God as a Hypothesis: A Response to Edward Feser

On his blog, Edward Feser argues that it is illegitimate to think of God as a hypothesis (Edward Feser: Is God’s existence a “hypothesis”?) I disagree. To begin, it is important to attend to what Feser means by "hypothesis." He adopts the following definitions, which he sees as being complementary to one another:

Hypothesis:

• [A] conditional or provisional explanation of observed facts or of their connection with each other; a tentative explanation suggestive of further experiment and verification.
• As used in the natural sciences, a predictive judgment about an empirical event that will occur under a describable set of conditions.  (Hypotheses are sometimes generated by more general theories; if the predicted events in fact occur, the hypotheses are said to be confirmed, and this in turn provides additional rational support for the theories in question.)

Thinking of a hypothesis in this way is similar to the way that a hypothesis is conceived of in Bayesian epistemology, although Bayesians often don't treat evidence as having to be "empirical" in any significant sense. A hypothesis is any kind of belief, supposition, proposition, or something similar that (usually) can be confirmed or disconfirmed by learning new things. Such learning does not have to be empirical in nature, but it can be. Suppose that we are considering a certain hypothesis H and we learn E. In Bayesian terms, we say that E is evidence for H means that Pr(H | E) > Pr(H), while E is evidence against H means that Pr(H | E) < Pr(H). If E is neither evidence for nor against H, then Pr(H | E) = Pr(H). In words, to say that E is evidence for H means that the probability of H given E is greater than the probability of H prior to learning E. To say that E is evidence against H is to say that the probability of H given E is less than the probability of H prior to learning E. Finally, to say that E is neither evidence for nor against H is to say that the probability of H given E is equal to the probability of H prior to learning E.

The probability in question is epistemic probability. We are not essentially concerned with the objective chances of things (propensities) but rather with our degrees of belief (credences) in things. We are concerned with how likely we think a hypothesis is given what we know or believe. With this being said, when we do know the objective chances of things, then our credences should match such chances (this is referred to as the "principal principle" in Bayesian epistemology). Often, however, we do not know the objective chances in question, and so we must make do with our subjective confidence in this or that hypothesis being true. Even a metaphysically necessary hypothesis can have an epistemic probability that is less than 1 if we do not actually know that the hypothesis in question is metaphysically necessary. This point will be important later on.

Getting back to Feser, how does he defend his contention that God cannot be thought of as a hypothesis that might be confirmed or disconfirmed by empirical evidence? First, he gives an illustration of the way in which hypotheses about the causes or explanations of observed effects are formed. Suppose that some effect E occurs under conditions of type T. From here, suppose that we form hypothesis H according to which a cause C is responsible for E. We can then test this hypothesis by bringing about C under T and observing whether or not E occurs. If it does, then we have confirmation of H. In Bayesian terms, Pr(H | C & E & T) > Pr(H). Even if, however, we get confirmation of H in this way, Feser notes, “it will be possible that something other than C is the cause, so that the most that further testing can do is render this supposition improbable (even if, perhaps, highly improbable).” 

From here, Feser argues that the relationship between C and E is not like the relationship between God and the universe according to theism: 

Now, this sort of relationship between C and E is simply not like the relationship between God and the world as that is understood by classical theism. God’s creating the world is not a matter of making it the case that this specific thing happens in the world rather than that specific thing. Rather, creation is a matter of making it the case that there is any world at all. Moreover, theism holds that the fact that there is any world at all is something that could not even in principle have obtained in the absence of divine creative action. For classical theism, if we’re talking about a view according to which the world might have existed apart from God, but simply happens not to do so, then we’re not really talking about theism but rather about something that only superficially resembles it.

So, the argument, as best as I can tell, is that according to theism, God is a necessary being, a being that must exist and that is necessarily the explanation of there being anything at all. The world could not have even in principle existed without God. Since, therefore, empirical confirmation does not get us to the conclusion that theism, taken as a hypothesis, must be true, it follows that God cannot be understood as a hypothesis, something that can be confirmed or disconfirmed by empirical evidence. We have reason, therefore, to think that what is liable to being confirmed or disconfirmed by empirical evidence (a hypothesis) must fall short of being God. So, God is not a hypothesis. We might succinctly summarize this argument as follows:

1. If God is a hypothesis (that can be confirmed or disconfirmed by empirical evidence), then it might be the case that God does not exist.
2. But it is false that it might be the case that God does not exist (since God is a necessary being).
3. Therefore, God is not a hypothesis.

In response, Feser’s argument seems to me to trade on an ambiguity between metaphysical and epistemic modality. To say that something is epistemically possible, for instance, is to say that it could, for all I know, be the case. For example, for all I know, it could rain tomorrow. This kind of possibility is distinct from metaphysical possibility, which refers to objective, mind-independent possibility. A simple example will illustrate this distinction. Consider the Riemann Hypothesis (perhaps the most famous unproven conjecture in mathematics). As a mathematical statement, the Riemann Hypothesis is either (metaphysically) necessarily true or necessarily false. However, since it has yet to be proven, it may for all we know be true, and it may for all we know be false. Even if the hypothesis is necessarily true (metaphysically), it may be false for all we know. That is to say, it is epistemically possible that it is false even if it is metaphysically necessary that it is true. Another thing to make note of is that unlike metaphysical possibility, epistemic possibility is person-relative. Something could be epistemically possible for me that is not epistemically possible for you, and this is because I know things that you don't, and you know things that I don't.

Now, the ambiguity in Feser's argument is with respect to whether the "might" in the first and second premises is meant to express metaphysical possibility or epistemic possibility. I'll begin with the second premise. Here, it seems clear that Feser intends for "might" to express metaphysical possibility. For when Feser speaks of God as a necessary being, he evidently has metaphysical necessity in mind, for it is metaphysical principles (such as the essence/existence distinction—see his article for more details) that necessitate God's existence. Since it is the metaphysical necessity of God's existence that rules out it being the case that God might not exist, it is evidently the case that to say that it is false that God might not exist is to say that God's nonexistence is not metaphysically possible. With respect to the first premise, however, it seems like the "might" must express epistemic possibility. For it is false that a metaphysically necessary truth cannot ever be confirmed or disconfirmed by evidence (empirical or otherwise). So, if the "might" expresses metaphysical possibility, then the premise is simply false. On the other hand, if the "might" expresses epistemic possibility, then the conclusion will no longer follow as there is an equivocation in the argument with respect to the term "might." Moreover, epistemic possibility does not entail metaphysical possibility.

Even if God’s existence is metaphysically necessary, it might not be epistemically necessary, i.e., God’s existence, though objectively necessary, might not be absolutely certain to me given what I know. In Bayesian reasoning, as previously explained, we are concerned with epistemic probabilities (credences), and there is nothing problematic whatsoever about assigning credences that are less than 1 to metaphysically necessary propositions. Now, if our credence in some metaphysically necessary proposition P is less than 1, i.e., if Pr(P) < 1, then it could very well happen that we obtain some evidence E that, upon conditionalizing, raises our credence in P. In other words, if Pr(P) < 1, then it could be the case that Pr(P | E) > Pr(P). We are concerned here with subjective probabilities. Of course, by the principal principle, if we know that the objective probability of P is 1, then our credence in P should also be 1. But we might not know this.

There are readily available examples from mathematics and theoretical computer science to illustrate these points. By the nature of the case, if Goldbach’s Conjecture, the Riemann Hypothesis, and the conjecture that P ≠ NP are true, then they are necessarily true. As it happens, though, we are not sure that any of these hypotheses are true. As such, we should not assign credence 1 to any of them even though if they are true then their objective probabilities are all 1. As such, there is nothing illegitimate about treating these mathematical conjectures as “hypotheses” that can be confirmed or disconfirmed by empirical evidence. Goldbach’s Conjecture in particular enjoys empirical evidence in its favor: it has been verified to hold for trillions of natural numbers. This is generally taken as evidence that the conjecture is true. It is quite intuitive to think that our confidence in Goldbach’s Conjecture should be higher given the knowledge that it is true for the first trillion natural numbers than it is in the absence of such knowledge. But then it is clear that the truth of (metaphysically) necessary propositions can be confirmed by empirical evidence.

The only way for a proposition to not be susceptible of being confirmed by evidence in the sense of having its (epistemic) probability raised by evidence is for that proposition to already be certain, i.e., probability 1. Since, therefore, it has been shown that metaphysical necessity does not entail epistemic certainty, it follows that a metaphysically necessary proposition can in principle be confirmed by evidence, including empirical evidence. Consequently, if our credence in the existence of God is less than 1, then in principle the existence of God could be confirmed for us by empirical evidence. For this very reason, therefore, there is nothing in principle illegitimate about treating God as a kind of hypothesis that can be confirmed (or disconfirmed) by empirical evidence.

Of course, if we were to have a true demonstration of God's existence, then empirical confirmation would become irrelevant to the existence of God in the same way that a proof of Goldbach's Conjecture would make empirical confirmation of its truth irrelevant. Given that Feser defends the existence of such demonstrations in his excellent book Five Proofs of the Existence of God, it is understandable why he thinks that empirical confirmation "is at best irrelevant to actually establishing God’s existence." Nevertheless, for those who are not at present persuaded by the cogency of such demonstrations, I think it is perfectly legitimate to treat the existence of God as a kind of hypothesis that can be confirmed by empirical evidence such as, for example, the fine tuning of the universe for the existence of life. Such empirical confirmation will fall short of proving that God exists, but it can still help to make God's existence more (epistemically) probable than not, and this is valuable to the project of natural theology and apologetics.