Simplicity

Consider two theories.

Theory 1: There is a single asexually reproducing ancestor of all life on earth, Ag, who came into existence at time A and split into two almost genetically identical descendants, Bof and Bok, at time B, and there was no biological life before Ag.

Theory 2: There is a pair of almost genetically identical ancestors of all life on earth, Bof and Bok, who came into existence at time B, and there was no biological life before Bof and Bok.

Both theories fit our observed data equally well, and will always do so, since we have basically no chance of identifying a fossil of Ag. The question I want to ask is which theory is simpler.

An easy thing to say is that Theory 2 is simpler, as it posits one fewer entity, namely Ag, but Theory 1 compensates for its greater complexity through having an additional explanatory merit--it explains the genetic similarity between Bof and Bok, which Theory 2 leaves unexplained. Moreover, the difference in complexity is small, because while Theory 1 posits one more entity, it is an entity of the same kind as Bof and Bok.

But I want to consider a different evaluation: Theory 1 is simpler, because when we consider the simplicity of a theory in terms of entity or kind counting, we only count the entities or kinds not explained by this theory (or, better, entities or kinds weighted by the degree to which they are unexplained by the theory, if explanation comes in degrees). Thus, Theory 1 posits one theory-unexplained entity while Theory 2 posits two theory-unexplained entities. So Theory 1 wins not only on explanatory grounds, but also on simplicity grounds.

Why go for this method of evaluation? First, in cases where the explanation is deterministic, it coheres with information-theoretic compression-based measures of complexity, which is a plus. Second, I think this fits with our intuitions about other examples. Consider two theories about the origin of life on earth.

Theory 3: A meteorite deposited some organic chemicals 4.1 billion years ago that combined to produce life.

Theory 4: A meteorite deposited some organic chemicals 3.9 billion years ago that combined to produce life.

As far as the details I gave of the two theories, there is no difference in complexity. But Theory 3 commits us to way more organisms in the history of the earth--200 million years' worth of organisms. And when we conjoin with evolutionary theory, Theory 3 will commit us to significantly more kinds of organisms as well--over those 200 million years, surely there would be a lot more species. But these added entities (or kinds) should not by themselves count as increasing the complexity of Theory 3 over Theory 4 (or Theory 3 + evolution over Theory 4 + evolution). Why not? The best explanation of why not seems to me to be that these added entities and kinds are easily explained by the theory in question.

The entities that are unexplained by one theory may, of course, be explained by another. It is only entities posited but unexplained by the theory in question that I am considering here. Nor am I saying that this is the only contribution to complexity--there are, no doubt, many others.

All this casts helpful light on the question whether theism or naturalism is simpler. At least it undercuts simple arguments that naturalism is simpler as it posits one fewer entity or even kind of entity.