the explanatory power of theism

Philosophy of Religion 25:129-146 (1989) �9 1989 Kluwer Academic Publishers. Printed in the Netherlands

The explanatory power of theism *

KELLY JAMES CLARK Department of Philosophy, Gordon College, Grapevine Road, ICenham, MA 01984

1. Introduction

What does it mean to say that the hypothesis of theism (T) explains the existence of the actual world (14/)? In The Existence o f God by Richard Swinburne, The Miracle o f Theism by J.L. Mackie, Religion and Scien- tific Method by George Schlesinger and Religious Belief and Religious Skepticism by Gary Gutting 1 this is understood as analogous to the broader question of a scientific hypothesis explaining certain phenomena. They use versions of Bayes' theorem as the appropriate method of confirmation and consider the arguments probabilisticaUy rather than deductively. Bayes' theorem may be expressed as

P(h/e&k) = P(e/h&k) P(h/k) P(e/k)

where h= hypothesis to be confirmed, e= the evidence, and k = general background knowledge. On the Bayesian analysis the confirmation of the hypothesis by the evidence is a function of the following three factors: (i) the antecedent likelihood of the hypothesis [P(h/k)], (ii) the antecedent likelihood of the phenomena to be explained [P(e/k)] ; and (iii) the degree to which the hypothesis explains the phenomena [P(e/h&k)]. This final factor must be considered relative to the antecedent likelihood of the evidence; that is, the explanatory power of a hypothesis is how much the hypothesis increases the likelihood of the phenomena, or in probablistic terms, is P(e/h&k)>P(e/k)? And especially, for our purposes, how much does the hypothesis of theism raise the probability of the existence of the actual world; that is, what does it mean to say that the hypothesis of theism explains the world?

* Special thanks to Alvin Plantinga, Michael Detlefsen and William Alston for many helpful suggestions.

130

What we will analyze is the explanatory portion of a Bayesian argument for the existence of God. Is the existence of the actual world more probable, given the hypothesis of theism than on background knowledge alone? Our analysis will discuss how one might possibly assign the relevant probabilities to such an argument for the existence of God. It should be noted at the outset that the aforementioned authors reach wildly divergent conclusions regarding the confirmation of theism. Mackie and Gutting, for example, are quite skeptical of probabilistically justifying the hypothesis of theism; whereas Swin- burne and Schlesinger believe that their arguments demonstrate the (probable) truth of the hypothesis of theism. It will be one of the tasks of this paper to account for this disagreement with respect to methods typically considered objective and conducive of convergence.

What criteria must be met for a good explanation? This explanation will provide only necessary conditions although jointly they may be sufficient conditions. Swinburne says that to explain the occurrence of phenomena E is to state truly what brought E about and why it was efficacious in bringing E about. In a scientific explanation, Swinburne contends, the causal powers of objects in the appropriate circumstances jointly bring about the phenomena E. Thus, a proper explanation will be in terms of the powers and liabilities of bodies in certain circumstances to cause certain events. He says: "On the amended Hempelian account the occurrence of a phenomena [sic.] E is explained if laws of nature L and other particular phenomena, C, called the initial conditions, physically necessitate (or make highly probable) the occurrence of E. ''2 Of course, this detYmition of a scientific explanation will not prove useful in a Bayesian argument for the existence of God. In this case, the explanatory power of the hypothesis is not in terms of the powers of objects in the appropriate initial conditions, but in terms of the intentions and abilities of a personal agent. Hence, a personal explanation would explain the phenomena by the postula- tion of an agent with the appropriate intentions and capacities for bringing about the event in question.

Let the above discussion suffice for placing constraints on appropriate explanations. Given the hypothesis of theism as an appropriate potential explanation of the world, how is that hypothesis justified or confirmed? Swinburne, Mackie and Gutting take T to be the hypothesis of theism (that there is an omniscient, omnipotent , and wholly good God), W to be the actual world, and K to be general background

131

knowledge. 3 The difference between the specification of T and K on the one hand and the specification of If on the other hand should be noted. The former are propositions and the latter is a complex collection of things and events. In order for the argument to be successful If must be stated as a proposition or a set of propositions. Let us take If to be a complete description of the universe that is maximal but does not contain any propositions that entail that T or -T . Because the ambiguity persists throughout, for example, Swinburne's argument, our discussion will not continually correct this notation and will pre- serve the ambiguity.

The relevant formula which we shall consider, the explanatory power of theism, is a consequence of Bayes' theorem: P(W/T&K)>P(W/K). 4 Thus, the justification of the explanatory power of the hypothesis of theism will consist in how much P(W/T&K) surpasses P(W/K). The following sections will assess the P(W/T&K) and compare it to P(W/K). We will begin with some general considerations and then turn more specifically to the arguments of the aforementioned authors. It will be assumed, until Section 5, that the P(W/K) is exceedingly low (although non-zero).

2. P (W/T&K) = 1

First, explanation may be taken to be an instance of the entailment relation. That is, to say that the hypothesis explains the phenomena is to say that P(e/h&k) = 1. Thus, h&k consist in all of the causally relevant factors which are sufficient for the occurrence of e; if h&k obtain then e obtains. That is to say that the hypothesis entails the phenomena. Now surely this is not the sense which could prove useful in an argument for thg existence of God. It is simply nonsensical to say that T entails If, for T is not a sufficient condition for the occurrence of If. Now it is possible that God actually be the cause of If, but that is not to say that T entails W since T is compatible with the denial of If, or T is compatible with a world like If in every respect except with eight planets, or with a world like If in every respect except with only half as many grains of sand, etc. Therefore, given only T, the existence of If is not necessary; T is compatible with too much. Thus, for a Bayesian analysis to work, the hypothesis explaining the phenomena cannot mean P(e/h&k)= 1 in a probablistic argument for theism, s

132

3. P(W/T&K) is significantly greater than P(W/K)

A second sense of a hypothesis explaining the phenomena is: P(W/T&K) is significantly greater than P(W/K). Of course, the first sense of explanation may be taken as a limiting case of this view. Swinburne en- dorses this position: 6 "A theory has explanatory power in so far as it entails or makes probable the occurrence of many diverse phenomena which are all observed to occur, and the occurrence of which is not otherwise to be expected. ''7 Let us suppose that P(W/K) is very low. In this case, does T significantly raise P(W)? It seems that P(W/T&K) is very difficult to assess. Given only the hypothesis of theism, T, a whole host o f worlds are possible. Given only T (God is an omniscient, omnipotent , wholly good, perfectly free spirit), there seems to be an infinity of universes possible.

Swinburne discusses the explanatory power of theism as follows:

The choice before God among world to create includes a world where there is just God: a world where there are one or more finite non-physical objects (e.g. non-embodied spirits); a world consisting of a simple physical universe (e.g. just one round steel ball); and a world which is a complex physical universe. For such a universe can be beautiful, and that is good; ... But I cannot see that God has overriding reason to make such a universe. (It is not obviously superior to any other sort o f world; ...) Nor can I see that he has overriding reason to make any alternative world. 8

On Swinburne's view W is exceedingly unlikely to occur unexplained. However, it is not unlikely to occur given T (although it is not especially likely given T either). God has, he contends, a good, but not overriding reason for creating a complex physical universe. The only constraints on possible worlds that such a being might create would be constraints with respect to his goodness. That is, such a being must create worlds which exhibit beauty and which have a preponderance of good over evil. Thus, Swinburne thinks that P(W/T&K) is, indeed, greater than P(W/T&K)

But such a being need not create a world with a moral overtone at all (he could create a world containing only beautiful, non-sentient steel balls). Or such a being need not create at all. And what is the probabili ty that such a being would create the actual world? 9 Perhaps this probabili ty may be represented by a fraction as follows: 1 / eve ry

133

possible world compatible with T. Now T is compatible with: the world consists only of one steel ball; the world consists only of two steel balls; the world consists only of three steel balls; etc. There seems to be an infinite number of possible worlds consistent with T. Now there is no reason to believe that W, the actual world, has anything to recommend it over the other possible worlds (given only T), so all of the possible worlds consistent with T must be equi-probable. And since there are uncountably many possible worlds consistent with T, the probability of W given T must be very low indeed; and there is no reason to believe that P(W/T&K) does not have a zero probability.

Given these considerations, how does P(W/T&K) compare to P(W/K)? How could one make this judgment given our specification of W? We assumed earlier that P(W/K) is exceedingly low; but P(W/T&K) is also exceedingly low. And both seem to be zero. So how do these probabilities compare? There seems to be no way to intelligibly make the comparisons unless some rather precise probabilities can be determined. And this is just what is lacking. So far we have only relative probabilities, both components of which are exceedingly low. The relative probabilities simply do not make the comparative probabilities per- spicuous. Hence, this understanding of a hypothesis explaining the phenomena could not advance an argument for the existence of God.

4. P(W/T*&K) is significantly greater than P(W/K)

It should be clear from the preceding discussion that, given only that God is omniscient, omnipotent , and wholly good, there is no reason to expect this world, or a world like this one (except with some moral or aesthetic constraints). But perhaps the theistic hypothesis may be amplified in a way which would make W likely. George Schlesinger in Religion and Scientific Method takes this approach in his argument for theism. He believes that the following properties are entailed by T and may, therefore, be added to the explanatory hypothesis: "Let [T*] stand once more for the theistic hypothesis which, among others, contains the statement that God, who is interested in creatures capable of responding to him, exists. ' ' '~ Adding God's desire for free creaturely fellowship to T, he contends, necessarily entails the existence of such creatures: "Thus by [T*] , there is a God who is interested in such creatures, and being all-powerful - therefore capable of realizing any-

134

thing he wishes - it follows that such creatures must exist. ''11 Schle- singer believes that T plus God's desire to create beings capable of responding to him entail that the world contain laws of nature and initial conditions which allow for the existence of such creatures. He contends, further, that, P(W/K) is very low. That is, the hypothesis of naturalism (N), that there are no supernatural forces responsible for the laws of nature) does not lead us to expect the existence of a world like this one. An infinite number of universes in which no human beings exist is compatible with N. Thus, N does not imply anything about the existence of the actual world, which is only one of the infinite set of possible universes compatible with N. If W is entailed by T plus God's desire to create responsive beings (T*), and if W is not entailed by N then T* explains W.

This raises two issues. First, the probability of the actual world would still be zero even given the theistic hypothesis and knowledge of God's intentions. Schlesinger contends that the hypothesis of theism entails a world with laws of nature and initial conditions something quite close to our world. If either the laws of nature or the initial conditions were altered in the slightest, then human life would not be possible. But the hypothesis of theism plus God's desires do not entail that the universe must be something like this one. Rather, it only entails that there be persons - nothing else is implied about the laws of nature or the initial conditions. The reason is that because of God's omnipotence, he could create sentient creatues with any laws of nature or initial conditions (or with no laws of nature if he deigned to create, say, angels). Thus, there is nothing special about this universe which gives it a higher probability than any other universe. Thus, the probability of this universe even given the hypothesis of theism and knowledge of God's intentions is not non-zero. However, perhaps it is appropriate to include in T* that God desires to create a world with natural laws in which creatures exist without regular supernatural sustenance. The appropriateness of thus expanding T* will be discussed shortly.

Secondly, it may not be legitimate, at this point, to bring in beliefs about God's intentions or desires. Swinburne, for example, contends that with a good C-inductive argument the premisses "should be known to be true by those who dispute about the conclusion. ''12 Hence, for Swinburne, with an argument for the existence of God, the premisses must be known to be true by both atheist and theist alike. Unless the premisses are known to be true, the argument is not a good C-inductive

135

argument. 13 It does seem that an appeal to God's intentions is likely to be contested by the nontheist. Hence, for Swinburne anyway, this cannot be the hypothesis to be considered in a good C-inductive argument for the existence of God.

How could one know a priori God's intentions? Schlesinger believes that God's desire to create is entailed by the hypothesis of theism. If God has every perfection, then he has omnibenevolence. And if God is omnibenevolent, then he will create creatures to share in his love. There are two flaws in this argument. First, even if the hypothesis of theism entails God's omnibenevolence, it does not follow that God will necessarily desire to create creatures at all. In the Christian tradition, God is considered perfectly loving but under no necessity to create. God is considered triune in this tradition and there is perfect love experienced among the Father, Son, and Holy Spirit. God does not need to create in order to express his omnibenevolence. Thus, God's desire to create free beings does not necessarily follow from his omnibenevolence. If it does not necessarily follow from omnibenevolence, then its justification must come from somewhere else.

And what is the justification for postulating that God has the intention or desire to create? How could one know or be justified in believing that God has this or that desire? Gutting raises this issue:

More generally, theistic explanations of any of the classes of facts listed above require assumptions about what God would want or how he would act. Thus, an explanation of religious experience as- sumes he would want to communicate with us, an explanation of moral experience that he would try to help us be good, etc. But it is hard to see how we could have reason to think that God will have any specific intentions or will act in any specific way. 14

Gutting objects to postulating God's intentions for two reasons. First, "because we lack his omniscience, we have no way of judging what specifically he would be likely to do. ''is Any judgments we might make about how God would act, he contends, would be viciously anthropomorphic. They would be projections about how we might act in analogous situations. But how could we know a priori that God would act as we do? Further, somewhat definite judgments are needed to determine the relative probabilities. But the analogy is not close enough to determine God's specific intentions and, therefore, we cannot make even a close guess concerning the relevant probabilities of God creating a world like ours.

136

Second, Gutting argues, the theist appeals to the inscrutability of divine knowledge for the problem of evil and, hence, his appeal to divine knowledge in this case is unfounded. The atheologian says that God has no good reason for allowing evil and the defender of theism rebuts that claim by appeal to the inscrutability of the divine purpose. The fact that we don't know God's reason for creating a world containing evil, the theodicist claims, is no justification for believing that God has no reason for creating such a world. From God's omniscient standpoint there may be a good reason for allowing evil. But Gutting argues that if we can't know God's purposes in creating a world with evil (due to the inscrutability of the divine purpose), then we ought not think we can know in any case what God intends to do: "But then the theist must admit that the same principle applies in other cases and hence that our understanding never gives us a basis for anticipating God's actions. ''16 In summary, Gutting believes that we do not have knowledge of God's intentions and that an explanation which crucially relies on those intentions is irreparably dam- aged. 17

Gutting believes that God's desiring to create (D) is an assumption which must be added to the theistic hypothesis (T) in order to get an explanation of the existence of the world. But perhaps (contrary to Gutting) D need not be considered an assumption at all, let alone a questionable one. It seems that it is difficult to delegate D to realm of 'questionable assumptions.' Granting the minimal conditions which an explanation must satisfy (as outlined in the Introduction to this section), it is hard to see why one cannot legitimately amend one's hypothesis in order to sufficiently explain the data. When scientists devise a theory to explain a body of data, they develop precisely the theory which is required to explain the data. That is, the explanatory hypothesis in combination with the relevant initial conditions must either entail or make more probable the data to be explained. If a hypothesis failed to do this it would either be abandoned (if there were a better alternative) or it would be improved to the point where it did entail or make probable the data.

Now suppose one discovers that T neither entails nor makes probable the occurrence of 14/, one can hardly fault a hypothesis T* which does make W more probable than on T. For the sake of parsimony, one may begin with a hypothesis like T and assess its explanatory power. When it is found wanting, it is legitimate for one to consider

137

a hypothesis more worthy of the explanatory task. Furthermore, T* does not seem to be an inappropriate explanatory hypothesis. In fact, it seems to be an extension of T. T is a personal explanatory hypothesis stating that God is omnipotent , omniscient, and wholly good. These properties do not entail God's desire to create free creatures, nonetheless, this is a legitimate extension of the theory. That is, the properties of a personal, omniscient, omnipotent , wholly good being suggest that such a being might have the desire to create free, moral agents.

This is a legitimate progression for explanatory hypotheses in physical theory. The Bohr model of the atom, for example, pictured atoms like the solar system, maintaining that electrons were like orbiting planets. It was later noticed that electron spin might be postulated in order to better explain atomic phenomena. Whereas, the original Bohr model was sufficient to explain the initial phenomena, it was subse- quently determined that the original Bohr model was insufficient to explain other phenomena. The explanatory power of the Bohr model was reasserted by a simple extension of the model itself; since planets spin, so may electrons. And electron spin was postulated merely to explain the phenomena. It should be noted that the planetary model of the electron does not entail that electrons have spin. However, it is suggested by the model and it certainly was an appropriate extension of the model. Hence, whereas Schlesinger mistakenly believes that T implies T*, it does seem that T* is a legitimate extension of T. There- fore, Gutting's charge that D, God's desire to create, is questionable and should be rejected is unfounded. The appropriate theistic hypothesis is T*, not T. 18

Now it might be objected that T* violates the principle of parsimony somehow. Mackie charges that parsimony is violated when one postulates that God has and fulfills certain intentions. Swinburne re- jects the existence of the world as self-explanatory because it is not simple: it's complexity, particularity, and infinity require an explanation. However, Mackie contends that postulating divine intentions is also a violation of simplicity: "Second, the particularity has not been removed, but only shelved: we should have to postulate particularities in God, to explain his choice of the particular universe he decided to create. ''19 This only raises the complexities of simplicity. In defense of T*, T* postulates only one being, just as T did. Thus, one's on- tology is not increased in the shift from T to T*. Now it might be charged that whereas entities are not multiplied, properties are. But,

138

if T* is suggested by T then there can be no great qualitative difference between the two. T contains the property of being personal, and T* expands T by stating that God desires to create personal creatures like us. If T* is less simple than T, it is only slightly less so. Hence, the criticism that T* violates a principle of parsimony carries little weight at best.

In conclusion, it seems that T* is the appropriate hypothesis for consideration. However because the actual world is only one of an infinite number of equi-possible worlds like this world, one is still left with the problem that P(W/T*&K) is not non-zero.

5. Explanation and measure theory

So far it has proven impossible to make any non-zero assignment to the probability of the existence of the world on the hypothesis of theism. The problem is that there are an infinite number of possible worlds which are consistent with the hypotheses of theism, both T and T*. But perhaps the project is not completely hopeless. It does seem that a person might justifiably believe that while the probability of this world on the hypothesis of theism is exceedingly low, the probability of a world like this worm might have a significant probability on the hypothesis of theism. This may be Swinburne's point when he says that the cosmological argument considers (in its most usual form) that there exists a complex physical universe. 2~ This is a much leas specific conclusion than the one we have been considering and, hence, is more easily confirmed. As argued in the previous section, a person may legitimately take as the hypothesis of theism that God desires to create creatures like us. If our analysis proceeded as before there are, nonetheless, an infinite number of possible worlds in which creatures like us exist, so that the probability of this world would still not be non-zero.

But suppose we approach the project in a different manner. It seems that the appropriate method for the assessment of the probability of the existence of the actual world would be better served not by considering every possible world but by considering classes of possible worlds. On this view the prior probability of the existence of the actual world may be exceedingly low because it may be just one of an infinite number of possible worlds. It also may be exceedingly low

139

because this world may be assigned to a class of worlds like this one, and there may be, depending on one's partitions of logical space, an infinite number of classes of worlds of which its class is merely one member.

Now, considering assigning the actual world to a class, what can be said for the hypothesis of theism explaining the existence of the actual world? Let us suppose that one assigns the actual world to the class of worlds like the actual world. Every world in this class will have general, natural regularities conducive to life; and some of the creatures in these worlds will be free, rational, moral beings. The issue which remains is: is it possible to compare one class of worlds with the totality of classes of worlds? What one is doing is picturing, or representing how P(W/T&K) may be sensibly understood. On this representation W is assigned to a class; but W is a member of many classes. Suppose one partitions logical space into only two classes: those worlds like W and those worlds that lack one or more of the properties which were listed above for a world's being similar to W. In this case one must compare only two classes of possible worlds. It is also clear that logical space may be divided up into only three classes of possible worlds, or only four classes of possible worlds . . . . , or a million classes of possible worlds, ... ad infinitum. Thus, one's interpretation depends on how one partitions logical space and there seems to be an infinite number of ways to partition logical space.

The problems with the required comparisons are that not only does each class contain an infinite number of possible worlds, there also may be, depending on one's partitions of logical space, an infinite number o f classes of possible worlds. However, these classes may be sensibly compared by employing density measures to assess each class. This method for representing or picturing may be applied to probabilities in mathematical contexts. Suppose one wanted to assess the probability of every third number in an infinite randomly chosen sequence of integers (which sequence is marked by the successor relation) being a number divisible by three. To assess this probability, one would compare the class of possible random sequences with the class of random sequences divisible by three. In this case, both the reference and attrib- ute classes contain an infinite number of members. However, their comparison may be represented by weighting and, then, comparing the classes. This representation pictures the class of possible random sequences as three times larger than the class of random sequences in

140

which every third number is divisible by three. Of course, these two classes cannot be actually compared. It is not the case that the former class is only one-third the size o f the latter class. Hence, this method won't serve to determine the probabilities. If one did not know before- hand that the probability was 1/3, one would not be able to make the appropriate partitions. Thus, this method will not determine probabilities, it only provides a picture which makes these probabilities meaning- ful or sensible. Therefore, one can sensibly hold that the probability of every third number in an infinite randomly chosen sequence (as described above) being divisible by three is 1/3. Thus, classes with an infinite number of members can be intelligibly represented by measure theory.

Carnap's logical interpretation of the probability calculus is best seen as an instance of measure theory. Carnap contends that certain problems in confirmation theory may be solved by shifting consideration from the individual to classes of individuals. As Salmon puts it: "The only thing that distinguishes individuals from one another is some qualitative difference, not a mere difference of name or identity. Hence, the fundamental possibilities to which we assign equal weights should not discriminate on the basis of individuals. ''21 For Carnap state descriptions are descriptions of possible state of affairs: "Each state description is a conjunction of simple statements, each of which asserts or denies that a given individual has the property in question; moreover, each state description contains one such assertion or denial for each individual. ''22 Comparisons need not be made according to individual state descriptions; state descriptions themselves may be conjoined by picking out relevant characteristics which obtain in similar state descriptions. These are called structure descriptions: "Carnap says that state descriptions that differ from each other only in arrangement of the individual names are isomorphic; a collection of all the state descriptions isomorphic to each other is a structure description.'23

Salmon sets up a system of state descriptions and structure descriptions using a simple logical language. The language consists in three terms "a," "b," and "c," as the names of individual entities and one descriptive predicate " F " referring to a property which the individuals may have or lack. The possibilities for state and structure descriptions in the language may be summarized as follows:

141

State description

Weight Structure Weight description

1. Fa&Fb&Fc

2. -Fa&Fb&Fc

3. F a & - F b & F c

4. F a & F b & - F c

5. - F a & - F b & F c

6. - F a & F b & - F c

7. F a & - F b & - F c

8. F a & - F b & - F c

one-fourth one-twelfth

one-twelfth

one-twelfth

one-twelfth

one-twelfth

one-twelfth

one-fourth

I. All F one-fourth

II. 2F, 1 -F one-fourth

III. 1F, 2 - F one-fourth

IV. No F one-fourth

On Carnap's account each structure description is assigned equal weight whereas state descriptions are assigned different weights. 24

On this interpretation of the probability calculus, probability is a measure of possible states of affairs, either of possible worlds, state descriptions, or of classes of possible worlds, structure descriptions. The problem which Salmon recognizes is that there does not seem to be one determinate means for assigning the measures:

There are many alternative ways of assigning such a measure; for instance, there are infinitely many ways of assigning nonnegative weights to the state descriptions of our simple illustrative language in such a way that together they total one .... Alternative methods of weighting have, of course, differing degrees of intuitive plausibili- ty. The inescapable question is: How are we to select the appropriate weighting or measure from the superdenumerable infinity of candi- dates? 2s

The answer to Salmon's rhetorical question, at least with respect to the explanatory power of theism, is that there is no theory-free way of assigning the appropriate weightings. The weights which one assigns will depend on other beliefs that one has.

Given a measure theory analysis, what can be said for the theistic hypothesis explaining the existence of the world? If one takes the hypothesis as Swinburne does (God is omnipotent, omniscient, and wholly good) then there are not only an infinite number of possible

142

worlds consistent with that hypothesis, there are also an infinite number of classes of worlds consistent with that hypothesis. On this hypothesis the existence of the actual world is, therefore, not non-zero. But if one may rationally consider the hypothesis that God also desires to create creatures like us in a world with natural laws (T*), then one may get a non-zero probability. That is, one may sensibly believe that the probability that God would create a world like this one is quite high. This is done by assigning the actual world to a class of possible worlds like IV in the relevant senses (specified by a structure description). Now suppose there are other structure descriptions (in one's partitions) which are also compatible with T*; the assessment of the probability of God's creating the actual world will be made in comparison with those classes of worlds. That is, one compares the structure description to which one assigns IV with all of the structure descriptions with which the hypothesis of theism is compatible. Thus, the P(W/T*&K) will be equal to: the structure description to which one assigns Iv/the structure descriptions with which the hypothesis of theism is compatible (IV*). And this will depend on how one partitions logical space. So, as with the number example, this method will not serve to determine P(W/T*&K); that will depend on how one partitions logical space. Thus, this method will only provide an interpretation of one's belief that P(W/T*&K)=X, it will not determine that P(W/T*&K)-X.

Of course, in order to determine the explanatory power of theism one must also determine the a priori probability of the existence of the world. We have assumed throughout this discussion that the a priori probability of the existence of the world is exceedingly low. On the measuring analysis, the theist's intention is to provide an interpretation of the explanatory power of theism [P(W/T&K)] which is greater than the a priori probability of the existence of the world [P(W/K)]. Of course, the latter may be stated in terms of structure descriptions, that is, what is the likelihood of the existence of a world like the actual world? On the measuring analysis this would be determined by assigning the actual world to a class of possible worlds in which all of the worlds are isomorphic, in the relevant respects, to the actual world. Presumably the theist will also believe that there are an infinite number of classes of possible worlds or structure descriptions. Hence, the a priori probability of the existence of the world will be: the structure description to which one assigns the actual world/

143

every structure description. Since all of the structure descriptions are assigned equal weights, this value will be exceedingly low.

However, the non-theist may partition logical space in such a manner that this does not follow. He may partition logical space into only two classes: the structure description specifying those worlds with which the actual world is isomorphic in the relevant respects, and the structure description specifying all of the state descriptions which are not isomorphic to the actual world in the relevant respects. Thus, this measuring analysis consists of only two structure descriptions. Given the means for assessing the a priori probability of the existence of the actual world in the previous paragraph and assigning equal weightings to the structure descriptions, the value assigned on this partitioning is 1/2. Unless the non4heist 's partitioning of logical space entails an assignment to P(W/T*&K) which is greater than 1/2, it will not follow that the existence o f the actual world confirms the existence of God.

Since the values which one assigns depend upon one's partitionings of logical space, and since one's partitionings of logical space depend upon one's intuitions, the values assigned will not serve to advance an argument for or against the existence of God. That is, this sort of probablistic argument for the existence of God will not constitute a successful piece of classical natural theology. 26 The best that such an argument can accomplish is to persuade someone who already shares some of one's basic intuitions.

6. Conclusion

On the measure theory interpretation of P(W/T*&K) one may sensibly believe that P(some world like W/T*&K) is a significant non-zero probability. If so, P(W/T*&K) may be significantly greater than P(W/K); in which case one may sensibly believe that the hypothesis of theism explains the existence of the world. However, this analysis is not without its problems. First, on T, the hypothesis that God is omnipotent , omniscient and wholly good, one is still left without a non-zero probability. If it is not legitimate to consider a hypothesis like T* (although I have argued that it is), then one is left with the problems specified in the preceding sections. Second, this argument depends on one's partitions of logical space. There seems to be no right way to partition logical space or, at least, no way to determine that right way. Mackie

144

may partition logical space one way, the theist another. The measure theory analysis is incapable of determining T probabilities; it merely provides an interpretation of one's intuitions. Thus, measure theory will not advance an argument for the existence of God. Mackie's beliefs suggest that he would partition logical space in such a way that P(W/T* &K) is not significantly greater than P(W/K)o As Mackie says:

Against the rival theistic hypothesis we should have to score the (significant) improbability that if there were a god he (or it) would create a world with causal laws, and one with our specific causal laws and constants, but also the great improbability of there being a process of the unmediated fulfillment of will, and, besides, the basic improbability of there being a god at all. 27

Thus, while measure theory does make sense out of P(W/T*&K) it will not prove polemically useful. ~

In conclusion, we have tried to make sense out of what one could mean, in a Bayesian cosmological argument for the existence of God, by the explanatory power of theism or in formal terms P(W/T&K)> P(W/K). This analysis assumed that sense could be made of the prior probability of the brute existence of the world [P(W/K)] and that it is exceedingly low. The reasoning for assigning the exceedingly low antecedent probability to the existence of the actual world is that there are an infinite set of possible chaotic worlds or worlds without free, conscious, moral agents which are consistent with the naturalistic hypothesis. The argument for theism does not need to prove that the existence of the actual world is impossible without God, but only that it is antecedently more probable that the world be like it is given the theistic hypothesis than without the theistic hypothesis (because God might prefer this kind of world). The argument of this essay has shown that it is very difficult to make sense of the claim that it is a priori more probable that God create this world than that the world exist simpliciter, and that the only way to make sense of this claim is by measure theory; a method which will not serve to advance an argument for or against the existence of God. Yet a measure theory analysis seems to have some intuitive appeal and it does provide an interpretation for one's intuition that the hypothesis of theism does, indeed, explain the existence of the world.

145

Notes

1. Richard Swinburne, The Existence of God (Oxford, 1979); J.L. Mackie, The Miracle of Theism (Oxford, 1982); George Schlesinger, Religion and Scientific Method (Dordrecht-Netherlands, 1977); Gary Gutting, Religious Belief and Religious Skepticism (Notre Dame, 1983).

2. Swinburne, p. 51. 3. I have taken l iberty with the notat ion to standardize it for this essay. Swin-

burne, in his cosmological argument for the existence of God, takes K to be mere tautological information, and Mackie does not. The significance of this is considered in note 27. Schlesinger has an enriched hypothesis of theism which is considered in Section 4.

4. More precisely, it is a consequence of Bayes' theorem plus another theorem, P(T/W&K)>P(T/K), which asserts that a theory T is confirmed by evidence W given background knowledge K.

5. It is an assumption of this essay that everything logically compatible with a hypothesis is equally probable on that hypothesis. Unless there is some reason for the hypothesis to exclude a state of affairs then it will be considered equi-possible on the hypothesis. For our purposes, we will consider which possible worlds are compossible with.a given hypothesis.

6. This, as we shall see, is misleading. Swinburne has a rather different specifica- t ion of W which will be explicated shortly.

7. Swinburne, p. 53. 8. Ibid., pp. 130-131. 9. This specific criticism will not apply to Swinburne's argument because he is

not at tempting to explain the existence of the actual world. Rather, he is trying to explain the existence of a complex physical universe. See Section 5.

10. Schlesinger, op.cit., p. 182. 11. Ibid., p. 183. 12. In addit ion he says on page 7: "What are clearly of interest to men in an age

of religious skepticism are arguments to the existence (or non-existence) of God in which the premisses are known to be true by men of all theistic or atheistic persuasions."

13. Swinburne's distinctions are as follows: "Let us call an argument in which the premisses make the conclusion probable a correct P-inductive argument. Let us call an argument in which the premisses add to the probabil i ty of the conclusion (i.e. make the conclusion more likely or more probable than it would otherwise be) a correct C-inductive argument. In this case let us say that the premisses 'confirm' the conclusion." Swinburne, p. 7.

14. Gutting, op.cit., p. 129. 15. Ibid. 16. Ibid., p. 130. 17. This criticism is surely unfounded. Not all theists appeal to the inscrutabili ty

of divine knowledge in their discussions of the problem of evil. Swinburue, for example, offers just such a theodicy. See, Swinbume, op.cit., pp. 2 0 0 - 2 2 4 .

146

18. This somewhat overstates Gutting's argument. Gutting contends that the original hypothesis T is a strong explanation and that T* is a weak explana- t ion because it adds assumptions to T which we have no reason to think are true. My argument would counter this weaker claim as well.

19. Mackie, op.cit. , p. 100. 20. Swinburne, op.cit., p. 129. 21. Wesley Salmon, The Foundations of Scientific Inference (Pittsburgh, 1966),

p. 72. 22. Ibid., pp. 7 0 - 7 1 . 23. Ibid., p. 72. 24. Ibid., p. 73. For a fuller discussion of the issues see ibid., pp. 6 8 - 7 9 . 25. Ibid., p. 75. 26. A successful piece of natural theology employs premises which all rational

creatures are obliged to accept. Our intuitions into the nature of logical space are so tenuous, that they cannot be considered rationally obligatory.

27. Mackie does this by rejecting Swinburne's intention to take K to be mere tautological information. He argues that on our experience the existence of a disembodied spirit directly fulfilling intentions (say, to create the world) is extremely unlikely. See, Mackie, op.cit., pp. 100.

28. If God's existence is contingent as Mackie and Swinburne contend, then in how many possible worlds does he exist? And in how many possible worlds does he create worlds like the actual world? In how many possible worlds are there disembodied spirits directly fulfilling intentions? If we consider epistemic probabil i ty, given our background beliefs, what is the degree to which one ought to believe that disembodied spirits directly fulfill intentions, i.e. what is the rational ratio of such worlds to the remainder of possible worlds? These considerations suggest the difficulty, again, of determining these probabilities.

the explanatory power of theism

Documents