## Friday, October 5, 2012

### A method for probabilistic reasoning, with an application to closure and naturalism

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:

1. p is no more implausible than q
2. p is at least as plausible as q
3. e1 supports p1 at least as much as e2 supports p2.
I think that where weighing of evidence and of plausibility is involved, it is valuable to formulate arguments using things like (1)-(3) rather than formal Bayesian ways. An advantage of this for apologetics is that one's arguments can be more widely understood. An advantage of this for seeking truth is that one's judgments of the form (1)-(3) are likely to be more reliable than asking oneself "What is my prior probability for naturalism?"

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:

1. Every physical phenomenon has a physical explanation.
2. Some physical phenomenon has a nonphysical explanation.
3. 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:

1. Either (5) or (6) is true.
2. But (5) is no less likely than (6).
Moreover, unless we are certain of the Principle of Sufficient Reason, in which case we are certain that (6) is false, we will think that:
1. It might be that both (5) and (6) are true.
But (7)-(9) imply that (5) is more than 50% likely. Moreover, if we think the PSR is true, then (5) will be our only option. So in either case, (5) is more than 50% likely.

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.