It's really hard to assign probabilities in a systematic and reliable way. But I think we are fairly capable of making comparisons of the form:
- p is no more implausible than q
- p is at least as plausible as q
- e1 supports p1 at least as much as e2 supports p2.
I used this method here. I will now give another application, namely an argument that a priori we should think that naturalism and closure of the physical are less likely than not to be true.
Start by observing that at least one of the following propositions must be true:
- Every physical phenomenon has a physical explanation.
- Some physical phenomenon has a nonphysical explanation.
- Some physical phenomenon has no explanation.
Next observe that (6) is no likelier than (5). Granted, it might be somewhat counterintuitive if a physical phenomenon had a nonphysical explanation, but it is no more counterintuitive (my undergraduates by and large think: much less counterintuitive) than a physical phenomenon lacking explanation.
Now observe that (4) is surely false. For instance, very plausibly, there is no physical explanation of why there ever are any physical states, since physical explanations cite physical states, and to cite a physical state to explain why there ever are any physical states would be circular (it would be like saying: "There has existed at least one zebra, because once there was a zebra and it had offspring"). Moreover, that physical things behave according to the fundamental laws seems a physical phenomenon, but not one explainable physically.
Furthermore, the argument for the falsity of (4) did nothing to favor (6) over (5). So:
- Either (5) or (6) is true.
- But (5) is no less likely than (6).
- It might be that both (5) and (6) are true.
But (5) is incompatible with the causal closure of the physical and with naturalism.
So in the absence of further evidence, we should think that naturalism or even the causal closure of the physical is less likely to be true than not.