Friday, February 1, 2019

God, probabilities and causal propensities

Suppose a poor and good person is forced to flip a fair and indeterministic coin in circumstances where heads means utter ruin and tails means financial redemption. If either Molinism or Thomism is true, we would expect that, even without taking into account miracles:

  1. P(H)<P(T).

After all, God is good, and so he is more likely to try to get the good outcome for the person. (Of course, there are other considerations involved, so the boost in probability in favor of tails may be small.)

The Molinist can give this story. God knows how the coin would come out in various circumstances. He is more likely to ensure the occurrence of circumstances in which the subjunctive conditionals say that tails would comes up. The Thomist, on the other hand, will say that God’s primary causation determines what effect the secondary creaturely causation has, while at the same time ensuring that the secondary causation is genuinely doing its causal job.

But given (1), how can we say that the coin is fair? Here is a possibility. The probabilities in (1) take God’s dispositions into account. But we can also look simply at the causal propensities of the coin. The causal propensities of the coin are equibalanced between heads and tails. In addition to the probabilities in (1), which take everything including God into account, we can talk of coin-grounded causal chances, which are basically determined by the ratios of strength in the causal propensities. And the coin-grounded causal chances are 1/2 for heads and 1/2 for tails. But given Molinism or Thomism, these chances are not wholly determinative of the probabilities and the frequencies in repeat experiments, since the latter need to take into account the skewing due to God’s preference for the good.

So we get two sets of probabilities: The all-things-considered probabilities P that take God into account and that yield (1) and the creatures-only-considered probabilities Pc on which:

  1. Pc(H)=Pc(T)=1/2.

Here, however, is something that I think is a little troubling about both the Molinist and Thomist lines. The creatures-only-considered probabilities are obviously close to the observed frequencies. Why? I think the Molinist and Thomist have to say this: They are close because God chooses to act in such ways that the actual frequencies are approximately proportional to the strengths of causal propensities that Pc is based on. But then the frequencies of coin toss outcomes are not directly due to the causal propensities of the coin, but only because God chooses to make the frequencies match. This doesn’t seem right and is a reason why I want to adopt neither Molinism nor Thomism but a version of mere foreknowledge.


Walter Van den Acker said...


Does your version of mere foreknowledge entail that P(H)=P(T)?

scott said...

I think I have a hazy idea of how your argument here goes. But I don't think I *exactly* get it. So here is a question/objection that might just reflect a misunderstanding on my part.

In the setup of your argument you consider a case in which someone flips a fair indeterministic coin with one direct outcome of the toss being bad for the good person and another direct outcome being very good for him. Later in the post you drop explicitly talking about that particular case and just talk in general about fair indeterministic coin flips. So one question I have is:

Q1: At the end of the post, are you still talking about particular cases in which a coin flip has one very good outcome for a virtuous person and one very bad outcome for him?

If the answer to Q1 is "no", then couldn't the Molinist/Thomist say that we have lots of observations of coin flips. But we don't have lots of observations (do we have any?) of the sort of coin flip you start the post with in which the direct consequences are so good/so bad. It seems to me that the only motivation for denying that P(H)=P(T)=1/2, given Molinism, would be observations of the outcomes of coin tosses in which there is a different balance in direct consequences of the outcomes of the toss. But since most coin flips don't have that difference in direct consequences, Molinism, given the relevant assumptions, predicts that P(H)=P(T)=1/2.

If the answer to Q1 is "yes", then couldn't the Molinist say that we don't have many observations of the relevant coin flip you've discussed. So maybe the relevant probabilities are skewed in exactly the way Molinism would predict?

Apart from all this, although our world isn't quite deterministic, it is awfully close. Or at the very least, it is awfully close when it comes to coin flips. There probably has never been an indeterministic 50/50 fair coin.

So this makes me wonder: is it that the coin flip example you are using is just a toy example that stands in for a more general or more complicated actual example that we've observed and you're talking about coin flips just for simplicity? If so, could you say a bit about how the coin flip example generalizes to a phenomenon we actually observe? Or am I just totally missing your point.

I have a couple of other questions. But they'll be pointless to ask if my first question just reflects a misunderstanding of your argument.

scott said...

Typo: Should instead have said: "It seems to me that the only motivation for *believing* that P(H)=P(T)=1/2, given Molinism, would be observations of the outcomes of coin tosses in which there is a different balance in direct consequences of the outcomes of the toss."

scott said...

One other quick thought: Consider the Molinist solution to the puzzle about Divine Hiddenness you offered a few posts ago. The rough idea was that some virtuous people are such that if they were to believe in God they would become vicious. God loves them and wants them to enjoy lives of virtue and unbelief rather than suffer lives of believe coupled with vice and opposition to God. So he sets the world up in such a way that they are able to refrain from believing in God.

Maybe your solution to the stuff about Divine Hiddenness could be applied in this case. One of the ways in which God can allow a world in which unbelief is possible for such people is by scaling back the evidence for His existence so that it is not decisive. Maybe one of the ways in which he could accomplish such scaling back is by setting the probabilities of P(H) and P(T) so that they aren't too far of from P(H)C and P(T)C.

Brandon said...

The argument for expecting (1) seems to me to be highly dubious; from a general consideration like divine goodness one can't draw any conclusion about what God would be more likely to do in a case of this sort. The assumptions you have to make start mounting up very quickly -- that God regards financial security for a good person as a matter of providential import for the administration of the whole universe, that this particular outcome is the particular kind of good that God wants for the particular good person in question, that there is no other options open to divine omnipotence that can be known by divine omniscience, that God will not compensate for it so that P(A)=P(B) if the coin is tested, that the deviation from the ideal is great enough to be distinguished from just the ordinary deviations of the real from the ideal, etc. And analogous problems seem to arise regardless of the particular kind of scenario.

Even if that's set aside, I'm not convinced that you are doing either the Thomist or the Molinist justice in your last paragraph. Neither has any reason to regard it as merely happenstance that frequencies and propensities are related, since they are both concerned with the causal disposition, in different ways. To cause a causal power and cause its effect to be other than its natural effect is precisely what we call a miracle (the strongest kind, in fact, a contranatural one), so the notion that they could be expected to diverge significantly is already ruled out by the scenario qualification, "even without taking into account miracles". The whole puzzle seems to consist of originally setting up the scenario so that we are assuming that God has made the coin such that P(H)=P(T) (within the ordinary approximation that comes from applying an ideal equality to real events) and then assuming that God as a further thing has to make P(H) and P(T) approximately equal in reality. But the former seems already to include the latter, even if it's defeasible with respect to the divine power to work miracles.

Heath White said...

Isn't any kind of divine guidance of history going to face a version of this same problem? Suppose you think the arc of the universe is long, but it bends towards justice. Still, there are going to be natural explanations (I include human free choices in "natural") about why some states prosper and others fall, why moral norms come into and go out of style, etc. What kind of explanation would explain the (hypothetical) observation that, although the long arc of the universe bends toward justice, the events in this universe *very closely* match the historical or social-scientific explanations we are able to provide?

And if you think God has simple foreknowledge, why would you think the long arc of the universe bends toward justice? (Why would you think there was any *providence* at all?)

Williams Pater said...
This comment has been removed by a blog administrator.
The Potato Philosopher said...

But can you describe what's going on in terms of substance and accident? Or are you just the run of the mill spammer?

Alexander R Pruss said...


No, because God can work miracles.


But isn't it astronomically unlikely that all the infinitely many considerations that God bears in mind when deciding how to guide the coin toss end up *always* being *exactly* a wash, so that the probabilities always come out exactly like the creature-only causal chances?


I think the problem exists for theories on which there is divine guidance of the outcomes of indeterministic events that are nonetheless fully natural. There is no problem for God guiding things by setting up initial conditions in ways that determine particular outcomes (or probabilities of outcomes) or by doing miracles in virtue of which the guided events are not fully natural. The simple foreknowledge view would allow for these two kinds of guidance.

Alexander R Pruss said...


Regarding your second paragraph, even if a thousand coins are tossed at once and they all come out heads, that need not be a miracle. It isn't what we would *expect* if nature were to have its way, but it's a *naturally possible* outcome (and no less likely than any other fully precise description of the thousand coin toss outcome). There need be nothing contranatural there.

Alexander R Pruss said...


At the end, I mean to be talking of the general case. I suspect that on Molinism or Thomism, in very, very few cases will the actual all-things-considered heads probability of the coin is 1/2.

Your challenge, then, is this: So doesn't this mean that we've just misidentified the actual chances?

I say: That makes sense if we identify the chances by high level observations. But let's move to the quantum level, which is presumably the root of all the indeterminism in the world with the possible exceptions of miracles and free will. There, we have the Born rule which moves us from the quantum state to the probability of an observation. Thus, the electron in state a|up>b|down> has probability |a|^2/(|a|^2+|b|^2) of being observed in the up state, and hence an electron in state |up>+|down> has probability exactly 1/2 of being observed in the up state. The analogue of your move would then, I think, be that the Born rule is very close to true, but only an approximate. I think this is attractive, but on general grounds of theoretical simplicity we should prefer a view on which a simple theory is true *simpliciter* rather than merely approximately true.

Again, I don't think it matters for my argument whether the creaturely and all-things-considered probabilities are close. I myself expect they are extremely close. But all I need for my argument is that we need to be able to make sense of both probabilities and their difference.

Brandon said...

On the first point, I don't see why it would be any more unlikely than anything else; indeed, since we're not omniscient, we don't really know how likely or unlikely it is given literally all possible considerations. If we're assuming financial status could be of providential significance, I don't see why the integrity of the fair coin toss is a possible consideration that is ruled out of bass.

My primary point on the miracle point was that there doesn't seem actually to be a problem here; it's not more a problem that the frequencies can diverge from the purely abstract probabilities here than that they do under any other suppositions. God is causing the causal power that is described by the abstract probabilities and whose actual effect is described by the frequencies, so the scenario involves God causing something that we have already, ex hypothesi, assumed has a tendency to approximate 50/50 frequency and then being surprised that the frequency is approximately 50/50. Of course you'd already expect them to be roughly the same; given a genuinely fair and indeterministic coin, the frequency would tend, in the long run, approximately, to be characterizable by P(A)=P(B), because the tendency and the frequency are related -- they are two different measures of the same causal capability. The fact that the freaky frequencies are possible shouldn't lead us to be surprised when the frequency is non-freaky.

Essentially what seems to be going on is that there is an assumption that the way real probability works, there is first an abstract probability and then a God-puts-his-thumb-on-the-scales probability. But it's unclear why a Molinist or a Thomist would accept such a separation; for both, the only thumb-on-the-scale is the creation of the thing characterizable by the abstract probability to begin with. To split them you have to introduce a miraculous intervention, which is ruled out by the conditions of the scenario.

It's not what I was going for with my original point, but it's worth noting that there are other miracles besides contranatural ones; a thousand heads all at once is at least a very good candidate for a preternatural miracle.

scott said...

I see. That is helpful. In that case lets compare your two hypotheses:

H1: The creaturely probability that an electron will be in the upstate equals its actual probability which equals .5

H2: The creaturely probability that an electron will be in the up state is .5 but the actual probability is a bit different.

I think the relevant question is not whether H1 is simpler simpliciter. But whether H1 is simpler relative to a particular background theory. Is H1 is simpler given mere foreknowledge? And is H1 simpler given Molinism?

Given mere foreknowledge, H1 is indeed the simpler hypothesis. It would introduce an unexplained complication to suppose that H2 is true.

But given Molinism, H2 does not cost us any relevant sort of simplicity. The Molinist already thinks God has knowledge of the outcomes of indeterministic processes prior to creation. The Molinist already thinks God used that knowledge when He was setting up creation. Given just these facts that the Molinist already accepts, there is nothing mysterious or obscure or complicated about the creaturely probability being .5 but the actual probability being a bit off. So, given Molinism, H2 is the product of the interaction of two simple laws-one about the creaturely probability of the electron being in an upstate and the other is that a perfect being has providential control of the world. Since the slightly off probability can be explained in terms of the interaction of two simple laws, it does not cost us simplicity.

If we had empirical observations that distinguished between the actual probability being .5 rather than a bit off from that, then we would have evidence against Molinism. And I grant that on other grounds Molinism isn't as simple as mere foreknowledge and that is a cost. But I'm skeptical of the idea that the truth of H2, given Molinism, yields any sort of cost in simplicity. For the very sort of features of Molinism that would lead us to predict H2 is true also, it seems to me, show that H2 isn't an unduly complicated hypothesis given Molinism.

Heath White said...

Alex, I think you are right about what kinds of divine guidance are available for the "simple foreknowledge" theorist. It just seems to me that a lot of folk ideas about divine guidance -- "everything happens for a reason", "God has a wonderful plan for your life" -- need more like the Molinist or Thomist offerings.

Alexander R Pruss said...


I think that's right. The Molinist and Thomist should simply embrace the existence of the two kinds of probabilities.

But what worries me most about the Molinist and Thomist proposals is something like the problem in the last paragraph of my post. It's a hard problem for me to get clear on, but it goes something like this. If God's choices determine the actual frequencies, then it seems that the creaturely probabilities only guide the frequencies in an occasionalist way. I.e., the reason about half of the coin tosses come out heads is that God is trying to stay close to the creaturely probabilities. Here is a poor analogy. Suppose you have the power and curse that whenever a die is tossed in your vicinity, you *have to* control it with your mind. Two of your friends want to play a die game and don't know about your superpower. You want them to have a good time, but you can't help but control their throws. So you make sure that the frequencies of throws are pretty much what the intrinsic probabilities of the dice say. Then the intrinsic die probabilities do explain the frequencies, but do so in the wrong way.

I think this is what is going on in Thomism and Molinism.

scott said...

OK. I think I understand the problem now. The reference to occasionalism helps.

Your point is this: Most of us think regular occasionalism is false. You've identified an occasionalism like feature of Molinism/Thomism. It isn't something that could easily be detached from those views. So, given that we think occasionalism is false, we should think Molinism and Thomism are false.

And then the challenge for the Molinist/Thomist is to find some relevant difference between ocassionalism and the ocassionalism-like feature of Molinism you identify that would make it not so bad to stick with Molinism but still bad to stick with regular occasionalism.

Cool argument!

Apologetics Squared said...

Molinist here!
I think I have a point that damages this argument.

You say:
"If either Molinism or Thomism is true, we would expect that, even WITHOUT TAKING INTO ACCOUNT MIRACLES [emphasis added]: 1. P(H)<P(T)."

You give your reasoning:
"The Molinist can give this story. God […] is more likely to ensure the occurrence of circumstances in which the subjunctive conditionals say that tails would comes up."

But how does God ensure the occurrence of these circumstances? Well, He needs to intervene in the natural order of our world to set up those circumstances; He needs to perform a miracle. Thus, the only way P(H)<P(T) IS when God performs a miracle.

But, obviously, if we allow for the occurrence of miracles, then on absolutely any view of God's foreknowledge, our probabilities get messed up. The point I'm making is that if we disallow miracles, then on Molinism and Simple Foreknowledge alike, the coin is going to be "left to its own devices" and turn up heads as often as it turns up tails, because disallowing miracles also disallows God's ordering of circumstances.

Wesley C. said...

Can't God set up initial conditions that would guide an indeterministic event simply on the basis of foreknowledge? Say God knows if He creates things in one way an indeterministic cause would have effect A, while there is a different world where it would create effect B in the same context, and God by His foreknowledge chooses to create a world where an indeterministic cause would have effect A rather than B.

This would be a type of domino-effect but indeterministically - God is transcendent enough to be able to make it the case that an indeterministic cause would have effect A without forcing it to become deterministic.

Alexander R Pruss said...

This would require not merely foreknowledge, but middle knowledge.

Wesley C. said...

About the probabilities of created events in relation to God's creative preferences - could we say that there are two different probabilities at work here; the intrinsic probabilities in the indeterministic fair coin itself as to what result it would produce, and the extrinsic probabilities of God creating a world where the result would be one particular outcome rather than another?

Since God creating a world to assure one specific outcome is something that transcends the indeterministic event as such - and actually works within the created order without imposing anything on the fair coin, just using one particular outcome for a specific reason - it doesn't increase the probability of the fair coin giving one specific result as such, or in a way that is intrinsic to the coin itself.