Jeffery Jay Lowder recently debated Frank Turek on the topic “Naturalism vs. Theism” (see https://youtu.be/ENZYEPpR2Jc). In this post and the next, I wish to examine the arguments that Lowder advances in his opening statement in support of naturalism (the view that physical reality is the ultimate reality and that no supernatural, non-physical beings, such as God, exist). In his opening statement, Lowder defends the following three propositions:

(1) The best explanation is the explanation with the overall greatest balance of intrinsic probability and accuracy.

(2) Naturalism is an intrinsically more probable explanation than theism.

(3) Naturalism is a more accurate explanation than theism.

In this post I will evaluate Lowder’s defence of (1), and in the next post I will evaluate his defence of (2) and (3).

*Inference to the Best Explanation*

Before we look at Lowder’s defence of (1), let’s try and understand the two common methods of assessing rival hypotheses, namely, Inference to the Best Explanation (IBE) and Bayesianism. IBE is a type of reasoning in which one tries to find which hypothesis in a set of rival hypotheses best explains some set of facts. In order to determine the best hypothesis, one examines how well each hypothesis complies with specific criteria. Commonly accepted criteria include the following:

**Coherence**: Is the hypothesis internally and logically consistent?**Consistency**: Is the hypothesis consistent with our background knowledge and other accepted hypotheses and facts?**Explanatory scope**: Does the hypothesis explain all the relevant facts?**Explanatory power**: How well does the hypotheses explain each fact?**Modesty or simplicity**: Does the hypothesis postulate entities only when necessary?**Refutability**: Can the hypothesis be falsified by some imaginary scenario or evidence?

The hypothesis that complies the best with these criteria is then accepted as the best explanation of the facts.

Bayesianism, on the other hand, is concerned with probabilities. Bayesianism tries to find the most probable hypothesis by assigning a probability to each hypothesis. This is done by evaluating whether our background knowledge and/or the relevant evidence increases the probability of the hypothesis. When speaking about relative probability, we use the term “P(H|E)” to mean “the probability of hypothesis H given evidence E”. “P(H|E)” must not be confused with the term “P(E|H)” because, unlike the former, the latter means “the probability of evidence E given hypothesis H”. When we know that a set of facts E is true, and we wish to know which hypothesis E supports the most, we investigate P(H|E). However, when we know that a hypothesis H is true, and we wish to know which uncertain fact (or evidence) H supports the most, we use P(E|H).

Bayesians make use of Bayes’ Theorem to investigate P(H|E). The simple (and common) form of Bayes’ Theorem is the following:

P(H|E & B) = [P(H, B) x P(E|H & B)] / P(E & B)

where H is some hypothesis, E is some evidence or set of facts, B is our background knowledge, P(E & B) ≠ 0, and 0 ≤ P(x) ≤ 1. One may leave out B in the equation:

P(H|E) = [P(H) x P(E|H)] / P(E)

but this is uncommon and not advised, since our background knowledge helps us determine (and sets some constraints when determining) probabilities. Our background knowledge includes our past experiences, self-evident truths (such as that the external world is real), accepted theories (such as that the earth is round), and so on. We can see, then, how important background knowledge is for assigning probabilities. For example, since B includes the fact that the universe exists, P(H) is greater than P(H & B) when H denotes the hypothesis that “nothing exists”!

It is obvious, then, that IBE and Bayesianism are very different methods. In fact, scholars disagree about which method is preferable or whether the two methods compliment one another. Nevertheless, if one wishes to use the two methods in a complimentary way, then one should follow Peter Lipton’s (2004, chapter 7) suggestion to use IBE to guide one in determining probabilities, since explanatory considerations (IBE) may help one see how probable something is. With this ground work in place, we may now evaluate Lowder’s defence of (1).

*Lowder’s Defence of (1)*

Lowder claims that “the best explanation is the explanation with the overall greatest balance of intrinsic probability and accuracy.” By “intrinsic probability”, he simply means P(H), which he believes is determined solely by modesty and coherence. By “coherence”, Lowder is referring to the criterion discussed above.

However, by “modesty”, he does not mean the simplicity criterion above but, rather, “a measure of how much the hypothesis asserts.” He continues: “The more a hypothesis claims, the more ways there are for it to be false and so, before we start looking at evidence, the less likely it is to be true.” The problem here is that Lowder is thinking of linguistic modesty. However, when evaluating competing hypotheses, modesty (or “simplicity”) should not be understood in terms of linguistic modesty but, rather, in terms of ontological modesty. *Linguistic modesty* refers to the number of claims (or propositions) a hypothesis asserts. But this type of modesty is problematic, since one proposition can be broken down into numerous (sometimes an infinite number of) propositions. Consider, for example, the proposition (P): “Naturalism is true”. Let N be the hypothesis that (P) is true. N, then, makes one claim, namely, that (P) is true. However, (P) encapsulates (or can be broken down into) many propositions, including the following:

- Physical reality exists.
- Physical reality is the ultimate reality.
- If the mental exists, the physical explains why the mental exists.
- There are no purely mental beings which can exist apart from a physical body.
- Christianity is false.
- Islam is false.
- God does not exist.
- It is false that one supernatural being exists.
- It is false that two supernatural beings exist.
- …

We can see, then, that the hypothesis N can be expressed as asserting many claims. Thus, if we use linguistic modesty as our criterion for modesty, then we can define our hypotheses such that they make as many assertions as we want, and then we can choose as the most modest the hypothesis that makes the least number of claims (as Lowder does). So, for example, we may define N as the hypothesis that asserts the above 1-9 propositions, and we may define T as the hypothesis that asserts only one proposition: “God exists”. According to Lowder’s criterion of modesty, then, it follows that T is more modest than N. But this is clearly wrong-headed. Thus, linguistic modesty is not what philosophers have in mind when evaluating competing hypotheses, since it allows one to rig the process of inference to the best explanation (IBE).

It is *ontological modesty*, then, that is commonly used in IBE. This type of modesty is associated with Occam’s razor, which is the principle that we should not assert the existence of more entities than are necessary. Accordingly, hypothesis H1 is more modest than hypothesis H2 if the former asserts the existence of less persons, physical objects, events, etc. than the latter hypothesis asserts. This is the type of modesty Lowder should be concerned with, which he overlooks.

Moreover, modesty and coherence alone cannot tell us what the intrinsic probability of a hypothesis is. The intrinsic probability of a hypothesis refers to P(H), the probability that the hypothesis is true when we ignore any evidence for it. Now, as noted above, to evaluate intrinsic probability we need to consider, not only modesty and coherence, but also our background knowledge. Ignoring our background knowledge, as Lowder does, results in many absurd hypotheses being more intrinsically probable than plausible hypotheses. For example, according to Lowder’s standard of intrinsic probability, the following hypotheses are far more intrinsically probable than naturalism:

- Nothing exists.
- Only you exist and the external world is a figment of your imagination.
- God alone exists (and thus no physical reality exists).

I doubt that Lowder wishes to claim that these hypotheses are truly more intrinsically probable than naturalism. Nevertheless, the point is that, when evaluating the intrinsic probability of a hypothesis, no scholar (that I know of) ignores our background knowledge. Therefore, Lowder’s use of “intrinsic probability” in (1) is confused and unsatisfactory.

What about Lowder’s understanding of “accuracy” in (1)? By “accuracy”, Lowder means “the degree to which a hypothesis’s predictions correspond to reality”. As far as I am able to tell, Lowder is here simply referring to the explanatory scope criterion discussed above, which asks whether the hypothesis entails or explains all the evidence. So far so good. But when Lowder explains “accuracy” further, he mixes IBE with Bayesianism:

We measure accuracy by looking at “evidence.” By “evidence” I mean something which makes something else more probable than it would have been otherwise. … Mathematicians have a formula called Bayes’ Theorem, which can be used to specify the relationship between intrinsic probability, accuracy, and the overall or final probability of a hypothesis.

Lowder is using Bayesianism in an unusual way: to support IBE. However, as discussed above, if one wishes to use both IBE and Bayesianism, one should do it the other way around, that is, one should use IBE to help determine the probabilities used in Bayes’ Theorem. Thus, as with Lowder’s use of “intrinsic probability” in (1), his use of “accuracy” is muddled. It turns out, then, that Lowder is really defending the following claim:

(1) The best explanation is the explanation that best satisfies the criteria of linguistic modesty, coherence, and explanatory scope.

However, since (1) ignores the criteria of consistency, explanatory power, simplicity, and refutability, and since Lowder’s defence of (1) is muddled, confused, and unsatisfactory, we should reject (1). It is unfortunate for Lowder that his entire case rests on (1). Since (1) is implausible, even if Lowder succeeds in showing that naturalism is a better explanation that theism in terms of (1), he will not succeed in showing that naturalism is *more probable* than theism. Nevertheless, in the next post we will turn to Lowder’s defence of (2) and (3).

*Bibliography*

Lipton, P., 2004. *Inference to the best explanation*, 2nd ed. Routledge, London.