Philosophy of Religion 30: 45-59, 1991. 9 1991 Kluwer Academic Publishers. Printed in the Netherlands.

The antinomy of divine necessity* DAVID E. SCHRADER Philosophy Department, Washington and Jefferson College, Washington, PA 15301-4801

1. Introduction It has often been held by both friends and foes of theistic belief that God's existence must be either logically necessary or logically impossible. Yet from that common starting point, these theists and atheists move in different directions, arriving at mutually contradictory conclusions. While particular forms of each type of argument vary, nevertheless the following two arguments are fair representations of these two ways of coming at the issue of God's existence.

T) 1. If God's existence is logically possible, then His existence is logically necessary. (logically equivalent to 'Either God's existence is logically impossible or God's existence is logically necessary.') 2. God's existence is logically possible. 3. Therefore, God's existence is logically necessary. 4. Therefore, God exists.

A) 1. Either God's existence is logically necessary or God's existence 2. 3. 4. 5.

is logically impossible. There is nothing whose existence is logically necessary. Therefore, God's existence is not logically necessary. Therefore, God's existence is logically impossible. Therefore, God doesn't exist.

*This paper arose out of a discussion of a paper, "Necessity and Explanation," presented by Robert Prevost (University of Texas at Arlington) at the Spring 1986 meeting of the North Texas Philosophical Association. An earlier version was presented to the 1987 meeting of the Society for Philosophy of Religion. I particularly want to thank Professor Billy Joe Lucas (Manhattanville College) for his very helpful comments on that earlier draft.

46 Obviously both argument A) and argument T) are valid. Equally obviously, they cannot both be sound. Their conclusions are mutually contradictory. Yet surely when a common premise leads us to contradictory conclusions there is another way of dealing with the situation. Very possibly we should conclude instead that the common premise is mistaken. We might, then, entertain a third argument: M) 1. 2. 3. 4.

There is nothing whose existence is logically necessary. Therefore, God's existence is not logically necessary. God's existence is logically possible. Therefore, God's existence is not logically necessary and is not logically impossible. 5. Therefore, it is not the case that God's existence is either logically necessary or logically impossible.

Clearly there is much to be said for the claim that God's existence is possible. Not only all theists, but a good many atheists as well would acknowledge God's possibility. Equally, there is much to be said for the claim that there is nothing whose existence is logically necessary. Not only the advocates of argument A), but a good many other people regardless of religious persuasion would regard that as a fundamental truth of modal logic. The remaining question is whether there is as much to be said for the disjunction upon which arguments A) and T) rest. In the present paper I shall argue that the disjunction in question ought to be rejected, that argument M) is the argument, of those presented above, that ought to be accepted. The high level of development given to modal logic during the present century has done more than enable us to give a variety of new formal treatments of the venerable ontological argument for God's (logically necessary) existence. It has also enabled us to gain clearer understanding of a fair variety of different notions of necessity. Not only are there natural and intuitive modal systems other than $5, but even within $5 we can characterize notions of necessity other than logical necessity. 1 Clearly theism must require God to be more than "merely" contingent. God cannot be simply one being among all other beings. It is, I take it, for something like this reason that advocates of the various versions of ontological argument have wanted to maintain that God's existence is necessary. Yet I shall argue that whatever legitimate explanatory power the hypothesis of divine necessity possesses, and whatever other good purposes are served by our taking God's existence to be necessary, all that is perfectly well accomplished by a notion of divine necessity a bit more modest than logical necessity. Moreover, such a somewhat more modest notion of divine necessity, unlike the notion of divine necessity as logical

47 necessity, does not run afoul of any kind of natural notions about the infinite variability of the domains of other possible worlds.

2. God's existence is logically possible In J.N. Findlay's now-famous article, "Can God's Existence Be Disproved? ''2 Findlay presents an argument which is substantially that given as A) above. Findlay claims that an "adequate object of religious attitudes" must be such that "His own non-existence must be wholly unthinkable in any circumstances. ''3 This is another way of saying that if God's existence (an adequate object of religious attitudes) is logically possible, then God's existence must be logically necessary. Findlay goes on to claim that, Those who believe in necessary truths which aren't merely tautological, think that such truths merely connect the possible instances of various characteristics with each other: they don't expect such truths to tell them whether there will be instances of any characteristics. 4 Here he claims that there are no logically necessary existential propositions, that there is nothing whose existence is logically necessary. He goes on to draw the obvious conclusion of argument A). Note that Findlay's conclusion that God's existence is impossible depends on the truth of the disputed disjunction, depends on the claim that an adequate object of religious worship must be logically necessary. That, of course, is precisely the claim that I wish to dispute in this paper. We might ask at this point, then, whether there is any other reason to doubt the logical possibility of God's existence. Questions of logical possibility are always something of a problem. Clearly we can establish the logical impossibility of certain things. Some things, like square circles, would involve the instantiation of patently selfcontradictory concepts, and hence are logically impossible. Other things, like the set of all sets that don't include themselves, are such that supposition of their existence leads to contradictions, and hence are logically impossible. Yet a third way of establishing logical impossibility would be to show that some essential characteristic of the putative type of entity in question falls into one of the two above-mentioned categories. Beyond these techniques for establishing logical impossibility, we seem to be limited to our own notoriously unreliable intuitions about possibility. Yet surely it has generally been presumed that something which we seem able to imagine should be regarded as logically possible unless there is some clear reason to suppose otherwise. Is there any clear reason to suppose that God's existence is not logically

48 possible? There is, of course, Findlay's argument. It, however, rests on just the proposition whose truth I am arguing against in this paper. (I shall have something to say about what is to be expected of a religiously adequate object of worship later in this paper.) Beyond Findlay's argument what can we say about the possibility of God's existence? Clearly the concept of God is not obviously self-contradictory. There have, of course, been any number of attempts to show that some characteristic or set of characteristics alleged to be essential to our concept of God either lead to logical inconsistency in and of themselves or are logically inconsistent with what we clearly know to be true of the world in which we live. Such traditional problems as the paradox of divine omnipotence, the problem of evil, and a whole collection of other topics which have kept philosophers of religious busy, then, might give us some reason to question the logical possibility of God's existence. Each of these paradoxes and problems has itself been the topic of many a philosophical paper. To examine any one of them would carry me well beyond the scope of this one. It is sufficient for my present purposes, however, to note that to date none of these problems has been shown to be intractable. No one has yet been able to show, to the satisfaction of any very large number of people at least, that any of these problems poses a successful challenge to the logical possibility of God's existence. Given all of this, it appears that we do not have much of any reason, beyond Findlay's argument, to doubt the logical possibility of God's existence. Lacking any such positive reason, and given the very widespread belief in the actual existence of God, and the even more widespread belief that such a being is at least conceivable, it seems most reasonable to suppose that God's existence, whether actual or not, is at least within the realm of the logically possible.

3. There is nothing whose existence is logically necessary While Findlay has claimed that there are no logically necessary existential propositions, a whole host of contemporary philosophers, perhaps the most noteworthy of whom would be Charles Hartshorne, Norman Malcolm, and Alvin Plantinga, 5 have argued for the opposite conclusion. Similarly, it is clearly arguable that a significant number of earlier philosophers from Anselm to Leibniz also argued that God's existence is logically necessary. They clearly held that God's existence was necessary in some sense, and most contemporary scholars have taken them to have held that divine necessity was what we would now regard as logical necessity.

49 Clearly these contemporary reformulations of the ontological argument make it quite clear that the Kantian problem of whether 'exists' is a logically proper predicate is a "red herring." Let us take Plantinga's formulation of the argument as he develops it in God, Freedom, and Evil. In that formulation, Plantinga provides us with two crucial notions: "maximal excellence" and "maximal greatness." While Plantinga does not give us a full characterization of either notion, he does tell us that maximal excellence entails omniscience, omnipotence and moral perfection, and that maximal greatness "entails maximal excellence in every world. "'6 Plantinga then goes on to develop the argument as follows: (25) (26) (28) (29)

It is possible that there be a being that has maximal greatness. So there is a possible being that in some world W has maximal greatness. A Being has maximal greatness in a given world only if it has maximal excellence in every world. A being has maximal excellence in a given world only if it has omniscience, omnipotence, and moral perfection in that world. 7

Clearly Plantinga's notion of maximal excellence includes those properties, omniscience, omnipotence and moral perfection, which we usually take to be definitive of God. Moreover, the notion of maximal greatness implies having those properties in every possible world. Thus (25) and (26) assert the logical possibility of God's existence. Yet (25) and (26) assert a good deal more than some of us would take to be implied by the assertion of the logical possibility of God's existence. (25) and (26) assert the logical possibility of the existence of a logically necessary being. That is precisely what Findlay denied. Given (25), however, the existence of a maximally great being (God) in every possible world follows validly in the modal system $5. Of course Plantinga simply assumes that it is possible that this logically necessary being exists. Yet I take it that all of those who have denied that there is anything whose existence is logically necessary have not held that this is merely a contingent fact. Rather, they have denied precisely what Plantinga wishes to assume here, namely that logically necessary existence is logically possible. What reason have we, then, for assuming the existence or even the possible existence of a logically necessary being. I take it that there are three possible responses to this question. First, it is a consequence of one approach to giving a semantics for quantified modal logic that whatever exists in one possible world must exist in every possible world. (This would, of course, not be very helpful in the end.) Second, advocates of some forms of ontological argument often allude to the alleged logical necessity of numbers. 8 Finally and most importantly, it

50 has been claimed by a wide variety of writers, Findlay among them, that only a being whose existence is logically necessary could be a worthy object of religious worship. In their discussion of "Modality and Existence" in An Introduction to Modal Logic, Hughes and Cresswell raise the question of "what kinds of worlds or states of affairs other than the actual one we [are] prepared to envisage or count as possible . . . . ,,9 They go on to respond that: One answer might be that we could envisage only certain words containing just the same objects as the actual world does, though with new properties and standing in different relations. We could think of the semantics of Chapter 9 as expressing this kind of answer, since each model there assigned a single invariant domain for all worlds. 1~ Clearly, on such a semantics, a being would exist in one possible world if and only if it existed in every possible world. It would clearly follow that if God's existence were logically possible (if He existed in some possible world), then God's existence would be logically necessary (He would exist in every possible world). This, however, would be a hollow victory indeed. For in this type of situation victory would be purchased at the price of a semantic collapse of necessary existence and possible existence into actual existence. God's existence would be logically necessary, but then so would the existence of my dog, Ginger. This is surely not the kind of logical victory that any advocate of an ontological argument could desire. Obviously a far more interesting claim is that the existence of numbers is logically necessary. This claim, if it were true, would clearly remove any plausible objection in principle to the logical necessity of God's existence. Unfortunately, it is simply not the case that the existence of numbers is logically necessary. While the early history of foundational studies in mathematics was dominated by the hope that logicians might be able to develop some way of deriving arithmetic from logic, that hope was given up long ago. It is now clearly accepted that arithmetic cannot be constructed solely on the basis of the predicate calculus. Rather, a foundational system for arithmetic requires the addition of non-logical axioms. The fact that these axioms are non-logical means they can be denied without fear of contradiction, that there are logically possible worlds in which they are not true. Clearly, of course, numbers must exist in any very interesting world. In any world that is even remotely like the actual one, any world in which there are intelligent creatures, perhaps even any world in which there is temporal succession, there will be numbers. As will become clear later on in this paper, I think that Plantinga and others who have at least implied

51 that the kind of necessity which attaches to the existence of mathematical objects is at least very close to the kind of necessity which attaches to God's existence are substantially correct. However the kind of necessity at stake is not logical necessity in either case. Finally, there is the claim that only a being whose existence is logically necessary can be a worthy object of religious devotion. It would seem that Findlay is right in saying that: ... we can't help feeling that the worthy object of our worship can never be a thing that merely happens to exist, nor one on which all other objects merely happen to depend. 11 Yet to move from that claim to the claim that a worthy object of religious devotion must exist by logical necessity would seem to depend on our seeing the domain of possible objects as simply divided into the logically necessary and the merely contingent. One of the results of the development of modal logics during the present century has been the possibility of distinguishing formally among a rather wide variety of notions of necessity. We are surely not forced to say that God's existence is either logically necessary or merely contingent. In the next section of this paper I shall look at a sample of the different kinds of necessity that we may distinguish with the tools of modal semantics. At present I shall not provide any argument for the claim that an adequate object of religious worship need not exist by logical necessity. I shall reserve that task until after I have looked at some of the alternative understandings of necessity which are available to us. At present let it suffice to say that it is by no means clear that the existence of an adequate object of religious devotion must be logically necessary. If I should turn out to be right in claiming that an entity does not have to exist in all possible worlds in order to be an adequate object of religious devotion, then we seem to have lost any positive reason to assert that God's existence must, if it is logically possible, be logically necessary. Indeed beyond this, it seems to me that we have good positive reasons for believing that there is nothing whose existence is logically necessary. Apart from the kinds of considerations which Findlay and others have raised about the character of necessary truths, the kinds of modal intuitions which I, and I strongly believe most other people, have about the range of contents of other possible worlds would also lead us to believe that there is nothing which exists in every one of those worlds. It seems to me, for example, that I can image a possible world in which there is only one green marble, doing nothing, and that in so imagining I need not fall into imaginative inconsistency. If this intuition of mine is correct, then since I

52 can image a large number of possible worlds with no green marbles at all, it will follow that there is no single object (God or anything else) that exists in the domains of all those possible worlds. I f that is the case, then there is nothing whose existence is logically necessary. So far I have argued that God's existence is logically possible, but not logically necessary. If I am right, then both certain forms of the ontological argument for God's existence and Findlay's ontological argument against God's existence are defeated. Yet clearly tradition has long held that God's existence is not merely contingent. Divine necessity has long been held to serve certain explanatory functions. This, I take it, is what lies behind the claim that God's existence must be either logically necessary or logically impossible. Thus, without showing that we may attribute some alternative notion of necessity to God, a notion which will provide a grounding for religious veneration while at the same time according with our normal intuitions about the variety of the domains of logically possible worlds, we may still find a variant of Findlay's position carrying the day. We may be forced to conclude that the only notions of God which are logically tenable are notions of God which are theologically uninteresting.

4. Modal logic and kinds of necessity The formal development of modal logic in the present century has made possible a level of clarity in philosophical discussions of the notion of necessity which was frequently lacking in earlier discussions of that issue. Moreover, the development of a large variety of different systems of modal logic has made it possible for philosophers to talk with increased clarity about a variety of different notions of necessity. While logical necessity may enjoy a position of some privilege in general discussions of necessity, it should be abundantly clear that contemporary discussions of necessity are not faced with a simple alternative between logical necessity and mere contingency. The semantic development of modal logic has been a particularly valuable tool in the attempt to distinguish different notions of necessity. We say that a proposition p is necessarily true in a given world G if and only if p is true in every possible world which is accessible to G. By specifying different accessibility relations we can specify different notions of necessity. If accessibility is taken to be reflexive, symmetrical and transitive, then we are talking about logical necessity, and we are working in the modal system $5. Similarly, we might take the accessibility relation to be just reflexive, reflexive and transitive, or reflexive and symmetrical. Were we to do so, we would be using somewhat different notions of

53 necessity, 12 and we would be working, respectively, with the T modal system, the $4 modal system, or the Browerian system. Yet even beyond these modal systems, we can generate a wide variety of other modal systems, either axiomatically or semantically. Some of these will give us yet additional notions of necessity. Others of these can be most reasonably interpreted to express non-alethic modal notions. Given that we have available to us such a broad range of different notions of necessity, we should at least be very cautious about accepting the claim that an adequate object of religious worship must exist by logical necessity. Clearly the claim that if God is logically possible He must be logically necessary cannot be accepted as simply following from the fact that no merely contingent being can serve as an adequate object of religious veneration. Rather a more reasonable procedure would be to look at what role the notion of divine necessity is supposed to play in an adequate theology, and then see what kind of view of necessity satisfies the demands of that role. If I am fight in my contention that the notion of divine necessity which will best serve our theological needs is not, in fact, logical necessity, then there is no need to choose between Findlay's and Plantinga's equally unpalatable arguments.

5. What we want from divine necessity

Findlay's article presents, I would submit, perhaps the most profound challenge to the legitimacy of theistic belief yet developed. The reason for this is that Findlay starts out with an analysis, far more careful and sensitive than what is usually given by defenders of theistic belief, of what is involved in the notion of an adequate object of religious reverence. Over the span of two pages of his article, Findlay gives a remarkably lucid and almost reverent explication of what Christian theologians and philosophical apologists over the past two thousand years have meant by an understanding of God as perfect and without limit. What I take to lie at the heart of that explication is as follows: And hence we are led on irresistably to demand that our religious object should have an unsurpassable supremacy along all avenues, that it should tower infinitely above all other objects . . . . But we are also led on irresistably to a yet more stringent demand . . . . : we can't help feeling that the worthy object of our worship can never be a thing that merely happens to exist, nor one on which all other objects merely happen to depend. The true object of religious reverence must not be one, merely, to which no actual independent realities stand opposed: it must be one

54 to which such opposition is totally inconceivable . . . . And not only must the existence of other things be unthinkable without Him, but His own non-existence must be wholly unthinkable in any circumstances . . . . ... Not only is it contrary to the demands and claims inherent in religious attitudes that their object should exist "accidentally": it is also contrary to those demands that it should p o s s e s s its various excellences in some merely adventitious or contingent manner. It would be quite unsatisfactory from the religious standpoint, if an object merely happened to be wise, good, powerful and so forth, even to a superlative degree, and if other beings had, as a mere matter o f fact, derived their excellences from this single source . . . . And so we are led irresastibly, by the demands inherent in religious reverence, to hold that an adequate object of our worship must possess its various qualities in some necessary manner. 13

Findlay rightly notes that God cannot be simply another being among beings, cannot be just another in the order of contingent things, but must be, in some appropriate sense, necessary. Yet when he goes on to say that, "necessity in propositions merely reflects our use of words, the arbitrary conventions of our language, ''14 Findlay is clearly assuming that analyticity, logical necessity, is the only adequate alternative to m e r e contingency. Similarly, Plantinga takes the latter part of Findlay's analysis of an adequate object of religious reverence, that part which deals with the manner in which such an object must possess its various qualities, as the point of departure for developing his notion of maximal greatness as entailing the possession of maximal excellence in every (logically) possible world. 15 Yet I still do not think it follows from Findlay's explication of the notion of an adequate object of religious reverence that the theistic believer is committed to the belief that the description of a (putative) logically possible world containing a large green marble and nothing else must involve a logical contradiction. When the theistic believer says that the non-existence of God is "wholly unthinkable in any circumstances," I do not think that the believer would take that to imply that no consistent description lacking reference to anything that might reasonably be called 'God' can be put together to constitute what modal logicians would regard as a possible world. Rather I take it that what the believer means to say is that there could be no universe even remotely like the actual one (accessible to the real world on some appropriate characterization of an accessibility relation) without a God. This is attributing to God's existence a very important kind of necessity, but it is not attributing logical necessity to His existence. Theistic belief ought not wish to deny that God's existence is a brute fact which is not susceptible to further explanation.

55 Rather it should assert that God's existence is the brute fact on which all other facts do and must depend. In saying that this is what theistic belief ought to be committed to, I am saying that to commit theistic belief to more than this will carry it well beyond the traditional affirmations of God as the creator and sustainer of the universe into a set of claims which are logically peculiar and theologically irrelevant. Suppose, for example, that theistic belief were to present itself as an answer to the age-old question of why there is something rather than nothing at all. What kind of answer would the logical necessity of divine existence give to that question? It is, I think, worth noting that for Plantinga, who believes that both God and numbers have logically necessary existence, theology and arithmetic would have to answer the question of why there is something rather than nothing at all in precisely the same manner. Neither of those answers, however, moves us a bit closer to an answer to the questions that most religious people would regard as theologically interesting, questions like, "Why am I here?" and "What is my relationship to God?" Answers to these latter questions depend for their answer on an appeal to God as the ground of all existence. Moreover, unless we want to lose contingency of any sort in the created universe, they must depend on an appeal to God's creative activity as basically and fundamentally free activity. An answer to the questions that are religiously significant, those noted above, as well as questions surrounding the redemption of God's creation, must invariably carry us to God's free activity, God's contingent choices. Beyond that, taking God to be logically necessary gives us nothing of religious significance. To say that the modal logician can describe a wide variety of arcane logically possible worlds whose domains lack God is not to say that the theistic believer can imagine a genuine, flesh and blood universe without God the Creator. The question remains, then, as to how we may distinguish the sense of necessity which is importantly a part of theistic belief. How may we distinguish those logically possible worlds which are also interestingly accessible to the real world? In what follows I shall put forward two suggestions as to the kinds of possible worlds which the theist most likely will want to affirm must involve a God. Earlier in this paper I claimed that in any world in which there are intelligent creatures, and perhaps even in any world in which there is temporal succession, there will be numbers. Along similar lines, I think that theists will most likely want to affirm that in any logically possible world in which there is any kind of action, and also likely in any logically possible world in which there is temporal succession there will have to be God. These kinds of worlds are the ones which have traditionally given rise

56 to arguments for God's existence. The arguments of St. Thomas Aquinas which argue from the fact of motus in the world, for example, would seem to be committed to the claim that God must exist in any world in which there is temporal succession. While those arguments are not successful as arguments, they do nevertheless tell us something important about what has traditionally been taken as the realm of God's sovereignty. Similarly, even St. Anselm starts out his version of the ontological argument with a world in which there is a fool. Perhaps we should take the claim of St. Anselm to be merely that any logically possible world that contains a fool must also contain God. Various writers have developed modal logics which are given their standard interpretation as logics of action. 16 These logics customarily give one or more praxiological modalities and two sets of individual symbols, one of which is a set of individual agent symbols and the other of which is a set of individual non-agent symbols. One of the praxiological modalities will be so interpretable as to allow one to express something like, 'Agent i brings it about that p', where p is the state of affairs expressed by some well-formed sentence of the language. We might say that a logically possible world w contains genuine action as long as there is some expressible state of affairs p such that the sentence standardly interpreted as 'There is some agent which brings it about that p, and there is some agent which does not bring it about that p' is true in w. We could then go on to designate as A the subclass of all possible worlds composed of all those logically possible worlds which also contain genuine action. Given such a class A, we could also define a praxiological interworld accessibility relation R A as AxA. That is, all the worlds included in A would be praxiologically accessible to each other, but no world outside of A would be praxiologically accessible to any world in A. This would allow us to identify a notion of praxiological necessity according to which a proposition p is praxiologically necessary in a world w if and only if p is true in every world which is praxiologically accessible tOW.

Similarly we can define a notion of necessity which I think we might appropriately call "metaphysical necessity" according to which a proposition p is metaphysically necessary in some world w if and only if p is true in every world which is metaphysically accessible to w. The metaphysical accessibility relation R M is definable in the same manner as R A above except that is definable over a subclass M, which includes those logically possible worlds in which there is also temporal succession. Hughes and Cresswell note a modal system, $4.3,17 developed by Dummett and Lemmon, 18 in which the modal sentence Lp is interpretable as 'It is and will always be the case that p'. Given this, we can identify those logically

57 possible worlds containing temporal succession as those in which there is some sentence p, such that p&-Lp is S4.3-true in that world. That is, some sentence is true, but will not always be so. Such a world would have to involve succession to another time at which p was false. I have now given two notions of necessity, praxiological necessity and what I have chosen to call metaphysical necessity. It seems that the legitimate demands placed on the notion of divine necessity by the concern that God be the Creator, Sustainer, and Redeemer of the universe, that God be the ground of all being, etc., are perfectly well satisfied by either of the above notions of necessity. Moreover, Plantinga's argument from God, Freedom, and Evil turns out to be nicely reconstructible by replacing the notion of logical necessity with that of either praxiological necessity or metaphysical necessity. Whether such a revision of Plantinga's argument would turn out to be an "argument triumphant''19 must remain an open question. That revision cannot, however, be dismissed on the ground that there are no logically necessary existential propositions.

6. Conclusion

I have argued for three claims in this paper: 1) God's existence is logically possible. 2) There is nothing the existence of which is logically necessary. 3) The kind of necessity which is required of an adequate object of religious veneration is not logical necessity. Claims 1) and 2), taken together, constitute a denial of common premise of the arguments labeled A) and T) at the beginning of this paper. The fact that those two arguments share the common disjunction, that each contains one additional premise which is true, and that they result in mutually contradictory conclusions, might lead us to see them as constituting an antinomy of divine logical necessity, a disproof of the claim that God must be a logically necessary being. The more important result of this paper, however, is that a denial of divine logical necessity does not relegate God to the status of mere contingency, just another among beings. Rather, there are many other kinds of necessity which we can identify. I have suggested two kinds of necessity which seem to me to be good candidates for the variety of necessity which must be demanded of an adequate object of religious worship. Certainly the precise demands of adequacy for an object of religious worship can only be worked out through careful theological development. Yet it is certainly important to note that the theologian is not stuck with logical necessity or nothing.

58 The tools of formal modal logic which have been developed in the present century have had a profound impact on the philosophy of religion. In particular, the venerable ontological argument of Anselm and others has gained new life. Twentieth-century philosophers of religion have given a wide variety of formally developed arguments for the existence of a logically necessary being. Yet if I am correct in my contention that logical necessity is not necessary, and perhaps not even desirable in an object of worship, then perhaps contemporary philosophers of religion with training in the techniques of modal logic would serve the religious community better by using those tools to identify the sense of necessity in which we do want to claim that God is a necessary being, the Alpha and Omega, the foundation and the redemption of the universe.

Notes 1. The notion of logical necessity is itself far less clear than we might desire. If logical necessity is construed as truth in every logically possible world, and a logically possible world is taken as a complete set of mutually consistent propositions, then logical necessity amounts to analyticity. This is the understanding of logical necessity which I adopt in this paper. By contrast, logical necessity may also be construed as provability within some given logical system such as the first-order predicate calculus with equality. If construed in this latter way, then some existential propositions, e.g. '(Ex)(x=x)', are necessarily true. Yet even this does not imply that there is any entity which exists in every possible world. On the former construal however, as long as an empty world is taken to be a logical possibility, even that proposition will be false in that one possible world. If the logical possibility of an empty world is denied, then my claims that there are no logically necessary existential propositions must be revised. However, my claim that there is nothing whose existence is logically necessary will still stand. 2. J,N. Findlay, "Can God's Existence Be Disproved?" Mind 57 (1948): 176-183. 3. Ibid., p. 180. 4. Ibid., p. 181f. 5. See, among other works, Charles Hartshome, The Logic of Perfection and Other Essays in Neoclassical Metaphysics (LaSalle, IL: Open Court, 1962); Norman Malcolm, "Anselm's Ontological Argument," The Philosophical Review 69.1 (January 1960): 41--62; and Alvin Plantinga, The Nature of Necessity (Oxford: Oxford University Press, 1974), and God, Freedom, and Evil (New York: Harper and Row, 1974). 6. Plantinga, God, Freedom, and Evil, p. 108. 7. Ibid., p. 108. 8. See ibid., p. 105. 9. G.E. Hughes and M.J. Cresswell, An Introduction to Modal Logic (New York: Methuen, 1968), p. 177.

59 10. Ibid., p. 177. 11. Findlay, op. cit., p. 180. 12. For some suggestions as to the senses of 'necessity' that may be involved in these different modal systems, see E.J. Lemmon, "Is There Only One Correct System of Modal Logic? Aristotelian Society Supplementary Volume XXXIII (1959): 23-40. 13. Findlay, op. cit., pp. 179ff. 14. Ibid., p. 182. 15. See Plantinga, op. cit., pp. 107f. 16. See, for example, G.H. von Wright, Norm and Action (London: Routledge and Kegan Paul, 1963), and An Essay in Deontic Logic and the General Theory of Action (Amsterdam: North-Holland Publishing Company, 1968); also, Ingrnar P~im, The Logic of Power (Oxford: Basil Blackwell, 1970). 17. See Hughes and Cresswell, op. cit., pp. 261ff. 18. See M.A.E. Dummett and E.J. Lemmon, "Modal Logics between $4 and $5," Zeitschrift fiir mathematische Logik und Grundlagen der Mathematik 5 (1959): 250--64. 19. See Plantinga, op. cit., p. 11.