Q&A: Does a Chain of Probabilities Still Indicate a Rational Choice?
Does a Chain of Probabilities Still Indicate a Rational Choice?
Question
Hello Rabbi Michael Abraham,
As I understand it, your faith-based line of reasoning goes something like this: it is likely that God exists (in light of various arguments). Given that He exists (and in light of several additional considerations), it is likely that He revealed Himself. In other words, there are two probability arguments stacked on top of each other. Now, I know there is some difficulty in quantifying this, but to sharpen my question I’ll assign numbers to these probabilities.
Suppose:
a — God exists. Probability: 60%.
and:
b — God revealed Himself. The probability — given a — is 70%.
You can see that even though each step along the way is probable on its own (that is, more likely than not), it still comes out that the probability that b happened is only 42% (0.6*0.7). In other words, it is more likely that b did not happen. So ostensibly it would not be rational to believe in that scenario — despite the fact that each step is probable.
On the other hand, one could say that it is the single most likely scenario (just a and not b — probability 18%; not a — probability 40%). So one could seemingly argue that it is still rational to believe in b. But in our case there is no practical difference between “just a and not b” and “not a,” since in both cases God was not revealed and therefore there is no obligation to keep the commandments. So it does make sense to examine this from the perspective of the probability that b is true in itself, and not from the perspective of which scenario is the most likely among the options. And that would mean that belief in revelation is not rational, even if each step in the chain is probable.
I’d be glad to hear your opinion. Since in the end you do argue that keeping the commandments is the rational choice, I assume either that you would disagree with this analysis, or that in your view “the percentages are higher” (even if only intuitively and not really something that can be quantified this way. The numbers are just meant to clarify the point). I’d be glad to hear which of those two possibilities you think is correct.
Thank you!
Answer
I disagree with the quantification. The probability that this happened by chance is negligible. The probability that He would reveal Himself is very high. In any case, it is hard to quantify, so you have to make decisions based on an overall impression. Plausibility, not probability. I would note that you could insert additional stations along the way: the probability that He exists. The probability that He created. The probability that He has a message for us. The probability that He revealed Himself in order to convey the message. The probability that we understood it correctly. The probability that it was transmitted to us properly, and so on. That way you will end up with tiny percentages.
By the way, even in a legal discussion involving two claims, where each claim has a 2-to-1 majority, we still accept the majority decision, even though the probability that both claims are correct is 4/9. Search here on the site for “the doctrinal paradox.”
Discussion on Answer
As an engineer, I’ll add:
times the probability that the engineer who built each and every component built it well, and chose the right components, and took care of component shelf life, and protections, or understood his goal correctly. Multiply that by the number of engineers involved. Then by the assemblies, and then by the connections between the assemblies. (At almost every such stage, the chance of a screw-up is not zero).
Anyway, Rabbi, do you have a good solution to the doctrinal paradox? I really struggled with it, and if I remember correctly I didn’t see a solution on the site.
It’s called the doctrinal paradox, but there isn’t really any paradox there. You have to choose whether to go by the majority on the bottom line or by the majority at each stage.
By the way, in light of what was said here, it also makes a lot of sense to go by the bottom line, because if you calculate the probability that the majority is right, you’ll find that it still comes out that way even if you do the calculation for each stage and multiply.
By the way, it would be worth doing a parallel calculation of the probability that the airplane you’re about to board will not crash: the probability that the law of gravity is correct, times the probability that all the laws of aeronautics and aerodynamics are correct, times the probability that the pilot won’t fall asleep or make a mistake, times the probability that the materials won’t fail along the way, times the probability that the principles of causality and induction that underlie all science and technology are correct. And that’s still at an extremely coarse resolution.