Some time ago I received “a few questions from an amateur philosopher” about my article “The Laws of Nature and of Nature’s God: The Theological Foundations of Modern Science.” With his permission, I’m reproducing them here with some brief answers.

**1) I agree that it seems unlikely for natural selection to actively select for higher order thinking, but isn’t it possible that the same logical reasoning that natural selection would select for to allow for higher probabilities of survival also provides the faculties that allow the higher order thinking, i.e. that the first being “truth-oriented” by necessity simply provided a general “truth” oriented system of thinking that we use in all our conscious thought? Are those things really so different? Relatedly, it seems strange to assume that natural selection only selects for physical traits – why wouldn’t it also select for cognitive advantages?**

I’ll start with the last question. The reason that evolutionary processes would only select for physical traits is that, given naturalism and the causal closure of the physical world, only physical traits can *causally influence* behavior. Mental events would be epiphenomena at best: caused *by* underlying physical (brain) events, but not making any causal contribution *to* those events. There would be no “top down” causation from the mental to the physical. Thus, cognition (understood as mental processes, not merely brain processes) would be ‘invisible’ to natural selection and to evolutionary forces in general. I actually explained this at some length in the article (see the three paragraphs in section II beginning “In the first place…”).

But suppose that natural selection could select for cognitive advantages and thus for lower-order thinking. Isn’t higher-order thinking just a natural extension of lower-order thinking? I don’t think so. For example, our ability to do integral calculus isn’t merely an extension of our ability to count. It requires a grasp of concepts that go beyond simple addition and subtraction. Likewise, our ability to use language to express complex abstract ideas goes far beyond our ability to ‘name’ (i.e., attach labels to) the physical objects we experience with our senses. There’s simply no good reason to think that undirected evolutionary processes, driven by sheer biological efficiency, would select for these higher-order cognitive capabilities over time. (Remember that on the standard Darwinian gradualist view, it’s not enough for the “final product” to be advantageous; every incremental step of the development must be advantageous enough to become fixed in the population.)

**2) “The problem of induction” clearly has no easy solution, but I don’t see how it follows that the only solution is divine. Isn’t this presupposing the absence of an eventual Galileo in this area and ascribing something we don’t understand to divine machinery? Further, I’m unfamiliar with any revelation that would justify reliance on induction or the uniformity of nature, so even if we were to look to the divine for guidance, it would appear that relying on induction or the uniformity of nature is still unfounded.**

This isn’t a God-of-the-gaps argument, and holding out hope for a Galileo-of-the-gaps does nothing to address the argument. Knowing *directly* that nature is uniform across space and time (including the future) is impossible for creatures like us who are so spatiotemporally limited; it would require a divine (or close to divine) epistemic perspective. Knowing it *indirectly* would thus require dependence on a divine source (i.e., *our* knowledge of the uniformity of nature would be dependent on *God’s* knowledge of the uniformity of nature).

Would this knowledge have to come through a divine revelation? Not necessarily. Certainly there are biblical texts that speak of God’s creation and sustenance of the natural universe (e.g., Gen. 1:1; Heb. 11:3; Rev. 4:11; Jer. 31:35; Jer. 33:20, 25). But even if there were no such special revelation, general revelation would be sufficient for us to know that the universe is created and sustained by God, and thus to know that the natural universe will operate in a generally orderly, regular, and predictable fashion.

Moreover, if one adopts an externalist epistemology like Alvin Plantinga’s proper function account, one wouldn’t even need a divine revelation of the uniformity of nature for inductive inferences to be warranted. Our cognitive faculties could be designed by God such that a true belief in the uniformity of nature arises immediately and intuitively, as a properly basic belief. Likewise, inductive inferences would be warranted insofar as they’re performed by properly functioning cognitive faculties operating according to a design plan well-aimed at truth. But note that these accounts depend on theism. The author of our cognitive faculties would have to *know* that nature is uniform for those faculties (specifically, whatever faculties are involved in inductive reasoning) to be *well-aimed at truth*. If the creator of our cognitive faculties were “flying blind,” so to speak, we would be too.

The upshot is that there are various ways in which we could account for our knowledge of the uniformity of nature, and the reliability of inductive inferences, given the truth of biblical theism. But all of them depend crucially on a prior *divine* knowledge of the uniformity of nature. Remove that foundation and the epistemological building collapses.

For a deeper treatment of the theistic foundations of laws of nature, see Chris Bolt’s excellent book *The World in His Hands*.

**3) Your argument regarding mathematics struck me as akin to acquiring a hand-tailored, made-to-order suit and then wondering at how well the body was designed to fit in it. As you note, mathematics isn’t a concrete thing – it is a descriptive system created by humans to measure, assess, and communicate about the world around them. In that sense, it’s no wonder it often describes the world in a simple way. (And some times it doesn’t: pi, Planck’s constant, e, the Golden ratio, the height of a tree or a house). By way of example, you ask “why not c to the power of 2.179635?” Couldn’t it be partly because our mathematical system is based on easily communicating our empirical observation of the world we built that system to describe?**

The analogy fails because we are clearly not the authors (or ‘tailors’) of the mathematical order of the universe. The objection implies that our descriptive systems are *assigned* to the universe, imposing a mathematical order upon it (or upon our experiences of it), rather than accurately capturing an objective mathematical structure that exists prior to and independently of those descriptive systems. Basic mathematical truths are objective and necessary. We didn’t *decide* that two plus two equals four (although we did invent the *symbols* we now use to express that truth). Two plus two equals four regardless of our descriptive systems (2+2=4, II+II=IV, 010+010=100, etc.). Likewise, the physical laws of the universe are objective realities; they are what they are regardless of what we happen think about them or how we choose to describe them. We didn’t *decide* that E=mc^{2}. That was true before any of us existed. We merely discovered it.

So any mathematical simplicity or elegance we discover in the universe cannot be attributed to *our* cognitive activities (unless we’re prepared to take a radically anti-realist and ultimately relativistic stance). The difference between 2 and 2.179635 isn’t merely a matter of degree or arbitrary convention; it’s a difference of kind. Whole numbers are *objectively simpler* than fractional numbers. Whole numbers, as the very name indicates, have a completeness to them. (Just consider the difference between having 2 children and having 2.4 children; the latter would be a lot messier than the former, for starters.)

It’s true that not all physical and mathematical constants have simple numerical values (e.g., whole numbers or simple ratios). Even so, it’s often the case that those that don’t still have a kind of simple internal or algorithmic structure. For example, Euler’s constant is the sum of an infinite series of rational numbers that track the series of natural numbers:

There’s also a rather neat relationship between Euler’s constant and π:

I could go on, but the main point here is that the physical universe has an undeniable mathematical order and elegance to it, a fact recognized by scientists on all sides of the religious debates. That fact isn’t surprising on a Christian theistic view, but it is rather surprising on a non-theistic view, and it’s *especially* surprising on a naturalistic view. Indeed, there are two aspects that a metaphysical naturalist will struggle to accommodate: first, that there is a realm of abstract mathematical objects (numbers and their relations), and second, that there is a real connection between the mathematical realm and the physical realm (i.e., the space-time system of concrete material objects).

For some fairly high-level discussions of this (and related issues) see the recent exchanges William Lane Craig had with Roger Penrose (here) and Graham Oppy (here).

**4) Are you familiar with Matthew Stewart’s book arguing that the founder’s understanding of the phrase “The Laws of Nature and Nature’s God” is derived from Epicurean/Spinozian understanding of the divine as constrained by or co-extensive with the laws of nature? If so, I’d be interested in your perspective.**

Sorry, I’m not familiar with it, although it does sound interesting. It wouldn’t surprise me to learn that there were significant non-theistic influences on Jefferson et al. But it strikes me as very implausible to think that such were the *primary* influences on the appeal to natural law in the Declaration of Independence, given the more direct and obvious influence of John Locke. In any case, even if Stewart’s thesis is correct, that wouldn’t undermine the main arguments in my article at all.

Marshall WallIn your original lecture, you mentioned toward the end that you had five additional theistic preconditions of science which there wasn’t time to develop. Would you mind listing what those were?

James1. Moral norms/values

2. Language

3. Fine-tuning for scientific discovery

4. Existence of persistent selves

5. Objective truth and laws of logic

I don’t call these “theistic preconditions” as such; rather, they’re preconditions of science that (I would argue) are far better accommodated by a theistic worldview than by a naturalistic worldview.

BálintHi James,

Maybe this is a bit tangential, but do you see a fundamental difference between abductive and transcendental reasoning when it comes to worldview comparison? You probably know why I’m asking :)

JamesI think transcendental arguments have to be deductive arguments, in the nature of the case. However, there remains a question about how one supports the key conditional premises of the argument (according to which X is a precondition of Y, where Y is some cognitive operation that the skeptic is relying upon). Are these premises supposed to be simply self-evident? That doesn’t seem plausible, except in fairly trivial cases. So these premises need some sub-arguments, and it may be that these sub-arguments are sometimes abductive in form. I don’t see anything wrong with that in principle.

JamesBy the way, when I spoke of “preconditions” in my earlier comment, I was using the term in a looser sense than we would use in discussions of transcendental arguments. For example, I don’t take the physical fine-tuning of the universe to be a

transcendentalprecondition of scientific reasoning. But it’s still a precondition in the sense that it’s necessary for the development of advanced scientific knowledge.Ben WallisI’m a mathematician, not a physicist, so my response here will be somewhat limited. For instance, I’m very tempted to respond to your bit about E=mc^2, but I will bite my tongue.

What I *can* respond to with great confidence are comments like this: “The difference between 2 and 2.179635 isn’t merely a matter of degree or arbitrary convention; it’s a difference of kind.”

Yes and no. Rational numbers require an additional layer of abstraction that natural numbers do not. But at the end of the day, they’re both abstract objects.

You also said this: “The analogy fails because we are clearly not the authors (or ‘tailors’) of the mathematical order of the universe.”

I’m not sure what difference there would be between ‘mathematical order’ and just plain ol’ order. It seems like any orderly system could be described mathematically.

If so, then the real mystery is not why the universe can be described by mathematics, but why it is orderly at all.

JamesHi Ben,

I don’t think it’s obviously the case that the referents of 2 and 2.179635 are the very same kind of abstract object. It could be, for example, that rational numbers are actually complexes of natural numbers. But really that’s irrelevant to my point, which is that there’s a qualitative difference between the

valuesof whole numbers and fractional numbers. Otherwise, why treat integers as special at all?Likewise, I’m not sure how your second remark is relevant to my argument. Suppose we grant that all order turns out to be mathematical order. (I don’t think that’s right — I think logical order is prior to, and distinct from, mathematical order — but leave that aside.) The point remains that we are not the authors of the order of the universe, and that orderliness is a datum that begs for explanation. If all order is mathematical (or mathematically describable) then the question why the universe is

orderlyat all is basically the question why the universe ismathematicalat all.Ben WallisWell, perhaps I shouldn’t have said that all order is mathematical order. But, it does seem plausible to me that any orderly system can be described mathematically. In your logic example, for instance, it certainly has such properties. So, on this hypothesis, there is a naturalistic explanation for why the universe is mathematical after all—it’s orderly!

Now, you’re always welcome to ask why it’s orderly, but that’s a different issue. At that point, we would no longer be talking about mathematics in particular.

And I admit, my hypothesis is just speculation—plausible speculation, but speculation nonetheless. But even if it turns out to be flawed, well, at least it underscores that it by no means follows from the fact that the mathematical properties of the universe are unexplained that therefore they are inexplicable. And it seemed to me you were relying on that inference, or something like it, in your original paper.