Q&A: Rarity versus Specialness
Rarity versus Specialness
Question
About a year ago I was with you, and we discussed the rational basis for Judaism, given the assumption that one believes there is a Creator (in the sense of the cosmological argument).
I argued there that the claim of the revelation at Mount Sinai, precisely because it is an event of vanishingly low probability (by definition, since nothing like it happened before it and nothing like it is supposed to happen after it), requires exceptionally powerful evidence—meaning that every existing alternative must be pushed to an absurdly tiny, near-zero probability.
You argued that reasonable evidence is enough. According to you, once there is God, it is possible either that He revealed Himself or that He did not, and reasonable testimony is enough to tell us which of those possibilities occurred. In that discussion you noted the distinction between “specialness” and “rarity,” where “rarity” is not a reason to reject a report (say, if I were told that a person of Mongolian origin was elected president of the United States), but “specialness” is (say, a report of a sequence of 6 million sixes in rolls of a fair die).
If I understood correctly—
“Rarity” is when one possibility is selected from among several that exist, even if they are not equally probable. In such a case, a reliable report is enough.
“Specialness” is when one possibility is selected from among several that exist, and it is both very low-probability and uniquely meaningful for the recipient of the report (provided that most of the possibilities are not meaningful).
Did I understand correctly?
Answer
Both a special possibility and a rare one are low-probability. It is like the difference between an ordinary outcome of rolling a die a hundred times and the outcome in which a 6 comes up every single time. Those two are equally probable (for any specific outcome); the difference is only in their specialness for us.
Something like this is distinguished in Jewish law between a majority and a presumption. The presumption that “a person does not pay before the due date” is really a kind of majority (most people do not pay before the due date). What distinguishes it from a majority like “most people who buy oxen buy them for plowing” (and not for slaughtering)? In the second case, if a person bought an ox for slaughtering, he belongs to the minority, but there is nothing at all problematic about that. What happened does not require an explanation. There is a minority of people who buy for slaughtering. Their number is small, but this is a normal phenomenon that does not call for explanation. By contrast, a person who paid before the due date did something unusual that does call for an explanation. Therefore his claim that he paid before the due date is not accepted, and it can even extract money, even according to the view of Samuel, which is the accepted Jewish law, that a majority does not extract money. Samuel was speaking about a majority like “most people who buy oxen buy them for plowing.” Of course, much more could be analyzed here, but this is not the place.
Discussion on Answer
In the comparison between a majority and a presumption, what is actually the reason for the difference?
Is the difference that a “presumption” is a majority that we assume has some underlying logic to it, and therefore deviating from it requires distinctive evidence, whereas an ordinary “majority” is one from which someone who deviates is not doing anything “strange,” and therefore no explanation is needed?
I’m trying to understand—
According to you, revelation is a rare event, but not a special one? Meaning: although statistically it has no probability, it is an existing possibility in a created world, and therefore reasonable testimony is enough for it?
I don’t know if I fully understand the concepts, but it seems to me that revelation does have “specialness for us.” It concerns a tiny minority within one species inhabiting one planet in a full universe. For that matter, there could have been all sorts of different revelations, more or less exceptional both in their intensity and in their content. Is a revelation specifically to us, one that suffers from further difficulties (why it does not repeat itself to spare doubts, why it contains mistaken contents such as its scientific content and its doctrine of reward and punishment, and more…), not “special”?
K,
because that is simply not true. If I assume there is a God on the basis of the cosmological argument, then indeed the probability that He created a world is 1. But the probability that He would stage such an event is undefined, and from our standpoint it is 0 or close to it (because it has never happened as far as we know, except for one time that defines itself as a one-time miraculous event, that is, one that is not at all likely to occur).
Sinai,
I’ll repeat once again what I already wrote and said. Assuming there is God, there is nothing preventing Him from revealing Himself. The fact that He has not revealed Himself many times makes the event rare, but not exceptional (unlikely). That is precisely why the discussion of whether or not there is a God in the philosophical sense also bears on the religious question. Once we reached the conclusion that there is such a thing, revelation changes from exceptional to rare, meaning that what stands against it changes from a presumption to a majority.
Sinai
If it is undefined, then why are you assuming in advance that it is 0? Maybe assume it is one half…
To the Rabbi,
does the Rabbi agree with the explanation I gave earlier?
To the Rabbi,
thank you very much, I think I understood. It may be that we no longer have the presumption “God does not reveal Himself,” but only a “majority”; but we still have the presumption that “people reporting revelations are liars / delusional” (it seems to me one could argue for such a presumption with fairly full confidence). That is indeed a weaker presumption, and therefore it really does take less powerful evidence to overcome it, but it still seems to me that there is a preference for any alternative explanation to revelation, so long as it is reasonable.
K,
I am not familiar with reliable documentation of revelations (other than ours, and even about that I have many doubts). For an event that has never happened, and is not part of the ordinary probability space, it seems to me reasonable to assign probability 0.
Even if our revelation is real, it itself testifies about itself that it is a total exception to the order of the world, and that there never was and never will be anything like it, which means “the probability is 0, but God performed a miracle.”
Why are you so sure that a breaking of the laws of nature cannot happen? Or of the correctness of our induction at 100%? It sounds like you’re really overdoing it. Especially since here you are talking about another factor such that, given that there is a God, revelation is not far-fetched.
Or in terms of the kind of evidence I like (and invented?)—the very fact that you are on this site is a sign that the revelation is probably true. Because insofar as there is no God and no true religion, the probability that we would invest and think about it is pretty low a priori.
And in general, how do you explain the progress of science?
K, I didn’t understand your explanation, so I can’t say whether I agree.
I don’t understand the question,
after all, you could argue that insofar as there is a God, the probability that He created a world and would stage such an event is 1.
Why are you assuming otherwise?