I recently read Josh Rasmussen’s recent book How Reason Can Lead to God. The book is accessible for the non-philosopher, but that’s not to say that the book doesn’t touch on many deep philosophical issues. Rasmussen says, “arguments do the most good when they are tools that promote an inquiry .” I think that’s exactly right, and Rasmussen’s arguments certainly do that. Rasmussen and Leon’s sister book Is God the Best Explanation of Things has a lot of the ideas of the first book and it goes much deeper. It’s set up as a dialogue between two expert philosophers—a theist and an agnostic. This one is more technical, and is aimed more towards those with some philosophical background; it helped me see some of the issues from the first book more clearly.
Rasmussen’s main point behind the two books is that we can use reason to discover that there must be a perfect foundation to reality. Reason further provides us with its many of its attributes. He summarizes his argument like so:
Premise 1. Reality in total is self-sufficient (with no outside cause or explanation).
Premise 2. Nothing can be self-sufficient without a perfect foundation.
Conclusion. Therefore, reality has a perfect foundation.
The idea behind premise 1 is fairly simple: nothing exists outside of reality (if it existed it would be in reality), therefore nothing outside reality can cause or explain reality, which is what it means to be self-sufficient. Premise 2 is supported in two ways: (1) the problem of arbitrary limits, and (2) the problem of construction.
The problem of construction is about looking at certain things in the world—minds, matter, morals, reasoning—and seeing that some foundation hypotheses lack the materials to construct those things. For example, he argues that just as white tiles are the wrong materials to construct a purple floor, molecules are the wrong materials to construct a mind, and likewise with matter, morals, and reasoning. The problem of construction is a big topic, so I intend to focus this post on the aspect that peaked my interest: (1) the problem of arbitrary limits, and corresponding issues with simplicity and intrinsic probability.
Rasmussen thinks that the foundation of reality cannot have unexplained arbitrary limits. First, what is an arbitrary limit? Rasmussen explains:
What I want to say, more precisely, is that a limit is arbitrary in this sense: The limit could conceivably have been slightly greater or slightly lesser. For example, if the foundation was the shape of an octagon, then its shape is arbitrary because it could conceivably have had nine vertices instead of eight. Why eight? That number is arbitrary in view of the conceivable alternatives (Rasmussen & Leon, 2019, p. 113-114).
On the view that a “limit could conceivably have been slightly greater or slightly lesser,” it seems even a perfect foundation is arbitrarily limited, since I could conceive of it being slightly less perfect. This is not a welcome result for Rasmussen. Suppose, instead, that we say something is an arbitrary limit if it could conceivably have been greater. This would fix the problem for a perfect foundation because nothing can be greater than perfect, but there is still another issue. Leon points out that a problem for quantitative features is that there are always greater infinities such that every quantitative feature would be limited. So I suggest we could understand Rasmussen’s view that an arbitrary limit is something that is not maximal in its fundamental qualitative features, as the following passage suggests:
My proposal so far, then, is that a maximal foundation would have no fundamental feature along a continuum of potentially (i.e., conceivably) surpassed magnitudes.
I should also clarify that maximal features are not the same as infinite magnitudes. I agree with Leon that even infinite magnitudes are conceivably surpassed. The fundamental features, then, would be nonquantitative features, like being independent, being foundational, having supreme power, and so on. (Note: having supreme power is not a quantity of power, but a quality or kind of power; or, if we want to call it a “quantity,” it a special, unsurpassable quantity (Rasmussen & Leon, 2019, p. 140-141).)
Given that properties like mass, number of vertices, size etc. are quantitative, they will count as limit; i.e. even an infinite mass, space, or velocity will be limited. My interpretation, then, is that anything that is not qualitatively maximal is a limit and hence requires an explanation. Rasmussen summarizes his argument:
All limits alike have an outside explanation upon which they depend. Yet the basic features of the foundation, by contrast, lack an outside explanation. Therefore, the basic features of the foundation have no limits (Rasmussen, 2019, p. 72).
This still leaves open that the foundation has limits that are explained. What Rasmussen objects to is unexplained limits. For example, if the foundation was the Trinity, the quantity of 3 persons could be explained by (perhaps) Swinburne’s suggestion of highest love.
Rasmussen thinks there are three reasons to think the foundation lacks arbitrary limits: (1) limits are less simple and hence less intrinsically probable, (2) limits block explanatory depth since that limit itself won’t be explained, and (3) limits are uniformly dependent such that they all require an explanation. I’ll go through each in turn.
Earlier in the book Rasmussen writes:
The complexity of a hypothesis flows from the quantity of basic components within it, not the quantity of words used to express it. Consider, for example, the following hypotheses: (1) “Adam is a bachelor” and (2) “Adam is a male.” Both hypotheses have four words. Still, the word bachelor contains more information than the word male. In fact, the concept of a bachelor includes the concept of a male plus the concept of being unmarried. For this reason, hypothesis (1) is more complicated than hypothesis (2). Simplicity, then, is not about how many words you use. Rather, it is about how many basic concepts are involved. The fewer the basic concepts, the simpler the proposition (Rasmussen, 2019, p. 63).
I think ‘perfect’ is conceptually or semantically simple—like Moore’s ‘good’, ‘perfect’ seems semantically irreducible—but I don’t think a perfect foundation hypothesis is as simple as it may seem. A lot of preconditions need to be in place for a being to be perfect, which lowers the intrinsic probability. For example, a perfect being must be at least omnipotent, omniscient, and morally perfect—in addition to other perfect-making properties; and, in order to be morally perfect, the being must have many good-making properties like being loving, generous, honest etc. To illustrate the hidden complexity, let’s compare two hypotheses:
H1: The foundation is perfect.
H2: The foundation is omnipotent and omniscient.
There’s a sense in which H1 is simpler—it has fewer basic concepts—but H2 is more intrinsically probable. Compare:
H1’: Bob knows that it will rain tomorrow.
H2’: Bob has a justified belief that it will rain tomorrow.
H1’ is simpler than H2’ in that it has less basic concepts, but H2’ is more intrinsically probable than H1’ since having knowledge entails justified belief but not vice versa. Concerning intrinsic probabilities, P(agent has a belief that p) > P(agent has a justified belief that p) > P(agent has a justified true belief that p). Having a justified true belief is a precondition to knowledge, and, similarly, the perfect-making properties are preconditions to perfection.
‘Making’ should be understood in a metaphysical grounding or explanatory sense rather than a causal sense; the perfect-making properties metaphysically ground or explain perfection. This can be shown with a Euthyphro-like question: Is the foundation perfect because it is omnipotent, omniscient, etc. or are these properties perfect-making because the perfect foundation has them. I think this direction of explanation is important because this means the perfect foundation hypothesis doesn’t explain the perfect-making properties like independence (i.e. not depending on something other); rather, the foundation is perfect partly because it is independent. Each additional perfect-making property adds to the complexity and hence lowers the intrinsic probability of the perfect foundation hypothesis.
Rasmussen explains that simpler hypotheses include less information and so have fewer ways to go wrong:
[The] reason the simpler hypothesis is more internally probable—is that the simpler hypothesis includes less total information and so has fewer ways to go wrong. To illustrate, suppose you have two hypotheses A and B. Suppose, next, that A is composed of basic parts, a1 and a2 and a3, while B is composed of just b1 and b2. Then A has three “opportunities” to be false, while B has only two. Now suppose you have no idea whether any of the components of A or B are true, and you have no idea whether the truth of one component depends on the truth of any other. Each component is equally plausible in your mind. Then, from where you stand, B is more probable than A because B has fewer components—and so fewer opportunities to be false (Rasmussen, 2019, p. 62).
Each perfect-making property—a precondition for perfection—adds information such that there are more ways things can go wrong. It’s not easy being perfect.
If I’m right, the simplicity of the perfect foundation hypothesis will depend on the simplicity of the cluster of perfect-making properties. Presumably Rasmussen will think that—following the arbitrary limits principle—power, knowledge, and moral value will be simpler if they are unlimited (i.e. maximal) rather than limited. This would be a favorable result for the perfect foundation hypothesis. In similar fashion, Swinburne thinks the God hypothesis is simple, based on what Gwiazda calls Principle P:
Hypotheses attributing infinite values of properties to objects are simpler than ones attributing large finite values. (Gwiazda, 2009)
Others have offered reasons for thinking the omni-properties are simple as well (Draper 2016; Miller 2016). Simplicity is being used as a guide to the intrinsic probability of the hypothesis: the simpler the hypothesis the higher the intrinsic probability.
An alternative way to assign intrinsic probabilities is to use the principle of indifference, where we apply a uniform probability distribution among the possibilities. For example, Tooley (2009) argues that, given an omnipotent and omniscient being, we should assign a 1/3 probability to the moral properties of being good, indifferent, and evil, such that the intrinsic probability of theism is less than 1/3. Similarly, we could apply the principle of indifference to power, cognitive ability etc. The result is that the intrinsic probability of the omni-properties is the same as any other particular degree of that property. This means that the intrinsic probability of the omni-properties is highly improbable, since there are many more ways to be limited than unlimited.
I don’t wish to settle the best way to assign intrinsic probabilities. I merely wish to point out that the principle of indifference is a plausible alternative method that would further lower the intrinsic probability of the perfect foundation hypothesis.
Consider next the problem of explanatory depth, which is another problem for an arbitrarily limited foundation.
The problem here is that if the foundation has arbitrary limits, then the foundation (or a theory of the foundation) has less power to explain the things that depend on it. Recall the theory just given: the foundation has (1) a mass of 241 grams, (2) the shape of a sphere, and (3) the capacity to produce exactly 288 particles. Focus on its mass. What might explain the fact that the foundation has a mass of exactly 241 grams (Rasmussen, 2019, p. 69)?
The point here is that if the foundation has 241 grams, not only is that left unexplained, the existence of mass in general is left unexplained. I’ll only offer a tiny sketch of a reply here, as I think it would take a lot of work to go through all Rasmussen’s points. I am the least confident in what I have to say here.
If God existed, I suppose the explanation would go something like this: God desires the good, and conjoined with his beliefs and powers, this would explain the good things we see. Even if the perfect foundation hypothesis is the best and only explanation for why there are limited things like shapes and mass, I feel like the perfect foundation hypothesis is so vague that the explanation isn’t good enough to warrant adding the perfect foundation onto our ontology. I do not clearly see that the perfect foundation predicts shapes and mass as a means to the good. Every theory of the foundation will have some brute facts, and we can try to explain those brute facts, but unless that theory has enough theoretical virtues, we shouldn’t add it onto our ontology.
Rasmussen’s final tool against unexplained arbitrary limits at the foundation is uniformity:
To illustrate the problem exposed by uniformity, imagine a mountain range. This mountain range has a particular shape along its mountaintops. No matter the shape, it has some explanation …. Whether the mountain range has two peaks or two thousand peaks, its shape does not appear from nothing … mere differences in shape between the mountains are irrelevant to their dependence on some outside explanation (Rasmussen, 2019, p. 70-71).
Rasmussen’s point here is that differences in limits—shape, size, mass etc.—are irrelevant towards being dependent—for how does having more vertices or weight or size help with being independent and uncaused? If all limits are uniformly dependent, then this would make sense of why differences in limits are irrelevant.
I agree that differences in limits are irrelevant to being dependent, which is to say, it’s hard to see how a particular shape, size, belief, desire etc. could be the difference-maker with respect to being independent. But I disagree that uniform dependence of limits is what accounts for the irrelevant differences.
What is the relevant difference that explains the difference between dependent things (that have an explanation) and the foundation (that has no outside cause or explanation)? Nothing explains it, or so I say.
It seems to me we have everything we need in Rasmussen’s argument in chapter 3:
- A realm cannot be self-sufficient without any independent layer (because independence is the root of self-sufficiency).
2. The blob of everything is a self-sufficient realm (because there is nothing beyond everything).
3. Therefore, the blob of everything has an independent foundation (Rasmussen, 2019, p. 22).
Dependent things are explained by the things that cause them, and the independent (and necessary) foundation lacks an explanation because non-existent things can’t explain it, and there can’t be anything more foundational than the foundation to causally explain it, and there doesn’t seem to be anything to conceptually explain it either. I do not see the need to posit some further property that explains the difference between dependent and independent (and necessary) things, nor do I see how this further property would explain the difference, because everything seems to me to be an irrelevant difference. Take perfection again. As I indicated before, I think it’s the perfect-making properties (like independence) that explain perfection and not the other way around.
To repeat, I have only focused in on the arbitrary limits principle and have not addressed the rest of the book including the ‘construction problem’ and predictive capabilities of the perfect foundation hypothesis; that is a big topic in itself. Rasmussen gave three reasons for thinking the foundation lacks arbitrary limits: simplicity, explanatory depth, and uniformity. Concerning simplicity, I argued that the perfect foundation hypothesis is not as simple as it initially seems given that perfect-making properties are preconditions to perfection; that the intrinsic probability depends on the intrinsic probability of the cluster of perfect-making properties; and that the intrinsic probability of the perfect-making properties is inconclusive given an alternative method based on the principle of indifference. Concerning explanatory depth, I gave a sketch of a reply that the perfect foundation hypothesis is too vague to be a sufficiently good explanation for limits. Concerning uniformity, I agreed that limits are irrelevant when it comes to explaining independence, but disagreed that we should think the foundation doesn’t have unexplained limits. I questioned whether we need to posit some property to explain the difference between dependent things and the foundation, and I questioned how any property could explain this difference.
Draper, Paul. “Simplicity and natural theology.” (2016).
Gwiazda, Jeremy. “Richard Swinburne, the existence of God, and principle P.” Sophia 48.4 (2009): 393.
Miller, Calum. “Is theism a simple hypothesis? The simplicity of omni-properties.” Religious Studies 52.1 (2016): 45-61.
Rasmussen, Joshua. How Reason Can Lead to God: A Philosopher’s Bridge to Faith. InterVarsity Press, 2019.
Rasmussen, Joshua, and Felipe Leon. Is God the Best Explanation of Things?: A Dialogue. Springer, 2019.
Plantinga, Alvin, and Michael Tooley. Knowledge of God. John Wiley & Sons, 2009.
Swinburne, Richard. The Existence of God. Oxford University Press on Demand, 2004.
 Rasmussen doesn’t exactly put it this way, but this is what I think follows from his view.
 For a defense of this view see Jeremy Koons’ Can God’s Goodness save the DCT from Euthyphro. Although he runs the argument based on goodness, a parallel argument can be applied to perfection. The idea is that if the perfect-making properties don’t explain perfection, then perfection becomes empty.
 Rasmussen has suggested to me that the order of explanation may depend on the sense of explanation (ontological, epistemic, conceptual, causal, etc.).