Compossibility and Divine Limits On Possible Worlds

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Tom Morris once proposed, in response to some otherwise cogent incompossibility arguments, that God is the delimiter of possibility. What Morris had in mind, inter alia, is that the contours of broad logical possibility depend on the essential properties of God. Or, at least, he had in mind that the Anselmian is in a position to insist that contours of broad logical possibility depend on the essential properties of God. If Morris is right, we have a devastating response to incompossibility arguments. It presents no problem at all that, as a matter of fact, we have a strong modal intuition that possibly an omnipotent being performs a morally wrong action. If God delimits possiblity, then that intuition is radically wrong: worlds in which an omnipotent being performs a wrong action are not in general possible. Similarly for every intuitive, but troublesome, claim about possible worlds in incompossibility arguments. We find quickly that the divine attributes are compossible!

Cheap victory, say I. We don’t want to insist that God is the delimiter of possibility in the sense that Morris describes. The reason is that many of God’s essential properties follow from free divine actions. So, free divine actions largely determine the contours of broad logical possiblity. It is presumably entirely up to God the number and kinds of worlds in which I exist. God, after all, freely chooses to actualize me in every world in which I am actualized. In general, God freely chooses which contingent beings are created in each world; he freely chooses which contingent states of affairs obtain in each world; he freely chooses the full contingent content of broad logical space. This follows from Morris’s assumption that God delimits possiblity. But this is bad news. The tradeoff is that we have next to no clue about the contours of broad logical space. We are in a deep modal skepticism. But, of course, we are not in such deep skepticism. So, Morris’s solution must be mistaken. That’s the good news.

44 Comments

But how can you stop God from having this power? For all I know God's dispositions might be such that he wouldn't have actualised a world in which I didn't exist. Then I'd be a necessary being. Can't we just say that, well, that might be true, and then again it might not, so let's just stick with our modal intuitions.

Mike:

I think you may be running different claims together here. When Morris says God is a "delimiter of possibilities," what he means - at least in the first instance - is that God's nature delimits broadly logical possibility. Since God exists and has His essential attributes in all possible worlds, there is nothing in any possible world inconsistent with God's existence and nature.

I don't much care for this view (for reasons I've spelt out elsewhere), but I don't think it should be confused with the view that God has or exercises a power to create broadly logical modal facts.

Now it's true that Morris also holds a tough-to-explain doctrine about how all properties (including God's own nature) somehow "depend" on God.

I've never been able to make much sense out of this further claim. But it shouldn't be confused with the thesis that God chooses which properties to create (as opposed to which properties to instantiate), or that God decides what broadly logical possibilities obtain, but could have created a completely different set of properties or decided on a completely different set of broadly logical possibilities. (That sounds more like Descartes!)

God doesn't get to "decide" the contents of "possible worlds." At least not within the "Plantingian" view of possible worlds that Morris is working with. At most, God gets to decide which possible world to ("weakly," perhaps) actualize.

This further claim of Morris's should also not be confused with the claim that God's (necessarily instantiated) nature is a "delimiter of possibilities." That could be so even if Morris's other claim about the ontological dependence of all abstracta on God were false.


Of course, God actualizes every possible world "at itself." And of course, all of God's world-indexed properties are among God's essential properties. I don't see how that's inconsistent with anything I wrote about the sense in which for Morris God's nature is a "delimiter of possibilities."

The context for Morris's discussion is essential divine goodness. His example (taken, I think, from Ted Guleserian) was a 'world' in which the only sentient beings are a bunch of rabbits that suffer terribly all the time. Morris says that this isn't a genuinely possible world because (a) God necessarily exists; (b) God is essentially good; and (c) an essentially good being could not actualize a world like that.

I'm not particularly sympathetic to Morris's argument here, but it's not clear to me what your objection to it is.

On Plantinga's view, all possible worlds necessarily exist and necessarily contain whatever they contain. All world-indexed propositions are necessary truths. (Remember that a possible world is a maximal consistent state-of-affairs.)

On this view, God doesn't create possible worlds at all. (Though they, like other abstracta, may "depend" on his mind in some other sense.) Nor is it true that God could have created a different set of possible worlds. Nor is it true that any possible world could have been different.

I don't see how anything in my last two paragraphs is inconsistent with saying that "at" each possible world God actualizes that world, or that "at" each world in which Almeida exists God has created him.

So in how many worlds do Mike or Wes exist? Quite a few, I should think. In all of them, God creates Mike and/or Wes.

So suppose that w is a world in which God creates Almeida. Then, as you rightly point out, it's necessarily true that in w God creates Almeida. You say that (for Morris) this too must "delimit" possibility. Well, yes, it's incompatible with there being any possible world in which it's not true that in w God creates Almeida.

That doesn't seem like an awfully serious problem to me. It's just what you'd expect if every possible world is "accessible" from every other. Is there something significant that's "delimited out" here? Something you'd really want to say is possible? I don't see what it could be.

Changing examples, you ask us to suppose that there is only one world in which God "creates Wes." That doesn't sound possible to me. I do in fact exist, and (at least in Plantinga's setup) lots of counterfactuals are true of me. So there must be lots of possible worlds (other than the actual one) in which I exist. Let w1, w2, and w3 be three such worlds. It's a necessary truth that in w1 God creates Wes, a necessary truth that in w2 God creates Wes, and a necessary truth that in w3 God creates Wes. That, too, is part of God's essence. But note that it follows neither that Wes must exist nor that Wes can't exist. So where's the problem?

You say:


God's essence will reflect what he chooses to do and broad logical possiblity will reflect God's essence.

What do you mean by "reflect what he chooses to do?"

God's essence includes what in w1 he chooses to do, includes what in w2 he chooses to do, includes what in w3 he chooses to do. But why is that a problem? And how does it lead us to be extremely skeptical about modal intuitions?

Remember that from the fact that God chooses something in w it does not follow that God (actually) chooses it. It's God's actual choices that I say are not responsible for making possible worlds contain whatever they contain. In Plantinga's scheme, God has exhaustive knowledge of all the possible worlds "prior" to choosing to create anything.

One last thought... Within God's essence, we might distinguish between properties that are, and properties that are not, world-indexed. There might be a sense in which many of the latter "depend" on the former. But I really don't see why you'd want to put world-indexed choices first and make them the ultimate delimiters of possibility.

But even if you did, that wouldn't make God's actual choices delimiters of possibility. On the contrary! God's actual choices are limited by what's possible!

Let's see. You say above that,

Of course, God actualizes every possible world "at itself." And of course, all of God's world-indexed properties are among God's essential properties. I don't see how that's inconsistent with anything I wrote about the sense in which for Morris God's nature is a "delimiter of possibilities."

But that is not consistent with your denial here,

God doesn't get to "decide" the contents of "possible worlds."

Take a world w. It is true in w that God freely actualizes S in w. It is therefore a world indexed property that God actualized S in w. It is therefore part of the essence of God that he actualized S in w. So God's free decision to actualize S in w made it the case that God instantiates the essential property of actualizing S in w. I think it is fair to say that God decides the content of that world.

But even if you did, that wouldn't make God's actual choices delimiters of possibility. On the contrary! God's actual choices are limited by what's possible!

That's just not true. Again, God freely actualizes Almeida in w. Because God freely did that, it is part of God's essence that he actualized Almeida in w. So, it is impossible that God did not actualize Almeida in w. This last delimits possiblity.

So in how many worlds do Mike or Wes exist? Quite a few, I should think. In all of them, God creates Mike and/or Wes.

I should think so, too. But not so if Morris is right. Look, what Morris does is make this very clever move. He argues that incompossibility arguments do not show that the Anselmian God does not exist. Instead, those arguments show that our modal intuitions about worlds incompatible with an Anselmian God are badly mistaken. Incompossibility arguments are in fact arguments that should lead us to question the (even near-) factivity of strong modal intuition. So, he calls into question those like Kripke, Plantinga, and Williamson, who think modal intuition provide something close to direct knowledge of modal fact.
So I understand why you should appeal to your counterfactual knowledge (as Williamson does) and I understand why you should appeal to your modal knowledge, as Plantinga and Kripke do. I agree that we have such knowledge. The problem is that Morris, if correct, undermines such knowledge. If we had direct knowledge of (even de re) modal fact, we could quite plausibly show that there is no Anselmian God. But if God delimits broad logical possiblity in spite of our inconsistent modal intuitions (as Morris is claiming) then we obviously do not have the kind of knowledge of modal fact that Kripke and others claim we have. This is what leads to an untenable (and frankly false) modal skepticism.

Let me take on just a tiny part of this.

In response to my claim that Plantinga's (and Morris's) God does not get to decide the contents of possible worlds, you write:

Take a world w. It is true in w that God freely actualizes S in w. It is therefore a world indexed property that God actualized S in w. It is therefore part of the essence of God that he actualized S in w. So God's free decision to actualize S in w made it the case that God instantiates the essential property of actualizing S in w. I think it is fair to say that God decides the content of that world.

Suppose w is a merely possible world and S some merely possible state of affairs such that in w God actualizes S in w. Well, both w and S are included in w. But w is not actual and S does not obtain. So God has not in fact made the "free decision to actualize" either w or S. So (according to your interpretation) is there some free decision God makes in the actual world that determines whether any of the following is true?

  • w contains S.
  • In w God actualizes S.
  • In w God actualizes w.

I'd have thought not, and that is ALL I was pointing out in the sentence you take exception to.

Let's think, for a moment, in terms of propositions. Let P be any proposition. Plantinga's God does not make P have the content it has (be the proposition it is), although God may well have the power to make P true (or false).

What goes for propositions goes for states of affairs. And don't forget that a Plantinga world just is a maximal consistent state of affairs.

More about moral skepticism later... (I think you may be onto something, but it has nothing to do with world-indexed properties.)

Mike,

Just trying to get a better handle on where you're coming from: On Plantinga's framework, what do you take the difference to be between God actualizing S in the actual world and God actualizing S in some non-actual world?

That helps, I think. But given that Plantinga (unlike modal realists) thinks that the actual world is in some objective sense different from non-actual worlds--the actual world is concrete, the others aren't--mustn't there be something different or special about God actualizing S in the actual world, as compared to God actualizing S in non-actual worlds?

Mike:

You write:


Because God freely actualizes S in w he acquires--through this act--an essential property: viz. the property of having actualized S in w.

There are a couple of problems with this formulation.

  • Essential properties are not "acquired." An individual necessarily possess all its essential properties. It doesn't "acquire" them by first existing in some possible world and then doing things "in" that world.
  • Why do you say "though this act?" It's not an "act." Merely possible acts are not acts.
I know you aren't really confused about this, but the sentence quoted above makes it sound as if you think of a possible world as a "place" where God actually does something and thereby "acquires" the "essential" properties of having done it in that "place."

Here's what's true. If, in w, God actualizes S, then necessarily God has the world-indexed property of actualizing-S-in-w. So if, in w, God actualizes S, then this world-indexed property is included in God's essence.

As far as I can see, these are just logical entailments. But your formulations makes it seem that you are making some further claim. Expressions like "because" and "acquires" and "through this act" leaves the reader with that impression.

You also write:

I might have a strong but mistaken intuition that S exists in more worlds than w.

A small quibble about terminology... S is supposed to be a state of affairs. In Plantinga's ontology, any state of affairs exists in all possible worlds. I think you must mean "obtains" here.

With that emendation, your argument against seems to go something like this:

Let's say we have the intuition that S obtains in many possible worlds. But we can't conclude that this is true, because, for all we know, God's essence might include world-indexed properties such that there is only one possible world in which he (strongly or weakly) actualizes S. That lands us in extreme modal skepticism.

If that is the argument, I don't see why Morris can't reply as follows.

Trust your original intuition, and conclude that God's essence does NOT include the world-indexed properties you are worrying about.

To continue (on behalf of Morris):

The only case in which we need to rule out the possibility of a state of affairs S on the ground that it's incompatible with God's nature is a case in which WE HAVE SOME REASON TO THINK that God's nature is incompatible with the actualization of S. (Think of God's essential goodness and the 'possibility' of a 'world' in which the only sentient creatures are miserable rabbits.)

Thanks, that's very helpful.

My general reaction to your argument is that I don't really have super-duper lots of confidence about what worlds there are anyways, independent of God delimiting them. If we keep things relatively straightforward, sure; I could've had corn flakes rather than toast this morning (even here there might be worries about determinism, I suppose). But if I'm thinking about (say) whether beings like us could exist in worlds governed by laws radically different from the actual ones, I have no idea.

Mike: World-indexed properties are acquired, and obviously so. Here is a world-indexed property.

1. Almeida-says-"hi"-in-@-at-2pm

I'm free in @. I can at 2pm say "hi" or not do so. If I do say hi, then I have the essential property of saying "hi"-in-@-at-2pm. If I don't say hi at 2pm, I don't have that essential property.

Alan: Hi Mike. I don't see how your-saying-"hi"-in-@-at-2pm can be both an essential property of yours and a property that you acquire. Granting S5, you have that property in every possible world in which you exist, so it's essential to you. But then how can it be up to you whether you have that property?

I think you're conflating '@' used as a variable denoting whatever possible world happens to be the actual one and '@' used as a name designating a particular world as the actual one. If you have free will, then it is in some respects up to you which world is @ (used here as a variable). World-indexed properties, however, name a particular world, and you don't have any say about those.

For simplicity's sake, suppose that there are only two possible worlds in which you exist, w1 and w2. And suppose these have the same history up until 2pm. At w1 you say "hi" and at w2 you don't. Well, then, it is up to you at 2pm whether w1 or w2 is the actual world. But it is not up to you whether you say "hi" at w1 or whether you refrain from saying "hi" at w2.

Mike:

It seems to me that we need to get the mechanics of Plantinga's possible worlds ontology straight before we can use it to talk about the main problem (which I do think is a very interesting one).

You say:


World-indexed properties are acquired, and obviously so.

You then explain:


I'm free in @. I can at 2pm say "hi" or not do so. If I do say hi, then I have the essential property of saying "hi"-in-@-at-2pm. If I don't say hi at 2pm, I don't have that essential property.

This makes it sound as if you think you get to decide what some of your essential properties are. You can't mean that!

Looking closely at your argument, it seems to me that it contains a subtle mistake. Let me explain.

It's true that you can say "hi," and that you thereby acquire the property of "saying-'hi'-at-2pm." But it is NOT true that you thereby acquire the property of "saying-'hi'-in-@-at-2pm." For any world w, either you have the property of saying "hi" in w, or you don't. You don't get to decide whether you have this property in a given world.

So what is up to you? Whether you say "hi" at 2pm, of course. Whether you do so makes a difference to which world is actual. But it makes no difference to what any world contains.

So where does that leave @? If "@" is a rigid designator for the world that happens to be actual, then if you say "hi" at 2pm, it follows that it's true in @ that you say "hi" at 2pm. But you do NOT thereby acquire any world-indexed property.

Look at it this way. Before you exist or do a thing, every world, including @, is completely specified down to the smallest detail. You can't make the slightest difference to what exists or happens or obtains "in" any world. What you can do do is make a difference to which world is actual.

...........

Sorry about misunderstanding your use of "S." I assumed it to be a state of affairs because we were both speaking about actualizing S. States of affairs are actualized. In Plantinga's lingo, persons are created, not actualized.

Mike:

Sorry to be so persistent. But here's another crack at it.

You say:


It is obviously true that I freely decide whether I say hi at 2pm in @ or not.

Really?

Either you're using "@" as a rigid designator for a Plantingian world (a maximal consistent state of affairs), or you're not.

If you are, then the quoted sentence is simply false. You do not get to decide what any maximal consistent state of affairs contains. Nobody - not even God - gets to decide that.

What you do get to decide is whether to say "hi" at 2pm, and that in turn makes a difference to which world is actual. Surely we can agree about that much?

If, on the other hand, you're using "@" in some other way (perhaps as shorthand for "whichever world happens to be actual"), then your statements about @ have nothing whatever to do with world-indexed properties.

If there is a real worry about extreme modal skepticism popping out of Morris's claim that God's nature is a "delimiter of possibilities," it has nothing to do with world-indexed properties.

Mike:

That's all well understood by both of us. But it's entirely consistent with the statement of mine that you quoted.

When we "actualize the rest via our free actions," we are helping to decide which world is actual. We are not helping to decide what's true "in" any particular world, or what the make-up of any particular world is.

Here's another way to say the same thing. When we "actualize the rest via our free actions," we are helping to decide which maximal consistent state of affairs obtains, and not what any particular maximal consistent state of affairs includes.

This too is just basic Plantinga.

I still think you need to face this dilemma. Either you're using "@" as a rigid designator for a particular maximal consistent state of affairs, or you're not. If you are, then it's simply not true that you get to decide what's true in @. If you aren't, then then your statements about what's true in @ are probably just statements about what's true in whatever world happens to be actual. In that case, no particular world is "indexed," and your statements about what's true in @ have nothing to do with world-indexed properties.

Mike,

Interesting discussion. I take it that your main point is that given Anselmian/Morrisian theism, what is possible depends in part on what God freely does in various worlds. You say, for example, "It is presumably entirely up to God the number and kinds of worlds in which I exist." But then this leads to unwanted modal skepticism.

I'm having trouble seeing why the number of worlds in which I exist would be up to God. Consider the galaxy G of worlds in which the counterfactuals describing who God would freely create in various circumstances are what they actually are. Presumably it is up to God which worlds are G-worlds if it is up to God which of his counter-factuals are true. Now I don't have much by way of modal intuitions as to the number and kinds of worlds within G in which I exist. But what does this have to do with the number of worlds in which I exist? Presumably, it is possible for God to have different counterfactuals, in which case 'G' would label different worlds. God may have control over which worlds 'G' labels, but I don't see how God would have control over the number and kinds of worlds in which I exist. After all, it seems to be logically compatible with an Anselmian God that there be infinitely many galaxies of worlds--galaxies in which God had different counter-factuals--in which I exist. The only delimiting factor I can imagine playing a role here is God's existence or moral perfection, not his choices in various worlds (except that those choices be limited by God's moral perfection). But I don't even think an Anselmian theist is committed to saying that God's moral perfection delimits any possibilities. See side note below.

(
Side note: if

(C) Every non-necessary situation--other than spontaneous actions--would always have a cause if actual.

and

(I) Any finite measure of greatness exemplified would be a non-necessary situation (because it could be surpassed instead)

Then I think we can run an argument for an Anselmian Being (with a few auxiliary principles, like no self-causation...). From there, it would be impossible for the only sentient beings to be suffering rabbits (assuming that a maximally great being would be sentient). Presumably, it would also be impossible for there to be rabbits suffering pointlessly.

However, if (C) is false, then even if an Anselmian God existed, it seems to me that it would still be possible for there to be pointless rabbit suffering. For if (C) is false, then a contingent situation in which rabbits are suffering pointlessly could obtain wholly uncaused. I don't see how even a maximally powerful being could prevent that.
)

My main point is that you seem to be drawing out modal skepticism from the idea that "God delimits possibility," but I'm having trouble understanding what you mean by that idea.

This is where the discussion between you and Wes comes in. Well, Wes is surely right that the contents of a world--the sofas that are entailed by a maximal sofa--are in no way dependent upon anyone's choices in a world. But you seem to be after another kind of dependence, perhaps having to do with which sofas are actualized, or which world-indexed properties one exemplifies. I'm having trouble getting clear what it is exactly.

Do you think it's up to God whether there are the "galaxies" of worlds that there are? If not, then why should "God delimits possibility" pose a problem for modal intuitions?

Mike:

4 does not follow from 3.

If, in a world w, S freely performs A, then it's eternally and necessarily true - not that S performs A, of course - but that S performs A in w. It follows straightaway that "performing A in w" cannot be an "acquired" property.

To see this, you need to take fully into account what a Plantinga world is. A world is a maximal consistent state of affairs. States of affairs are abstract entitles. As such, they are eternal and necessarily existent. A world is not built up piecemeal - though it may, of course, be actualized one bit at a time.

Prior to creating anything, God "sees" all worlds. Each world is a complete way in which things might go. What has to be decided is which world is to be actualized - not what any world contains.

I can't tell what your last paragraph here comes to, because you don't say how you're using the expression, "@." If it's a name of a maximal consistent state of affairs, then the claim made in this paragraph is false.

What does Morris mean when he says that God is a "delimter of possibilities?"

Here's what he does not mean: "God performs some act that makes it the case that certain things are impossible in the broadly logical sense."

Here's what he does mean. "God exists and has certain essential properties in all possible worlds. So anything that is incompatible with God's existing and possessing those properties is impossible."

It's hard to see how anyone could disagree with Morris's actual claim. Whether it leads to some sort of extreme modal skepticism is an interesting question, however.

Here's a worry that somebody might have. Let n be an extremely large natural number. It seems intuitively plausible to say that there could have been n atoms.

But now suppose our knowledge of God's essence is limited in the following way. For all we know, God might have an essential aversion to there being n atoms. Then, for all we know, it couldn't have been the case that there were n atoms.

Do these reflections undermine the intuition that there could have been n atoms?

I'd have thought not. If the original intuition is reasonably strong, then the right conclusion to draw is that God does not have an essential aversion to there being n atoms.

Mike:

You write:

Some of his essential properties depend on what he freely does.

So are you saying that God could have had essential properties other than the ones he actually has?!

4 follows from 3 almost trivially. So, finally, that's where the discussion ends

I'm with Wes on this one--it doesn't follow at all, as far as I can tell.

Let's go back to 3 and 4:


3. It is true in w that S freely acquired the property of having performed A. (From 1,2)
4. It is true in w that S freely acquired the property of having performed A in w. (from 3)

Let's say that in possible world w* I refrain from performing A. Then it is true in possible world w* that I freely acquire the property of having refrained from performing A.

But I still have (in w*) both the properties of having performed A in w and of having refrained from performed A in w*. I don't freely acquire either of those world-indexed properties through my choice to refrain from performing A.

Mike: let me try to put this in non-possible-world terms first, then translate back into possible-world and world-indexed-property talk.

By freely performing the action A, S acquires the property of having freely performed A. But he doesn't acquire the property of its being possible for him to have freely performed A, nor does he acquire the property of its being possible for him to have freely refrained from performing A. Both of those properties (that it's possible for him to perform A and that it's possible for him to refrain from doing so) already obtained independently of his choice--it's through his choice that one of those possibilities was actualized.

To try to put this back in possible-worlds talk: by freely performing A, S acquires the property of having performed A, and hence he helps makes w the actual world, because w is a possible world in which S freely performs A. But he doesn't make it the case that there is a possible world in which freely performs S and one in which he freely refrains from performing A. So he doesn't acquire the world-indexed properties either of having performed A in w or of having refrained from performed A in w*. Instead, he makes w actual and thereby acquires the property of having performed A.

Mike:

What do you mean when you say that S "acquires" a property? Does it entail that there is a time t at which S lacks that property, and a later time t at at which S possesses it?

Mike:

Thanks. This explains my difficulty in understanding your move from 3 to 4 in:

1. There is a world w in which person S freely performs an action A. Assumption

2. It is true in w that S freely performs A.
(from 1).

3. It is true in w that S freely acquired the property of having performed A. (From 1,2)

4. It is true in w that S freely acquired the property of having performed A in w. (from 3)

5. It is true in w that S freely acquired an essential property. (from 4)

In no world is there a time at which anything lacks one of it's world-indexed properties and later acquires it. I'm sure you will agree that on that reading of "acquires," 4 does not follow from 3.

But you say this is not what you mean by "acquiring a property" in 3, 4, and 6. Instead, you mean

... that having the property depends on S performing some free action A in some world or other. In performing that free action he acquires the property.

I don't know precisely what kind of dependence relation you have in mind. Your "omnitemporality" illustration is suggestive. But I'm still not quite sure what the relation is supposed to be. Is it a logical entailment relation? Or a truth-making relation? A relation of supervienence? Or do you have something else in mind?

Once that's settled, we need to replace all occurrences of "freely acquired" with a suitable reference to the proper dependence relation. How will 3, 4, and 5 read when that's done? And how will "freely" come into it?

Isn't this subject to a great-pumpkin objection?

Can someone please explain to me what it would mean to say that God exists in all possible worlds when God does not delimit the number of possible worlds? For example, is there not a possible world in which God does not exist (e.g. a possible world with no-maximality)? Or a possible world in which unjustified evil exists? These meet the criteria for possibility, right? But if so, it does not seem that God could exist in these possible worlds. In other words, if God does not delimit possibility, then is there not a possible world w, in which, given God’s essential properties, God could not exist? If this is so, what does it mean to say God exists in all possible worlds, given that he does not delimit possibility? What do those theists (is Plantinga one?) who disagree with Morris about God delimiting possibility have to say about this issue?

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