Wednesday, March 23, 2016

Near certainty and open theism

Suppose that in heaven there will everyday be a choice that we can make, and that we can make it without its coming to be a habit that we choose in a particular way, so that there is some approximate independence between the choices. For definiteness, let's suppose it's a choice of what to have for breakfast. For any infinite sequence B of possible breakfasts (pancakes, nothing, waffles, waffles, egg sandwich, ...) let EB be the proposition that B is the sequence of breakfasts I will eat. Also suppose that I am in heaven. Then the probability of EB is zero or infinitesimal, for pretty much the same reason that the probability of any infinite sequence of coin tosses has zero probability.

Given classical theism, God can just tell which infinite sequence B of possible breakfasts will be had by me. But given open theism, all he has are these probabilities. So for every infinite sequence B of possible breakfasts, God assigns zero or infinitesimal probability to EB, and hence assigns a probability of one or one minus an infinitesimal to ~EB. Say that an agent is nearly certain of p provided that the agent assigns a probability of one or one minus an infinitesimal to p. Then God is nearly certain of ~EB for every B.

So far it seems to me that open theists are likely to agree with me. But now let's explore some varieties of open theism in connection with this.

1. Suppose, as some open theists (van Inwagen and Swinburne) believe, that there can be a fact of the matter about future contingents. Then one of the EB propositions is true, even though God is nearly certain that it's false. This by itself seems incompatible with perfection. To be nearly certain of a falsehood is bad for you. But God is perfectly blessed. He doesn't suffer from bad states.

2. Suppose there are no facts about future contingents. Then God is nearly certain of ~EB even though he knows that there is no fact about ~EB. It is irrational to be nearly certain of that which one knows there to be no fact about.

3. Interestingly, the above line of thought so far fits well with Alan Rhoda's variety of open theism. Rhoda thinks all claims about contingent futures with a wide-scope "will" operator are false, and EB can be seen as a conjunction of such claims. Thus, God is not only nearly certain of ~EB, but he is actually certain. But now let NB be the claim that tomorrow my breakfast will be other than the first item in B, the day after tomorrow it will be other than the second item in B, and so on. On Rhoda's view, NB is false. But the probability of NB is one or one minus an infinitesimal. So on Rhoda's view, God ends up being nearly certain of something that he also knows to be false.


Michael Gonzalez said...

I'm not sure I see the problems with any of the 3 alternatives (though I have other reasons for thinking that #1 is wrong).

1) There is a fact about it, but, given that it is impossible to know it, the right thing to do is assign the zero/infinitesimal probability to it. God is perfect in that He knows that this is the right probability to assign to all of the possible sequences and He goes ahead and assigns it. I already don't see a problem here, but I could also add that one will never ACTUALLY complete any of these sequences (you never actually get to the end of an infinite series), so there will never come a time where the right probability to assign is anything other than the zero/infinitesimal one that God always assigns.

2) (My preferred view). If we genuinely took it to be the case that there is no fact of the matter at all, then there is no sequence to discuss, and God does not assign any probability at all. It would be like assigning the probability for the number of hairs on Harry Potter's head. There is no fact of the matter, so no amount of talking about maximal hair counts on a human head, etc, has any relevance to this case. It is fiction.

3) I'm not familiar with Rhoda's view, but, in my (very limited) experience, people who say that all such statements are false mean something similar to what I'm saying in #2. Even if I actually end up eating waffles tomorrow, it is still false TODAY to say that I WILL eat waffles tomorrow. There is no fact at all about what I will eat tomorrow until tomorrow comes around. So ALL such "will" statements are false for the moment.

Alexander R Pruss said...

Regarding 1: Isn't it a bad thing to be nearly sure of a falsehood?

Regarding 2: But doesn't probability theory give us a probability here?

Michael Gonzalez said...

1) I'm not sure. I mean, if He is equally "nearly sure" of every other possibility, then He's exactly right infinitely more often than the one time He's wrong. It just seems like the perfect state to be in, given that it is an unknowable truth.

2) I suppose so, but only in the same sense that it could give us a probability on hair counts for Harry Potter's head. It's fiction on top of fiction. If one takes probabilities to be rigorous treatments of what one "should expect" under certain circumstances, then the fact that the thing in question does not exist ought to preempt any further reasoning, since what we "ought to expect" is nothing at all.

This reminds me of the old joke about set theory (that, according to set theory, if there are 6 people in a room, and 7 people leave, you need 1 person to enter the room just for it to be empty). Mathematics is carried out to full limit of the rules and structures available to it. But, in practice, some of the results may be pure nonsense.

Alexander R Pruss said...

1. Being wrong AT ALL seems incompatible with divine dignity.

2. But the kind of probability we get *here* is one that it could make sense to act on, and hence the probabilities involved are ones that it could make sense to act on. After all, as time progresses, the various E_B hypotheses get disproved one by one.

Michael Gonzalez said...

1) If someone feels that way, then perhaps your argument ought to convince them to go with a view like #2 or #3. I just think that, if God has the appropriate level of confidence (or lack thereof), then He is perfectly-minded toward the matter.

2) I'm not sure how you could act on this. As time progresses, it doesn't make the particular line any more likely, does it? It's still zero or infinitesimal, right? I think that the probability calculus (like all of math) is an abstraction. When applying it to any actual situation, the parameters of the actual situation will limit the applicability of the mathematics.

Alexander R Pruss said...

As time goes on, however, some of the lines get ruled out completely.

You can also run a similar story with respect to a continuous instant choice, say an indeterministic random spinner that has infinitely many points it could land on. Then there will actually be a future time after the spinner has settled. So there will be a point such that God will remember having assigned probability zero or infinitesimal to that point being the one the spinner would land on. So God will remember having been quite sure of something that has turned false.

William said...

Can God create an object so heavy He cannot be lift it? Can God create a scenario so unpredictable He cannot correctly predict it?

Michael Gonzalez said...


Some of the lines get ruled out, but none ever become any more likely, do they? I mean, it's still the same zero/infinitesimal probability for any given line.

I don't think there can be infinitely many points on anything... but, I do think the spinner scenario is very interesting. I still feel a very strong inclination to say "God assigned the perfect probability and level of certainty, given the circumstances, and the circumstances can't actually happen anyway (there cannot be actual infinites), so there is nothing missing from the most perfect conception of God". It is an intriguing puzzle though....


"So heavy He cannot lift it" and "so unpredictable He cannot predict it" are meaningless phrases when it comes to God. They may as well be a string of nonsense letters. They both entail exceeding a nonexistent limit (to power or to predictive ability), which is the same thing as saying "exceeding and not exceeding" which is "X and not X" (the very definition of a contradiction).

So, it is no more a limit on God's power that He cannot create a rock too heavy for Him to lift, than it is a limit on His power that He cannot "akddmnkl;2903".

William said...


Agreed. If the original posting is of a paradox, this cannot happen (using the same classic arguments as are used for the rock lifting paradox).

Unknown said...

Hi Dr. Pruss,

Suppose there is exactly one infinite series of choices which is the you one you will make, but it is indeterminate which series is that one. (Each fully-determinately specified series is not definitely not it.) Then that one series is such that God knows for sure that it is the series of choices you will make. However, it is indeterminate which series it is of which God knows this for sure.