Modal Theistic Arguments (1993)
[This article was originally published as "Modal Theistic Arguments", Sophia, 32, 2, July 1993, pp.17-24]
A modal theistic argument is a proof of the existence of God which makes use of the premise that God is a being who exists in every possible world. Such arguments have been advanced by Alvin Plantinga, and more recently by Brian Leftow. In this paper, I provide a general ground for objecting to all modal theistic arguments. Moreover, I suggest that there is something important about recent conceptions of modality which can be learned from these arguments.
In On The Plurality Of Worlds, David Lewis defends the thesis that our world (= universe) is but one world among many. These worlds are all distributions of properties over connected spacetime points. An object possesses a property necessarily iff all of the counterparts of that object in all of the worlds possess the property. Sometimes, when we make a modal statement, we may mean only to quantify over some of the worlds: in that case, it will be true to say that an object possesses a property necessarily iff all of the counterparts of that object in all of the worlds over which we quantify possess the property. However, when we give our account of the layout of logical space, we mean to describe absolutely all the worlds that there are.
Lewis' modal realism is controversial. Perhaps we should prefer ersatz modal realism, which takes possible worlds to be abstract entities which represent ways that worlds might have been. Or again, perhaps we should prefer combinatorialism, according to which possible worlds are maximal combinations of entities which are formed by recombination of the primitive elements of the actual world. Or yet again, perhaps we should prefer modal fictionalism, according to which all modal claims belong to a gigantic fiction about alternative possible worlds. However, whichever of these accounts we choose, we shall still be committed to the possible worlds analysis of necessity and possibility. Moreover, from the standpoint of that analysis, it will make little difference if we choose to speak with the modal realist. (Of course, it will make some difference. The combinatorialist and the linguistic ersatzist offer fewer possibilities than does the modal realist. However, this difference is not relevant to our present concerns.) So the question which I shall ask is this: How should the theist who holds that God is a being who exists in all possible worlds modify the account of the nature of logical space which Lewis defends?
Since the theist wishes to hold that God exists in every possible world, the first difference between his account and Lewis' is that there must be a counterpart to God in every one of the worlds. This is no restricted quantification; when the theists say that God exists in every possible world, he means what he says unrestrictedly. Moreover, when the theist says that there must be a counterpart to God in every one of the worlds, he means that there must be exactly one counterpart in each of the worlds.
Of course, the theist does not merely think that God is some necessary being or other. If Lewis adopts a Platonistic account of numbers, then he is already committed to the view that there are countless necessary beings which have unique counterparts in all of the worlds. But, whatever numbers can and cannot be, one assumes that none of them is God. I shall suppose that the theist is committed to the view that all of the following are necessary properties of God: omnipotence, omniscience, omnigoodness, existing eternally, creating the world ex nihilo. (Perhaps there are other properties which should be added to this list; perhaps some should be omitted. However, this list certainly serves to capture the sort of view which I wish to investigate.) Thus, the theist holds that, in each one of the worlds, God has each of these properties--i.e. in each one of the worlds, the counterpart of God is omnipotent, omnisicent, omnigood, eternal, and the creator of that world ex nihilo.
There are questions about how God is tied to the world. It seems wrong to say that he exists in a particular part of spacetime, for why should He exist here rather than there? Perhaps, then, He exists everywhere. Or perhaps he exists outside of spacetime, yet is tied to a given world by the quasi-causal relation of being its creator. I do not know; I shall suppose that theists can make up their own minds about this question.
Not all of Lewis' worlds are compatible with the existence of God. In particular, there are Lewis worlds which contain vast amount of unmitigated evil. No omnipotent, omniscient and omnigood being could permit such worlds to exist (far less create them). However, the loss of these worlds does not mean that we lose very many of the modal judgements which we would ordinarily be prepared to accept. More precisely: the only modal judgements which we shall need to revise are those which neglected the (purported) fact that every world must contain an omnipotent, omnisicent, omnigood, eternal being which created that world ex nihilo. This represents a slight complication in the theory, but not one which is so great that it renders the theory unacceptable. (A combinatorialist could think of the hypothesis as a constraint on the principle of recombination: otherwise kosher combinations of elements may be made impossible simply because they are incompatible with the existence of God.)
That is more or less the full story. The underlying logic is of course the counterpart-theoretic version of S5. Moreover, the principles which Lewis uses to gain modal knowledge--recombination, imagination, etc.--are all available to the theistic modal realist, albeit with suitable modifications. Indeed, whatever benefits Lewis claims for his theory, the theistic modal realist can also claim. And if ersatzism or combinatorialism or fictionalism is to be preferred, then the theistic modalist can comfortably board those trains as well.
Given the theistic account of logical space just sketched, it is easy to explain why I think that there can be no modal argument for the existence of God.
For the sake of argument, I shall suppose that there are just two different accounts of the nature of logical space between which we must choose--the account offered by Lewis, and the account offered by the theist. Of course, this is an absurd simplification. Following Hume's lead, we can construct infinitely many alternative accounts of logical space, with different types of entities playing the role which our theist assigns to his God. Moreover, I think that we can argue that there are no good grounds to prefer any of these accounts above all of the others. But, for now, let us ignore these kinds of considerations.
How are we to choose between Lewis and the theist? By construction, there really isn't anything to choose between the accounts which they offer of modality--or content, or properties, or counterfactuals, or laws of nature. True, there are some Lewis possibilities which the theist does not recognise--but these seem to be fairly unimportant. Moreover, and far more importantly, it is surely the case that the only good way that we have of deciding whether or not these are genuine possibilities is to decide whether or not God exists. In general: the only good way to decide whether to follow Lewis or the theist is to decide whether or not God exists in the actual world.
But if this is right, then the question of which account of the nature of logical space to accept reduces to a purely non-modal question, viz: does God actually exist? In this context, we can't use modal intuitions--e.g. judgements based on imagination and recombination--because those judgements already rely upon assumptions about the nature of logical space. But that is just to say that there can be no modal argument for the existence of God. Any modal theistic argument must be question-begging, since it will rely on assumptions about the nature of logical space which can only be supported by the further claim that God actually exists.
In The Nature Of Necessity, Alvin Plantinga offers the following modal ontological argument:
1. There is a possible world in which unsurpassable greatness is exemplified.
2. In any world, an entity has unsurpassable greatness iff it has the world-indexed property of being-maximally-excellent-in-A for every world A.
3. (Hence) Unsurpassable greatness is exemplified in every possible world--i.e. there actually exists a being who is omnipotent, omniscient, morally perfect, etc., and who has these properties in every world.
As Plantinga notes, this is a valid argument. Moreover, the second premise is obviously true, since it is merely a definition. However, this is not to say that the argument is sound--for there is still the question of the truth of 1. What reason do we have to accept 1? It isn't enough to claim that we have an intuition that 1. is true--for the question of the truth of 1. is precisely the question whether we should accept the modal theist's account of the nature of logical space. But what other reason could there be?
Now, of course, Plantinga does not argue directly that the above argument is sound. In particular, he notes that we should also consider the following argument:
1. There is a possible world which has the property of no-maximality.
2. A world has the property of no-maximality iff no entity in that world has the property of unsurpassable greatness--i.e. iff no entity has the world-indexed properties of being-maximally-excellent-in-A for every world A.
3. (Hence) No-maximality is exemplified in every possible world--i.e. there actually exists no being who is omnipotent, omniscient, morally perfect, etc., and who has these properties in every world.
Once again, this is a valid argument with one premise which is true by definition. But, once again, the question of the truth of the other premise is precisely the question whether we should reject the modal theist's account of the nature of logical space.
Plantinga claims that the modal theist is free to accept the first of these arguments, and to reject the second. In a sense, this is so. However, the first argument does not give the modal theist a reason to believe in the existence of God--for one of the premises of the argument rests on the assumption that God exists. To a non-committed agent, each of these arguments is worthless--the modal considerations invoked can play no part in settling the question whether or not there is a God.
In "A Liebnizian Cosmological Argument" (Philosophical Studies, 1989), Leftow offers the following modal cosmological argument, which he claims has the consequence that "any Platonist would have to be at least a quasi-theist":
1. Necessarily, if there is a being which causes abstract necessary beings (e.g. numbers) to exist, then it is necessarily the case that there is a being which causes abstract necessary beings to exist.
2. It is possible that there is a being which causes abstract necessary beings to exist.
3. (Hence) There is a being which causes abstract necessary beings to exist.
As Leftow notes, this is a valid argument in S5. Moreover, the first premise is true by definition: if there is one being which causes abstract necessary beings to exist, then that being exists in every possible world (since abstract necessary beings exist in every possible world). However, Leftow's justification of the second premise is ultimately an appeal to intuition: surely we can conceive of a being which causes abstract necessary beings to exist! But that's no good. All that Leftow's second premise can mean is that, according to one account of logical space, there is a being which causes abstract necessary beings to exist. Yet, in order to determine whether that is the correct account of logical space, we need to find out whether there actually is a being which causes abstract necessary beings to exist--i.e. we need to find out precisely what Leftow's argument is supposed to prove. So there is no way that Leftow's argument can be made to work; Platonists can still be atheists, if they so choose.
I have drawn a distinction between ground-level modal judgements and higher-level judgements about the nature of logical space. However, it seems natural to express judgements about the nature of logical space in what sounds like ordinary modal terms: "Surely it's possible that there is a necessary being; after all, I can imagine that there is an omnipotent, omnisicent, omnigood, eternal being who created the world ex nihilo, who exists in every possible world, and who has all of these properties in every possible world." Does this mean that there is something wrong with the possible worlds account of modality? We know that David Lewis holds that sometimes possibilities are smaller than worlds; must we also hold that they are sometimes bigger?
No. Since the nature of logical space cannot be a contingent matter, some of our conflicting beliefs, desires and imaginings about the nature of logical space are beliefs, desires and imaginings of impossibilia. But, on any adequate analysis of propositional attitudes, there must be some account of beliefs, desires and imaginings of impossibilia. Maybe we won't give a possible worlds analysis of propositional attitudes; but, whatever we do say, we shall give an account of attitudes involving impossibilia which extends to cover the case of incorrect theories about the nature of logical space.
Perhaps Lewis will follow Stalnaker, and hold that what we fail to know is which propositions (= sets of worlds) are expressed by our sentences. I would prefer to say that the objects of belief are states of affairs under modes of presentation, where states of affairs can have impossibilia, such as impossible logical spaces, as constituents. But, for present purposes, the details are not important. What matters is that it would not be correct for the theist to respond by saying that, far from impugning modal theistic proofs, my argument shows that there is something wrong with standard analyses of modality. We must have some account of how one person can believe that Goldbach's conjecture is true when another believes that it is false; but that is a problem about propositional attitudes, not about modality. There is no new problem about modality here. (It is also worth noting that any quantificational analysis of modality will have the same problem: for all we know, there are many different ways that logical space "might" be.)
"Modal Theistic Arguments" is copyright © 1993 by Graham Oppy. All rights reserved.
The electronic version is copyright © 1998 by Internet Infidels with the written permission of Graham Oppy. All rights reserved.