Looking at clouds can’t refute it and therefore also doesn’t confirm it, but how is that connected?

A. I don’t know of an argument whose two premises are probabilistically dependent on one another. Can you give an example? In any case, in the argument about God that is certainly not the case.
B. Why do we also need to include the chance “that it is true even though one of the premises is not true”? As far as I’m concerned, without the proof for God we are talking about a celestial teapot that I’m not giving any chance to.
C. And let’s say there is indeed some independent chance that God exists even without the argument, and let’s say I give 60% credence to the premises—who says that the chance independent of the argument completes the product of the plausibilities to above 50%?
D. As for the raven paradox, like Yishai said, it seems to me one should distinguish between a case where an object happened to come before us that could have one of two properties, x or y, one of which would refute the argument and the other would not—in that case it really does strengthen the general law.
But when no object came before us that had the potential to refute the general law, then its opposite did not strengthen the general law either, for you cannot say of it that it “stood the test of possible refutation and was not refuted”; it never stood such a test at all.

A. For example: 1. All people are mortal. 2. Socrates is a person. The probability of the two premises depends in some sense on the existence of people (premise 1 can hold vacuously, but that’s not what is meant when one assumes it—you don’t use the word “people” to point to some unknown thing such that anything could hold of it, because then the predicate is arbitrary and the whole premise is meaningless).
B. He wrote to you on the level of principle. You can also assign a probability to other proofs or assign a probability to a celestial teapot (if you assign a probability to the possibility that the universe is not complex, then maybe it makes sense to assign some probability to the existence of a celestial teapot too).
C. Again, he answered you on the level of principle. If you think the chance that the two premises hold is 36% and the chance that God exists regardless is 2%, then you can work out for yourself what the overall chance is in your view—what is there to ask here?

By the way, it seems you are assuming that what matters is whether the probability is above or below 50%. That is not necessarily justified.

Actually, what I wrote about the raven paradox isn’t correct. Examining clouds can’t refute the claim, but examining colored things (= non-black things) can refute it. Still, that is a very large and diverse set that is hard to examine. After all, if I checked one raven, I wouldn’t adopt the claim about all ravens. Not even if I checked all the ravens within a 200-meter radius of my house. To become convinced that all ravens are black, I need to examine enough ravens under enough conditions that seem to me likely to matter. So it’s true that one could also do this with the set of colored things (and in fact if I examined all of it, I would prove the claim), but there it requires much more, and therefore examining one item or a few items there is completely marginal (far more marginal than examining a raven, which is itself completely marginal).

Everything has already been answered here. I’ll just add: more power to Yishai for his last answer. That really is the explanation of the raven paradox. Finding a white cloud does indeed confirm the thesis that all ravens are black, but because of the huge number of cases, the confirmation is minuscule. So Hempel was of course not right in his attack on induction.
The conclusion is that logical equivalence does not mean equivalence in confirmation. And in that respect this is similar to our case. For in a valid argument there is an equivalence between the premises and the conclusion (in fact this is implication, not equivalence, but let’s leave that aside). And yet I showed that the plausibility of the premises is not equivalent to the plausibility of the conclusion. Consider this carefully.

Just one more note about a mistake of Yishai’s. Of course examining clouds can refute the claim that everything non-black is not a raven. If we examine that white object in the sky and discover that it isn’t a cloud but a raven, the thesis has been refuted. The examination being discussed is obviously not an examination of the color of clouds (given that it is a cloud and I am checking what color it is), but an examination of the nature of white objects (given that it is white, I am checking whether it is a raven). Note this well.

So from now on, when I come to examine a logical argument, do I need to make sure I agree with its premises (assuming they are independent) at more than 70%? For some reason the Rabbi didn’t mention this in the notebooks when he told the reader to formulate a position after reading them. It seems to me this is a point that almost nobody notices, and it causes many people to form a mistaken position regarding the existence of God, Heaven forbid, and in other topics too. Do I now need to start re-examining my whole worldview?
And regarding ravens and clouds, I didn’t understand why a black raven strengthens the general law more than a white cloud does.

Yosef, how did you get from my words to the opposite claim from what I wrote? On the contrary, I wrote that there is no equivalence of confirmation.
As for the ravens, I explained that this is a function of the number of relevant objects. The claim “all ravens are black” speaks about all ravens. Let’s say there are one hundred thousand of them in the world. You checked one of them—you confirmed it a little. The claim “everything non-black is not a raven” deals with all non-black objects. There are very many billions of those. If you checked one, you confirmed it only a tiny tiny bit.

I understood the second part now.
But regarding the question itself, I didn’t understand.
Assuming that in the argument about God the premises are not dependent (that is the case in my humble opinion), and assuming that this is the only argument in the world in favor of God’s existence, then apparently it is obvious that I need to check to what degree the premises seem plausible to me. What is wrong with that? God is a celestial teapot without this proof. Even if there is a 1% a priori probability of His existence, that won’t close the gap when confidence in the premises is less than 70%.

Not true.
When you have 50% certainty that it is true, how can you say it’s a teapot? As for the rest, you can assume 50-50 for example.

As for my mistake, that is exactly what I wrote when I corrected myself—examining clouds is not helpful, but examining colored things is helpful, and that is what the honorable Rabbi wrote in the latter part of his second reply, and so it is clear to anyone who reads my words carefully, and clever indeed.

He is saying that assuming the premises of the proof are not true, then of course there is no 50% certainty, and so the probability of God’s existence is 1%. If there are two premises and he believes each of them at 60%, then he is still very far from 50%.

I didn’t understand. If they are certainly not true? Then obviously the proof has no significance. But if each has a probability above 50%, then obviously we have already moved beyond the realm of a teapot.

What I meant was that before the proof, God is like a teapot, so that even if I include the a priori probability (without proof) of His existence, that usually will not complete the argument’s plausibility to above fifty percent.
After the argument it is of course clear that God is no longer a teapot, but can I even be called a believer if my belief is less than 50%? And besides, if I had to bet on whether God exists or not, I would choose the option that He does not, because the probability gave me less than fifty percent.

You are making a mistake in the calculation. If the two premises are plausible in your eyes, then the plausibility that God exists is also higher than 50%. Put the teapots aside, and make the calculation assuming that beyond the plausibility of the premises all the other possibilities are equally weighted.
Suppose the proof of His existence is based on two premises, each at 60%. Now let’s divide into two possibilities:
1. Without the proof there is a 50% chance that He exists (because there is no indication either way and this is not a teapot).
2. With the proof He certainly exists.
The chance that there is a proof is 36%. If that is true—there is God with 36%.
The chance that there is no proof is 64%. If that is true—there is God with 32%.
Therefore the overall probability that God exists is: 68%.
I’m beginning to remember Euler jokes and this is not the place. Of course one should not take any such calculation seriously. It only comes to show that in general the conclusion is not weaker than its premises but even stronger than each one of them.
God exists. Which is what was to be shown.
God exists!!! (That is a cry of joy, of course). 🙂

I understand the whole calculation, but why do you claim that without a 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 have equal probability. The teapot argument says there is no reason at all to assume God exists, and therefore even in the absence of information one should assign probability 0. But in our case that is not correct, because if there is a proof with 50% probability, then even without the proof you cannot say this is a teapot case. Notice that the teapot argument always refers to what the situation is beyond what is before us.

Heaven is my witness that I cannot 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 win only if two coins I toss both come up tails, then the chance of winning is of course 25%, so it is not worth betting.
According to the Rabbi, since there is some chance of winning (25%), then a priori too there is some chance of getting tails twice, and therefore my chance of winning is more than 25%, and I really don’t understand that.
If, for example, someone comes and tells me that he saw a celestial teapot, then there is a 50% chance he is telling the truth (I have no information about his reliability), and since there is a 50% chance he is right (and thus that there is a teapot), then there is also an a priori 50% chance of the existence of such a teapot, and thus it comes out that there is a 75% chance there really is one.

Heaven be your witness that I’ll try one more time, and if not—then not.
The entire teapot argument is based on resorting to the alternative state without the information before us. Someone comes and says there is a teapot. We have information before us that this person says so. Apparently we are in doubt about his words. Then someone comes and asks: what would we have thought without this? That there is no chance at all; so even if he says it, we don’t really pay attention to him (especially since his statement itself has no basis. How does he know if we do not know?).
And what happens in our case? If there is a proof then there is God, except that it is not clear whether there is a proof. But even on the possibility that there is no proof, it is still a plausible argument (just not a proof). Therefore even without a proof the situation is not like the teapot. Add to that other arguments in favor of God’s existence, which also take us out of a teapot situation.
That’s it. Up to here.

Thank you.
I would just be glad for an explanation of this sentence:
“But even on the possibility that there is no proof, it is still a plausible argument”—why plausible?

Because even if it is not certain that everything has a cause, it is still plausible that this is so. And beyond that there are the other arguments for God’s existence.
Notice that every logical argument is built this way. Every logical argument begins from some basic premises. No basic premise is certain. If so, on your approach one could throw out all logical arguments. And if there are three premises, then even 80% would not be enough.

I’ll formulate it this way: even if it is not true that everything has a cause, you still cannot say that nothing has a cause (rather, only that it is not certain that everything does). If necessarily nothing has a cause, then you are right that there is no reason to assume there is God. But that is not the other side of our coin. The two sides are: 1. Necessarily everything has a cause. 2. It is not necessary that everything has a cause.

deus est! deus existit!

Oh… that is already clearer. [Let’s put aside the other proofs for God and deal with a situation where there is only one proof.]
Basically the claim is that if the causality premise (for example) is true with one hundred percent certainty (+ another premise that is certain with one hundred percent certainty), then the conclusion is certain, and if the premise is plausible at 70% (and the second premise is also plausible at 70%), then the argument is certain only at 49%. But we did not say that the premises are true only at 70%; rather, that they are certain only at 70%, so it is still possible that we may also count the remaining 30%, or at most half of it (because we are in doubt), and then the product of the premises should take into account 85% truth, so that the plausibility of the argument is above 50% even though the plausibility of the premises is only 70%.
Am I on the right track?
And if so, then your words are not necessarily correct for every argument. There are arguments where the two sides of the coin are black or white. (Statements that begin with the word “All…”)

If we formulate it differently, then one can assume that everything has a cause, and one can assume that not everything has a cause. Now the question is: if one assumes that not everything has a cause, then why do some things have one and others not? The claim “a thing has a cause iff it is green” would probably get a very low probability. The claim “a thing has a cause iff it does not include the whole world” could be given a higher probability. The question is whether there are such claims that one could assign significant plausibility to and from which it would come out that there is a God. If there are none, then the total plausibility is equivalent to a teapot.

I can think of: “a thing has a cause iff it is not eternal,” and then the question is whether the universe in a broad sense (including universes that collapsed into a singular point, if there was such a thing) is eternal, and if not then there is a proof of a Creator.

Beyond that I can’t think of anything that would increase the probability of God’s existence by more than epsilon.

Yosef,
The question is not whether the premises are certain or plausible. Every premise can be either a true claim or a false claim, and based on that you assign probabilities to it.
The claim is that even if the claim is not true, there is still some distance between that and its exact opposite. So there is a 30% chance that not everything has a cause, but within that 30% there are many possibilities. You have to assign each possibility (or at least each major possibility) some probability, and then check whether from that possibility it follows that there is a God. For example, if everything that starts with the letter A has a cause, then the world has a cause (this is of course a ridiculous example).

“When there is no information, all possibilities are equal” — only if the distribution is uniform.

Yishai, what you’re saying is interesting, but it’s a little funny.
When I look for what is included within the 30% doubt that maybe not everything necessarily has a cause, I’ll find many subcategories, among them your example. I’ll find possibility 1, that not everything has a cause, but only things that start with the letter A, and then after I remove all the irrelevant minorities (that things starting with B, C, D, etc. have no cause), I’ll be left in practice with the percentage I assign to the claim that the world itself has a cause. So apparently we are no longer dealing with the original logical argument (“everything has a cause”), but with the a priori question whether in my opinion the world has a cause—that is, whether there is a God—and then it really comes out that this is begging the question.
For example: 30% that not everything has a cause; a third of that because maybe things beginning with the letter A have no cause; a third of that because maybe things beginning with the letter Ayin have no cause; and a third of that because maybe things beginning with the letter Tav have no cause.
It turns out that the first and last possibilities are irrelevant to the argument and leave the claim standing, so that in practice the probability that the world has a cause is 90%.
Now I’ll check what is inside the group of words beginning with Ayin, and I’ll find there are three things: the world, a wagon, and an association. Of course the wagon and the association do not affect the argument, so in practice I am left with a 96.6% chance that the world has a cause, that is, a 96.6% chance that there is a God.
But where did the extra 26.6% come from? We agreed that I hold only at 70% that everything has a cause.
By the way, I have to say that you explain very well. Maybe you should open a site too, for those days when Rabbi Michi does not manage to attain the level of Rabbi Preida and despairs of us lesser folk? 🙂

The extra 26.6% was added from cases where not everything has a cause. If, again, everything that starts with Ayin has a cause but everything else does not, then roads have no cause and the world does have a cause. Meaning: God created the world, but the roads in it came about randomly.
So if I assign probability to only 3 possibilities:
1. Everything has a cause — 70%
2. Only things that start with Ayin have a cause — 4%
3. Nothing has a cause — 26%.
Then the probability that the world has a cause is 74%. Part of this probability is in the possibility that everything has a cause, and part is in the possibility that only some things have a cause but the world is included in that subset.

Of course, the probability of such a thing is 0%.
But one can think of more reasonable possibilities, as I wrote in an earlier message to our Rabbi, may he live long, ruler of the website, may he live long. One can think that everything that is not eternal has a cause. Let’s give that 14% and assume there is no other possibility except that nothing has a cause. Now if you think the probability that the world is not eternal is 12%, then the possibilities are:
1. Everything has a cause — 70%
2. Everything non-eternal has a cause — 14%
A. The world is not eternal — 12%. Therefore it has a cause: 14%*12=1.68%
B. The world is eternal — 88%. Therefore it has no cause: 14%*88%=12.32%.
3. Nothing has a cause — 16%.
Now it comes out that the probability that the world has a cause is 71.68%.

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

Suppose I am not completely sure of the premises, only 70%.
If so, it comes out that more likely than not (51%) Danny will not be punished today, despite the fact that I have fairly high confidence in the premises of the argument.
Will you now come and say that it is still more likely that Danny will be punished today, because premise B can be broken down into several possibilities?
Maybe the teacher didn’t say he would punish everyone who is late to class, but only whoever is late to class and whose name starts with D (and then Danny will be punished even though premise B is false), etc.?
Thanks in advance.

Certainly.
Though in truth it is not very likely that this is what the teacher said, so that probably won’t be what pushes it over 50%.
But note that there are other possibilities too. Even if Danny wasn’t late to class, he could be punished for other reasons (and here too there is a non-negligible probability that this will happen).

And it is definitely also possible that two children will be late and only one of them will be punished. Usually this is not related to the first letter of the name, but to overall behavior, how they look to the teacher, his mood at the moment he saw them, and so on and so on.
So think of a situation where Danny and Shlomo were late. Now there is a 70% chance that both of them will be punished, plus some 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? (In truth it certainly may, because it could be that the teacher’s punishment policy, consciously or unconsciously, is also tied to the number of latecomers and their identities.)

And to go back to my example—Socrates is a person and all people are mortal.
Even if Socrates is an enchanted snake or a demon, it is still possible that he is mortal. And even if not all people are mortal (say everyone except Elijah the Prophet), it is still possible that he is mortal.

So if you were 70% sure of premises A and B, and you were required to bet on the question whether Danny will be punished today or not, what would you choose? [As a criterion to check whether in your opinion it passes 50%.] I assume you would bet that he won’t be punished. So how is the argument about God different from this? (Assuming there are no other arguments.) Why does the side probability there cause the overall plausibility to rise above 50%?

I would ask what the probability is that the teacher would decide to punish him specifically for the lateness, and what the probability is that he would do something else that would cause him to be punished, and what the probability is that he would be punished for no particular reason, and on that basis I’d decide.
By the way, I repeat again my comment from the beginning that majority is not sacred. If, for example, they offered me to pay 100,000 shekels so that if Danny is punished I receive a million, I would not agree, and if they offered me the same deal in case Danny is not punished I also would not agree (if they offered me both, of course I would agree to both…). The fact that something has more than a 50% chance of happening does not in itself mean I would bet on it—the bet also depends on the consequences.

Okay, so in the example of Danny being late, you would estimate the chance that he would be punished regardless of his lateness today. Theoretically one can think of ways to estimate such a thing (how many students were punished this year, etc.). But if we return to the proof for God, how can you estimate the a priori plausibility of God? It’s not like in Danny’s case, where the question would be: how many students on average are punished each day, and of course how many students there are in the class.
But with God, the question would apparently lead us directly back to God Himself (and not to something like “how many universes are created by God and how many are not”), and then the matter cannot be known or estimated from outside the circle of the proof.

And how do I assign a probability to the premise “a complex thing does not arise by chance”? I simply assign it according to what seems right to me.
That is also how I assign a probability to any other premise. First one has to map out the possibilities, and that actually seems to me the harder part.

But that is exactly the difference.
I can ask myself what I think the probability is that a complex thing does not arise by chance, in order to arrive at an estimate of the chance that God exists.
But I cannot ask myself what the probability is that God exists in order to arrive at an estimate of the chance that God exists.
How would you assess such a thing? Only by means of other proofs for His existence—but we already said to put other proofs for His existence aside.

I’m not asking what the probability is that God exists.
I’m asking what the probability is that everything (except God) needs a cause. Then what the probability is that every complex thing needs a cause, and what the probability is that the world is complex (but one can ask: complex at what level? and assign a function that gives the probability that every thing at complexity level X needs a cause, and a function that gives the probability that the world is complex at level X, and then derive the probabilities from that with an integral). Then what the probability is that everything non-eternal needs a cause, and what the probability is that the world is non-eternal. Then what the probability is that every blue thing needs a cause, and what the probability is that the world is blue (and together with that you can include all the silly ideas, call them all together a teapot, and assign them roughly 0%).
So first of all one has to find all the possibilities that are not idiotic (there are infinitely many idiotic possibilities).
Of course one also has to factor in other proofs, such as the ontological one or proofs from history, if you assign them more than negligible plausibility.