Friday, August 15, 2008

More on Molinism and stochastic processes

In earlier posts and comments, here and on prosblogion, Mike Almeida and I have been discussing problems with Molinism and stochastic processes.

Here's a way to put a variant of the problem (this may well duplicate some of Mike's ideas). Let C be the following set of circumstances: a fair indeterministic coin is tossed, with a machine set up so that if the coin landed heads, then laws of nature specify that the machine would cause all creatures in existence suffer excruciating and undeserved pain for eternity.

We can now do two different calculations. Let G be the claim that omnipotent, omniscient and perfectly good God necessarily exists. On the one hand, P(Heads|C)=1/2 (because the coin is fair). On the other hand, P(Heads|C and G) is less than 1/2. For such a God would be unlikely to allow C to be actualized unless he knew that the counterfactual C→tails is true. He might of course be planning to miraculously intervene after the machine activates, and so P(Heads|C and G) is non-zero but it seems to be part of divine providential goodness to avoid having to intervene miraculously, but surely P(Heads|C and G) is less than 1/2.

But now we actually have a contradiction. For the probabilities in question seem to be objective probabilities, and when we're talking of objective probabilities, P(G)=1, since G is a necessary truth. Hence, 1/2 > P(Heads|C and G)=P(Heads|C)=1/2. In other words, 1/2 > 1/2, which is absurd.

Therefore, we must reject one of the two probability claims. In particular, it seems, we need to reject P(Heads|C)=1/2. But this means that given theism, we cannot consider the probabilities that come from empirical study to be the genuine objective probabilities governing the events. Granted, in the case above, we were talking of a catastrophic case. But presumably even if the consequences of heads are somewhat bad, P(Heads|C and G) will still be somewhat less than 1/2.

12 comments:

Brandon said...

It's an interesting argument, but I'm not really sure it shows anything but that it is highly improbable that God has set the laws of nature up so that if a fair coin lands heads a machine will cause all creatures in existence to suffer excruciating and undeserved pain for eternity. More precisely, the contradiction arises from assuming, in C, that God has set up events so that there's really a 50% probability of all creatures suffering endless undeserved pain; and then from concluding, from G, that God would not have set events up so that there's really a 50% probability of all creatures suffering endless and undeserved pain. Am I missing something?

Mike Almeida said...

Alex,

Why not say that the chances at t that the coin comes up heads is 1/2. That seems like it has to be true, assuming that there are genuine chances and the coin is fair. What you know is that the chances will be different at t+n. But there is no contradiction in this. Chances do vary over time: i.e., chance is time dependent. God has so chosen a coin that it's chances at t+n of landing heads is 1 and it's chances at t of landing heads is .5.

Alexander R Pruss said...

Mike,

I don't know what you mean by saying that the chance of E at t is p. Do you mean that the conditional probability of E given all of history up to and including t is p? (That's particularly tricky in cases where the past might contain a prophecy.)

Heath White said...

It seems to me that what follows from the assumption of Molinism is that the fairness or otherwise of a coin is not an intrinsic property of the coin. There is only a un/fair coin-in-C.

Think of it this way. You hook the coin up to the machine, flip it 100 times, and get all tails. You conclude it is not a fair coin. You unhook it...now God doesn't care how it lands, so you get 50 tails. Whether the coin lands fair depends on the circumstances. It is not a big step to conclude that whether the coin *is* fair depends on circumstances.

(How secure this inference is depends on the interpretation of probability. For frequentists it's deductive. For propensity theorists and classical theorists, it depends on what counts as a "propensity" and a "possibility" respectively.)

Now, since this never ever happens, is that an argument against Molinism?

Alexander R Pruss said...

Heath:

I think you may be right about the intrinsicness.

I wouldn't say that this never happens. One would expect that probabilities would be affected whenever there is a significant difference in the values of the prospective outcomes.

Mike Almeida said...

We'd probably want to say that chance is a dispositional property, possessed in virtue of cetain (intrinsic) categorical properties. In any case, Mellor argues along this lines.

I don't know what you mean by saying that the chance of E at t is p. Do you mean that the conditional probability of E given all of history up to and including t is p?

Yes, that's it. The history up to t determne what the chances are at t. Something like this has to be included in a right notion of chance, since the chances of, say, my finding my way out of a labyrinth by noon, definitely change as I start moving around.

But there's another approach to the problem you describe. I'm inclined to say that P(H/C) gives the chances of H. And, other things equal, my credence for H should mirror the chances of H. So C(H/C) = P(H/C)= 1/2. But when I learn that the Alpha Centurians A have taken over the world and, given their nature, are intent on mind-bending coin tosses to our disadvantage, my credence changes to (say) C(H/C & A) > .5. Whether God is manipulating the coins or the AC's are doing it, that information goes into my credence for tossing heads, not into the propensity for tossing heads.

Alexander R Pruss said...

A part of the history of the toss would be God's deciding to permit the toss, and that would in part be what we are conditioning on.

However, now we have a problem. Is the subjunctive C→heads a part of what we are conditioning on? One reason to think it should be a part of what we're conditioning on is that itseems to be a part of the explanatory history of the toss. God allows the toss because of that conditional.

Mike Almeida said...

If we came to know what CCF's God has chosen in directing chancy events, then of course we would include them in our credence for those events. From God's point of view, the chance of the coin coming up tails is 1 or 0; that's certainly the Molinist position. God is not taking chances. If we had God's information, we wouldn't be taking chances either. P(H/C & C -> Tails) = 0. That's compatible with P(H/C) > 0. That sounds right, no? We'd do the same thing if we got such information from a time traveler or an Alpha Centurian.

normajean said...

Speaking of Molinism, William Lane Craig has made some fine comments about you on his Reasonable Faith broadcast. Thought you would appreciate that.

http://www.reasonablefaith.org/site/PageServer?pagename=podcasting_main#rf

Click Blackwell Companion link and forward to 8:01 and go until 9:51

Enigman said...

Why not just say that P(C|G) = 0?

Alexander R Pruss said...

Because God might allow C, and then miraculously prevent the bad consequences. The chance of God's opting for that may be low, but it's non-zero.

Enigman said...

If it is possible for God to create such a machine, which either does something that could have been done more straightforwardly (without the coin toss) or else does nothing because God intervenes to stop it, then it seems (to me) that it is possible for God to create either pointlessly (which seems to me to violate PSR) since childishly (as I regard actually creating something just so that it can be overcome miraculously), which seems impossible.