I’ve thought of a simpler way of making the argument from my last post. Suppose Jack is the defendant, and the lawyer for the prosecution shares with the jury that Jack carries a knife around with him. In fact, as the lawyer for the prosecution well knows, Jack carries a butter knife around with him, but the lawyer chooses not to share this detail. Obviously the jury are going to be misled. It’s not that they’ve been told a lie: it’s true that Jack carries a knife around with him. The lawyer has misled the jury by giving them a less ‘filled in’ account of the evidence than is available.
This example (modified from an example due to Paul Draper) reveals a very important principle in probabilistic reasoning, a principle I would define as follows:
The Requirement of Total Evidence (RTE) – Never bypass the evidential implications of specific evidence in order to focus on weaker evidence.
(That ‘Jack goes around with a knife’ is weaker evidence than ‘Jack goes around with a butter knife’ because the latter entails the former but not vice versa).
It is this principle that is violated by those inferring a multiverse from the fine-tuning. The evidence that our universe is fine-tuned is striking to us because it raises the probability of something god-ish: simulation hypothesis, Nagel-style teleological laws, cosmopsychism, etc (I would not go for the omni-God, as the existence of suffering is powerful evidence against the omni-God). However, our culture tells us that god-ish hypotheses are ridiculous. And so, in general, those scientists who do find something compelling about fine-tuning bypass the god-ish evidential implications of ‘our universe is fine-tuned’ in order to focus on the weaker evidence that ‘a universe is fine-tuned.’ This is in violation of RTE and hence is a fallacious inference.
It’s exactly the same error we find in the classic Inverse Gambler’s Fallacy (IGF) case:
You walk into a casino and see someone roll all sixes with twenty dice. You infer that there must be lots of people playing in the casino tonight, as it’s more likely that someone will make such an incredible roll if there are many players.
The problem in this case is that the evidential implications of the specific evidence that ‘this roll was a double six’ (such an extraordinary roll raises the probability that the dice are loaded) are bypassed in order to assess the probability of the weaker evidence that ‘someone the casino rolled all sixes with twenty dice.’
It is commonly pointed out that there is a selection effect in the fine-tuning case which isn’t present in the casino case: we couldn’t have observed a universe that wasn’t life-conducive but we could have observed someone making a terrible roll. In my last post, I sketched the Jane analogy which has a selection effect but is still fallacious. However, a more direct response is to point out that the presence of absence of a selection effect has no relevance to the explanation of why the casino example is fallacious (which is that the reasoner bypasses specific evidence to focus on weaker evidence) and hence does nothing to block the multiverse inference being fallacious in the same way (as this inference also involves bypassing specific evidence to focus on weaker evidence).
If the multiverse theorist wants to resist this argument, they not only have to deal with the Jane analogy from my last post, but they also need to explain why the inference to the multiverse is exempt from RTE. I’ve seen some attempts at the former (although none I’m as yet convinced by) but I haven’t seen any attempts at the latter.
[I should credit a tweet from Thomas Metcalf with making me think that maybe we can simply modify our understanding of RTE rather than qualifying it, although I don’t quite agree with his way of doing that, which I hope to talk about in future work. This has been a ‘Eureka’ moment in my thinking on this. In his original article on this, White appealed to RTE, but I was mistakenly thinking it entailed we always have to focus on the strongest evidence we have, which is obviously false, and so I thought White must have got the theoretical underpinnings of his argument wrong (in a postscript to a re-published version of the paper, White gave up on RTE and offered instead a new theoretical justification, which I don’t agree with). But now I see that we can make the argument in terms of RTE, so long as we define it as I do above. Finally, for those following these Twitter discussions, I should also confess that I haven’t yet got around to reading Quentin Ruyant’s second response to me.]