Wednesday, January 20, 2010

Total nuclear war

Assuming non-theism, a global nuclear war in the 20th century would have been a reasonable prediction to make (and indeed some made it)—but a prediction that was falsified. On the other hand, given theism, such a war would be unlikely. I think there is an argument for theism here. Let me say a little more.

Given naturalistic assumptions about human behavior, there were several approximately independent occasions (whether a short crisis or a longer stretch) during the Cold War at which it was moderately likely—say, probability 1/2—that a global nuclear war would result. Let's say there were four such occasions. Then, given naturalistic assumptions about human behavior, the probability that global nuclear war would occur would be about 15/16. On the other hand, given theism (and especially given Christianity or Judaism—specifically, the promise of the non-repetition of the vast destruction of human life in the Flood), the probability that global nuclear war would occur is much smaller, let's say 1/8. (It would be an order of magnitude harder to come up with a theodicy for a global nuclear war than for such horrors as are already hard to come to come up with a theodicy for.) Well, these two conditional probabilities show that non-occurrence of a global nuclear war incrementally and significantly confirms theism over naturalism.

If initially theism and naturalism are take to have equal probability 1/2, and we plug the above numbers into Bayes' theorem, we get a consequent probability of 0.93 for theism given the no-global-nuclear-war evidence. If initially theism is taken to have probability 0.1 and naturalism 0.9, we get a consequent probability of 0.61 for theism.

Of course, I've made up the numbers about the probabilities of global nuclear war, though they don't seem crazy to me. A historian would be needed to give us better numbers.


PFS said...

I suppose a naturalist would say that there is something hardwired in us (and, so, in the leaders of these nuclear-equipped countries) connected to our survival. Behavior regarding nuclear war is different from say, wiping out another tribe, which would have survival benefits for the one plotting the destruction of the other tribe. With nuclear war one is undermining one's own survival probability because of the mutual destruction policy of the other ones with nukes. Thus, perhaps the probability of nation x nuking y--given the situation in which both x and y are nuclear-ready--are much lower than what you propose here.

Perhaps your argument would work better if you (or the historian) can identify scenarios where nation x has nuclear capabilities and y does not. This would just be similar to the one tribe wiping out the other, but on a much larger scale (which God would not allow, based on your assumption--I take it--that this such an action is inconsistent with his Divine Providence & Goodness). Under this condition, it would seem that the naturalist's recourse that I mentioned above is not available.

Alexander R Pruss said...

There certainly is a survival instinct. However, people are able, for better or for worse, to act contrary to it.

Think of something like the Cuban missile crisis. It seems things were pretty close. Or take the 1983 Petrov event, where a single individual's judgment call may have been essential.

Still, it may be that I've overestimated the probability. Based on an analysis of the Cuban missile crisis, Martin Hellman estimated the conditional probability of the use of a nuclear weapon given the Cuban missile crisis at 10-50 percent, and there was only one Cuban missile crisis. (Here is a chilling quote: "A Soviet submarine near the quarantine line had been subjected to signaling depth charges, commanding it to surface,
which it eventually did. Not until 40 years later did Americans learn that this submarine carried a nuclear torpedo and that the Soviet submarine captain, believing he was under attack, had given orders to arm it. Fortunately, the submarine brigade commander was on board, over-ruled the captain, and defused the threat of a nuclear attack on the American fleet.")

However, Hellman's estimates of the risk of total nuclear war may not be fully relevant, because they are partly based on the actual rate of crises over the past fifty years, while the actual rate of crises may be significantly lower than the expected rate of crises given naturalism.

It would be interesting to collect past estimates by smart people of the likelihood of a nuclear war. For instance, Lackey (in a JPhil article) in 1986 estimates the probability of a nuclear war over the (then) next 50 years at 0.01-0.00001.

Alexander R Pruss said...

I withdraw my commitment to the argument. It does not appear that my amateur estimates of likelihoods of nuclear war match those of experts, even ones like Hellman who are making a case where overestimating the risk would benefit them. (Still, maybe the experts are wrong.)

I still think there is a moderate boost to the probability of theism from the data, but the 15/16 chance of nuclear war during the Cold War does seem to be an overestimate.