THE PROBABILITY ARGUMENT FOR THE EXISTENCE OF GOD AND ALIEN PYRAMID BUILDERS

 

James Fieser

 

9/14/2006

 

 

Over the centuries, the design argument for God’s existence has taken many forms, most notably Aquinas’s version that nature is directed towards an end, and Paley’s version that natural design resembles the intricacies of a watch. Both of these versions are weakened by rival naturalistic explanations of apparent design in the world, specifically evolutionary and astrophysical theories. However, one version of the design argument seems resistant to that attack: the design argument from probability. I will examine this argument, and, in so doing, contend that it fails insofar as it rests on a basic fallacy of ad hoc reasoning.

 

THE PROBABILITY ARGUMENT STATED AND CRITICIZED

            The central idea behind the design argument from probability is that the physical conditions that make life possible on earth are extraordinarily delicate, and their occurrence is more probable under a theistic hypothesis than a non-theistic one. A good example of this is the following from Isaac Newton:

 

Were all the planets as swift as Mercury or as slow as Saturn or his satellites [i.e. its moons]; or were the several velocities otherwise much greater or less than they are (as they might have been had they arose from any other cause than their gravities); or had the distances from the centers about which they move been greater or less than they are (as they might have been had they arose from any other cause than their gravities); or had the quantity of matter in the sun or in Saturn, Jupiter, and the earth (and by consequence their gravitating power) been greater or less than it is; [then, in any of these cases,] the primary planets could not have revolved about the sun nor the secondary ones about Saturn, Jupiter, and the earth, in concentric circles as they do, but would have moved in hyperbolas or parabolas or in ellipses very eccentric. To make this system, therefore, with all its motions, required a cause which understood and compared together the quantities of matter in the several bodies of the sun and planets and the gravitating powers resulting from thence.... And to compare and adjust all these things together in so great a variety of bodies, [such a design] argues that cause to be, not blind and fortuitous, but very well skilled in mechanics and geometry. [Letters to Richard Bentley, 1]

 

There are two parts to Newton’s argument above. First is his list of ultra-precise physical factors that are needed to keep the solar system just as it is. Second his statement that these factors are not the result of blind forces, but, rather, a cause that is “very well skilled in mechanics and geometry.”

            300 years after Newton, we find the same general strategy in probability arguments for God’s existence, but with an updated list of stumbling blocks in the sciences of biological evolution and astrophysics. For example, the initial emergence of DNA molecules is not easily explained on purely scientific grounds. Other versions mention several ultra-precise physical conditions that are needed for supporting life on earth. If the initial big bang as physicists describe it had differed in strength by only the tiniest amount, life on earth would have been impossible. So too if gravity was slightly stronger or weaker. So too if the sun was slightly larger or smaller. So too if the size of the earth differed minutely. The list of such contingencies is very long and eye-opening. While probability arguments differ in the specific scientific examples they cite, most share a common theme which can be expressed as follows:

 

1. The existence of life-sustaining conditions on earth is probable under the theistic hypothesis.

2. The existence of life-sustaining conditions on earth is improbable under the non-theistic hypothesis.

3. When considering two competing hypotheses, we should accept the one that offers the more probable outcome.

4. Therefore, we should accept the theistic hypothesis as the explanation of the world’s life-sustaining conditions.

 

The notion of “theism” adopted in premise 1 refers to a specific concept of a supremely intelligent and powerful divine being who is sufficiently motivated to bring about life-sustaining conditions on earth. By contrast, the notion of “non-theism” in premise 2 refers to the idea that blind natural forces brought about those life-sustaining conditions, without any intervention from a divine being. The non-theist doesn’t necessarily disbelieve in a divine being; rather, the non-theist would maintain that if a divine being does exist, it is a vastly different entity than what the theist imagines, and that being played no role in the creation of the cosmos.

            The above argument doesn’t rule out the possibility that many of the life-sustaining conditions on earth are the result of natural causes such as evolution. The point is that a purely naturalistic set of causes is an unlikely explanation of the earth’s ultra-precise life-sustaining conditions. It’s thus more probable that a divine intelligence arranged the conditions, perhaps using some evolutionary forces in the process. Examples of ultra-precise life-sustaining conditions on earth, such as gravitational forces, are compelling, and even religious skeptics should except that life on earth hinges on exceedingly strict physical conditions. What’s at issue, though, is our lack of historical knowledge about what actually took place when the cosmos was formed. We unfortunately can’t travel back in time to the creation of the universe to see whether a divine being was involved in some way. The above argument attempts to fill this knowledge gap by assessing the probability levels of two competing hypotheses.

            Let’s set this argument for God’s existence aside for a moment, and examine a parallel argument that similarly rests on incomplete historical knowledge, specifically knowledge about who really built the pyramids in ancient Egypt. We’re all familiar with the accepted theory by academic historians that the pyramids were built by human Egyptians several millennia ago. But there are many lingering questions about how an early Iron Age civilization could, out of nowhere, develop the complex engineering skills to cut and assemble stones on a monumental scale with such mathematical precision. So mind-boggling were these marvels of the ancient world that contemporaries of the time believed that they were constructed under the supervision of the gods. Several thousands of years after the fact, try as we do, we can’t fully explain the organizational structure that led to their creation, and the explanations academic historians offer are riddled with improbability. Consider, now, an alternative theory that fully answers these questions: the pyramids were built under the guidance of advanced aliens from another star system who long ago traveled through outer space to ancient Egypt. They had superior knowledge and resources which enabled them to meet the pyramid-building challenges with the utmost expertise. With the help of human laborers, they did just that. We’ll call this the “alien hypotheses” in contrast with the traditional view that we’ll call the “non-alien” hypotheses. The specific argument in favor of the alien hypothesis is this:

 

a. The existence of pyramid-building technology is probable under the alien hypothesis.

b. The existence of pyramid-building technology is improbable under the non-alien hypothesis.

c. When considering two competing hypotheses, we should accept the one that offers the more probable outcome.

d. Therefore, we should accept the alien hypothesis as the explanation of the existence of pyramid-building technology.

 

            Clearly, we want to reject the conclusion of this argument, but where does the argument itself go wrong? The flaw is that it assumes a hypothesis in premise (a) which can always be stipulated to have a stronger probability than its rival. This is a case of the fallacy of ad hoc rescue. That is, to rescue a cherished belief from a problem, I specially fashion a new assumption that eliminates the problem. This constitutes a fallacy specifically when there is no good independent reason to accept the new assumption other than that it succeeds in saving my cherished belief. In this case, my cherished belief is that aliens built the pyramids. My new assumption is this: “I hereby stipulate that the ‘alien hypothesis’ entails the view that there are technologically advanced aliens who, upon visiting earth, would probably build pyramids.” This assumption is then used to fix the probability level in premise (a). Yes, this new assumption enables the alien hypothesis to overpower the non-alien hypothesis. However, I have no independent reason for accepting this assumption other than the fact that it rescues my cherished belief in alien pyramid builders.

            Even if the academic historian rejects premise (b) and insists that the non-alien hypothesis is probable, the alien defender can modify his stipulated assumption to match this. That is, he can stipulate that the alien hypothesis entails the view that “there are technologically advanced aliens who, upon visiting earth, would very probably build pyramids.” This surpasses the new probability of the non-alien hypothesis. Further still, if the historian insists that the non-alien hypothesis is extremely probable, the alien defender can match this by stipulating that the advanced aliens, upon visiting earth, “would unquestionably build pyramids.” Again, the alien hypothesis wins. Since we can’t travel back in time to watch the construction of the pyramids first hand, there will always be some gap in our historical knowledge of human Egyptian capabilities so long ago. Even the academic historian must grant that the non-alien hypothesis will never be 100% certain. But a carefully stipulated assumption in the alien hypothesis will always yield a higher probable outcome, and this is the heart of the fallacy.

            The point regarding the alien pyramid builder argument is, of course, that we find this same problem in the probability argument for God’s existence: both rest on the fallacy of ad hoc rescue. In the probability argument, my cherished belief is that a divine being created the world; my new assumption is the following narrowly stipulated view of theism: “I hereby stipulate that ‘theism’ entails the view that a supremely intelligent, powerful and sufficiently motivated divine being, upon creating the universe, would have probably made it to sustain life on earth.” This assumption is then used to fix the probability level of the theistic hypothesis in premise 1. And, as with the alien pyramid builder argument, I have no independent reason for accepting this assumption other than the fact that it rescues my cherished belief in a divine being as creator. Like the pyramid builder hypothesis, the theistic hypothesis can always be crafted to surpass the probability level of its rival. If scientists insist that the non-theistic hypothesis is probable, the theist could say more confidently “I hereby stipulate that ‘theism’ entails the view that an intelligent, powerful and sufficiently motivated divine being, upon creating the universe, would have unquestionably made it to sustain life on earth.” Even if the non-theistic hypothesis was highly probable, it still could not compete with this carefully-stipulated theistic hypothesis.

            Several specific elements of the theistic assumption are crucial for the theistic hypothesis to even appear probable on face value. Specifically, it’s not sufficient to simply stipulate that the divine being has supreme “intelligence”.  For all we know an intelligent divine being wouldn’t have any motivation to intervene in the development of the natural world at all.  Further, a supremely intelligent divine being might not have the power to intervene even if it wanted to. Thus, the theistic hypothesis must include assumptions about the divine being’s power and motivation, and not just its intelligence. These elements of the assumption, then, serve to establish the probability level of the theistic hypothesis in premise 1. But, like the alien hypothesis, all of these assumptions of the divine being are stipulated without any compelling independent knowledge. I may believe through faith that a divine being is supremely intelligent and powerful, and sufficiently motivated to help guide cosmic development; but that doesn’t count as independent evidence any more than my cherished belief that aliens built the pyramids. What I’m left with is an assumption about a divine creator in premise 1 that I can stipulate any way that I want to, just as I can an assumption about alien pyramid builders.

            There is a more impartial way of wording premise 1 that avoids the fallacy of ad hoc rescue. I might be less precise about the nature of the divine being in question -- its motivations, its level of intelligence and power. Accordingly, I might consider the probability of life-sustaining conditions on earth under “the set of all supernatural hypotheses.” I might also be less precise in the level of probability that I assign to the outcome. A revised wording of premise 1, then, is this:

 

1’. The existence of life-sustaining conditions on earth has probability X under the set of all supernatural hypotheses.

 

The problem with this revision, though, is that I cannot establish what “probability X” might be; there are an infinite number of possible supernatural hypotheses, some might involve ultra-precise life-sustaining activities of a supernatural agent, but others won’t. I have no independent evidence that tells me whether a given supernatural agent would be likely or unlikely to intervene in cosmic development. Without knowing what “probability X” is, I can’t compare the probability of the supernatural hypothesis to the non-theistic hypothesis. So, this modified design argument from probability fails.

 

ANSWERS TO OBJECTIONS.

            The essence of the above critique is that we can’t invent an unsupported hypothesis, arbitrarily assign it a high level of probability, and then proclaim victory when it surpasses the lower probability of a historically or scientifically grounded hypothesis. The above critique is rather concise, and undoubtedly raises questions that require more detailed explanation. For example, is the theistic hypothesis really without independent reason? Are the theistic and alien hypotheses really comparable? Are the non-theistic and non-alien hypotheses really comparable? Several potential objections are presented here with responses to each.

            Objection 1: The alien hypothesis is a pure invention with no independent reasons whatsoever to back it up. The theistic hypothesis, by contrast, isn't the same: it's part of a long cultural tradition that is grounded in personal religious experience. It, thus, has some independent reasons in its support, unlike the alien hypothesis. As such, the probability argument for God does not exhibit the fallacy of ad hoc rescue.

            Answer: The issue of what counts as “support,” “evidence,” “justification”, “warrant” – and a host of related concepts – is a rather thorny matter within epistemology that cannot be resolved here. However, we might very generally distinguish between two types of evidence which, following William James, we can call “tough-minded” and “tender-minded”. Tough-minded evidence is the sort commonly associated with science, which involves empirical observation and repeatable experiments. Tender-minded evidence, by contrast, is less scientific, more intuitive, and affects the choices that we make in our quests for happiness, personal fulfillment, love and community. For many people, religious tradition and experience undoubtedly qualify as tender-minded evidence in these more intimate areas of life; it would be uncharitable for the non-theist to deny this. But there is no tough-minded religious evidence. The road to religious knowledge is littered with failed attempts to scientifically demonstrate life after death, the effectiveness of prayer, the accuracy of prophecy, the veracity of miracle claims. To the extent that religious tradition and experience count as “evidence”, it seems to be restricted to the tender-minded realm. It may very well be the private choice of a theistic believer to give preference to the tender-minded aspects of life over the tough-minded, and the non-theist must respect that right. As such, the theist may personally opt to believe through faith that a divine being orchestrated the life-sustaining conditions on earth. However, the probability argument for God’s existence does more than this: it enters the tough-minded arena of science and attempts to combat the non-theistic hypothesis on its own tough-minded ground. In essence, it misrepresents tender-minded religious evidence as tough-minded evidence. This is most clearly seen in defenses of intelligent design theory, which boldly present their position as a scientific explanation. Thus, to the extent that the theistic hypothesis lacks tough-minded evidence, the probability argument for God is very much like the alien pyramid builder argument and commits the fallacy of ad hoc rescue.

            Objection 2: There’s an important difference between the alien and theistic arguments. In reality, the alien hypothesis has a very low initial probability -- and not a comparatively high one as premise (a) in the pyramid builder argument states. In fact, the initial low probability level of the alien hypothesis is assumed in the very fact that the alien argument is put forward as a parody of the theistic argument. To suggest that the theistic hypothesis has a similar very low initial probability begs the question against the theist.

            Answer: In many probability arguments for God’s existence, the initial probability levels of the rival hypotheses are set by something like gentlemen’s agreements. For example, where “1” is the highest level of probability and “0” the lowest, disputants may initially set the probability of both the theistic and non-theistic hypotheses midway at “.5”. Disputants then will increase or decrease the probability levels of the rival hypotheses based on relevant information about either. The key question, though, is why should we extend this gentlemen’s agreement to the theistic hypothesis but not the alien hypothesis? Both lack tough-minded evidence. Both would be supported by their respective advocates for tender-minded reasons. Both have stipulated assumptions that are tailored to support their respective ends – whether it’s pyramid building or the creation of life-sustaining conditions. One obvious difference between the two is that there are substantially more believers in the theistic hypothesis than in the alien one (although there are some actual believers in the latter). But the probability levels here cannot be set by a mere popularity contest; doing so would transform the probability argument for God into an argument from popular appeal, which is not the theist’s intent. In fairness, then, the alien hypothesis deserves the same gentlemen’s agreement that’s offered to the theistic hypothesis. With either hypothesis, an initial probability assignment of “.5” is arbitrary, and a different gentlemen’s agreement might result in probability levels as low as “.1” or as high as “1.” If through agreement we assign a “.1” to the alien hypothesis, the theistic hypothesis deserves the same; or, if we assign a “1” to the theistic hypothesis, the alien hypothesis deserves the same. The strategy of both the theistic and alien arguments, though, is for their defenders to assign probability levels to the theistic and alien hypotheses that are high enough to surpass their respective rivals, whatever the probability levels of those rival hypotheses may be. This begs the question against the rival positions, and the fallacy of ad hoc rescue emerges.

            Objection 3: The probability of the non-theistic hypothesis is so low that it entitles us to consider the theistic hypothesis, even when the theistic hypothesis isn’t backed by independent reasons. By contrast, in the alien pyramid builder argument, the probability of the non-alien hypothesis is high enough that it does not entitle us to consider the unsupported alien hypothesis.

            Answer: We need to be clear about what specific part of the non-theistic hypothesis is improbable, and what the term “improbable” means. On the one hand, if I arbitrarily pointed to some particular planet or moon in the universe, it may indeed be astronomically improbable for it to display life-sustaining conditions. On the other hand, if I am considering the probability that some planet in the universe has naturally-occurring life-sustaining conditions, that’s a different matter. The probability here depends on the size of the playing field – how many solar systems are in our galaxy and how many galaxies are in the known universe. The larger the playing field, the greater the chances. Many researchers believe that the probabilities are very good that life-sustaining conditions occur throughout the universe, and our planet is just one case in point. Premise 1 of the theistic argument states that “The existence of life-sustaining conditions on earth is improbable under the non-theistic hypothesis.” The term “improbable” is a concession that the non-theist may be willing to make, perhaps in the absence of any consensus among scientists about an exact probability level. Nevertheless, it is uncharitable for the theist to maintain that the existence of naturally-occurring life-sustaining conditions is astronomically improbable. While the evidence for the non-theistic hypothesis may be incomplete, it is still backed by enough scientific evidence to prohibit opponents from countering it with a rival hypothesis that lacks any scientific support.

            Objection 4: The purely natural occurrence of at least some life-sustaining features on earth is in fact astronomically improbable, such as the initial emergence of DNA molecules. Accordingly, with respect to these specific ultra-improbable features, the non-theistic hypothesis has no good independent reason in its support; as such it does not parallel the human-pyramid-builder hypotheses which does have independent support.

            Answer: True, some defenders of the probability argument maintain that current scientific evidence doesn’t come close to supporting the non-theistic hypothesis when it comes to these ultra-improbable features. The accuracy of their claim remains to be seen, and rests on biological and astrophysical evidence that is beyond the scope of this essay to explore. For the sake of argument, though, let’s assume for the moment that the non-theistic hypothesis is completely without good independent support with respect to these ultra-improbable features. This means that the non-theist is free to stipulate his notion of “non-theism” any way that he wishes (just as the theist can), such as the following: “I hereby stipulate that ‘non-theism’ entails the view that blind natural forces, upon creating the universe, would have unquestionably made it to sustain life on earth.” Accordingly, the non-theist can revise premise 2 as follows:

 

2.’ The existence of life-sustaining conditions on earth is virtually assured under the non-theistic hypothesis.

 

The probability argument for God’s existence now becomes a contest between two unsupported hypotheses: the theist’s and the non-theist’s. As worded in the new premise 2’, the unsupported non-theistic hypothesis surpasses the unsupported theistic hypothesis, and the probability argument for God falls flat. The theist could of course respond with a revised hypothesis that matches 2’. The contest will then end in a draw – or perhaps metamorphose into an ontological argument that rests on the hidden implications of “theism” and “non-theism”. The larger point, though, is that the theist is now locked between two horns of a dilemma. If the theist insists that the non-theistic hypothesis is without independent rational support, then there is no probability argument for God’s existence. If on the other hand the theist grants that there is at least some good independent reason to support the non-theistic hypothesis, then the probability argument for God’s existence commits the fallacy of ad hoc rescue.

            Objection 5: There are other versions of the probability argument that are less susceptible to the charge of ad hoc rescue, such as this:

 

(1) There are only three possible explanations of the ultra-precise life-sustaining conditions on earth: necessity, chance, and intelligence.

(2) The life-sustaining conditions on earth are contingent (that is, they could have been otherwise), which rules out necessity.

(3) The life-sustaining conditions on earth are so improbable that chance is an inadequate explanation.

(4) Therefore, intelligence is the only explanation left standing.

 

When the probability argument for God is presented this way, there is nothing ad hoc in its argument structure.

            Answer: There are two key problems with this alternative argument. First, of the three possible explanations listed (that is, necessity, chance and intelligence), the theist arbitrarily selects “necessity” and “chance” for analysis, eliminates them, and concludes with the “intelligence” option. The non-theist, though, could just as arbitrarily select “necessity” and “intelligence” for analysis, eliminate them, and conclude with the “chance” option. The non-theist’s counter argument, then, is this:

 

(1) same as above

(2) same as above

(3) There is no independent reason to believe that the life-sustaining conditions on earth are caused by intelligence, which makes this an inadequate explanation.

(4) Therefore, chance is the only explanation left standing.

 

To avoid the charge of arbitrary selection, the argument needs to independently analyze all three options – or, eliminating “necessity” on its face value, at least analyze the two main contenders of “chance” and “intelligence”. This, though, brings us back to the original wording of the probability argument that appears at the outset of this essay, and the fallacy of ad hoc rescue again emerges.

            The second problem with the alternative version of the probability argument is that it commits the fallacy of excluded middle. That is, it presents three options as the only logically possible contenders when there are in fact many others – the total number of which may perhaps be limited only by our abilities to conceive of different metaphysical categories and science fiction scenarios. Hume sufficiently makes this point here:

 

In this little corner of the world alone, there are four principles, reason, instinct, generation, vegetation, which are similar to each other, and are the causes of similar effects. What a number of other principles may we naturally suppose in the immense extent and variety of the universe, could we travel from planet to planet, and from system to system, in order to examine each part of this mighty fabric? Any one of these four principles above mentioned (and a hundred others which lie open to our conjecture), may afford us a theory by which to judge of the origin of the world; and it is a palpable and egregious partiality to confine our view entirely to that principle by which our own minds operate. [Dialogues Concerning Natural Religion, Part 7]

 

Without listing, analyzing and then definitively eliminating all of the logically possible contenders, the “intelligence” option cannot be supported by a simple process of elimination.

 

CONCLUSION

            Since the outset of the scientific revolution, theists such as Newton were quick to expose the inadequacies of purely natural explanations of life on earth and conclude instead that a designing mind must be behind the fabric of life. One especially remarkable theistic apologist of this period was William Derham (1657-1735) whose two works Physico-Theology (1713) and Astro-Theology (1715) cataloged virtually every known improbable state of affairs in the biological and celestial realms. But, as science moved forward over the succeeding decades and centuries, two things happened. First, scientists were able to offer compelling natural explanations for many of the phenomena that previously proved so baffling. Second, by pushing the frontiers of knowledge even further, scientists uncovered yet more highly-improbable natural phenomena. A new generation of theistic apologists then cited these new puzzles as clear proofs of a designing mind. Unfortunately the new apologists never set the record straight by conceding that the earlier apologists over-dramatized the old scientific puzzles. Rather, they just forged ahead by announcing to the world how the new puzzles definitively showed the footprints of God in the natural world. With this happening generation after generation, we might be suspicious of every new theistic argument from probability, just as we would the fabled “boy who cried wolf”. But older works like Derham’s are buried in obscurity, and we can’t readily see the historical pattern for what it is.

            Perhaps the perennial appeal of the probability argument is more emotional than it is a matter of the cool weighing of probabilities. It’s pretty scary to think that life on earth might not have existed if its life-sustaining conditions had been off just a little. But our lives our filled with “what if” scenarios. What if I turned left at the stoplight; I would have been killed in an accident. What if I didn’t look in the help wanted section of the newspaper; I wouldn’t have gotten this job. All of these “what ifs” involve ultra-precise conditions, but we should not push the issue to the point of concluding that a divine designer had his hand in these matters. Fortunate events naturally happen just as do unfortunate ones. The probability argument presents a big “what if”, but perhaps we should just be happy that life on earth emerged as it did, and leave it at that.

 

[Copyright 2005, James Fieser, all rights reserved. Revised 2006]