Dmitry Chernikov’s Blog

Here is Draper’s original article. Linked from Thinking Christian.

In (ST, I, 2, 3, obj 2) Aquinas writes that “it is superfluous to suppose that what can be accounted for by a few principles has been produced by many. But it seems that everything we see in the world can be accounted for by other principles, supposing God did not exist. For all natural things can be reduced to one principle which is nature; and all voluntary things can be reduced to one principle which is human reason, or will. Therefore there is no need to suppose God’s existence.” We need not consider his reply to the effect that natural causes are to be traced back to God as Alpha, and voluntary causes are to be traced back to God as Omega. It may be true that naturalism makes fewer claims about the world than theism does, though Draper himself points out that “It is not as easy to compare the scope of hypotheses like theism and naturalism.” At any rate, given only that information, it will follow that naturalism is more probable than theism.

But why limit ourselves in such a way? Einsteinian mechanics makes grander claims of how the universe works than Newtonian mechanics does. Does it make the former less probable than the latter? Perhaps it does to the uninitiated, to those who are unfamiliar with physics. But physicists have proof of the correctness of Einstein’s theories and similar proof of the limits of Newton’s theories. These serve to adjust the probabilities of both away from their “intrinsic” probabilities.

A second example is the debate between the German Historical school and the Austrian school in the early 20^th century on the issue of whether there is such a thing as an immutable body of economic law, valid at all times, in all places, and for all people. The Austrian school asserted that there were economic laws, and that praxeology — the science of human action — and its a priori methodology were legitimate. Thus, the Austrian school’s claims had a far greater scope that the claims of the German historicists. But the Austrians were correct in their theory, and the historicists mistaken in theirs.

A third example would be solipsism. By asserting that only I exist and everything else is a figment of my imagination I make a claim of a very narrow scope, as opposed to someone who does not doubt the real existence of the external world. Yet there is an external world, and solipsism is false, despite the fact that in describing the external world we take risks, because we can make mistakes in our investigation of it. In a reductio, consider the proposition “nothing exists.” Its scope is exactly zero. Of course, this proposition is false, which can be proven by “I think, therefore I am” or by noticing that when nothing exists, the number of existing things is 0, so 0 must exist; and now the number of existing things is 1, so 1 must exist, as well; and so on with all the natural numbers; further, numbers may be mind-dependent, so there must be a (divine) mind in which these numbers are kept, or by showing God’s existence to be necessary, etc. Once again, a proposition of a lesser scope turns out to be false, and a contrary to it proposition with a much greater scope turns out to be true.

Finally, let’s take Draper’s own excellent example. “There is a dog at the door” is less probable than “there is an animal at the door,” and concomitantly, “there is no animal at the door” is less probable than “there is no dog at the door.” This is because all dogs are animals, but not all animals are dogs. But what has this to do with God? Perhaps this: “There exist a God and Ford Motor Company” is less probable than “there exists Ford Motor Company.” But we know that Ford exists. So the previous statement is equivalent to “The probability that there exists a God is less than or equal to 1,” which is a rather trivial discovery.

The pattern should now be clear. What we are dealing with here are competing ontologies. In all of these cases A says that some X exists, and his opponent B says that X does not exist. If X exists, then its nature, behavior, and properties call for an explication. In the Draper’s case of theism vs. naturalism it is true that the theist talks of more things than the naturalist does, because the former countenances an additional entity in his ontology, viz., God, which the naturalist does not countenance. Thus, if God does not exist, then theology is so much nonsense, but if God does exist, then it is a genuine science of God. So, the issue here is not scope; in other words, the issue is not to how many entities our investigation extends; it is rather, does God exist? If He does, then we ought to discuss Him, and therefore the more limited scope of the naturalistic worldview buys you precisely nothing.

Now it is certainly true that in our study of God we can make mistakes. In this sense we are risking more by talking about God. The possibility of having an erroneous belief is greater in theism than it is in naturalism, because if God exists, then the naturalist will have only one erroneous belief, namely, “God does not exist.” On the other hand, a theist might conclude that God is temporally everlasting, when in fact He is atemporally eternal; or that God is not a Trinity, when in fact He is; and so on for many controversial theological problems. (Notice, however, that the naturalist’s single error is monumental, whereas the theist’s multiple errors are much less significant.) But this is so only because the theistic ontology is richer than the naturalistic ontology, which is why the crucial question to be answered has nothing to do with the scope of any hypothesis but asks rather whose ontology is the correct one. And there is no a priori reason why the sparser naturalistic ontology should be truer or more reflective of reality than the richer ontology of theism. Consequently, the lower “intrinsic” probability of the theistic hypothesis based on the scope of that hypothesis is no evidence against existence of God.

Conclusion. The scope argument is a trick. It proves far too much. It cannot entail that no new theories that build on or generalize old theories can be proposed, because such things are done lawfully every day. It cannot follow from it that the search for new knowledge is best abandoned, because every hypothesis that goes beyond what we believe to already know dangerously increases the probability of error in our web of beliefs. So, it’s of no use in this case.