God, purposes, and the misuse of probabilities 
Massimo Pigliucci and Mohan Matthen have blogged recently about probabilistic arguments against naturalism and evolution. Recent arguments by Alvin Plantinga and Thomas Nagel begin by considering how likely some development is given only natural causes and evolutionary processes: How likely are we to know anything? How likely was it that there would come to be conscious life? The answer is supposed to be unlikely and that these would be utterly to be expected if there were a God (Plantinga) or if there were purposive, teleological laws (Nagel). From this, it is concluded that there is a God or that there are teleological laws.*

Reasoning like this seems to misuse probabilities in at least two respects. I'll focus on the theological version.

First: It is unclear to me why the existence of God makes sentient knowers more likely than the absence of God does. Of course, the omnipotence of God entails that there will be sentient knowers if She wants there to be, but why suppose that She does? There does not seem to me to be any obvious probability metric over the space of possible gods, and I doubt that the space is well-defined. Theologians have often argued that there is only one possible god, namely God, but their arguments also typically entail that She exists. The probabilistic argument is superfluous at best if it relies on such an apodictic rationalist argument to establish one of its premises!

Second: Even accepting that sentient knowers are more likely given God than not, this only shows that the existence of sentient knowers should increase our credence in God. Whether we should think that She is likely to exist at the end of the exercise depends on the prior probability. There are two ways this could go. (A) Suppose the prior is objective. If the principle of indifference that is doing the work, so that the prior for "God exists" is .5, then we need to have winnowed down the space of alternatives to include only atheism and this specific flavour of monotheism. Again, the argument seems to be falling back on rationalist arguments about the space of possible gods. (B) So suppose instead that the prior is subjective. Then the conclusion is just that someone who believes that God is tolerably likely should, after looking around, be rather more confident. This will not and rationally should not convince those who start with strong atheist inclinations. Those who believe in God place a high prior probability on Her existence, and they might just as well have report that to begin with. The fideism of subjective probability makes the argument irrelevant.

These concerns apply to teleological laws, too. There is even more uncertainty about what would or wouldn't be likely given teleological laws and what the prior probabilities should be, because Nagel's proposal is dismally obscure. At least with God, there is a long philosophical history of worrying over what She might be like.


* Now that I've written it out in this form, it looks rather like the No-Miracles Argument for scientific realism. Naturally I think there are problems with base rates. A quick search also reveals that I've responded to Mohan blogging about Plantinga and Nagel before.

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