Swinburne and the Inductive Cosmological Argument
Richard Swinburne, in his book The Existence of God, presents what is easily the most careful, comprehensive, and plausible set of arguments yet offered in defense of theism as an explanatory hypothesis. He begins, admirably, with a detailed examination of the nature of inductive argument, the structure of explanations, and the principles of confirmation theory. He then examines six arguments supporting and one against theism construed as an explanatory hypothesis. His conclusion is that, though none of the theistic arguments considered in isolation makes it more probable than not that God exists, when taken together they show that the balance of probability favours the truth of theism.
One of Swinburne's theistic arguments, the one from miracles, will be examined in a later chapter. Another one from religious experience, does not readily fit into an hypothesis-confirming format and so is omitted from this thesis. The one anti-theistic argument that he considers, the problem of evil, will also be the topic of a later chapter. Two other of his arguments, the teleological and the argument from consciousness, have already been thoroughly and, in the present author's view, decisively criticized by J.C.A. Gaskin and J.L. Mackie respectively. Further, since Swinburne does not regard as sound one of the arguments he considers, the argument from morality, only his cosmological argument is left to be examined in this chapter.
A crucial distinction for Swinburne--mentioned earlier as having escaped Schlesinger's notice--is the difference between what he calls P-inductive and C-inductive arguments:
Let us call an argument in which the premisses make the conclusion probable [i.e. more likely than not to be true] a correct P-inductive argument. Let us call an argument in which the premisses add to the probability 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 premises 'confirm' the conclusion. Among correct C-inductive arguments some will obviously be stronger than others, in the sense that in some the premisses will raise the probability of the conclusion more than the premisses do in other arguments.
In asserting that the cosmological argument is a correct C-inductive argument, Swinburne is making a fairly modest claim. He does not claim that the existence of the universe makes it more probable than not that God exists, only that its existence constitutes evidence favouring the hypothesis that there is a God. In other words, all that Swinburne is claiming is that the intrinsic or a priori probability of theism is lower than its probability when the existence of the universe is considered as evidence for that hypothesis.
Swinburne recognizes that many will object that it is unintelligible to speak of the universe as a whole as evidence for anything. Since Hume it has been argued that, because the universe is by definition unique, it belongs to no reference class with respect to which any probabilities can be determined. Hence, it cannot be said that the universe is any more or less probable on one hypothesis than another. Therefore its existence cannot serve as evidence for any hypothesis.
Swinburne replies that cosmologists do in fact make statements about the origins, size, structure, etc. of the universe and are not the least deterred by its uniqueness in making these claims. Further, he contends that any object is unique under some description and that it has not been shown that the universe is unique in a different sense. Gaskin has cogently criticized Swinburne on these points and there is no need to dwell on them here.
Swinburne holds that Bayes' theorem provides the machinery for determining the probability of an hypothesis given a particular piece of evidence. The formula for Bayes' theorem is:
p(e/h.k) p(h/e.k) ---------- X p(h/k) p(e/k)
where h is whatever hypothesis we are considering, e is the particular evidence, and k is background knowledge, i.e. all relevant information not included in e. Bayes' theorem tells us that the probability of certain hypothesis relative to a piece of evidence plus our background knowledge--p(h/e.k)--is dependent on three factors: (1) p(e/h.k); the probability of the evidence's having occurred given that the hypothesis is true (plus our background knowledge), (2) p(e/k); the probability that the evidence took place independently of our hypothesis, i.e. its probability with respect only to background knowledge, and (3) p(h/k); the probability of the hypothesis being true independently of the particular evidence, i.e. the probability of its truth given only background knowledge. Therefore, the probability of a certain hypothesis given a particular piece of evidence will be directly proportional to the probability stated in factors (1) and (3) and inversely proportional to that stated in (2).
A stock example may be employed to illustrate the way that Bayes' theorem systematizes a number of basic insights into the relation of evidence to hypotheses. Suppose that Jones is found murdered and Smith's fingerprints are on the murder weapon. The probability of the hypothesis that Smith murdered Jones (h) given that Smith's fingerprints were found on the murder weapon (a) is determined by the three factors mentioned above. The probability of h given e is also increased (factor 1) to the extent that it is likely that if Smith did indeed murder Jones his fingerprints would be on the murder weapon. The probability of h given e is also increased (factor 3) to the extent that it is likely that Smith murdered Jones given all our evidence other than the presence of his fingerprints on the murder weapon. If, for instance it were part of our background knowledge that Smith had a strong motivation to kill Jones and had threatened to do so repeatedly, this would increase the probability of h given e. On the other hand, if our background knowledge included the fact that Smith had an ostensibly flawless alibi at the time of the murder, this would adversely affect the probability of our hypothesis. Similarly, if it were somehow quite likely that Smith's fingerprints would be found on the murder weapon whether or not he killed Jones (factor 2) this would decrease the probability of h given e.
In the remainder of this chapter it will be convenient to follow Swinburne's symbolizations of his arguments. Henceforth (except where otherwise noted) h will stand for the hypothesis that God exists, e for the existence of the entire physical universe, and k, since all possible empirical evidence has been included in e, will be mere tautological knowledge. Thus p(h/e.k) is the probability that God exists given that the universe exists, p(e/h.k) is the probability that the universe exists given that God exists, p(h/k) is the intrinsic probability of theism (i.e. the probability that God exists given only tautological background knowledge--in short, that God exists as the ultimate, uncaused fact) and p(e/k) is the intrinsic probability of naturalism (i.e. the probability that the universe is the ultimate, uncaused fact).
With these preliminaries in place, we may now turn to the cosmological argument. However, it should be noted in passing that many philosophers, including some eminent theists, do not believe that theism and naturalism have intrinsic, a priori probabilities. Alvin Plantinga, for instance, completely rejects the notion that hypotheses can have purely a priori probabilities. John Hick views theism and naturalism as total, all-encompassing interpretations which, by their very comprehensiveness, preclude the existence of a neutral scale for the weighing of their relative probabilities. Swinburne does not adequately address such objections.
Traditionally, defenders of the cosmological argument have viewed it as a sound deductive argument that succeeds in demonstrating the existence of God. Such defenders, e.g. Leibniz and Clarke, have based their case on the Principle of Sufficient Reason. That Principle is the claim, taken to be intuitively obvious and apodictically certain, that nothing can exist unless there is some sufficient reason both for its existence and its possession of the particular attributes that it has. A second pillar of the traditional cosmological argument is the claim that God is the only being who possesses a sufficient reason for his own existence.
Critics of the traditional cosmological argument have challenged both of its fundamental premises. It has been argued that the Principle of Sufficient Reason is not intuitively obvious; indeed, it has been claimed that it is demonstrably false. Further, it has been charged that no being, not even God, can constitute a sufficient reason for its own existence.
Neither of the above standard criticisms applies to Swinburne's version of the argument. Swinburne does not rely upon the Principle of Sufficient Reason; he readily admits that the universe could conceivably be an ultimate, unexplainable brute fact. Further, he does not conceive of God as possessing a sufficient reason for his own existence. God, if he exists, will simply be the ultimate (logically) contingent fact.
One consequence of Bayes' theorem is that a hypothesis is confirmed by a piece of evidence if and only if that evidence is more likely to occur if the hypothesis is true than if it is false. Symbolically, for any h, e, or k, p(h/e.k) > p(h/k) iff p(e/h.k) > p(e/~h.k). In other words, the truth of the hypothesis must be in some strong sense relevant to the occurrence of the evidence (hence this consequence is called the "relevance condition"--a condition that an hypothesis must meet if the cited evidence is to lend it any support). Therefore, for Swinburne to show that the existence of the physical cosmos confirms (i.e. raises the probability of) the claim that God exists, it is necessary and sufficient to show that the universe is more likely to exist if there is a God than if there is not. This is precisely what Swinburne claims to be shown by the cosmological argument.
For Swinburne, a cosmological argument is one that starts from the existence of any finite object. However, since most such arguments have begun with the existence of the entire cosmos, Swinburne restricts his attention to these. Cosmological arguments begin with evident facts of experience. It is, for instance, unquestionably true that there exists a complex physical universe. In order for there to be an argument from the universe to God it must be shown both that the universe somehow requires explanation and that God is the only, or at least the most likely, source of such explanation.
According to Swinburne there are two ways that the universe could require such explanation. If the universe has existed for a finite time, then, even if all states of the universe since the first are adequately explained in terms of earlier states, the initial state itself will be unexplained. Of course, since he repudiates the Principle of Sufficient Reason, Swinburne sees no incoherence in the notion of an unexplained first state. However, he will later clalm that such inexplicability is unacceptable even though it is coherently conceivable.
Further, Swinburne claims that it is a mystery why the universe should remain in existence over time, whether that time is of finite or infinite duration. That is, even if we allow that the universe is infinitely old and that each state of the universe has a complete scientific explanation in terms of earlier states and the laws of nature, it is claimed that the series of states and laws taken as a whole will have no explanation. It is this purported mystery that Swinburne holds to provide the strongest reason for invoking the theistic hypothesis.
Of course, the claim that a series can remain unexplained even if its individual members are explained runs head-on into a famous argument of Hume's:
In...a chain...or succession of objects, each part is caused by the part which preceded it, and causes that which succeeded it. Where then is the difficulty? But the whole, you say, wants a cause. I answer that the uniting of several parts into a whole like the uniting of several distinct countries into a kingdom, or several distinct members into one body, is performed merely by an arbitrary act of the mind and has no influence on the nature of things. Did I show you the particular causes of each individual in a collection of twenty particles of matter, I should think it very unreasonable, should you afterwards ask me what was the cause of the whole twenty. This is sufficiently explained in explaining the cause of the parts.
Swinburne opposes this with a rather brusquely worded counterclaim:
It would be an error to suppose that if the universe is infinitely old, and each state of the universe at each instant of time has a complete explanation in terms of a previous state of the universe and natural laws (and so God is not invoked), that the existence of the universe throughout infinite time has a complete explanation or even a full explanation. It has not. It has neither. It is totally inexplicable.
Swinburne begins his argument against the Humean claim by stating the principle that the cause of a collection of states is any collection of the causes of each state. Hence, if a is caused by a', b by b', and c by c', the cause of the collection a+b+c is a'+b'+c'. For instance, if lamp a lights because switch a' was thrown, lamp b lights because switch b' was thrown and lamp c lights because switch c' was thrown, then the cause of the lighting of lamps a, b, and c will the throwing of switches a', b', and c'. So far Hume would be in complete agreement.
However, when we have a collection of states wherein some states are caused by other states in that same collection, this principle must be modified:
... a full cause of the occurrence of a collection of states is any collection of (full) causes of each, which are not members of the former collection. Hence if a full cause of a is b, of b is b', of c is d, and of d is d', then a full cause, of a+b+c+d is b'+d'. If a full cause of a is b, of b is c, of c is d, and of d is e, then a full cause of a+b+c+d is e.
For instance, suppose Jones is killed by the house collapsing, the house collapses because the dynamite went off, the dynamite went off because the fuse was lit, and the fuse was lit because Smith set a match to it. Then we would say the cause of the whole chain of events--the lighting of the fuse, the explosion of the dynamite, the collapse of the house, and Jones's death--was Smith's setting a match to fuse.
Swinburne concludes that:
... in so far as a finite collection of states has a cause, it has its cause outside the set. Hence if the universe is of finite age, and the only causes of its past states are prior past states (i.e. scientific causality alone operates), the set of past states as a whole have no cause and so no explanation.
Swinburne contends that the same conclusion applies if the universe is infinite in age and the only causes invoked are past states of the universe and the laws of nature. In this case, though each state of the universe might have complete scientific explanation, the whole series will lack an explanation since there will be no causes of members of the series that are not themselves members of the series. Swinburne concludes that: "In that case the existence of the universe over infinite time will be an inexplicable brute fact. There will be an explanation [in terms of the laws of nature] ... of why, once existent, it continues to exist. But what will be inexplicable is the non-existence of a time before which there was no universe.
Further, there are certain permanent features of the universe, such as the amount of energy it contains, that Swinburne views as requiring explanation. Conservation laws tell us, given that the universe does contain a given amount of energy, that it will always contain just that amount. However, it is quite conceivable that the universe could all along have contained a different amount of energy. Therefore the universe lacks an explanation of why it contains just the amount of energy it does and neither more nor less.
Swinburne realizes that in order to show that the universe requires explanation it is insufficient to show merely that it lacks explanation. The repudiation of the Principle of Sufficient Reason entails that the ultimate, uncaused reality, whatever that might be, will be an inexplicable brute fact. But if there can exist a terminus of explanation for which no further explanation can be given, why cannot that terminus be the fundamental law and entities of the physical universe rather than God?
According to Swinburne, though there is no incoherence or absurdity in supposing the universe to be the ultimate brute fact, it is very unlikely that it will be. That is, p(e/k) is very close to zero. In fact, Swinburne regards the intrinsic probability of naturalism as so law that the notion of the universe as the ultimate brute fact is hardly more acceptable for him than it was for Leibniz or Clarke.
Further, Swinburne maintains that it is very unlikely that any being other than God will be the ultimate, uncaused cause of the universe. That is, he argues tht all hypotheses postulating a creator other than the God of theism have a very low order of probability.
It will be recalled that what Swinburne is trying to show is that it is more likely that the universe will exist given that God exists than that it will exist given that God does not exist, i.e., that p(e/h.k) > p(e/~h.k). Once this is shown, the "relevance condition" mentioned earlier will have been satisfied and it will be shown that theism is confirmed by the existence of the universe and hence that the cosmological argument is a good C-inductive argument.
The probability that the universe will exist given that God does not exist, p(e/~h.k), is equal to the probability that the universe is uncaused, p(e/k), plus the probability that the universe is caused by some entity other than God. Hence, if, as Swinburne claims, these last two probabilities are both exceedingly small, then it follows that the sum of these two probabilities , p(e/~h.k), is still very small. If it is thus extremely unlikely that the universe will exist unless God exists, and it is not equally or more unlikely that God exists, then a theistic explanation of the existence of the universe would seem to be warranted.
Further, if we have good reason to believe that p(e/h.k) is not too low, that is, that it is not too unlikely that this universe is the one that God would create, then we can with some confidence assert that p(e/h.k) > p(e/~h.k). If we are justified in doing this we will have shown that the theistic hypothesis satisfies the "relevance condition" and hence that the universe does supply confirming evidence for the existence of God.
Why, though, is it so very unlikely that the universe will be the ultimate, uncaused brute fact? Why is it also so very improbable that the universe has been caused by some entity other than God? The former question should be examined first.
According to Swinburne, anything so enormously complex as the physical universe cries out for explanation and so itself is not a good candidate for the terminus of all explanation:
A complex physical universe (existing over endless time or beginning to exist at some finite time) is indeed a rather complex thing. We need to look at our universe and meditate about it, and the complexity should be apparent. There are lots and lots of separate chunks of it. The chunks each have a different finite and not very natural volume, shape, mass, etc.--consider the vast diversity of the galaxies, stars, and planets, and pebbles of the seashore. Matter is inert and has no powers which it can choose to exert; it does what it has to do. There is just a certain finite amount, or at any rate finite density of it, manifested in the particular bits... There is a complexity, particularity, and finitude about the universe which cries out for explanation...
Swinburne justifies his claim that the universe, in virtue of its complexity, is unlikely to be the ultimate brute fact by appealing to confirmation theory. Swinburne defines the complexity and simplicity of hypotheses in terms of the number of entities, the kinds of entities, and, the types of relations between entities that they postulate. Hence, an hypothesis that postulates one or a few entities will, ceteris paribus, be simpler than one that postulates many entities. The same holds for hypotheses that postulate fewer types of entities or less intricate relations between entities than rival hypotheses. Given such an understanding of simplicity and complexity, the hypothesis that the physical universe is the ultimate, uncaused existent will be a very complex hypothesis indeed.
It is a fundamental tenet of evolutionary theory that extremely complex hypotheses have very low a priori probability unless that complexity is counterbalanced by redeeming virtues such as a very high degree of concordance with background theory. However, when our hypothesis concerns the postulation of an ultimate, uncaused terminus of all explanation, there seems to be nothing left to serve as background (except, of course, tautological knowledge). In other words, if we are seeking the ultimate terms for the explanation of everything, then, by definition, there will be no background entities, and hence no theories about such entities with which those terms must accord.
Since Swinburne regards naturalism as such an ultimate hypothesis, he holds that background knowledge is irrelevant to the assessment of its intrinsic probability. He maintains that simplicity is the only consideration that has much bearing on the a priori or any other such ultimate hypothesis. Having, he believes, established that naturalism is a very complex hypothesis, he concludes that it has a very low intrinsic probability.
Surely, though, some hypotheses other than theism could postulate very simple beings as the creators of the universe. Swinburne replies that, however simple the beings postulated by other hypotheses might be, the God of theism will be much simpler still.
Swinburne contends that theism is an extremely simple hypothesis because it postulates only a single entity of a very simple kind. Indeed, God is alleged to be the simplest conceivable kind of person. One reason that God is such an extremely simple entity is that his capacities are infinite:
To start with, theism postulates a God with capacities which are as great as they logically can be. He is infinitely powerful, omnipotent. That there is an omnipotent God is a simpler hypothesis than the hypothesis that there is God who has such-and-such limited power (e.g. the power to rearrange matter, but not the power to create it). It is simpler in just the same way that the hypothesis that some particle has zero mass, or infinite velocity is simpler than the hypothesis that it has a mass of 0.34127 of some unit, or a velocity of 301,000 km/sec. A finite limitation cries out for explanation of why there is just that particular limit, in a way that limitness does not... There is... a neatness about zero and infinity which particular finite numbers lack. Yet a person with zero capacities would not be a person at all. So in postulating a person with infinite capacity the theist is postulating a person with the simplest kind of capacity possible.
Hence, if Swinburne is right, theism, insofar as it postulates an omnipotent being, is simpler than any alternative hypothesis postulating a limited, finite entity as the creator of the universe.
Another factor cited as enhancing the simplicity of theism is that God's attributes are claimed to fit together in a particularly intimate and natural way. For instance:
It would seem most consonant with his omnipotence that an omnipotent being have beliefs which amount to knowledge (for without knowledge of what you are doing you can hardly have the power to do any action). The simplest such supposition is to postulate that the omnipotent being is limited in his knowledge, as in his power, only by logic. In that case he would have all the knowledge that it is logically possible that a person have, i.e. he would be omniscient.
For a person to act, he has to have intentions. His intentions might be determined by factors outside his control... It would, however, seem more consonant with his omnipotence for an omnipotent being to be entirely uninfluenced in his choice of intentions on which to act by factors outside his control, i.e. to be perfectly free. (For an omnipotence which you cannot but use in predetermined ways would hardly be worth having.)
Similar arguments are made with respect to God's eternity. An even stronger claim is made with respect to God's perfect goodness. It is argued that a being with complete knowledge and perfect freedom will always necessarily choose the good.
It follows that an hypothesis that postulates an omnipotent, unlimited being who fails to possess one or more of omniscience, perfect freedom, or eternal existence, will not be as simple as theism since these properties are the ones that it is simplest to suppose an omnipotent being to possess. Further, an hypothesis postulating a being possessing all these properties and less than perfect goodness is alleged to be incoherent. It appears, therefore, that whether an alternative hypothesis postulates a limited or unlimited being, that being will lack the simplicity of the theistic God.
In making an evaluation of Swinburne's arguments, it will be helpful to begin by stepping back and looking at the nature of his project as a whole. Swinburne unambiguously affirms that his aim in The Existence of God is to provide an argument for theism that is in all relevant essentials identical with certain types of scientific arguments:
The structure of a cumulative case for theism was thus, I claimed [in The Existence of God], the same as the structure of a cumulative case for any unobservable entity, such as a quark or a neutrino. Our grounds for believing in its existence are that it is an entity of a simple kind with simple modes of behaviour which leads us to expect the more complex phenomena which we find.
Just how similar, though, are Swinburne's theistic arguments to the grounds upon which physicists base their beliefs about quarks and neutrinos? It is true that much of the initial plausibility of the quark model was due to the fact that it provided a simple account of an enigmatic complexity. Physicists in the early 1960's were confronted with a baffling array of hundreds of species of hadrons--those particles, believed elementary at that time, that are affected by the strong nuclear force. Then, in 1964, Murrary Gell-Mann showed how the bewildering variety of hadrons could be accounted for by suggesting that they are composite particles, each constitutes by a different combination of a small number of point-like particles which he called quarks. Gell-Mann's quark hypothesis was regarded as plausible for precisely the reasons mentioned by Swinburne--it provided a simple account which, if true, would explain a confusingly complex batch of phenomena.
However, the story hardly ends here. As physicist Richard Morris observes, so long as experimental evidence for quarks was lacking, their actual existence was held in doubt:
At first, many physicists regarded quarks as nothing more than a useful mathematical fiction that could be used to impose order upon the chaotic world of subnuclear particles. They didn't believe that the quarks corresponded to anything real. When attempts to find free quarks in nature failed, their suspicions were confirmed. The quark, they concluded, was an imaginary particle that made the job of doing physics somewhat easier.
In other words, in the absence of experimental confirmation, the simplicity and explanatory power of Gell-Mann's model only sufficied to establish quarks as convenient fictions, not as actual entities.
Morris notes that the first experimental evidence for quarks came in 1968:
In that year, an experiment was performed which indicated that protons, at least, seemed to be composite particles. Beams of high-energy electrons were directed at proton targets in order to probe the internal structure of the latter. It was found that the protons seemed to contain pointlike charges. The quark hypothesis had been confirmed.
Another physicist writes:
... free quarks have never been observed. Yet circumstantial evidence for their existence has mounted steadily. One indication of the soundness of the quark model is its success in predicting the outcome of high-energy collisions of an electron and a positron... The case for the reality of quarks is also supported by the variety of energy levels, or masses, at which certain species of hadron, notably the psi and the upsilon particles, can be observed in accelerator experiments.
The above quotations indicates that the cumulative case for the existence of quarks is based on the experimental confirmation and predictive success of the model, not merely on its simplicity and ability to account for previously known data.
Swinburne's cumulative case for theism, on the other hand, rests upon no experimental evidence nor does it predict any previously unobserved phenomena. His case rests entirely upon the simplicity of the theistic hypothesis and its purported ability to account for data already within our possession. Hence, contrary to Swinburne's claim, his theistic arguments do not strictly parallel those whereby physicists seek to establish the existence of quarks and neutrinos (neutrinos, by the way, have also been experimentally confirmed).
This, by itself, may not be a particularly damaging criticism. Indeed, Swinburne anticipates such an objection and argues that with regard to Bayes' theorem: "It is a matter of indifference...whether e is observed before or after the formulation of h. All that matters is the relations of probability holding between e and h. And surely the theorem is correct in that respect." Swinburne argues that to deny this would render probability into a highly subjective matter rather than an objective relationship between evidence and hypothesis. Of course, we do normally confirm our hypotheses by subjecting them to experimental tests and by determining their predictive success or failure. However, this need is brought about by the particular hypothesis and evidence under consideration and is not a generalizable requirement.
Swinburne further supports the above claim by adducing the example of Newton's laws of motion:
Newton's theory of motion was judged to be highly probable on the evidence available to men of the late seventeenth century, even though it made no immediately testable predictions, other than the predictions which were already made by laws which were already known and which it explained (e.g. Kepler's laws of planetary motion and Galileo's law of fall). Its high probability arose solely from its being a very simple higher-level theory from which those diverse laws are deducible.
If, therefore, scientists do sometimes justifiably accept new hypotheses purely because of their simplicity and ability to account for presently known phenomena, there seems no reason not to accept the theistic hypothesis if it displays those same virtues.
However, there are important disanalogies between Newton's theory of motion and Swinburne's theistic hypothesis; disanalogies that show how far the latter strays from accepted standards of scientific argument. First, though Newton's laws of motion were not immediately tested, they were in fact testable. They received spectacular confirmation when Edmund Halley correctly deduced from them that the comet, consequently named for him, would reappear in 1758.
Swinburne's theistic hypothesis, on the other hand, not only fails to imply any immediately testable consequences, it appears to be untestable in principle. This is significant because, although scientists do sometimes accept new hypotheses even when they do not imply any immediately testable predictions, they also demand that such hypotheses be capable of making testable predictions. In chapter one testability was proposed as an intuitively plausible hallmark of every genuinely scientific endeavor. However, Swinburne's implicit challenge to this proposal demands that it be defended in some detail.
Underlying the insistence upon testability is the recognition that any hypothesis, no matter how simply it accounts for all presently known data, can be dead wrong, or at least not the whole story. It is entirely possible, as was actually the case with respect to Newton's laws, that a given hypothesis will be an oversimplification. Since any given hypothesis could conceivably be an oversimplification, it ought to be capable of being replaced by a more complicated one should the need arise. However, unless the testability of all hypotheses is insisted on, it is hard to see how this requirement can always be met. Once untestable hypotheses become entrenched they are very difficult to dislodge, even when better (albeit somewhat more complex) hypotheses are available.
The extreme tenacity of superstitious explanations in the face of conflicting, and more productive, scientific accounts is sufficient evidence of this claim. Explanations in terms of demonds, poltergeists, mental telepathy, magic, and other such occult entities and processes frequently possess a greater simplicity, as Swinburne defines the term, than rival scientific explanations. A demon, for instance, is a single entity, it is a spiritual being and hence not compounded of parts, it presumably exercises its power over persons and physical objects in some direct and simple way, and it is in all its deeds actuated by a single motivating drive--malevolence. Hence, explanation of a case of psychosis in terms of demon possession seems much simpler than any currently plausible psychological account. The simplicity and untestability (How could it ever be shown that demons do not cause psychoses?) of such hypotheses gives them great obscurantist potential.
More generally, if we allow untestable hypotheses to be accepted purely on the basis of their simplicity and ability to provide post factum explanations of known data, it is hard to see how science could ever progress. Virtually any phenomenon that we currently think possesses an adequate scientific explanation could be explained more simply in nonscientific terms. Occult powers wielded by disembodied agents could be invoked to cover just about any occurrence. Clearly, if scientific hypotheses are ever to win out over such nonscientific rivals, they must enjoy some advantage other than simplicity and post factum explanatory efficacy. Concordance with background theory will not suffice since every scientific background theory will also have a simpler nonscientific rival. Scientific hypotheses can have a clear advantage only when they are capable, even if only in a very circumstantial, roundabout, or partial manner, or being put to an empirical test. Hence, the insistence upon testability is a demand that lies at the heart of the entire scientific enterprise.
A second disanalogy further distances Swinburne's theistic hypothesis from the Newtonian model. Newton's laws of motion, unlike the quark model and the theistic hypothesis, did not achieve greater explanatory power by postulating the existence of previously unknown--and allegedly discovered or deduced--entities. Newton proposed a set of simple laws that systematically connected a complex set of phenomena previously thought to be disparate and unconnected. Although his laws later led to the discovery of new entities, such as the planet Neptune, they were initially proposed as laws, i.e. as nomological propositions telling us how certain kinds of entities can be expected to behave. The entities those laws applied to--stars, planets, cannonballs, etc.--were already known. The quark model and the theistic hypothesis, on the other hand, propose that new entities be postulated to account for known ones.
The above suggests that a fundamental distinction needs to be made between two different types of explanatory hypotheses: The first, let us call them L-hypotheses, explain known phenomena by postulating simplifying and unifying laws that govern the behaviour of and relations between those phenomena. A second type, call them E-hypotheses, explain known phenomena through the postulation of a new entity or set of entities.
The criterion of simplicity relates to these two types of hypotheses in crucially different ways. An L-hypothesis is confirmed when it is shown to be the simplest testable hypothesis compatible with the known date. With E-hypotheses, however, being the simplest testable hypothesis is not enough. Until the entities postulated by E-hypotheses are confirmed by hard experimental evidence, scientists tend, as in the case of quarks, to regard them as heuristically convenient fictions.
The theistic hypothesis is definitely an E-hypothesis, not an L-hypothesis like the Newtonian model. Further, Swinburne is clearly claiming that God is more than a heuristically helpful fiction. It is therefore quite inadequate to claim that simplicity and post factum explanatory efficacy are sufficient to confirm such an hypothesis.
A final way that Swinburne's theistic hypotheses diverges from the Newtonian model is with respect to its explanatory power. The great simplicity of Newton's laws only partially accounts for their rapid acceptance by Newton's contemporaries. Much of the reason for the initial acceptance of Newton's theory was that known laws, such as Kepler's laws of planetary motion and Galileo's law of fall, could be deduced from that theory. Swinburne, on the other hand, freely admits that no facts about the world can be deduced from the theistic hypothesis. In fact, the most that he ever argues is that the probability that this universe will exist given that God exists, p(e/h.k), is not too low. Hence, even the post factum explanatory power of the theistic hypothesis is quite low in comparison to the Newtonian model. This means that practically the entire support for Swinburne's hypothesis derives from its claimed simplicity. It would be highly instructive for Swinburne to adduce any example of an unquestionably scientific hypothesis that to a similar degree stakes its confirmation entirely upon the criterion of simplicity. Newton's laws of motion do not constitute such an example.
We have seen that Swinburne's claim that his theistic hypothesis parallels accepted scientific ones is open to serious question on a number of points. Swinburne claims that his arguments for theism are much like those that scientists employ when they argue for the existence of unobservable entities such as quarks. This is not so, however. Scientists have experimental evidence for quarks and refused to regard them as real entities until such evidence was forthcoming. Swinburne attempts to circumvent this objection by comparing his hypothesis to Newton's laws of motion. Newton's laws, though incapable of immediate empirical testing, were accepted because of their simplicity and ability to account for known phenomena. However, we have seen that Swinburne's hypothesis diverges from the Newtonian model. These divergences appear significant enough for a reasonable person to be justified in demanding more of the theistic hypothesis than the kind of support upon which Newton's laws were initially established.
Some doubts have been raised about Swinburne's project as a whole. Such doubts do not spell doom for that project; they merely show that, contrary to Swinburne's claim, there is no very strict affinity between his hypothesis and unquestionable scientific ones. This merely reaffirms the conclusion of Chapter One. There it was concluded that whenever theists propose to treat the existence of God as a strictly scientific hypothesis, they inevitably lapse into pseudoscience. We saw that the utter untestability of "scientific" creationism guaranteed its pseudoscientific and obscurantist status. "Scientific" creationism is untestable because it "explains" phenomena in a irremediably unscientific manner and because it predicts nothing that would allow it to clash empirically with evolutionary theory. These features seem to be shared by all theistic hypotheses, including Swinburne's: viz., they specialize in unscientific post factum explanations while making no predictions of a sort that could serve to discredit them in favour of a competing hypothesis. Hence, if Swinburne is construed as claiming that his hypothesis is on all fours with unquestionably scientific ones, the above arguments, and those of Chapter One, force the conclusion that he is simply engaging in pseudoscience.
Perhaps, though, Swinburne would be ready to admit that his hypothesis does indeed diverge rather far from any unquestionably scientific model. He might then contend that to deny strictly scientific status for his hypothesis does not deprive it of cogency. However, Swinburne must admit that his hypothesis will not enjoy confirmation of the same kind or degree as a well-supported scientific hypothesis. This means that Swinburne ought not to be surprised if his hypothesis fails to command consensus among the qualified discussants in the same way that a well-confirmed scientific hypothesis does. That is, he should admit from the start that there will be more room for rational dissent from his hypothesis than there currently is with respect to, say, quantum mechanics. To see exactly how cogent Swinburne's arguments are, each must be examined on its own merits. Hence, we now turn to a detailed examination of his cosmological argument.
We have seen that Swinburne repudiates the Principle of Sufficient Reason and the allied notion that some being can account for its own existence. Hence, both Swinburne and the atheist hold that something exists as the brutally factual terminus of all explanation. Swinburne's cosmological argument boils down to the claim that God is a more satisfactory candidate for such terminus than any other imaginable entity. In order to evaluate this claim we must first see exactly what it is that atheism leaves unexplained.
It is Swinburne's opinion that science has not yet put forward any solid reasons for thinking either that the universe had or did not have a beginning. Hence, he chooses to disregard the problem that arises for atheists only if the universe is of finite age, viz., the inexplicability of the initial state. Instead, he concentrates on the weakness that, he argues, afflicts all forms of atheism.
Swinburne contends that if scientific explanation is the only sort allowed, there can be no explanation for the entire series of the universe's states. Scientific explanation will only countenance explanations of the states of the universe in terms of the earlier states of the universe and the laws of nature. As we saw, Swinburne argues that the explanation of a sequence of states taken as a whole must be something that lies outside that sequence. Thus, if the sequence to be explained is the lighting of the fuse, the explosion of the dynamite, the collapse of the house, and Jones's death, the cause of that sequence as a whole is Smith's setting a match to the fuse. It is this requirement, that the explanation of an entire series be something outside the series, that Swinburne deploys against the Humean claim that if each member of a series is explained the series as a whole will be explained. Hence, if a whole series can be explained only by something outside that series, then clearly the set of states of the universe cannot be explained in terms of any member of members of that set. Swinburne concludes that atheism therefore leaves unexplained the existence of the universe over time, whether that time is of finite or infinite duration.
Now we do normally explain an entire causal series in terms of something outside that series. It is quite natural to speak of the cause of the sequence of events ending in Jones's death (the fuse being lit, the dynamite going off, the house collapsing) as simply being the fact that Smith set a match to the fuse. However, we must not forget that in grouping the above events together in the way that we have we are performing what Hume called an "arbitrary act of the mind." To say that the above sequence as a whole lacks an explanation (suppose we did not know who lit the fuse) does not in the least vitiate the explanation of Jones's death in terms of the house collapsing. In fact, every event in our above sequence is perfectly well explained except the last, i.e., we know everything up to who lit the fuse. Further, what we do know in such a case is not one whit augmented when we come to know who lit the fuse: Smith was just as surely killed by the collapse of the house whether or not we ever know who lit the fuse.
The upshot of the above is that the inexplicability of a finite causal chain boils down to the inexplicability of its first term. Once that is given, the whole series is explained. It is therefore very hard to see how the atheist who holds that the universe is finite in age leaves anything unexplained except the existence of the initial state of the universe. To say that the series of states as a whole is unexplained just seems to say that all such states are explained but the first.
Suppose, though, that the universe is infinite in age, i.e., it lacks an initial state. Swinburne wants to argue that since the causal chain stretches back infinitely, we cannot regard any past states of the universe as standing outside that chain. Hence, he argues that the infinite series of the universe's past states lacks an explanation on the atheist's scheme. But why not stand this argument on its head? That is, why not argue that because the past states of the universe constitute an infinite series (and thus, by definition, there cannot be any states standing outside of the series) the demand that it be explained in terms of something outside the series no longer applies? This argument seems plausible since in an infinite series, unlike a finite one, each state will always have an adequate explanation in terms of a preceding state. In fact, it seems that it is the very finitude of a finite series that makes us look beyond that series for its explanation. That is, because a finite series comes to an end, it will always stop short of the cause of the first member of that series. Hence, the first member will be unexplained and, as a result, the series as a whole will be unexplained. However, with an infinite series there will, by definition, be no first term and, it seems to follow, no reason to look beyond that series for an explanation of the series.
Further, as Gaskin notes, it is not at all clear what it means to speak of an infinite series 'taken as a whole':
It does not appear to me to make sense to talk about any sort of explanation (internal or external to the universe) of an infinite series of states considered 'as a whole'. No 'whole series' exists to be explained. If a real infinite series means anything, it means a series incapable of being gathered as a whole--whatever whole you take, there is limitlessly more. It is impossible to take such a whole, and yet every state has a sufficient explanation [emphasis in original].
It seems, therefore, that the demand for an explanation of an infinitely old universe 'as a whole' is either incoherent, or, if its coherence can be made out, does not demand an explanation in terms of anything 'beyond' the universe.
What then does the atheist leave unexplained upon the supposition that the universe is infinite in age? The permanent features of the universe mentioned by Swinburne, such as the amount of matter it contains, no longer seem to present any mystery. The universe presently contains the amount of matter it does because it contained just that amount of matter in its past states and the laws of conservation have always assured that just that amount was preserved as the states of the universe evolved. Of course, it is possible to imagine the universe all along having had a different amount of matter, but this does not create a mystery. When was it ever possible for the universe to have had a different amount of matter? On the supposition that the universe is infinitely old such a possibility has simply never arisen.
Also, what are we to make of Swinburne's accusation that atheists who propose an infinitely old universe leave unexplained "... the non-existence of a time before which there was no unknown."? It is hard to know what to make of this statement because it seems scarcely intelligible. At any rate, the non-existence of anything does not present a mystery unless we have some reason to think it should exist. The non-existence of a rhinoceros in my bedroom is not a mystery that requires explanation; there is simply no reason to think that a rhinoceros ought to be in my bedroom. Likewise, unless we have some reason to think there should have been a time before the universe existed, the non-existence of such a time just is not a problem.
Perhaps, though, the real battle between theists and atheists ought to be whether and how the laws of nature can be explained. Even if an infinite succession of states does not in itself present any problems, what atheists still leave unexplained are the laws of nature that govern the transitions from one state to another. For instance, it does not seem that atheists can explain why the universe has the particular set of laws it has or why those laws remain constant over time.
Before proceeding we need to get clear on what exactly it will amount to for Swinburne if atheists concede that they cannot explain the ultimate laws of nature, whatever they may be. Swinburne endorses what he calls a 'powers and liabilities' account of the laws of nature. He argues, plausibly, that we must not make the mistake of reifying the laws of nature by turning them into additional entities that somehow exist alongside or parallel to material bodies. Rather, laws of nature should be conceived as powers or liabilities possessed by those material bodies themselves:
A power of a body is a capacity of it to bring about effects. A liability of a body is a disposition of it to suffer change under various circumstances--among the liabilities of a body are that it has (of physical necessity or probability) to exercise its power when subjected to various stimuli. Thus instead of saying that the ignition of a certain mass of gunpowder plus a natural law of chemistry explained some explosion, earlier scientists would have said that the gunpowder caused the explosion, the power to cause an explosion being among the powers of the gunpowder, and a liability necessarily to exercise that power when ignited being among the liabilities of the gunpowder; and the explosion was to be explained by the gunpowder's exercising its powers in virtue of its liabilities.
Hence, for Swinburne, to say that a law of nature is unexplained is to say that there is no explanation of why a certain material body possesses the particular powers and liabilities that it has. Of course, the powers and liabilities of one body may be explained in terms of the powers and liabilities of constituent bodies and those in turn by even more fundamental entities. Presumably, though, rock bottom is eventually reached. At present, rock bottom would be the powers and liabilities of such entities as quarks and electrons. Since, by definition, the ultimate features of the universe will constitute the ultimate terms of scientific explanation, science clearly cannot account for those absolutely basic features. Hence, atheists must concede that they cannot explain why the ultimate laws of nature are as they are. In Swinburne's terms, they cannot explain why the fundamental constituents of the universe, whatever they might be, have the characteristic powers and liabilities that they do.
What though, does this concession really amount to? To say that there is no explanation of why a quark, given that it is a fundamental particle, has the powers and liabilities it possesses, seems tantamount to saying that there is no explanation of why a quark is a quark. Surely anything with a different set of powers and liabilities than those possessed by quarks would simply not be a quark. After all, what is a fundamental particle over and above a particular set of irreducible powers and liabilities? It appears, therefore, that when our inquiries have reached the fundamental stuff of nature, and hence the terminus of scientific explanation, there just is not anything left to be explained. Quarks are just quarks; that is the bottom line.
Perhaps this misses the point. Maybe the difficulty is not that quarks, given that they do in fact exist and that they are fundamental particles, have the powers and liabilities they have. Rather, the question is why quarks exist in the first place rather than something else or perhaps nothing at all. However, it must be recalled that on the hypothesis of an infinitely old universe there is no 'in the first place' when it was possible for nothing or something else to exist instead of what does in fact exist. Of course, it is conceivable that nothing or something different might have existed. But again, it is difficult to see how this creates problems for the atheist. If the universe has always existed, then it has never been possible for there to be nothing or for something else to exist.
In conclusion, on the hypotheses that the universe is infinitely old, atheism appears to explain everything that can reasonably be thought explicable. Each state of the universe is explained by a previous state and the laws of nature. The demand to know the cause of the set of states 'as a whole' is incoherent, or, if allowed, does not require an answer in terms of anything transcending the universe. The laws of nature reduce in the final analysis to the powers and liabilities of the fundamental physical stuff. The demand to know why the ultimate physical stuff has the powers and liabilities it has is incoherent. This is because the fundamental stuff just would not be that stuff if its powers and liabilities were different. Finally, though we can imagine there never having been anything or there all along having been something else in existence, the presupposition that our universe has always existed explains why these other "possibilities" were never actualized.
If the atheistic hypothesis thus explains everything that can be explained, why should a theistic hypothesis ever be invoked? The only possible answer seems to be that as a total system theism will be simpler than atheism. In other words, as ultimate theories of existence theism and atheism both adequately explain the totality of things, but theism does so with greater simplicity than does atheism.
This, however, seems plainly false. On the presupposition that the universe is infinitely old, the universe, in all of its complexity, will have always existed on both the theistic and the atheistic accounts. However, on the theistic hypothesis something else, namely God, will have always existed. Further, the theist must also postulate a power continuously exercised by God to keep the universe in existence (otherwise God just exists in parallel with the universe and has no creative input with respect to it). Unless it can be shown that the universe somehow needs to be kept in existence, Swinburne's theism thus seems to be a paradigm case of multiplying entities without cause.
It appears that if Swinburne's cosmological argument is to have any chance of making headway, it must presuppose that the universe is finite in age. That is, it must assume that the cosmos had an initial state and then argue that God is a more acceptable terminus of explanation than that first state.
Whereas classical systems of atheism such as the De Rerum Natura, presupposed the eternal existence of matter, most atheists would now likely be willing to accept that the universe had a first state. This is because the bulk of scientific opinion, pace Swinburne's earlier-mentioned skeptical reservations, now appears to favour some sort of "big bang" cosmology. That is, various converging lines of evidence seems to indicate that the entire cosmos, indeed space-time itself, originated instantaneously in a primeval explosion occurring some fifteen to twenty billion years ago. Further, "big bang" cosmologists believe that the current state of the universe--its configuration, its laws, and the entities that constitute it--are all explicable in terms of events that occurred within the first split seconds of the universe's existence. Indeed, some physicists hold out the hope that particle physics and "big bang" cosmology will soon be united under a single theory that will show the four basic forces of nature evolved from a single "superforce" believed to have existed in the first instant of creation. The boldest theorists are pushing even farther by offering scenarios that would explain how the universe arose uncaused literally ex nihilo.
Of course, even the most optimistic of the cutting-edge cosmologists admit that their wilder ideas are still entirely speculative. More cautious physicists point out that the models so far offered stretch accepted theories and concepts far beyond their tested range of application. Some philosophers are more skeptical still. Patrick Suppes, for instance, denies outright that science can ever be brought under a single unifying theory and regards the quest for such unification as a quixotic remnant of the decayed positivist program.
Fortunately, our interests here do not turn on the question of whether science will ever achieve the sort of ultimate success that presently eludes the searchers for "superforce." Swinburne clearly holds that no matter how successfully science explains phenomena, it will always be warranted to pass beyond science to theistic explanation. In other words, Swinburne holds that theism provides a more acceptable stopping-place for explanation than any possible scientific theory. This being so, it will here be assumed that the boldest aspirations of science will in fact be rewarded with success. That is, it will be taken for granted that science can succeed in showing that all natural phenomena are ultimately explicable in terms of a single theory lying at the apex of all hierarchies of scientific explanation. In such a case, all that the atheist will have to regard as permanently inexplicable will be the ultimate terms of that ultimate theory. Swinburne's job is therefore to show that God is a more acceptable terminus of explanation than any such conjectured ultimate scientific explanation.
To get right to the point, why is it better to end explanation with God than, say, with an uncaused first state of the universe? Perhaps God is simpler than any conceivable initial physical state and therefore a priori more likely to existed uncaused. We have seen that much of the reason for God's claimed simplicity is that his attributes are infinite in quality. Swinburne apparently assumes that no physical entity could possess such infinite properties and therefore cannot emulate God with respect to simplicity. Physicist Paul Davies directly addresses such an assumption:
According to our best scientific understanding of the primeval universe it does indeed seem as though the universe began in the simplest state of all--thermodynamic equilibrium--and that the currently-observed complex structures and elaborate activity only appeared subsequently. It might then be argued that the primeval universe is, in fact, the simplest thing that we can imagine. Moreover, if the prediction of an initial singularity is taken at face value, the universe began in a state of infinite temperature, infinite density and infinite energy. Is this not at least as plausible as an infinite mind?
In short, it does in fact seem that naturalistic hypotheses can emulate (or surpass) theism with respect to simplicity. Even the possession of infinite attributes is not a privilege restricted to God alone.
At any rate, what is it about unlimited attributes that prevents them from crying out for explanation in the same way that limited ones supposedly do? In other words, why should the possession of unlimited attributes ipso facto make a being simpler than one having limited properties? Swinburne is not much help here. As we have seen, all he tells us is that
... an omnipotent God is a simpler hypothesis than the hypothesis that there is a God who has such-and-such limited power...It is simpler in just the same way that the hypothesis that some particle has zero mass, or infinite velocity is simpler than the hypothesis that it has a mass of 0.34127 of some unit, or a velocity of 301,000 km/sec. A finite limitation cries out for an explanation of why there is just that particular limit, in a way that limitlessness does not.
Unquestionably, an hypothesis postulating zero power for some entity will, other things being equal, be simpler than one postulating some degree of power. Zero power just means no power at all, and, as noted earlier, the nonexistence of something does not demand any explanation unless there is some reason that it should exist. However, with respect to infinite power, Swinburne's claim seems to be that it lacks a particularity possessed by finite degrees of power. But, on the contrary, omnipotence seems to be a highly specific and determinate degree of power, viz., the highest logically possible degree of power. If omnipotence is thus a particular, determinate level of power, it is not clear why it would fail to demand an explanation just as much as any other degree of power. The alternative would seem to be to deny that omnipotence is a specific degree of power. It seems, though, that power just is the sort of attribute that must be possessed in some degree or other if it is to be possessed at all. To say that something has power but does not have it in some degree or other (whether finite or infinite) does not appear to make sense.
For the sake of argument, let us suppose that it can be shown that the theistic hypothesis is simpler than any possible naturalistic hypothesis. This leads us to the most central question for Swinburne's entire project: Why is it more likely that the ultimate, uncaused entity will be a simple rather than complex entity? Anthony O'Hear has said all that needs to be said here:
... against what standard of probability can we possibly judge in general terms what type of thing is most likely to exist? If experience is anything to go by, and what is likely to exist in the abstract is rather like what we do have experience of as existing, then we will have to conclude that what is likely to exist is rather more complex than it need be. (We can easily imagine possible worlds a lot simpler than ours such as a Parmenidean, block universe.) If, on the other hand, we do not take our actual experience into account, we might wonder what the probability assessment is being based on. It hardly seems reasonable to say, in the absence of any evidence, that what is most likely to exist is that possible world which the human mind finds more simple. Indeed, in the absence of any way of deciding what is correct here, one doubts whether the question has any meaning at all. In a way, the point being made is the old one made by Peirce, that universes are not as plentiful as blackberries, that, in other words, we have no sample of universes to inspect to infer what is a priori more likely or unlikely in an actual world.
O'Hear's remarks have the ring of finality. What then are we to make of the fact that some confirmation theorists do recommend that a higher a priori probability be accorded to an hypothesis which, other things being equal, is simpler than a competing hypothesis? Other confirmation theorists, most notably Popper, do not make this recommendation (even most of those who do would doubtless be very surprised to learn that they thereby implicitly endorse grandiose metaphysical theses about the nature of Ultimate Existence). How then do we account for the scientific preference for the simplest of empirically equivalent hypotheses if we do not construe it as an endorsement of the probable truth of that hypothesis?
The answer is that simplicity is a desideratum for hypotheses, not because of the nature of reality, but because of the nature of science. As O'Hear puts it:
... science aims at more than truth; it aims also at a system of simple and wide-ranging hypotheses. Without such a preference, scientists would have no reason for preferring theories that postulate underlying unifying causes for diverse phenomena, rather than remaining content with mere summaries or digests of past observations. For similar reasons, preference may be accorded theories which postulate one entity, rather than many, one kind of entity rather than many kinds, and zero or infinite degrees of a given quality, rather than some intermediate figure. Some may indeed be prepared to mark these preferences by according theories which are simpler in these respects greater degrees of prior probability...
In other words, it is an (if not the) aim of science to make systematic sense of the farrago of ostensibly disjoint and unconnected events we encounter in experience. Science endeavours to reveal hidden conspiracies in nature, unsuspected relations and regularities that permit a unified explanation of diverse phenomena. In this sense, scientific discovery just is simplification. However, it must be emphasized that such simplification is one of the aims of science; there is no prior assurance that such hopes will meet with complete success. There just is no way of knowing a priori whether the ultimate terms of explanation will turn out to be as simple as they could be. The preference for simple hypotheses therefore appears to arise from the fundamental aims of science, not from a misplaced trust in how reality will ultimately turn out.
Other criticisms have been made of Swinburne's project. However, enough has been said here to bring into doubt the core claim of Swinburne's cosmological argument--that God is significantly more likely than the universe to be the ultimate, uncaused existent. In Bayesian terms, Swinburne has failed to show that p(h/k) is significantly higher than p(e/k). If this is so, then, since Bayes' theorem tells us that
p(e/h.k) P(h/e.k) = ---------- X p(h/k), p(e/k)
p(h/e.k) will not be much higher than p(e/h.k). This means that the probability that God exists given that the universe exists, p(h/e.k) will be quite low since Swinburne admits that p(e/h.k) will be low. Hence, if the existence of the universe adds at all to the probability that God exists, it adds a very small amount. Thus, even if Swinburne's argument is, technically speaking, a good C-inductive argument (and we have seen no reason to hold that it is), it only succeeds in showing that e confirms h to a very small degree. It seems, then that theists will have to look elsewhere to find any substantial degree of confirmation of their hypothesis.
 The Existence of God will hereafter be abbreviated as EOG.
 J.C.A. Gaskin, Hume's Philosophy of Religion, (London: Macmillan, 1978); in the course of defending Hume's critique of the design argument Gaskin answers all of Swinburne's objections to Hume. See Mackie's critique of the argument from consciousness in Chapt 7 of his book.
 EOG, p. 7.
 Ibid., p. 131.
 Ibid., p. 117.
 Gaskin, pp. 20-23.
 Alvin Plantinga, "The Probabilistic Argument from Evil," Philosophical Studies, Vol. 35, #1 (1979).
 John Hick, Arguments for the Existence of God (London: Macmillan, 1970), pp. 32-33.
 One classic statement of the traditional cosmological argument is found in G.W. Leibniz, On the Ultimate Origination of Things, trans. M. Morris, in The Philosophical Writings of Leibniz (London: Everyman, 1934), pp. 31f.
 This criticism is made by Antony Flew in God and Philosophy (London: Hutchinson, 1966), pp. 83-84.
 See Terence Penelhum, Religion and Rationality (New York: Random House, 1971) pp. 37-46.
 EOG, p. 120.
 Ibid., p. 128.
 Ibid., p. 131.
 Ibid., p. 116.
 David Hume, Dialogues Concerning Natural Religion in Richard Wollheim, ed. Hume on Religion (London: Fontanta, 1963), p. 164.
 EOG, p. 122. "Complete" and "full" explanations are technical terms for Swinburne (see pp. 22-24 and pp. 73-75). Unfortunately, his definitions of these terms are extremely convoluted and unilluminating. As far as I can tell, a "full" explanation of an event E is one that mentions all of the factors (entities, initial conditions, laws of nature, etc.) that are jointly sufficient to bring E about. An event E is "completely" explained if it is fully explained at a givent ime but none of the factors in terms of which E is explained can themselves be explained in terms of further factors operating at that time.
 Ibid., pp. 123-124.
 Ibid., p. 124.
 Ibid., p. 124.
 Ibid., pp. 124-125.
 Ibid., p. 128.
 Ibid., p. 287-288.
 Ibid., p. 130.
 Swinburne's clearest definition is found in his reply to Mackie's criticism of his cosmological argument: "Mackie, Induction, and God" in Religious Studies 19 (1983), p. 386.
 Swinburne summarizes his views on the factors affecting a priori probability in EOG pp. 51-57.
 Ibid., p. 65.
 Ibid., p. 129.
 Swinburne explains the reasons for the simplicity of theism in detail on EOG pp. 90-102.
 Ibid., p. 94.
 Ibid., pp. 94-95.
 Ibid., p. 95.
 Ibid., pp. 96-97.
 Ibid., pp. 97-102.
 Swinburne, "Mackie, Induction, and God," p. 386.
 This problem and how quark theory has resolved it are brilliantly explained by Chris Quigg, "Elementary Particles and Forces" in Scientific American, 252, #4 (April 1985), pp. 84-95.
 Richard Morris, Dismantling the Universe (New York: Simon and Schuster, 1983), p. 195.
 Ibid., p. 195.
 Quigg, pp. 86-87.
 Ibid., p. 84.
 EOG, pp. 66-67.
 Ibid., p. 67.
 Ibid., p. 131.
 Ibid., p. 121.
 J.C.A. Gaskin, The Quest for Eternity (New York: Penguin Books, 1984) p. 63.
 EOG, p. 126.
 Ibid., p. 42-44.
 Ibid., p. 43.
 "Big Bang" cosmology is clearly explained in Davies, chapt. 2.
 See Davies' Superforce (New York: Simon and Schuster, 1984).
 Ibid., chapt 12.
 Patrick Suppes, Probabilistic Metaphysics (Don Mills, Ont.: Oxford University Press, 1984).
 Davies, God and the New Physics, p. 49.
 EOG, p. 94.
 Anthony O'Hear, Experience, Explanation, and Faith (London: Routledge and Kegan Paul, 1984), pp. 116-117.
 Ibid., p. 115.
 Good examples of such criticisms are: Michael Martin, "The Coherence of the Hypothesis of an Omnipotent, Omniscient, Free, and Perfectly Evil Being," International Journal for Philosophy of Religion, 17 (1985); and Robert Prevost, "Swinburne, Mackie, and Bayes' Theorem," International Journal for Philosophy of Religion, 17 (1985).