And if I may add—there should also be a clear probabilistic tendency here. (A rational consideration, and not only a purely cognitive one.) After all, in the simpler explanation you posit fewer assumptions. For example, explanation A and explanation B. Let us say explanation A is “simpler” (?), meaning it has fewer assumption-points, say 3. But explanation B is “more tangled,” meaning it has more assumption-points, say 5 (3+2=5). Assuming both are acceptable explanations, then there is doubt between A and B as to which is the correct explanation.

When there is doubt, there are a priori rules of doubt (you don't have to be a great genius for this), and now we have to investigate what is correct—A or B. Of these two theses, the thesis that posits *fewer assumption-points* has a much higher probability. [A]
Alternatively, B, which posits more assumption-points (each additional assumption-point is on the one hand a much greater approximation to the required conclusion, but at the same time the skepticism about the truth of the assumption itself is doubled), has a much lower probability of being closer to the truth.

That's how I understood the principle of “Occam's Razor” (by the way, if the Rabbi agrees or disagrees, I’d be happy to hear his opinion).

I’d be glad if the Rabbi could expand on the answer above; I didn’t completely understand it.
1. Did you mean that there is empirical evidence for the razor principle, because theories determined according to it worked, while those determined against it did not? Could you give an example?
2. You argued that the razor principle is derived from cognition, from the “mind’s eye.” I didn’t completely understand that either.

Daniel explained the razor principle through statistics. I’m not sure Occam’s Razor is subject to statistical rules. I don’t have a good example at the moment, so let’s take Rabbi Chaim of Brisk’s formulation regarding the signs of a madman: he loses what is given to him, tears his clothing, and sleeps in a cemetery. It is preferable to determine that the person is insane, which is one explanation, rather than interpret him with three separate explanations.
To determine what is more correct probabilistically, you need to place on one side the probability of a person being insane according to the distribution in the population, and opposite that the probability of performing the three strange behaviors (calculating the probability of each behavior and multiplying them together p1*p2*p3).
(By the way, it would be more correct to calculate “conditional probability” regarding the person—that is, what is the probability that he is insane given that he behaves in this strange way in these three areas.)

If probabilistically it turns out that the chance of the person being insane is lower, and we still prefer the interpretation that he is insane, that would be a sign that Occam’s Razor does not depend on probability.

What does the Rabbi think—is Occam’s Razor connected to statistics?

1. All scientific theories are examples of this.
2. My claim is that the razor principle is a result of observation and not of reasoning. We see the correct theory; we do not think that it is correct.
See all this in my article here:

עוד בעניין תערו של אוקהאם

Clearly statistics does not work in all cases. This is a very general principle. But I think there are cases in which it can be grounded in statistics: assume reasonable assumptions about the distribution and see.

A good and blessed week.

Dear Oren, I actually think that probabilistically, positing more assumption-points is certainly less likely.
For example, suppose there are 2 Daniels (1—Daniel Koren, and 2—Daniel Leibovitz [by the way, these are my two last names, one from my father and teacher, may he live, and the other from my mother and teacher, may she live]) on planet Earth who are world chess champions—they and only they are established as such. All the other Daniels are only known as half-clutch backgammon players (and one can derive from this an a fortiori argument for chess).
One of them lives—say Koren—in Australia. And the other lives in Israel.
And then a shocking report comes out publicly about the crushing defeat of the *Australian chess champion* by a person named “Daniel.”

Now we have an Occam investigation—according to Occam, of course Daniel Koren (the Australian) is the winner.
On the other hand, you can cast doubt on this and ask: who says it wasn’t Daniel Leibovitz (from Israel)?! After all, he’s also called Daniel, and he too is an established chess champion. Why should Koren prevail over Leibovitz?! I am astonished. Doubt. (As long as it is not established 100% that Daniel Koren is the winning competitor, we should not rush to conclude—even though it is simpler, and maybe even more logical, because why would Danny Leibovitz fly all the way to Australia… much less likely, since Danny Koren actually lives there.)
And you can raise a further difficulty: “Wait a second, and who says there isn’t some other mysterious Daniel from Australia who was discovered after the fact to be a world chess champion…?”
Or maybe there is even a more far-fetched possibility in both scenarios: an *Israeli* (mysterious) named “Daniel Levy” who flew there especially… [this could go on forever].

Now I ask you, my friend Oren: don’t you think that every additional assumption-point (a Daniel from some distant district, or a Daniel not known at all as a player, etc. etc.) greatly lowers the probability?

Sometimes it is more plausible to assume fewer entities, and sometimes not. If I see a mouse in the yard enter a hole and a split second later hear a scream from the living room that there is a mouse there, I may very well assume that there are at least two mice rather than one mouse with spaceship speed. Wherever something seems more plausible, one can identify that the reason it seems more plausible to us is that it requires positing fewer entities or fewer arbitrary assumptions.
I like the example from Rabbi Chaim himself. If after seeing three puzzling things we assume the person is insane, and do not settle things for ourselves with local explanations for each of the three, then why did Rabbi Chaim himself bother to explain dozens of difficult passages in Maimonides rather than dismiss Maimonides as senile and be done with it? Obviously because he thought the probability that Maimonides’ book was written carelessly and without proper supervision was lower than the product of all the probabilities of all the assumptions in all his explanations put together.
However, the Talmud’s own example regarding a madman is statistically pure, as Aharon wrote, and there in truth one need not reach for principles at all, but only for probability calculations given full information about the population.

The term “product of probabilities” isn’t precise, since Rabbi Michi distinguishes between plausibility and probability, but the principle is clear.