A little over a year ago, one of my favourite physics YouTubers, Sabine Hossenfelder, posted a video explaining why she doesn't think the fine-tuning argument is sound. To boil her argument down to what I think is the most important part, she doesn't think we can know whether the universe is fine-tuned because we can't know what the probability distribution is of the constants of nature. And the reason we don't know what the probability distribution is is because we can only observe one universe. We'd have to be able to observe many universes before we could know what the probability distribution is for the values of the constants, and only then could we know whether the universe was fine-tuned. Since we can't know whether the universe is fine-tuned or not, fine-tuning cannot be used as a premise in an argument for God or for a multiverse.
I think this is a decent argument, but it's not a satisfying refutation of fine-tuning. It plays on two other objections to fine-tuning that are pretty common, and which I'll talk about in a minute.
Notice, though, that Sabine has given us an undercutting defeater rather than a rebutting defeater for fine-tuning. In other words, she hasn't shown that the universe is not fine tuned, only that we can't empirically demonstrate that the universe is fine-tuned. It could be fine-tuned, and we just have no way of knowing it. But she is right that if we can't know whether it's fine-tuned, then we can't use fine-tuning as a premise in an argument for God or a multiverse. If we did, such an argument could still be sound (since the premises could still be true); we just couldn't know if it was sound (since we couldn't know whether the premises were true).
One problem I have with her argument is the assumption that an empirically demonstrated probability distribution is the only kind of probability we have to go on. In her dice analogy, she said that to get a probability distribution, we'd have to roll the dice many times to see the frequency with which it lands on each side. But that is not typically how people come up with the probability of things like dice. Instead, the probability is arrived at by making a ratio of 1 divided by the number of possibilities. If it's a six-sided dice, then there's a 1 in 6 chance of it landing on any given side.
The same sort of thing is true with the lottery. We say the probability of winning the lottery is one divided by the number of possible outcomes. We don't have to run the lottery a gazillion times to come up with an empirically demonstrated probability distribution.
In the case of poker, there are different kinds of probabilities we can come up with. There's the probability of any given hand, whether it's a meaningful hand or not. Then there's the probability of certain kinds of hands, like two pairs or a royal flush. Then there's the probability that you will randomly deal any worthy hand. You'd get a different probability in each of these cases, but it wouldn't be based on empirically observed frequency.
In the same way, fine-tuning arguments do not use empirically observed frequency to come up with probabilities. Instead, the probabilities are based on a ratio between the life permitting range of the contants and the possible values of the constants. One of the major objections brought against fine-tuning is that we don't know what the full range of possible values they could have is. But this is a weak argument because we can know something is highly unlikely without knowing precisely how unlikely. As Luke Barnes pointed out one time (I can't remember where), we can artifically limit the range to what is mathematically coherent. Robin Collins has a different approach to dealing with this problem, but that'll take us on a rabbit trail, so nevermind about that.
The only problem with using these kinds of probabilities (let's call them "statistical probabilities") is that it assumes the probability is evenly distributed among all the possibilities. We know that in nature, probabilities are not always distributed this way. Consider the path an electron might take when it goes through a double slit. Pretty much any spot on the wall behind it is a possibility, but the probability takes the form of a wave. If you shoot a bunch of electrons through the double slit (whether all at once or one at a time doesn't matter), a pattern will emerge that takes the form of a wave. There are peaks and valleys of probability. The wave can be described by the Schrodinger equation, so there's a law that describes the probability distribution.
In the case of the dice, the observed probability would only be evenly distributed if the dice were a perfect cube. If it has a funny shape, and we rolled it many times, the observed frequency with which it landed on each side would be different than the statistical probability would suggest.
That may be the case with the constants of nature. It may be that if we generated many universes while randomly shuffling the constants, that the frequency with which we got each combination would not be evenly distributed between all the possibilities. That is the heart of Sabine's objection to fine-tuning.
If you think about it, though, this is really just another version of the "deeper laws" objection to fine-tuning. According to the deeper laws objection, it's possible that there's some unknown law of nature that makes it to where the constants we observe in nature had to be that way or had to be very close to their current values. Well, the only way Sabine's argument could serve to undermine fine-tuning is if the probability distribution makes it to where life-permitting values happen to be more probable than life-prohibiting values. That means there has to be a hidden law that determines the uneven probability distribution. Sabine's argument fails for the same reason the "deeper laws" objection fails. It's because if there were a deeper law that made life-permitting universes more probable than life-prohibiting universes, then the law itself would be fine-tuned. So Sabine hasn't undermined fine-tuning. She's only artifically moved it back a step by suggesting the possibility that there's a deeper law that makes life-permitting universes more probable on the probability distribution curve than life-prohibiting universes.
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