An Analysis of Richard Swinburne's The Existence of God (2010)

1. The Argument

2. Where the Argument Fails

2.1 The Premises

2.2 Simplicity

2.3 Which God?

3. Conclusion



Richard Swinburne is an icon of rational theism. He has been praised as being "perhaps the most significant proponent of argumentative theism today" and "one of the foremost rational Christian apologists."[1] These, among many other accolades, have been conferred upon him as a distinguished philosopher of religion. His arguments for theism are broadly held in high esteem as being rational and rigorous, providing highly reasonable grounds for holding conviction in the existence of God. In disputes on theism, he is often held as an eminently reasonable exemplar to counter atheistic charges that a belief in God is intrinsically irrational.

Although Swinburne has written prolifically on various aspects of religion—specifically, Abrahamic monotheism—The Existence of God (Oxford University Press, 2004) is his centerpiece. Whether God exists is central to the Abrahamic constellation of convictions, and so arguably must take precedence over all other questions, as they would be moot without its unequivocal resolution. Undoubtedly to the applause of many theists, the back cover of the book claims that "No other work has made a more powerful case for the probability of the existence of God." If one wants to challenge the notion that God exists, or that it is rational to believe in God, one needs to tackle the arguments in Swinburne's book.

The Existence of God reveals Swinburne's signature positions and the methodology used to support his thesis. Central to his reasoning is Bayes' Theorem on conditional probability, augmented by methods of inductive reasoning, confirmation theory, intrinsic probability of simple hypotheses, substance dualism, and moral realism—terms I will clarify shortly—all held together in what appears to be a highly structured, coherent, and rigorous framework. I don't intend to critique any of these tools and positions individually, as that would take me too far afield—and others have already done so quite skillfully.[2] Rather than picking apart Swinburne's methodology, I will examine whether the entire structure of his argument is rigorous and whether it implies the conclusion that he expects the reader to affirm. Focusing only on the major flaws in his argument, I will analyze how and to what degree each flaw undermines the structure of his argument, and alters the force of his conclusions.

As I don't assume that the reader has any familiarity with The Existence of God, I will briefly outline Swinburne's primary argument, focusing on the essential elements of the structure of the argument. Where appropriate, I will explain within the outline which elements are necessary to the argument and how they relate to each other. This is not readily apparent in a casual reading of the book due to its many long-winded and rambling parts. Since I provide a road map of Swinburne's argument, hopefully readers will more clearly see the impact of flaws in particular elements upon the entire argumentative structure. This outline will be followed by an examination of the major structural flaws that I think make Swinburne's argument less rational and rigorous than it appears on a casual reading. (In fact, a serious reasoning blunder seems to derail his project from ever attaining the intended conclusion.) Finally, I attempt to show that even if we ignore Swinburne's reasoning errors and take his conclusion at face value, a confirmed but astute theist could not derive much consolation from it.

1. The Argument

Swinburne immediately states his purpose in the Introduction—"to reach a conclusion about whether on balance the arguments indicate that there is a God or that there is not" (p. 1)—with his allegiance self-evident. The implication is that by the end of the book, we will have that answer. But he cautions: "I shall, however, argue that, although reason can reach a fairly well-justified conclusion about the existence of God, it can reach only a probable conclusion, not an indubitable one" (p. 2). Thus, we have a fairly modest aim, and fair warning that we will soon be knee-deep in probability calculus.

An outline of the argumentative structure of the book follows.

Chapter 1 is devoted to a discussion of inductive arguments.

Traditional deductive arguments to the existence of God are useless because the premises are disputed, that is, are not known to be true by those who argue about religion (p. 6). Swinburne defines two kinds of inductive arguments (p. 6): A correct P-inductive argument is one in which the premises make the conclusion probable (the probability is >1/2). A correct C-inductive argument is one in which the premises add to (confirm) the probability of the conclusion. Having eschewed deductive arguments to God, he endorses probabilistic inductive arguments because "the premisses are known to be true by people of all theistic or atheistic persuasions" (p. 6) He continues, "I therefore define arguments from premisses known to be true by those who dispute about the conclusion which are valid deductive, correct P-inductive, or correct C-inductive arguments, respectively good deductive, good P-inductive, and good C-inductive arguments" (pp. 6-7) [italics mine]. It is crucial to note this definition. As we shall see further on, had Swinburne stopped at this point and not written the rest of the book, he could have quit while he was ahead. But he didn't, so let's press on. Swinburne gives an outline of his strategy: He will only discuss a posteriori arguments—those from experience and evidence—not a priori arguments from logically necessary truths (p. 8). He will examine a number of separate arguments which he takes to be good C-inductive arguments in isolation, but then he will reexamine them "cumulatively." That is, he will attempt to place a series of arguments, A, B, C, D, ..., one on "top" of the other, such that A supports B, A and B support C, A and B and C support D, and so on. Here Swinburne attempts to ratchet up a number of C-inductive arguments which independently do not attest to the probability of anything, but which cumulatively provide a good P-inductive argument, and thus attain his goal of a probable conclusion (pp. 13-14). Next Swinburne provides an outline of confirmation theory and the notation for conditional probability (pp. 14-19). He explains that P(p | q) is the notation for the probability of p given that q is the case. Next he introduces P(h | e & k) , which contains the main variables that he uses in the rest of the book. h stands for some hypothesis to be evaluated, e is the evidence that one examines in support of h, and k is the "background knowledge" of what we take the world to be like in general. This notation and explanation leads naturally to the Bayesian formulation, which later plays a prominent part in the rigorous aspect of Swinburne's argument and his aim of arriving at a probabilistic conclusion. In the book h generally stands for the hypothesis that "God exists" while e represents phenomena observed in the world. Swinburne's ultimate goal is to show the probability of h. Further along, Swinburne tells us that "all important a posteriori arguments for the existence of God ... purport to be arguments to a (causal) explanation of the phenomena described in the premisses in terms of the action of an agent who intentionally brought about those phenomena" (p. 20). This statement makes sense of a great deal of what Swinburne argues next. In terms of the notation introduced earlier, he says that h explains e, thus lending support to h. Consequently, we need to understand what "explanation" is, and so Swinburne soon invests a great deal of effort expounding what constitutes an explanation. Swinburne's statement also portends his later discussion of the role of "agency" and "intentionality" in explanation. Finally, Swinburne briefly raises the question of the "proper terminus" of explanation, to be discussed in more detail later. This issue—essentially the thorn of infinite regress—plagues every hypothesis where a "prime mover" lurks.

Chapter 2 provides an outline of various types of explanations.

The need for this follows from point f of the outline of chapter 1 above. A full explanation of some phenomenon E is one where nothing remains unexplained about E in the sense that the factors that precipitated E necessarily entailed it (p. 25). Pages 25-35 are devoted to "scientific explanation" along the lines set out by C. G. Hempel—in terms of initial conditions and natural laws. Swinburne also presents an alternative view in terms of the "powers" of "substances" (what they can do) and their "liabilities" (the exercising of those powers). Scientific explanations undergird the naturalistic worldview, against which the next type of explanation is counterposed. Pages 35-45 see the development of "personal explanation" where E, a phenomenon, is simply brought about by a person P intentionally, that is, by "meaning so to do" (p. 35). Here the terminus of explanation is nothing more than the intention to bring about E. More specifically, Swinburne asserts, "Having an intention is not something that happens to an agent, but something that she does" (p. 43). And further on he clarifies, "To act intentionally is to exercise causal agency in a certain direction, which will succeed in producing the intended effect if the agent has the requisite power" (p. 43). It is clear that Swinburne does not intend to look behind the intention, that is, at how intention itself is explained; intention is simply inscrutable, presumably a mental "brute fact." This is no less than substance dualism, the notion that there are two distinct types of substances in the world, one material and the other mental. Science objectively deals with and knows much about material substances, but we know about the mental only through direct personal access. Without further explanation he admits that "Some sort of dualism is unavoidable here" (p. 41) [italics mine], and does eventually try to defend substance dualism in particular in chapter 9. We'll later discover that he has good reason to shy away from explicitly defending substance dualism here, so as to avoid being too overt about his presumptions at the outset of his program. Note that personal explanation will be one of the main pillars of Swinburne's overall argument. Pages 47-51 give a taste of things to come as Swinburne generalizes explanations concerning the action of God. For example, he states: "God's own intentions alone explain his doing what he does" (p. 49) [italics mine]. And regarding God's intentions, he explains: "Nor are God's intentions scientifically explicable." Substance dualism simply deflects investigation beyond this terminus—you simply can't go there!

Chapter 3 deals with the justification of explanation. How can we know that an explanation is true? If a hypothesis is to adequately explain some phenomenon, we must have grounds for confidence in the truth of this hypothesis; otherwise we might contrive any outlandish ad hoc hypothesis merely to fit the phenomenon without any regard for its truth.

Chapter 3 is important because it addresses the criteria by which we judge the quality of a hypothesis. On page 53 Swinburne introduces the concept of "prior probability"—the likelihood of a hypothesis or theory before we consider any evidence in its favor. This is judged as a function of the hypothesis' simplicity, scope, and fit with background knowledge. Swinburne eventually dismisses the significance of scope and fit and focuses entirely on simplicity, writing: "The best theory may be less than perfectly simple; but other things being equal, the simpler, the more probably true" [italics mine]. Despite his inclusion of the caveat here, from this point forward he virtually ignores "other things being equal" and considers only pure simplicity as he judges it. He also provides a brief outline of the factors by which a theory may be characterized as simple (p. 53), but again largely ignores them beyond this point. Nevertheless, the evaluation of hypotheses in terms of their simplicity plays a constantly recurring and central role in his arguments to follow. Page 66 introduces the Bayesian probability formulation that plays such a central role in the remainder of the book. In terms of the notation Swinburne introduced earlier, Bayes' Theorem is:



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



Swinburne's ultimate aim is to show that P(h | e & k) >1/2 ; that is, that h (God exists) is probable given our observational evidence of phenomena e and our background knowledge of the world k. This of course depends on the factors on the right-hand side of the Bayesian equation, and Swinburne spends the remainder of the chapter exploring what these factors mean, and what he needs to show about them in order to arrive at his intended target. P(h | k) describes the prior probability of h discussed by Swinburne earlier, and his goal is to show that h is simple and thus probable even without considering the evidence. Of course, he also needs to account for the ratio P(e | h & k) / P(e | k) , which he characterizes as the "explanatory power" of h—that is, how well h explains e, as alluded to in point f of the chapter 1 outline. It all ties together.

Chapter 4 explores in detail item g of the chapter 1 outline—the proper terminus of explanation. Swinburne realizes that the possibility of an infinite regress of explanations can't simply be ignored, so he tries to head off any salvos from that direction in this chapter.

He argues for the existence of phenomena that are "too big" or "too odd" either for science to explain, or to be explicable by the actions of an embodied agent. This leaves such phenomena explicable as actions of a nonembodied agent (pp. 74-75). He defines various categories of full explanation: A complete explanation is one where all the factors are there at a particular time (p. 78). An ultimate explanation is one which terminates in an inexplicable "brute fact" at some earlier time (pp. 78-79). An absolute explanation is one that is based on self-explanatory or logically necessary factors (p. 79). On page 80 he takes the actions of God to have complete explanation since they are rooted in God's intentions at the time of the action, and those which intentions are, by hypothesis, perfectly free (and uncaused). For the remainder of the chapter he argues that science has historically rested upon states of affairs for which no further explanations were sought, so why not allow God's intentions to serve as a terminus in the case of the God hypothesis. His solution for avoiding an infinite regress is thus greatly aided by the intractable mystery inherent in substance dualism.

Chapter 5 begins with a detailed examination of the factors in Bayes' Theorem. First Swinburne tackles P(h | k), the prior or intrinsic probability of h given only our general background knowledge of the way the world is.

Things finally get interesting as Swinburne must now define precisely what h means. It is clearly useless to argue for the intrinsic probability of the vague hypothesis "God exists" without a fairly clear idea of what "God" means; the term is notoriously subjective and varies greatly among religions. It is important to note that once the definition is given and the hypothesis has been spelled out, Swinburne has committed himself to it! He cannot later add, modify, or subtract from h. Although he continues to use the simple notation h for his hypothesis, "God exists," I will more explicitly call it h(S) for reasons which will become clear later. This is what h(S) looks like: God is a nonembodied person (a spirit) that has always existed and always will exist, and is "omnipresent." Thus he knows about "goings-on" everywhere, and he can control the states of affairs everywhere. God is the source of being and power of all substances. God is perfectly free in that nothing in any way causally influences his choices (by his intention). God is "omnipotent"—able to do whatever is logically possible. God is "omniscient"—he knows at any time whatever it is logically possible to know at that time. One logical restriction on his knowledge is that he is unable to know the future acts of a free agent (p. 95). This limitation avoids the possibility of conflict between an agent having free will and God having perfect foreknowledge. Swinburne posits the existence of God as a "brute fact" that simply does not have an explanation. Take it or leave it! It's his hypothesis and he can frame it any way he pleases. God is a person (and only one person), and as a person he has intentions, beliefs, and basic powers (p. 97). It now seems clear why Swinburne expended so much effort defending personal explanation in chapter 2. In my chapter 3 outline Swinburne argued in point a. i. that the simpler a hypothesis, the more likely it is to be true—that is, the greater its intrinsic probability. Given this he now argues that h(S) is very simple and thus intrinsically probable. He bases this on the part of h(S) that says that God is just one person, not many, and that his properties are infinite ("omni" this and "perfect" that). And Swinburne claims that infinity is exceedingly simple compared to some specific value. I will say much about this rash assertion later. Starting on page 99, Swinburne presents an argument for adding "perfect goodness" as an attribute of God as deductively entailed by the other properties of h(S) proper. Had Swinburne earlier included perfect goodness as a defining attribute in h(S) he would have introduced additional complexity and thus diminished its intrinsic probability. Much will rest on God's perfect goodness in Swinburne's later arguments. And Swinburne's argument to God's perfect goodness itself rests on moral realism, the position that there are objective moral truths irrespective of subjective moral judgments. I will shortly show that Swinburne's argument to God's "perfect goodness" contains some serious flaws that contaminate anything that rests upon it.

Chapter 6 examines the remaining factors in Bayes' Theorem, the ratio P(e | h & k) / P(e | k). This ratio is the explanatory power of h in explaining e, as noted in chapter 3.

Swinburne reiterates: "Now let h be the hypothesis of theism, that there is a God" (p. 110). He does not add the caveat as I have defined God, however, and this is a critical qualification because he soon discusses ~h as the hypothesis that there is no God! Although ~h excludes God as Swinburne defines God, it also excludes other God hypotheses, such as "there is no Yahweh." Yahweh may have some overlapping traits with h(S) , but Yahweh also has far more features and traits than posited in h(S) . Yahweh is not a member of the set specified by h(S) , nor is any other God of an actual religion! Hence, Yahweh and gods of other religions belong to the set specified by ~ h(S) . Using just the simple h in the book, Swinburne reiterates an earlier relation showing the bottom factor of Bayes' formula, namely



P(e | k) = P(e | h & k) P(h | k) + P(e | ~h & k) P(~h | k)



which expresses the intrinsic probability of the phenomena e that we observe, conditional upon h and ~h. On page 112 he reformulates this by expanding ~h to give



P(e | k) = P(e | h & k) P(h | k) + P(e | h(1) & k) P(h(1) | k) + P(e | h(2) & k) P(h(2) | k) + ...



where h(1) , h(2) , ... are competing hypotheses to h, such that one and only one of them is true. As I said earlier, Yahweh would be one of the h(n), as h in the above relation is specifically just h(S) . That Swinburne's h is indeed my h(S) is shown by the remainder of the argument in this chapter, dealing with the type of world that God is likely to create and with what type of denizens (divine, human, and animal) God is likely to populate the world. This argument derives entirely from the traits of God given in h(S) plus his purported perfect goodness.



This argument thus deals with the factor P(e | h & k) . That is, given the existence of God h and our background knowledge k, what is the likelihood of the things we observe in the world e? Swinburne also intends to show that this probability is greater than P(e | k) , the likelihood that we will see e if there is no God.



At this point in the book Swinburne's formerly sober and largely rigorous style of argument has been abandoned and replaced with rambling flights of subjective speculation. Consequently I will give subsequent chapters short shrift in this outline.

Chapters 7 to 12 deal with traditional arguments for the existence of God, such as the cosmological and teleological arguments, as well as defenses against the traditional arguments from evil and God's hiddenness. All of these arguments are highly speculative, but what is noteworthy about them is that Swinburne usually concludes that he has presented a good C-inductive argument for God's existence, and demonstrated that evil and hiddenness do not provide good C-inductive arguments against theism.

Chapter 13 deals with the argument from religious experience. Here Swinburne argues for a somewhat different conclusion, one which will be used in an unexpected manner in chapter 14. Again the reasoning is rambling and highly speculative. It rests on the following two principles which he argues for. The Principle of Credulity (p. 303) is that, for the most part, we should assume that things are the way that they appear to be. The Principle of Testimony (p. 322) is that, for the most part, things really are the way that people report them. If it looks like a duck, swims like a duck, and quacks like a duck, it's probably a duck. The upshot is that if there is a God, people will likely have religious experiences, and they can, for the most part, trust that these experiences are what they appear to be. Furthermore, others may mostly trust the testimony of those having these experiences, and one's confidence in one's own experiences would be bolstered by the testimony of others with similar experiences.

Swinburne ultimately aims to reason that we have no good grounds to doubt the veridicality of religious experiences in light of these principles unless the prior probability of God based on other factors is very low. Alternatively, if the prior probability of God is at least a draw, these principles would tip the scales to make it probable—that is, P-inductive—that God exists.

Chapter 14 attempts to tie all of this together to yield the conclusion that Swinburne's overall argument to the existence of God is a good P-inductive one.

On page 339 Swinburne reformulates Bayes' Theorem in this form:



P(h | e & k) = P(e | h & k) P(h | k) / (P(e | h & k) P(h | k) + P(e | ~h & k) P(~h | k))



where the original divisor P(e | k) is replaced by its equivalent shown in point b of my chapter 6 outline. Swinburne further decomposes P(e | ~h & k) P(~h | k) into



P(e | h(1) & k) P(h(1) | k) + P(e | h(2) & k) P(h(2) | k) + P(e | h(3) & k) P(h(3) | k)



where h(1) stands for "many gods or a limited/lesser God," h(2) stands for "no God but a physically lawful universe," and h(3) stands for "no explanations at all, just brute facts." These are all summarily dismissed as unlikely, and the sum of these three probabilities is hence claimed not to exceed P(e | h & k) P(h | k) , the other term in the divisor. From this it is simple to see back in the Bayesian equation that:



P(h | e & k) !< P(e | h & k) P(h | k) / (2 x P(e | h & k) P(h | k))



or



P(h | e & k) !< 1/2



where !< stands for "not less than." In the decomposition of ~h (there is no God) into h(1) , h(2) , and h(3) here, Swinburne continues to equivocate the hypothesis h as noted in point a of my chapter 6 outline. Since his definition of the term "God" in h (as outlined in chapter 5) makes no reference whatsoever to the God of any actual monotheistic religion, those Gods must logically belong to ~h. Now Swinburne clearly has an allegiance to a specific theistic religion, whose God he would certainly not regard as a limited or lesser God—that is, a member of h(1) . Furthermore, it is unlikely that the purpose of this book is to promote his generic h(S) over actual theistic religions. Consequently, Swinburne's h implicitly appears to represent the Gods of actual theistic religions, yet shies away from explicitly and logically acknowledging that commitment. Swinburne now cleverly invokes his conclusion from chapter 13. He claims to show that P(h | e & k) is not a very unlikely consequent in his "cumulative" argument, hence not less than 1/2. Alongside the argument from chapter 13, this forces the conclusion that God's existence is probable (that is, P-inductive). Q.E.D.

2. Where the Argument Fails

Initially, Swinburne's argument is measured and sober. Although he makes a valiant effort using a clear methodology, the length of his book goes against his own dictum of simplicity. Early on he warns with justification, "the more you assert, the more likely you are to make a mistake" (p. 55). And throughout the book, he asserts a great deal, not just h(S). I will return to his assertions shortly.

It is clearly problematic whenever someone tries to derive a somewhat quantitative result using a precise quantitative formula where variables can only be examined qualitatively. The somewhat quantitative result sought here is to show that some probability is greater than 1/2. But the hypothetical being of h(S) has no necessary quantitative aspects at all in relation to either e or k. Hence the book is permeated with terms such as "perhaps," "maybe," "it seems to me," "intuitively," "I am inclined to suggest," "probability ... not be nearly as low," and so on—terms of ambiguity and imprecision. Swinburne tries to overcome this imprecision by introducing numerous examples and analogues, but this just muddies the waters even more. His use of Bayes' Theorem to evoke an air of precision is akin to using a micrometer to measure the location of the exact edge of a patch of fog. Furthermore, Swinburne's constant reliance on ambiguity in a lengthy, involved argument lends itself to the magnification of error in his final result, casting a great deal of doubt upon any outcome that he derives. Of course, this kind of objection itself is rather broad and imprecise, but it illustrates why the reader should be rather uneasy about Swinburne's ultimate conclusions. In any case, there are far more specific failures in Swinburne's argument, failures to which I now turn.

2.1 The Premises

At the outset Swinburne expressed dissatisfaction with traditional deductive arguments to the existence of God because their premises themselves were in dispute. He had written:

Since the premisses are not common items of knowledge to those who argue about religion, they do not form a suitable jumping-off ground for such argument. What are clearly of interest to people in an age of religious skepticism are arguments to the existence (or nonexistence) of God in which the premises are known to be true by people of all theistic or atheistic persuasions. (p. 6) [italics mine]

Swinburne's very definitions of good C-inductive and P-inductive arguments rest on this condition. The promise seems to be that the argument to follow will be based on such indisputable premises. But Swinburne fails in this promise with respect to a number of major premises, as well as many minor ones.

The first premise to fail the indisputability test is that substance dualism is true, yet Swinburne's entire case for personal explanation in chapter 2 depends upon it. It is curious that Swinburne defers his defense of substance dualism until chapter 9, where the first chapter's promise of working from undisputed premises is no longer fresh in the reader's mind. In any case, substance dualism is hardly an uncontested position within the philosophy of mind, as Swinburne finally acknowledges in chapter 9, writing: "Dualisms of the physical and mental are not popular philosophical positions today" (p. 199). The sense of "popular" used here is not the sense that bowler hats are not popular items of apparel today; rather, it is the sense in which a geocentric model of the universe is not "popular" with cosmologists today. There is no point in getting embroiled over the truth of substance dualism here—it is enough to note that Swinburne's argument fails his own criterion of resting on "premisses known to be true by people of all ... persuasions" (p. 6). And this is not a trivial matter because substance dualism bolsters his defense of personal explanation, which in turn bolsters his hypothesis that God is a person with beliefs and intentions. Absent his defense of personal explanation, the nagging question of what explains God's beliefs and intentions cannot avoid infinite regress. And then Swinburne simply loses his terminus of explanation.

Another pillar of Swinburne's overall argument—which undergirds his supporting argument to God's perfect goodness—is the highly contested premise of moral realism. Even a cursory survey of the relevant literature reveals a range of attitudes toward the truth value of moral propositions. Swinburne himself is (somewhat belatedly) forthright about this: "The truth of this view is, of course, a contentious philosophical issue" (p. 99). But his only defense is rather petulant: "Surely the person who says that there was nothing morally wrong in Hitler's exterminating the Jews is saying something false" (p. 100). Is this emotion-laden example supposed to settle a question that has perplexed philosophers for ages and continues to do so? At least this time Swinburne promptly admits:

For reasons of space I shall assume rather than argue for the view that moral judgements have truth values. But if they do not have truth values, it would be misleading to call perfect goodness a property of God, for it would be neither true nor false to say of him that (for example) he does no morally bad acts (p. 100).

Again, grounding his argument in a hotly disputed premise contradicts Swinburne's dictum to start from uncontroversial premises. And moral realism is certainly not a trivial premise; Swinburne's argument to God's perfect goodness, by his own admission, is dependent on it, and God's perfect goodness serves in turn as a recurring explanation for many other points in the book. As outlined in chapter 1, Swinburne aims to present a "cumulative" argument—but what are we to make of his approach when he stumbles right from the start by using arguable premises which he had promised to avoid?

Moreover, even if we grant Swinburne the truth of moral realism, his argument to God's perfect goodness equivocates the meaning of the term "good." He starts with a fairly uncontroversial assertion: that an agent always acts for some reason (some intention or purpose), and that this reason is that the agent thinks that the act is good. He says that "performance of ... [an act] is in some way a good thing" (p. 100) [italics mine]. But he does not specify in what way the agent views the act as a "good thing." There is not even an intimation of a moral dimension to the issue yet. For example, one could easily substitute the phrase "[for] a good thing" with "for the agent's gratification," and the meaning would be clear. The agent might get immediate sensual gratification from the act (such as eating a tasty meal), or emotional gratification (such as that derived from performing a kind deed). Deferred gratification may even be the substitute (such as when saving money now in order to buy some desired item later). Even performing an objective moral good (if there is such a thing) could be considered good in the eyes of the agent not because it is morally good, but because it brings the agent emotional gratification. One generally feels "good" when gratified, or when doing a "good" deed in an objective moral sense. But the two "goods" are not necessarily equivalent.

Next Swinburne examines the term "good" strictly in a moral sense, as if he was still talking about the same "good" he discussed earlier. After a long-winded examination, he concludes that unless the agent is under some nonrational influence like "weakness of will," he will not choose a morally inferior act over a morally superior one against his better judgment. Since God as defined in h(S) has perfect freedom, and thus is not under the influence of nonrational motives, he will never choose to commit morally inferior acts against morally superior ones. Furthermore, since h(S) posits that God is omniscient, he knows precisely the objective moral reality, and hence cannot act immorally—that is, is perfectly good. Or so Swinburne's argument goes.

In addition to this equivocation, the only factors which Swinburne considers in an agent's rational comparison of "good" and "bad" (or less good) are along a moral dimension. There is no mention of factors like personal gratification in such rational judgments. Should we consider personal gratification, personal safety, and other nonmoral considerations as nonrational factors in deliberating upon an action? Take a case with three factors, two of which—A and B—are moral considerations. Let A be objectively morally superior to B. Now let a third factor, C, be simple personal gratification, which we will take in this argument to be significantly greater when conjoined to B than to A. If no other factors come into play, a rational agent would clearly choose B and C, rather than A and C. This is even clearer when the agent is a sophisticated sociopath who feels little or no empathy for his victims, upon whom he inflicts some harm or hardship. Sociopathy is orthogonal to the dimension of rationality; a sociopath can be highly intelligent, rational, and functional. Being sophisticated, this criminal can intelligently plan and commit his morally reprehensible acts in a fully rational manner for personal gratification. He would likely be more rational in this sense than someone with relatively normal personal empathy, for the sociopathic criminal is actually "freer" than someone "fettered" with a normal level of interpersonal conscience. If God is by hypothesis perfectly free, he is totally unfettered. One could only guess and shudder at what rational choices he would make.

Since moral realism remains contentious, Swinburne equivocates the term "good," and his argument is susceptible to my counterexample, his case for God's perfect goodness is very naïve. And since God's perfect goodness is not entailed by h(S), we are led to the hypothesis of a personal being who has no particular reason for doing anything whatsoever—a very hollow, aimless, and possibly terrifying God whose actions, if any, would be inexplicable since h(S) itself posits no specific personality attributes for God.

We have now seen the eviscerating effects of Swinburne's dubious two main premises. A number of minor premises also pepper the book, particularly in the speculative sections. For obvious reasons, I will not tackle these one by one, but treat them as a whole. They are typically bald assertions about what is good, better, bad, valuable, and so on, often in a moral sense, where the argument to follow requires their affirmation. Some representative examples follow. On page 117 we are told that "a good being will inevitably try to make other good things." On page 118, that "A conscious life is a good thing." Page 119 states: "A solitary God would be a bad state of affairs" and "The goodness of significant free choice is, I hope, evident." These constant bald assertions are not patently false, but most are highly subjective and thus questionable as premises in a purportedly rigorous argument. Worse still, Swinburne himself undermines their impact on the argument, writing: "Our understanding of what is [morally] good or bad is very limited" (p. 113). Presumably he suffers from this limitation himself! He tries to redeem himself by writing: "But it is wildly implausible to suppose that our understanding of what is morally good and bad is totally in error" (p. 114) [italics mine]. On his own analysis, our confidence in the truth of each of his assertions about good and bad should range from "totally in error" at worst to "very limited" at best. This greatly undermines the individual arguments that these assertions are meant to support. Cumulatively, these layered arguments might incorporate so many "small" errors along the way that the truth of Swinburne's final conclusion is entirely up in the air.

The overall effect of all these contentious and suspect premises is to undermine Swinburne's entire argument. As previously stressed, his definition of good C-inductive and P-inductive arguments presupposes premises "known to be true by those who dispute about the conclusion" (p. 6). Swinburne fails to meet this condition repeatedly. Consequently, the cogency of his C-inductive arguments are doubtful, which in turn undermines his cumulative argument (via chapter 13) to his P-inductive conclusion. These failures alone seriously damage the foundations of his argument, and thus its conclusion. Worse still, independent considerations—to which I now turn—also gnaw away at the rigor of Swinburne's argument!

2.2 Simplicity

Swinburne's probabilistic argument for the existence of God presumes that simple hypotheses are more likely to be true. He repeatedly uses this premise to dismiss competing hypotheses as more complex and thus less probable. In what follows I will pass over an examination of the veracity of this premise itself, for it is a commonly held, if ambiguously applied, philosophical principle. One reason for its imprecise application is the absence of any agreed upon method for measuring simplicity.

Simplicity is a highly subjective attribute that one can unwittingly project on to the world rather than discover in it. For example, elementary arithmetic may appear simple to an adult but complex and mysterious to youngsters, while the process of learning a new language may be complex to an adult but "child's play" to children. On page 53 Swinburne takes a stab at what simplicity means with respect to hypotheses, but he necessarily produces rough, subjective guidelines, and does not purport to have discovered a precise metric of simplicity. For the most part, these guidelines rest on the criterion of paucity of variables, attributes, and relations.

It doesn't take long, however, for Swinburne to argue for the dumbfounding notion that "infinity" is itself a very simple thing. Why? On page 97 he says that this is the primary means by which he can claim that h(S) is very simple. The various "omni" attributes of God and his perfections may be viewed as infinite "values" along those dimensions. A God who is "omnipotent," for example, is "infinitely powerful" (p. 97). Such a God is also simple because he is "one" God rather than some complex consortium of gods. Fair enough. But on what agreed upon criterion does Swinburne argue for the simplicity of infinity? He compares infinite "values" to any specific numerical value, claiming that the specific numerical value (say the speed of light) "cries out for an explanation of why there is just that particular limit, in a way that limitlessness [infinity] does not" (p. 97). Here the absence of an objective, precise metric of simplicity is painfully apparent; crying out for an explanation is a highly subjective measure. And curiously, "not crying out for an explanation" is not included in Swinburne's outline of what constitutes a simple theory on page 53.

Most people are used to dealing with particular values to measure things—three wishes, 50 km/hr, 10 digits, etc. But no one (to my knowledge) has direct experience with infinite "values." Why would a person want to know the reason for some particular value of a thing, yet fail to be perplexed by some infinite, limitless value? If someone were to hand me a wallet with the instructions that I may spend the seven bills it contains in any way that I please, I may wonder why it contains seven bills and not six or eight or some other value. But if my benefactor instructed that I may indefinitely and without limit continue to remove bills from the wallet without replenishment, the notion that it wouldn't occur to me to seek an explanation stretches my credulity to the extreme. I think that most people would suspect that this state of affairs howls for an explanation in comparison to the one in which there are just seven bills to spend.

So much for the value of "crying out for an explanation" as a measure of the simplicity of the infinite. What of infinity itself? Swinburne say that infinity is comparable to numerical values, as if it was a value itself, and sometimes treats "infinite" as a synonym for "limitless"—but otherwise says nothing about what constitutes "infinity." The second notion is mathematically more accurate. But under any view, "infinity" is very perplexing and hardly something simple. For one, the notion of infinity is notorious for spawning paradoxes, such as Zeno's paradox[3] and Hilbert's hotel.[4] Simple notions and paradoxes make strange bedfellows.

If infinity were so simple, it would be one of the first things taught in mathematics, along with the natural numbers. Yet mathematical education proceeds from arithmetic through algebra before tackling the differential and integral calculus based on limits as values approach infinity. Finite series are studied before infinite series; finite sets before infinite sets; spaces of finite dimension before spaces of infinite dimension; integers, rational numbers, real and complex numbers, before transfinite numbers; and so on. Infinity is in no sense mathematically simple!

Swinburne says that God has infinite powers in the sense that "he can do whatever it is logically possible that he do" (p. 94). On this definition, we may put the powers of God into a denumerable infinite set {p(1), p(2), p(3), ... }, where p(n) represents some power possessed by God. Clearly, creating four-sided triangles is not one of these powers, as that would contradict the requirement that God only have the ability to do logically possible things. But curing cancer, constructing solar systems, moving galaxies about, creating the law of gravity, and so on would be powers that are members of this set, among an infinite number of other distinct powers. Earlier Swinburne had characterized the simplicity of a theory as "postulating ... few properties of entities, ... few kinds of properties" (p. 53). And "the preference [in terms of simplicity] for the infinite over the large finite applies only to degrees of properties" (p. 55) [italics mine]. But curing cancer is not a degree of moving galaxies about, of creating a universal law, or of collapsing the wave function of a proton. As powers, these are also attributes, or properties, of God. Though these properties fall under broad categories, such as the category "powers," that does not make them indistinct.

For instance, a building has distinct and independent properties of height, width, and length, even though these may also be subsumed under the single property "dimensions." Without some deeper explanation, we can only view powers—hence properties—as distinct and independent. And no such explanation—such as an account of how God's distinct powers are accomplished by some common but infinitely variable mechanism or property—is anywhere to be found in the book. I would certainly not view my power to hammer a nail as a degree of my power to calculate my taxes; they do not appear to be properties of mine along a single dimension. Given the prima facie distinctness and independence of God's various powers, an infinite number of divine powers shows that an omnipotent God fails Swinburne's own test for the simplicity of hypotheses, and of understanding the infinite in terms of degree. This argument also applies to God's omniscience, which may be viewed as a denumerable set of distinct and independent facts that God knows.

Since infinity seems to be anything but intrinsically simple, and Swinburne's hypothesized God prima facie must possess infinite distinct properties, h(S) appears to be complex to a mind-boggling degree. Swinburne's frequent arguments presuming the simplicity of h(S) are thus brought into serious doubt. The pillars of his overall argument continue to crumble. But he also commits a fairly common blunder in the reasoning process itself.

2.3 Which God?

Earlier I stressed that once h(S) was precisely defined in chapter 5, it could not be modified later as Swinburne built up his cumulative argument. Thus h(S) states that there exists a God such as defined by points (i) to (vii) in part a of my chapter 5 outline. The God of h(S), who Swinburne posits to exist, has just these attributes and whatever is deductively entailed by them—no more and no less. Is this God identical to that of actual theistic religions? Is this God Yahweh, or the Trinity, or Allah? That would only be possible if all of the properties of the God of h(S) match one-to-one with all of the properties of one or more of these other Gods. Certainly there appear to be some general commonalities, but that is hardly enough for a precise match. The problem is that although h(S) is laid out with an attempt at precision, the attributes of the other three Gods are highly inferential from the scriptures of the pertinent religions. No precise match could be made and hence no equivalence could be established. We could only consider these other Gods as separate, somewhat subjectively laden hypotheses competing with h(S) and one another (with their attributes conforming to the details of the pertinent scriptures). Only h(S) has no included scriptures. Furthermore, since the religions of Gods other than that of h(S) are split into various sects, we are actually dealing with a large number of competing hypotheses, which I will label as h(R1), h(R2), h(R3), etc. Strictly speaking, these h(Rn) belong to the set specified by ~h(S).

We now need to revisit phrases such as "God exists" and "the existence of God." Before Swinburne made clear the specific details of h(S), we didn't have a precise referent for the term "God." After h(S), we did. After h(S) and Swinburne's use of it in his arguments, any reference to "God" is a reference to the God of h(S), and we must hold him to this implication. Where he states that ~h means "there is no God," precisely it means that there is no God of h(S), but there may well be a God of h(R1), or h(R2), and so on, or none at all, and we have to hold him to that as well. Following these strictures and sticking precisely to the God of h(S) is the only way that Swinburne can claim to present a rigorous argument. Has he in fact adhered to this stricture? Sadly, no.

The first hint of trouble appears as early as chapter 6. In points b and c of my chapter 6 outline, Swinburne presents the formulation

P(e | k) = P(e | h & k) P(h | k) + P(e | h(1) & k) P(h(1) | k) + P(e | h(2) & k) P(h(2) | k) + ...

where h is the way he represents "there is a God" and h(1), h(2), etc., are competing hypotheses to h, only one of which can be true. The hint of trouble stems from what Swinburne fails to say here. What he does say is: "Among these theories will be the theory that e has no cause ... or [is] caused by some lesser being or beings" (p. 112).

These are the only alternatives that Swinburne considers in competition to his h. He does not say that Yahweh or Allah—presumably not lesser beings—are also in competition with h, where one would think that such a distinction needs explicit clarification. At the same time, he never claims that his h also represents a God from any actual theistic religion. In fact, throughout the book he deliberately shies away from including in h the tenets of any actual faith, or the many said properties of any actual theistic God, for fear of burdening h with complexities that would undermine his claims to simplicity. Swinburne is thus curiously silent about what relation h in fact holds to the Gods of actual theistic religions. Implicitly, he must hold that h is not identical with any God of an actual religion, for his definition of h contains no such references and is functionally independent of such connections. But given his explicit Christian commitments elsewhere, Swinburne is clearly motivated to provide rational support for some or most actual theisms. And his statement that notable alternatives to h are simply "no cause" or "lesser being or beings" seems to imply that h does in fact represent real world theisms by proxy. All in all, there is equivocation here regarding h—not a very pleasing state of affairs in a rigorous argument.

So what would be the correct rigorous formulation? Discarding the ambiguous h and taking h(Rn) as defined recently, we should have,

P(e | k) = P(e | h(S) & k) P(h(S) | k) + P(e | h(R1) & k) P(h(R1) | k) + P(e | h(R2) & k) P(h(R2) | k) + ... + P(e | h(Rn) & k) P(h(Rn) | k) + ...

+ P(e | h(N1) & k) P(h(N1) | k) + P(e | h(N2) & k) P(h(N2) | k) + ...

where h(Ni) are nontheistic hypotheses.

Again, h(S) has no scriptures nor, I should add, any adherents in the traditional religious sense. What are we then to make of the argument from religious experience in chapter 13? No one has ever had a religious experience arising from h(S)! Typically, Jews would not have religious experiences of the Virgin Mary, Catholics of Allah, and so on and so forth. Certainly a generic h(S) would not have had a role in anyone's religious experience. How, then, would anyone's religious experience provide support for h(S)? Would a rabbi's religious experience of the Virgin Mary provide support for h(J), the Judaic hypothesis, or would a Catholic's similar religious experience provide support for h(J)? Not in any rigorous sense according to the precepts of confirmation theory if these are distinct, even if kindred, hypotheses. All religious experience must be of some actual religion, and certainly not of the merely hypothetical h(S). Yet Swinburne, I suspect innocently, turns a blind eye to this equivocation in chapter 13 in support of h(S), and simply borrows the notion of religious experience from the only possible source—other theistic hypotheses. Consequently, no conclusion drawn in chapter 13 is relevant as support for his argument to just h(S).

The 14th and final chapter, where all of this is tied together, thus fails on both the equivocation of h and the impertinence of the conclusion drawn from the argument from religious experience, which itself is based on an equivocation of h. Since Swinburne takes h(1), h(2), and h(3) as the only alternatives to h, he fails to account for h(Rn)—other theistic hypotheses. To make the argument rigorous h needs to be just h(S), and since h(S) needs to be simple (else Swinburne would not have reached this point in the argument), the h(Rn) would need to be grouped with h(1), h(2), and h(3), and counterposed against h(S). But this is probably not the conclusion which Swinburne desires, for it argues for h(S) at the expense of h(Rn). If he argues that P(h(S) | e & k) is not less than 1/2, then the various P(h(Rn) | e & k) would have to share what little remaining probability they have with each other and nontheistic hypotheses. And regardless of that, the conclusion of chapter 13 would not even be available to tip the balance of probability of h(S) over 1/2.

3. Conclusion

The question "Is there a God?" is rather like the question "Is there a dog?" Both "God" and "dog" are universals, even if that is counterintuitive with respect to the former, since one normally thinks of universals as having multiple instantiations. And inherent in the idea of God is that he is a solitary instance of his kind, a singleton. It is much easier to accept "god"—with lower case g—as a universal. But "God," like "dog," is merely an idea. Yahweh and Allah are possible (hypothetical) instantiations of the universal "God." For the purposes of reviewing Swinburne's book, we are not really interested in any sense in the existence of "God," the universal idea or abstraction; that is a question for Plato. We are interested in establishing if any instantiation of "God" exists.

"Is there a dog?" is a much easier question to tackle, but the method is the same. I would first posit a hypothesis that some particular instance of "dog" possesses certain attributes by which his/her existence may be verified by evidence; my dog, for example. He is, as I write, occupied with shedding his hairs on my sofa. I don't need to argue intrinsic probabilities for my hypothesis; simply applying the Principle of Credulity, I quickly come to the conclusion that it is quite likely that he exists. Therefore, it is quite likely that "there is a dog," and my work here is done. Note that my confidence in the existence of my dog sheds no light whatsoever on the existence of my neighbor's dog. That is a separate hypothesis that needs to be verified on its own merits.

h(S) is a hypothetical instance of the abstract universal "God," along with Yahweh and various others. They are distinct hypotheses and need to stand on their own merits, up to and until the time when someone can rigorously show that any two or more of these hypotheses are one and the same by matching them property for property. Although Swinburne has argued for h(S) and only h(S), I'm nevertheless left with the impression that he has forgotten that fact somewhere in the course of his argument.

What can an atheist take away from this book, notwithstanding Swinburne's optimism on page 6? I think that a person holding an atheistic view of the world, which is often based on a healthy skeptical attitude, would find great difficulty in overlooking the problems with Swinburne's argument outlined here, especially where the argument purports to be based on premises undisputed by all.

Even disregarding all of these deficiencies, astute theists have have little reason to derive consolation from Swinburne's conclusion. In order to claim rigor and rationality, Swinburne would have to acknowledge the distinction between h(S) and the other "God" hypotheses h(Rn), and that the latter cannot ride free on the coattails of the former. And what does h(S) alone promise the faithful? It promises a simple God who is almost robotic in nature. God's actions are bound by logic and a perfect reading of the objective morality that moral realism posits, and that God must follow by dint of his perfect goodness. In principle, a computer that could access the "scroll" of objective morality, and that possesses actuators which can accomplish anything logically possible, could be programmed to act exactly as the God of h(S) would act.

Would such a robotic, simple God engender any admiration, love, and worship from his adherents? Worse still, this God promises very little benefit to his adherents in this life other than some platitudinous growth in sanctity and insight, the opportunity to make a difference, and the opportunity for significant responsibility through suffering, all a consequence of the "greater good" mandated by moral realism. But take heart! We're quickly informed that God may compensate any sufferers by providing "a [less than eternal] compensatory period of good life after death ... and perhaps he also shares the suffering of humans and animals by becoming incarnate" (p. 265) [italics mine]. Oh joy! These modest hopes betray Swinburne's concern with promising too much lest h(S) become weighed down by too much complexity. And this is the catch-22 that confounds h(S): if it is a rich, promising hypothesis, it is too complex and intrinsically improbable, but if it is to remain simple and intrinsically probable, it is necessarily threadbare.

Notes

[1] Stated in the brief biography preceding Richard G. Swinburne, "The Justification of Theism" (Truth Journal, Leadership University website, 2002), and the brief biography of Richard Swinburne prepared for "The Origin of the Laws of Nature and the Existence of God" panel discussion sponsored by the John Templeton Foundation, respectively.

[2] See: Nicholas Everitt, "Substance Dualism and Disembodied Existence" (Secular Web, 2000); Richard Gale, "Swinburne's Argument from Religious Experience" (Secular Web, 1994); Yujin Nagasawa, "Review of The Evolution of the Soul" (Secular Web, 2005), Graham Oppy, "Is God Good By Definition?" (Secular Web, 1992); Keith Parsons, "Swinburne and the Inductive Cosmological Argument" (Secular Web, 1986); Quentin Smith, "The Anthropic Coincidences, Evil and the Disconfirmation of Theism" (Secular Web, 1992); Quentin Smith, "Swinburne's Explanation of the Universe" (Secular Web, 1998); and Jordan Howard Sobel, Logic and Theism: Arguments for and Against Beliefs in God (New York, NY: Cambridge University Press, 2004), especially the Appendix to Ch. VII.

[3] Say Achilles is in a race with a tortoise who is generously given a starting position say 100 meters ahead of Achilles. If both run at a constant speed where Achilles runs faster, he still cannot catch the tortoise. For when Achilles reaches the point where the tortoise was at the start, the tortoise would already have advanced some small distance as well. When Achilles reaches this new position, the tortoise is again some smaller distance ahead, and so on indefinitely. The paradox is, of course, that Achilles does in fact catch and pass the tortoise.

[4] In a hotel with an infinite number of rooms, each one of which is now occupied by a guest, there is still room to add one more guest. Simply move the occupant of room 1 to room 2, that of room 2 to room 3, room 3 to 4, and so on. Now the new guest may lodge in room 1 without expelling any current guest. Even more perplexing is the case where the guest of room 1 moves to room 2, that of room 2 to room 4, that of room 3 to room 6, and so on, freeing all the odd numbered rooms into which a countably infinite set of new guests may then lodge.