This argument is an intuition-pump. I don’t know if it can be made rigorous.
Start with some observations. Let Q0 be the nomic parameters of our universe—the exact values of all the constants in the laws of nature. To avoid serious problems with higher infinities and probability, I will make a technical assumption, which I will assume to be neutral be theism and atheism:
- There are at most countably many universes.
Now:
For no non-zero countable cardinality n does theism have a bias against the hypothesis that there are countable many universes with cardinality at least n.
The parameters Q0 are life-permitting.
For any fixed countable cardinality n of universes, theism has a significant bias in favor of distributions of parameters that include more universes with life-permitting parameters.
If (2) and (3), then for any countable cardinality n of universes, theism has a significant bias in favor of at least one of them having the parameters given by Q0.
Thus, theism has a bias in favor of a universe with Q0.
Thus, the obtaining of Q0 is evidence for theism.
Some thoughts on the premises.
Regarding 1: Theism actually seems to have a bias in favor of the hypothesis that there are at least n universes. After all, theism has a bias in favor of the hypothesis that there is at least one universe: that there is a universe is quite surprising on atheism, but not so on theism, given that God is by definition perfectly good, and the good tends to spread. But the same reasoning suggests a bias on theism in favor of larger numbers of universes.
Regarding 2: Obvious.
Regarding 3: I think the main way to challenge (3) is to say that God would only care about having one universe with life-permitting parameters, and wouldn’t care about having a larger number. But I think this is implausible given that the good tends to spread. In fact, it seems likely that God would create only universes with life-permitting parameters, which would induce a strong bias in favor of such parameters.
Regarding 4: This is a very substantial assumption. It won’t hold for every set of exact parameters, because some sets of parameters might be life-permitting but would be likely to generate a universe that is really unfortunate in some regard. I don’t think the parameters Q0 behind our universe are like that, but this is a matter of dispute, and intersects with the problem of evil. Note also that it is important for the “significant” in (4) that even if n is (countably) infinite, the probability getting exactly Q0 on atheism is low (in fact, infinitesimal).
The big technical difficulty, which makes me doubtful that the argument can be made rigorous, are the infinities involved.
3 comments:
Won't this depend on how you do anthropic reasoning? If you adopt the self-sampling assumption, then you'll think that, though more universes on theism makes it likelier our exact laws would exist, it doesn't raise the probability that they'd be our laws in particular? Seems that would hold on any view of anthropics other than compartmentalized conditionalization.
I am just ignoring the anthropic stuff here, and only using standard conditionalization. My justification is that there is no method of handling self-locating evidence that doesn't have some serious problems. So I am just ignoring the self-locating part of the evidence. Ignoring which also has some serious problems, of course. :-) But as I said, the argument is just an intuition pump.
You're right that the argument doesn't work on self-sampling. But I think it works on self-indication and compartmentalized conditionalization. That's two out of three. :-)
Yes, I think that's right. I think one can make a very similar argument (one I've made elsewhere https://benthams.substack.com/p/the-best-argument-for-god and is the argument for theism that moves me the most). If either compartmentalized conditionalization or SIA is true, theories that say there are more worlds are better. God is good, so he'd make a bunch of worlds, because worlds are a good sort of thing. Thus, your existence, on those views (especially SIA, which I think is more plausible), gives you strong evidence some big cardinality of infinity worth of people exist, which favors theism.
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