The Probability of God

Betrand Russell, famous for his agnostic views as much as for his theories on logic, was once asked how he would answer if he turned out to be wrong about God. Russell was delighted with the question and answered, “Why, I should say, ‘God, you gave us insufficient evidence.’”

I suspect that upon their meeting, God corrected the ol’ Brit, showing how the evidence was there and that Russell had simply chosen to ignore it. But it does raise the question of why different people when presented with much the same evidence, come to such varying conclusions about the existence of God.

Presumably, rational people weigh the evidence of God’s existence or non-existence in order to determine the probability of one being more likely than another and proceed from there. After all, since we can’t know the answer with absolute certainty, we have to base it on our best probabilistic assumption.

But how can we determine what is more likely when applied to an issue such as the ontological status of God? That is the question British theoretical physicist Stephen Urwin attempts to answer in his book, The Probability of God.

By applying Bayesian probabilities, a statistical method devised by eighteenth-century Presbyterian minister and mathematician Thomas Bayes, Urwin attempts to determine the probability of God’s existence. Since 50-50 represents “maximum ignorance,” Unwin begins with a 50 percent probability that God exists (or 50 percent probability that God does not exist) and then applies it to the following modified Bayesian theorem:

The probability of God’s existence after the evidence is considered is a function of the probability before times D (“Divine Indicator Scale”):

10 indicates the evidence is 10 times as likely to be produced if God exists

2 is two times as likely if God exists

1 is neutral

0.5 is moderately more likely if God does not exist

0.1 is much more likely if God does not exist

Unwin then uses the following lines of evidence and applies his own, admittedly subjective, figures for their likelihood:

Recognition of goodness (D = 10)

Existence of moral evil (D = 0.5)

Existence of natural evil (D = 0.1)

Intra-natural miracles (e.g., a friend recovers from an illness after you have prayed for him) (D = 2)

Extra-natural miracles (e.g., someone who is dead is brought back to life) (D = 1)

Religious experiences (D = 2)

Plugging these figures into the above formula (in sequence, where the P after figure for the first computation is used for the P before figure in the second computation, and so on for all six Ds), Unwin arrives at the conclusion that the probability that God exists is 67 percent.

While I generally agree with Unwin’s assessment, my own calculations would be slightly different:

Recognition of goodness (D = 10) — I agree that the existence of goodness is more probable in a world in which God exists.

Existence of moral evil (D = 1) — I believe that the existence of evil is a neutral factor in regards to God’s existence. As Alvin Plantinga shows with his “free will defense” argument, moral evil is just as probable in a world in which God exists as it would be in a world in which He didn’t.

Existence of natural evil (D = 1) — Since “transworld depravity” could apply to nonhuman moral agents, Plantinga’s argument still applies.

Intra-natural miracles (D = 2) — I’ve personally had a sufficient number of these types of experiences to believe that it is two times as likely that they are divine actions rather than coincidences. Since the mathematical probability of them being coincidences are impossibly high, though not outside the realm of possibility, I can only rate this a 2 rather than a 10.

Extra-natural miracles (D = 2) — I would put them in the same category as the ones above.

Religious experiences (D = 2) — I give my personal religious experiences the same weight as I did the intra-natural miracles.

When I plug these number into the formula (fortunately, Urwin provides a calculator) I come up with the probability that God exist to be 99 percent. Even if I had started with the presumption that there was a 98 percent chance that God does not exist, when I factor in the evidence it still puts the probability at 62 percent. Clearly, based on my interpretation of the evidence, it would be more reasonable for me to believe that God exists than to doubt it.

My actual confidence that God exist is higher than 99 percent, so while the formula is useful, it is not exact.

[Note: By using Urwin’s calculator, we can perform this analysis based on any seven lines of evidence. We just assign each a designator (E1 - E7) and plug them in to come up with the probability.]

Addendum & Objections

Let me clarify that this argument is not intended to be used as a proof of God’s existence. The sole intention is to put in quantifiable terms the probabilities that we should form a belief about such a Being’s existence. In other words, this is not an ontological proof but a means of justifying a particular epistemic stance toward the idea of the existence or non-existence of a deity.

The argument is that starting from an epistemically neutral point (50 percent/50 percent), we can factor in specific evidence for the existence or non-existence of a deity. After evaluating each line of evidence, we can determine if it is more or less likely that it would entail the existence of God.

The numbers we assign are not completely objective (since we don’t have an objective standard to compare them to) but neither are they assigned arbitrarily. For example, the claim that a specific piece of evidence is two times (.2) more likely to be true if God exists does not mean that it is the only possible explanation. It is simply stating that from a neutral and objective viewpoint, it would be more likely to have occurred if a God exists then if he doesn’t.

The lines of evidence that Unwin presents are, of course, not the only ones that we could use. If better evidence should be considered we could take that into account also. We could keep plugging in numbers to this formula for every criterion that we deem important. My contention, and the reason for the post, is that the more evidence we consider the more the probability of God’s existence increases above the 50 percent point. If my point is correct it would mean that it is more rational to believe in the existence of God (in the purely theistic sense) than to disbelieve it.

I’ll try to answer some of the more specific objections that might arise:

If good exists, there is necessarily the possibility of evil as the absence of good.; Neither good nor evil could be defined if the other did not exist.

The existence of evil has very little to do with the argument at hand. As philosopher Alvin Plantinga shows, the existence of evil is as possible in a world where God exists as in one where he does not. Some people might still claim that the appearance of evil tilts the scales in favor of the non-existence of God. To make that claim, however, they must first refute Plantinga’s argument.

Your choice of criteria is totally arbitrary. What about D (pretty flowers) = 145 or D (this beer is stale) = 0.2

My ratings are subjective but not arbitrary. D (pretty flowers) would imply the existence of an aesthetic sense and might raise the number above neutral. D (stale beer), on the other hand, would be neutral in regards to God’s existence. We could have taste buds and stale beer in a world without a deity.

No matter how much evidence is provided, it seems to me that you still decide whether or not you want to believe the evidence. Didn’t Nieztche state something along the lines of “Now it is our preference that decides against Christianity, and not arguments”?

Exactly!

One problem that I see with this approach is that if I start from a 50-50 prior probability, I should state which god am I talking about. If I’m going to be totally “neutral” with respect to the triune God of the Bible, I should also be “neutral” with respect Allah, Zeus, Loki, Baal, and every other god I can think of. I would have to calculate the probabilities for all these gods. What do I do with those probabilities? Do I just pick the one that gives me the highest posterior probability?

The short answer: yes.

You realize, of course, that this entire argument is based on a false dilemma, right? Either God (i.e. the Christian God) exists, or He does not, according to your argument.

That’s not what my argument says at all. I’m saying that based on the evidence I have at hand, I have more reason to form a belief that the Christian God exists than I do to form a belief that he doesn’t.

It completely rules out any non-Christian God possibility, as well as various polytheist possibilities. But even granting your either-or assumption, the logic is flawed anyway, insofar as it arbitrarily assigns numerical values to very subjective things. You can’t just do that where it suits you.

Again, I should point out that this is not an ontological proof. And subjective is not the same as arbitrary.

It should be noted that the 50 percent prior probability is completely without base. No one would assign a 50 percent probability to an entity without some reason to do so, and since the reasons Urwin gives add their own probability, I’m not sure what he used to justify 50 percent.

Urwin uses 50 percent/50 percent because it is a mathematically neutral starting point.