The best naturalistic alternative to theistic explanations of fine-tuning is a multiverse where there are infinitely many variations on the constants in the laws of nature, generating infinitely many universes, such that in infinitely many of them there is life–and we only observe a universe where there is life. Typical multiverse theories are committed to:
- For any situation involving a finite number of observers, stochastically independent near-duplicates of that situation are found in infinitely many universes.
I will argue that if (1) is true, then ordinary probabilistic reasoning doesn’t work. But science is based on ordinary probabilistic reasoning, so any scientific argument that leads to the typical multiverse theories is self-defeating.
The argument that if (1) is true, then ordinary probabilistic reasoning doesn’t work is based on a thought experiment. You start by observing Jones roll a fair six-sided indeterministic die, but you don’t see how the die lands. You do, however, engage in ordinary probabilistic reasoning and assign probability 1/6 to his having rolled six.
Suddenly an angel gives you a grand vision: you see a countable infinity of Joneses, each rolling a die in a near-duplicate of the situation you just observed. You notice tiny differences between the Joneses, but each of them is rolling an approximately fair indeterministic die, and you are informed that all of these situations are stochastically independent.
You still can’t see what anybody has rolled. At this point, you reasonably assign approximately the same credence to every proposition of the form <Jonesk rolls six>, and if ordinary probabilistic reasoning is to work, this credence has to be about 1/6. This is just symmetry plus your initial ordinary probabilistic reasoning about the first Jones you saw. The angel then informs you that infinitely many of the Joneses rolled sixes and infinitely many didn’t. This doesn’t surprise you and you don’t change any of your credences. You already expected this from the Law of Large Numbers.
The angel then informs you that he’s made a list of all the Joneses, where each Jones who got a six is paired with a Jones who didn’t. You think to yourself: “So what? I already knew that such a list was possible.” And you don’t change any of your credences.
Then the angel then promises to transport you to meet every pair of paired Joneses, pair by pair, in a heavenly meeting room to which the Joneses are transported. And he does it. Let’s say you meet Jonesn and Jonesm. You know that exactly one of the two rolled a six but have no information as to which one it was. If you still assign approximately 1/6 to each proposition of the form <Jonesk rolls six>, you will violate the probability calculus, since given your information, P(Jonesn)+P(Jonesm) is close to 1, while 1/6+1/6 is definitely not close to 1.
So maybe you need to change your credence that Jonesn rolled six, either to an undefined probability (perhaps an interval) or to 1/2–symmetry allows no other options. But why change your credence now upon meeting the two? As soon as you heard that the angel made the promise to introduce you to the paired Joneses, you would have been able to figure out that you’d need to change your probabilities. So, why wait? Shouldn’t you change them right away? Van Fraassen’s Reflection Principle certainly would suggest you shouldn’t wait. But if you should change your probabilities then, why not earlier? After all, the angel’s promise that he’d transport you to meet all the pairs is quite evidentially irrelevant to the probabilities that a particular one of the Joneses rolled six. So you should have changed your probabilities of a particular Jones rolling six to 1/2 or no-probability even earlier, maybe when you heard that the angel made the paired list. But again, why then? That the angel made the paired list is quite irrelevant, as long as you already knew that such a pairing was possible. So you should have changed your credence from 1/6 to 1/2 or no-probability even earlier, when you found out that there were infinitely many of each outcome, as that was enough for you to know that a pairing was possible. But that won’t do, since as soon as you learned there were infinitely many Joneses, you knew (with probability 1) that infinitely many rolled six and infinitely many didn’t.
So it seems that the only reasonable place to put the probability shift is when you find out that there are infinitely many Joneses who rolled a die. In other words, learning that there are infinitely many Joneses who rolled the die makes it impossible to assign probability 1/6 to six being rolled by the Jones you see. And so learning (1) is true undercuts ordinary probabilistic reasoning, since such reasoning requires assigning 1/6.
The challenge to anybody who thinks that you can still maintain probability 1/6 after learning there are infinitely many Joneses rolling is either to say at which point in the process you need to change your probabilities or to defend the idea that you should assign a different probability to the first Jones you happened to see from all the others. I think the first option is the somewhat less unappetizing, and if I were forced down that route, I might insist that it’s the actual meeting of the paired Joneses that changes the probabilities, pace Reflection. But this is an unhappy conclusion, I think.
A somewhat different version of this argument is given here.