According to the Internet Encyclopedia of Philosophy, “Divine simplicity is central to the classical Western concept of God.”[1] There are a variety of apologetic motivations for this claim, largely to show God’s unity, transcendence, uniqueness, immutability, and so on. Richard Swinburne, emeritus professor of philosophy at the University of Oxford, has a unique take on this notion and a somewhat different motivation. He argues that, yes, God is very simple, but specifically that this is because he has attributes of infinite magnitude, which is how he characterizes the various well-known “omni-traits.” Swinburne explicitly claims that infinite attributes, in general, are as simple as possible, whether pertaining to God or not. I intend to show that this claim is not only dubious, but even worse, leads to a contradiction.
It is fair to give warning at the outset that the following contains some technical terms and concepts, and even an equation from basic physics. A strong grasp of these is not essential to understanding the whole argument, though, especially the conclusion. The one technical concept that is essential to understanding the gist of the argument is that of reductio ad absurdum. With that out of the way, let’s dive in.
Being finite creatures, with the exception of those who are highly mathematically adept, most of us struggle with the concept of infinity. Our personal worlds are confined and limited in space as well as in time, and the notion of infinity is the opposite of confinement and limitation. Thus we have no direct contact with this abstraction. Only in the loftier, complex realms of mathematics, physics, and philosophy does the notion of infinity attain some semblance of manageability, and even there it does not become manageable with great ease. Consequently, it’s not too much of a stretch to say that simplicity, commonly construed, would not be considered naturally associated with infinity.
To make matters more confounding still, infinity itself appears to be multifaceted, not a single “value,” if indeed it can be thought of as a value at all. In the mathematics of transfinite numbers, following on the work of Georg Cantor, there are at least two distinct cardinalities (“size”) of infinite sets: that of the set of natural numbers, designated by the term aleph-zero, and that of the set of real numbers (with some caveats), designated by aleph-one. The latter can be formally shown to exceed the former. Thus, not all infinities are the same “size.” To put it another way, there are multiple infinities, which complicates matters.
Now the notion of infinity has also made a curious appearance in theological narratives, in particular with respect to the Abrahamic concept of God. This deity is typically presented as possessing various attributes such as power, knowledge, wisdom, and goodness that are, in some sense, perfect, unbounded, and without limitation. It is then easily surmised that these attributes can be described as infinite in magnitude, although the scriptures do not use that term.
Such an innocent lexical move would ordinarily not elicit much attention, except in one notable case that is the subject of this article. The philosopher Richard Swinburne famously proffered the assertion that the hypothesis of the existence of the Abrahamic God is a simple one, and that consequently the intrinsic probability of the God hypothesis is large in comparison to competing, purportedly more complex hypotheses—no God or lesser gods.[2] In a lengthy argument resting largely on the assertion of divine simplicity, Swinburne claimed to show that the intrinsic probability of the truth of his hypothesis was not less than ½, or in other words, was greater than or equal to ½. This essentially amounts to the claim that the hypothesis that God exists is more likely than not.
This result, of course, is hardly spectacular, as it leaves completely uncertain how far beyond a simple 50/50 toss-up the probability of the God hypothesis actually is; Swinburne never attempts to proceed beyond this milestone and enumerate a specific probability greater than ½. Viewed another way, prior to Swinburne making his case for God, the intrinsic probability of God’s existence was, axiomatically, in the range 0 to 1. This, of course, is just the limit of the range of any probability, from 0 (completely impossible) to 1 (utterly certain). At the end of making his case, Swinburne’s essential claim, and no more than that, was that this range was reduced by half to the range 0.5 to 1! That is, anywhere from a 50/50 toss-up to complete certainty. As I stated above, he did not proceed to show where in this range the probability of his hypothesis actually landed. I have critically examined his argument in much greater detail in an earlier article, pointing out various notable flaws in his reasoning that cast doubt on even this modest achievement.[3]
What connects the above to the notion of infinity is that Swinburne argues that his God hypothesis is simple on account of God’s attributes possessing infinite magnitudes. In addition, he also argues that simple hypotheses are more likely to be true than more complex hypotheses, that is, they have a larger intrinsic probability. These are the two primary pillars of his argument.
Taking the latter claim first, there is some intuitive preference for simpler hypotheses over more complex ones, a notion embodied in Ockham’s razor, or Albert Einstein’s maxim “Everything should be made as simple as possible, but not simpler.” Now that this preference for simplicity can be justifiably extended to the claim that simple hypotheses are more likely to actually be true is questionable. I will not examine the validity of this claim in detail here, as there are others who share my concern about this leap who have well addressed the issue.[4]
Rather, I will focus here on Swinburne’s claim that an attribute of God that has an infinite magnitude somehow confers simplicity on God, and thus on the hypothesis of his existence. Considering my earlier reasons for feeling that simplicity would not naturally be associated with infinity, this claim seems counterintuitive. How does Swinburne justify this claim?
He asserts: “Interestingly, however, hypotheses attributing infinite values of properties to objects are simpler than ones attributing large finite values. For we can understand, for example, the notion of an infinite velocity (the velocity being greater than any number of finite units of velocity) without needing to know what the googleplex [sic: googolplex] is (10^10^10.)”[5]
Further along he states:
He [God] is infinitely powerful, omnipotent. This 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…. There is a neatness about zero and infinity that particular finite numbers lack. Yet a person with zero powers would not be a person at all. So in postulating a person with infinite power the theist is postulating a person with the simplest kind of power possible.[6]
Let’s look at the first justification that an infinite magnitude is simple in comparison to some specific large value because it is more understandable. He uses the example of infinite velocity. Now something traveling at infinite velocity would necessarily get from point A to point B instantaneously—in 0 time—given that
time = distance/velocity
In the equation above we are dividing a finite distance by an infinitely large velocity, giving the result of 0 time.
Thus, this single object would be at point A and point B simultaneously (at the same time), and at all the points in between as well! I fail to comprehend how this strange state of affairs is more understandable than the case of the object being at only one location at a time, which would be the case if it had some finite velocity. Some may raise the objection that quantum mechanics does describe a realm where a particle is, in some manner, considered to be at a superposition of locations at the same time, that is until it is observed, at which time it “collapses” to a single location. But even this mysterious superposition is not a consequence of infinite velocity; rather, it occurs at any velocity. Furthermore, no one has the foggiest idea of how to make sense of this even though the mathematics is precise and empirically well supported. It is not, by any means, considered easily understandable, and it has befuddled physicists for a century.
The second justification is no more edifying. It rests on notions of “crying out for an explanation” and “neatness.” Again taking the example of infinite velocity and its logical consequence of simultaneous positions, infinite velocity appears to be much more in need of explanation, based upon our experience of the world, than some finite velocity. As for the notion of “neatness,” this is rather subjective. I take it to mean that an infinite magnitude is a single term—barring objections from Cantor—whereas other possible finite values of magnitude can be quite numerous, possibly infinite. The concept of neatness seems to rest on how many choices are possible. With infinity, as commonly construed, there is only one choice.
Granted, forming hypotheses where you reduce your choices is definitely simpler than having to come up with some reason for one of many possible specific values. But as shown with the example of infinite velocity, opting for such artificial neatness comes at the cost of concocting a stillborn hypothesis that makes no sense.
Nevertheless, let’s grant Swinburne his assertion that “in postulating a person with infinite power the theist is postulating a person with the simplest kind of power possible”[7] and see where this leads. To generalize his assertion, we can state that postulating some entity possessing an attribute with an infinite magnitude is postulating an entity with the simplest kind of this attribute possible. This generalization is well in keeping with his earlier claim that “hypotheses attributing infinite values of properties to objects are simpler than ones attributing large finite values.”[8] Swinburne never does seem to specify that the assertion applies only to the attribute of power.
Now let’s take “complexity” as an attribute of our hypothetical entity, that is to say, just how complex this entity is. Clearly this is a fundamental attribute of any entity. Complexity is the inverse of simplicity; the greater the one, the less the other, and vice versa. If we now postulate that the magnitude of the complexity attribute of our hypothetical entity is infinite, we would then have an infinitely complex entity. So far so good—this is simply following Swinburne’s method. But if we follow the logic of Swinburne’s assertion above with respect to infinite attributes implying simplicity, then we are now forced to the conclusion that our entity possesses the attribute of complexity that is as simple as possible.
There seems to be something distinctly unsettling about this result! What does it even mean? Does it mean that there can be such a concept as simple complexity vs. complex complexity—in other words, complexity of complexity? That would not make sense. Instead, one could reasonably interpret the above conclusion to mean that if the complexity of an entity is as simple as possible, then it has no complexity at all: it is zero. Thus we are forced to the conclusion, by Swinburne’s assertion, that our hypothetical entity is as simple as possible.
Yet we postulated at the outset, by hypothesis, that the entity is infinitely complex. Thus we have arrived at a contradiction, a reductio. That is, initially assuming the general assertion that postulating some entity possessing an attribute with an infinite magnitude is postulating an entity with the simplest kind of this attribute possible, leads to a contradiction. Hence, the assertion is false. And then so is the specific assertion “in postulating a person with infinite power the theist is postulating a person with the simplest kind of power possible.” This pretty much unravels Swinburne’s claim that the hypothesis of God’s existence is very simple and thus intrinsically more probable than competing hypotheses. Without these pillars, Swinburne’s overall argument flounders, as he admits, “Simplex sigillum veri (‘The simple is the sign of the true’) is a dominant theme of this book…”[9]
Notes
[1] Peter Weigel, “Divine Simplicity” in The Internet Encyclopedia of Philosophy ed. James Fieser (Martin, TN: University of Tennessee at Martin, 2019). <https://www.iep.utm.edu/divine-simplicity/>.
[2] Richard Swinburne, The Existence of God, 2nd ed. (Oxford, UK:: Oxford University Press, 2004), chapters 3 & 6.
[3] Gabe Czobel, “An Analysis of Richard Swinburne’s The Existence of God” (March 4, 2010). The Secular Web. <https://infidels.org/library/modern/gabe-czobel-swinburne/>.
[4] See: Emily Qureshi-Hurst, “Is Simplicity that Simple? An Assessment of Richard Swinburne’s Argument from Cosmic Fine-Tuning.” Theology and Science Vol. 19, No. 4 (2021): 379-389; Emma Beckman, “Richard Swinburne’s Inductive Argument for the Existence of God—A Critical Analysis” (master’s thesis, Linköping University, 2008). DiVA [Digital Scientific Archives]. <https://www.diva-portal.org/smash/get/diva2:208388/FULLTEXT01.pdf>, pp. 37-38; and Kevin T. Kelly, “Simplicity, Truth, and the Unending Game of Science” in Infinite Games: Foundations of the Formal Sciences ed. V. S. Bold, B. Loewe, T. Raesch, & J. van Benthenm (Roskilde, Denmark: College Press, 2007): 223-270, pp. 266-268 [16. Conclusion: Ockham’s Family Secret].
[5] Swinburne, The Existence of God, p. 55.
[6] Swinburne, The Existence of God, p. 97.
[7] Swinburne, The Existence of God, p. 97.