teapot argument is based on the need for the other situation without the information in front of us. A man comes and says that there is a teapot. We have information in front of us that this is what that man says. Ostensibly, we are content with his words. Then a man comes and asks what we would think without it? That there is no chance, so even if he says it we don't really pay attention (especially since his statement also has no basis. How does he know if we don't know).
And what happens with us? If there is proof, then there is a God, but it is not clear whether there is proof. But also on the side that there is no proof, but it is still a reasonable argument (but not proof). Therefore, even without proof, the situation is not like the teapot. Add to this other arguments in favor of the existence of a God that also break us out of the teapot situation.
That's it. That's it.

Thank you.
I would just like to clarify this sentence:
“But even on the side that there is no proof but it is still a reasonable argument”, why reasonable?

Because even if it is not certain that everything has a reason, it is still likely that it is. And beyond that, there are the other arguments for the existence of God.
Note that every logical argument is structured like this. After all, every logical argument starts from some basic assumptions. Not even a basic assumption is certain. If so, according to you, you can throw away all logical arguments. And if there are three assumptions, then even 80% will not be enough.

I will put it this way: Even if it is not true that everything has a reason, it is impossible to say that all things do not have a reason (but only that it is not certain that there is). If nothing necessarily has a reason – then you are right that there is no reason to assume that there is a God. But this is not the other side of our coin. The two sides are: 1. Everything necessarily has a reason. 2. Not everything necessarily has a reason.

God is! God exists!

Or… that's more understandable. [Let's put aside the rest of the proofs for God, and deal with the situation in which there is only one view].
Basically, the argument is that if the assumption of causality (for example) is 100% correct (+ another assumption that is 100% certain), then the conclusion is certain, and if the assumption is 70% probable (and the second assumption is also 70% probable) then the argument is only 49% certain, but we didn't say that the assumptions are only 70% correct, but that they are only 70% certain, so it's still possible to consider the remaining 30%, or at most half of them (because we are doubtful), and then the product of the assumptions should take into account a correctness of 85%, so that the probability of the argument is more than 50% even though the probability of the assumptions is only 70%.
Am I on track?
And if so, then I'm not sure that what you're saying is true for every argument, there are arguments that have both sides of the coin as black or white. (Sentences that don't start with the phrase “all…”).

To put it another way, then we can assume that everything has a reason and we can assume that not everything has a reason. Now the question is whether we assume that not everything has a reason is why there is and why there is not. The claim “there is a reason for things but they are green” is probably given a very low chance. The claim “there is a reason for things but they do not include the whole world” can be given a higher chance. The question is whether there are such claims that can be given significant probability and from which it follows that there is a God. If there are none, then the sum of the probabilities is equal to a teapot.

I can think of “there is a reason for things but they are not ancient”; and then the question is whether the universe in the broad sense (which also includes universes that collapsed to a singular point if there was such a thing) is ancient, and if not, then there is proof of a Creator.

Beyond that, I can't think of anything that would increase the likelihood of God's existence by more than epsilon.

Joseph
The question is not whether the assumptions are certain or reasonable. Every assumption can be a true or false claim, and accordingly you give it chances.
The claim is that even if the claim is not true, there is still a distance between it and its exact opposite. So there is 30% that not everything has a reason, but within that 30% there are many possibilities. You have to give every possibility (at least a central possibility) a chance, and then check whether this possibility leads to the existence of God. For example, if all things that begin with ’ have a reason, then there is always a reason (this is of course an idiotic example).

"When there is no information, all options are equal" only if the distribution is uniform.

Yishai, it's interesting what you say, but it's a bit funny.
When I look for what the 30% doubt that not everything necessarily has a reason includes, I will find many subcategories, including your example. I will find option 1, that not everything has a reason, but only things that start with the letter A, and then after I remove all the irrelevant minorities (that things that start with A, B, C, etc. have no reason), I will actually be left with the percentages that I give to the world itself having a reason, and then seemingly this is no longer the original logical argument (everything has a reason), but rather an a priori question of whether in my opinion the world has a reason, that is, whether there is a God, and then it really turns out that this is the desired assumption.
For example: 30% that not everything has a reason, a third of this because maybe things that start with the letter A have a reason There is no reason, a third of that because maybe things that start with A have no reason, and a third of that because maybe things that start with B have no reason.
It turns out that the first and last possibilities are irrelevant to the argument, and leave the claim intact, so in fact the probability that there is a reason for everything is 90%.
Now I will check what is within the group of words that start with A, and I will find that there are three things: the world, a wagon, an association. Of course, an wagon and an association do not affect the argument, so in fact I am left with a 96.6 chance that there is a reason for everything, that is, a 96.6% chance that there is a God.
But where did the additional 26.6% come from? After all, we agreed that I believe that only 70% of everything has a reason.
By the way, I must point out that you explain very well, maybe you too will open a website, for the days when Rabbi Michi does not get to reach the level of Rabbi Frida and gives up on us little ones? :).

The additional 26.6% were added from cases where not everything has a reason. If, again, everything that starts with a has a reason but everything else has no reason, then roads have no reason and the world has a reason. In other words, God created the world but the roads in it are created randomly.
So if I give a chance to only 3 possibilities:
1. Everything has a reason 70%
2. Everything that starts with a has a reason and only 4%
3. Nothing has a reason 26%.
So the chance that the world has a reason is 74%. Part of this chance is in the possibility that everything has a reason, and part is in the possibility that only some things have a reason but the world is included in that part.

Of course, the chance of such a thing is 0%.
But one can think of more logical possibilities, as I wrote in my previous message to Rabbi Shalit of the Shalit website. We can think that everything that is not ancient has a cause. We give it 14% and assume that there is no other possibility except that nothing has a cause. Now if you think that the chance that the world is not ancient is 12% then the possibilities are:
1. Everything has a cause 70%
2. Everything that is not ancient has a cause 14%
A. The world is not ancient 12%. Therefore it has a cause 14%*12=1.68%
B. The world is ancient 88%. Therefore it has no cause 14%*88%=12.32%.
3. Nothing has a cause 16%.
Now it turns out that the chance that the world has a cause is 71.68%.

Bravo, I understand.
But do you think this calculation would be valid in any logical argument?
Let's take the following argument for example:
A. Danny was late for class.
B. The teacher said today that anyone who is late for class will be punished. (The teacher must keep his word).
Conclusion: Danny will be punished today.

Let's say I'm not completely sure of the assumptions, but only 70%.
So it turns out that the probability (51%) that Danny will not be punished today, even though I have quite a high level of confidence in the assumptions of the argument.
Will you now come and argue that it is still most likely that Danny will be punished today, because assumption B can be broken down into several possibilities?
Maybe the teacher didn't say that he would punish everyone who is late for class, but only those who are late for class and whose name begins with D. (Then Danny will be punished even though his assumption is wrong), etc.
Thanks in advance.

Sure.
Although it's really not very likely that's what the teacher said, so it's probably not what will get the 50%.
But note that there are other possibilities. Even if Danny wasn't late for class, he could be punished for other reasons (and here there is also a not insignificant probability that this will happen).

And it is certainly possible that two children will be late and only one will be punished. Usually it is not related to the letter of the name, but to the general behavior, how they look to the teacher, his mood as soon as he saw them, etc. etc.
So think about a situation where Danny and Shlomo were late. Now there is a 70% chance that both will be punished, and another chance that only Danny will be punished. Now let's go back to the situation where only Danny was late - does his chance of being punished change now? (The truth is that it is certainly possible because the teacher's punishment policy, whether consciously or unconsciously, may also be related to the number of latecomers and their identity).

And to return to my example – Socrates is a man and all men are mortal.
Even if Socrates is a charmed serpent or a demon, he may be mortal. And even if not all men are mortal (say all except Elijah the prophet), then he may be mortal.

So if you were 70% sure of assumptions A and B, and you were required to bet on whether Danny would be punished today or not, what would you choose? [Criteria to check whether it exceeds 50 in your opinion], I assume you would bet that he would not be punished. So how is the argument about God different from this? (Assuming there are no other arguments), why does the side chance in his case cause the overall probability to rise above 50?

I would wonder what the chances are that the teacher will decide to punish him specifically for being late and what the chances are that he will do something else that will get him punished, and what the chances are that he will just be punished, and decide accordingly.
By the way, I repeat my comment from the beginning that Rob is not a saint. For example, if they offered me 100 thousand NIS, so that if Danny is punished I will get a million, I would not agree, and even if they offered me the same deal in case Danny is not punished I would not agree (if they offered both, of course I would agree to both). The fact that something is more than 50% expensive does not mean at all that I will bet on it – the bet also depends on the consequences.

Okay, so in the example of Danny being late, you would estimate the probability that he will be punished regardless of his lateness today. It is theoretically possible to think of ways in which such a thing could be estimated (how many students were punished this year, etc.), but if we go back to the proof of God, how could you estimate the a priori probability of God? It is not like in the case of Danny, where the question would be: how many students on average are punished each day, and of course how many students are in the class.
But with God, the apparent question would return us directly to God (and not something like: “How many universes are created by God and how many are not”), and there it is no longer possible to know or estimate the matter outside the circle of proof.

And how do I determine the probability of the assumption “a complex thing did not come into being by chance”? I simply determine according to what I think.
This is how I also determine the probability of any other assumption. First, you have to map out the possibilities, and that seems to me to be the hardest part.

But that's exactly the difference.
I can ask myself what I think the probability is that a complex thing did not come into being by chance, in order to arrive at an estimate of the chance of God's existence.
But I can't ask myself what the probability is of God's existence in order to arrive at an estimate of the chance of God's existence.
How would you test something like that? Only by other proofs of its existence, but they've already said that there are few other proofs of its existence.

I'm not asking what the probability is for God to exist.
I'm asking what the probability is that everything (except God) needs a cause. Then what the probability is that everything complex needs a cause and what the probability is that the world is complex (but you can ask complex at what level, and give a function that gives the probability that everything of complexity level X needs a cause, and a function that gives the probability that the world is complex at level X, and then extract the odds from that with an integral). Then what the probability is that everything that is not ancient needs a cause and what the probability is that the world is not ancient. Then what the probability is that everything blue needs a cause and what the probability is that the world is blue (and along with that you can put in all the stupid ideas, call them together a teapot and give them a chance of about 0%).
So first of all you have to find all the possibilities that are not idiotic (there are endless idiotic possibilities).
Of course you also have to weigh other evidence such as ontological or evidence from history if you give them more than negligible probability.