It seems to me that most theories involve postulated objects, and then various laws that describe how those objects must or can relate to each other. So, you might postulate an id, ego and superego, or genes, or electrons, protons and protons, etc. It also seems to me that there are at least two types of "simple" when talking about explanations. There's a brevity "simple" -- like a maths proof or a piece of computer coding with minimal steps. And there is also an ontological "simple" -- an explanation relying on as few postulated objects as possible. If it's true that there are at least these two types of "simple", well, does that render parsimony often difficult to apply, if you're committed to it as a good rule of thumb when deciding what to believe in? One candidate theory could be ontologically complex but brevity-simple, whereas the alternative theory might be ontologically simple but convoluted. Here are some things that worry me: (1) does appealing to deities lead to simpler explanations that ones that don't involve deities? Does OCcam's razor cut in favour of gods or against them? (2) philosophers are interested in all sorts of things that apparently aren't physical -- like universals, concepts, propositions, meanings, mental states, laws of logic. If one is commmitted to physicalism (on the basis of ontological simplicity), should one endeavour to be eliminativist about anything you can't jab with a stick, even though you can land yourself in explanatory difficulties by trying to do without these notions?

Good questions. The philosopher David Lewis (1941-2001) rightly insisted on distinguishing two kinds of ontological simplicity or parsimony: quantitative and qualitative. Quantitative parsimony concerns the sheer number of postulated entities; qualitative parsimony concerns the number of different kinds of postulated entities. Lewis argued that only qualitative parsimony matters. It's not the sheer number of (say) electrons but the number of different kinds of subatomic particle posited by a theory that makes the theory parsimonious or not, compared to its rivals. (Maintaining this line required Lewis to treat "the actual world" as an indexical phrase and to hold that each of us has flesh-and-blood "counterparts" in nondenumerably many other universes.)

All else being equal, then, theories that posit deities are qualitatively less parsimonious than theories that don't, because (I take it) deities are supposed to be of a different kind entirely from the phenomena that they're invoked to explain. Furthermore, any simplicity had by deity-invoking theories is likely to come at the cost of explanatory power. Theistic explanations, for example, typically say that beyond a particular stage of explanation reality is the way it is simply because God wants it that way, there being in principle no explanation of why God wants it that way rather than some other way. (In On Genesis, St. Augustine writes, "Anyone who asks 'Why did God want to make heaven and earth?' is looking for something greater than God's will, but nothing greater can be found.") As I see it, naturalists need never give up on seeking contrastive explanations for the facts.

The relationship between naturalism, as I define it, and abstract objects (universals, propositions, etc.) is tricky. I think the two are compatible: that is, I don't see naturalism as implying physicalism. But I recognize the tension, which makes me a reluctant Platonist about abstract objects. If I saw a way to make sense of the world without positing any abstract objects, I'd be strongly tempted to take it. I hasten to add that abstract objects are by no means easy for theism to explain either, because of the necessary existence and ontological independence that (many) abstract objects are supposed to enjoy.

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