# «THE MAD/BAD/GOD TRILEMMA: A REPLY TO DANIEL HOWARD-SNYDER Stephen T. Davis [ABSTRACT:] The present paper is a response to Daniel Howard-Snyder’s ...»

**THE MAD/BAD/GOD TRILEMMA:**

## A REPLY TO DANIEL HOWARD-SNYDER

Stephen T. Davis

[ABSTRACT:] The present paper is a response to Daniel

Howard-Snyder’s essay, “Was Jesus Mad, Bad, or God?...Or

Merely Mistaken?”

I

Many Christians are familiar with a popular apologetic argument in

favor of the divinity of Christ called “the Trilemma” or “the Mad/Bad/God

argument.” (I will call it the MBG argument.) It has been defended most famously by C.S. Lewis,1 but also by other Christian apologists since Lewis.

I have recently argued that the MBG argument can be used to establish the rationality of belief in the incarnation of Jesus.2 But now Professor Daniel Howard-Snyder has subjected the MBG

**argument to a rigorous critique.3 He summarizes the argument as follows:**

(1) Jesus claimed, explicitly or implicitly, to be divine.

(2) Either Jesus was right or he was wrong.

(3) If he was wrong, then either a. he believed he was wrong and he was lying, or b. he did not believe he was wrong and he was institutionalizable, or c. he did not believe he was wrong and he was not institutionalizable; rather, he was merely mistaken.

(4) He was not lying, i.e., a is false.

(5) He was not institutionalizable, i.e., b is false (6) He was not merely mistaken, i.e., c is false.

(7) So, he was right, i.e., Jesus was, and presumably still is, divine.

1 Interestingly, Howard-Snyder is prepared to grant the truth of premise (1), which many people would consider the most controversial premise of the argument, as well as the truth of (4), and (5). It is premise (6) that he questions. That is, Howard-Snyder denies that the MBG arguer can sensibly rule out the possibility that Jesus was “merely mistaken” in believing himself to be divine.

II Let us then consider the case that Howard-Snyder makes. I will focus on just two of his arguments: (1) his use of the “dwindling probabilities” argument (the DPA); and (2) the stories he uses to rationalize the possibility that Jesus was neither mad nor bad but merely mistaken in claiming to be divine.

The DPA is a strategy that Howard-Snyder borrows from Alvin Plantinga. In his Warranted Christian Belief,4 Plantinga argues that a faithful acceptance of the Christian gospel must be a gift of God. It is not something that human beings can, so to speak, recognize and accept quite on their own.

Nor can a convincing natural theological argument show that the Christian gospel is true or even probably true. It involves crucial and controversial claims about (among other things) God, revelation, sin, incarnation, resurrection, atonement, and the church. So any rational argument in favor

damaging fact—even if you show that one crucial point in it has a certain fairly high degree of probability, that probability will be reduced when you try to argue for the high probability of the next crucial point, and the one after that, and etc. Each time a new point is added, the relevant probabilities have to be multiplied. So there is no way that the entire package will end up with anything like a high degree of probability.

Let me make two main points in response to Howard-Snyder’s use of the DPA. The first has to do with the forma and application of the argument.

The second has to do with the actual probability numbers that he supplies to the premises of the MBG argument.

(1) The form and application of the DPA. I should point out first that Howard-Snyder apparently is not deeply committed to the DPA. I read him as saying that if the proper way to assess the MBG argument is in terms of the probability calculus, then the DPA can be raised against it. In other words, Howard-Snyder is not asserting that this is indeed the proper way to evaluate the MBG argument, but he suspects that many people will hold that it is. Still, just in case those people are correct, I need to reply to HowardSnyder’s (so to speak) hypothetical use of the argument.

chain of probabilistic inferences. Suppose we are trying to argue on behalf of a hypothesis H. And suppose we argue as follows: “P, therefore very probably Q; Q, therefore very probably R; R, therefore very probably S; and S, therefore very probably H.” In such a case, the dwindling probabilities objection can ruin the argument. This is because the probability numbers (once actual values are supplied) have to be multiplied at each step, and accordingly may well result in H having a value of less than 0.5.

Plantinga’s argument works against a certain way of doing natural theology. For example, a natural theologian might first try to argue on the basis of our background knowledge that it is probable that God exists, and then try to argue on the basis of our background knowledge plus the probability of the claim that God exists that it is probable that God reveals things to human beings, and then try to argue on the basis of our background knowledge plus the probability of the claim that God exists plus the probability of the claim that God reveals things to human beings that it is probable that human beings are sinners, etc. At each new point, the probabilities will diminish.

Now there is some reason to think that Howard-Snyder holds that the MBG argument takes this form. On this interpretation, the MBG arguer must

is high; and then show, on the basis of our background knowledge and the probability of (1), that the probability of (4) is high; and then show, on the basis of our background knowledge and the probability of (1) and the probability of (4), that the probability of (5) is high; and finally show, on the basis of our background knowledge and the probability of (1) and the probability of (4) and the probability of (5), that the probability of (6) is high. Now if MBG arguers must present their case in this way, then the probabilities that will emerge at the end might well dwindle to the point of being unimpressive.

However, this is not the logic of the MBG argument. What then is that logic? Using Howard-Snyder’s version of it as a rough outline (but

**supplying new numbers for the premises), it is more like this:**

Note that the arguments for any one of steps (10a), (10b), or (10c) do not depend probabilistically on the arguments for the other two. For example,

probability of the case that he was not bad, etc.

This is the proper strategy of MBG arguers. First they try to show that it is highly probable on our background knowledge that Jesus claimed to be divine. Then they try to show that it is highly improbable on our background knowledge that Jesus was lying in claiming to be divine. Then they try to show that it is highly improbable on our background knowledge that Jesus was mad in claiming to be divine. Finally, they try to show that it is highly improbable on our background knowledge that Jesus was “merely mistaken” in claiming to be divine. If they can succeed in doing those things, then the probability will be high that Jesus was right in claiming to be divine.

This creates a different logical situation. By the disjunctive axiom of the probability calculus, we add, rather than multiply, exclusive alternatives like Howard-Snyder’s (3a), (3b), and (3c). Accordingly, the probability of the disjunction [(3a) v (3b) v (3c)] is the sum of the probabilities of each disjunct. (If they overlap—which I do not believe that they do, in this case5—it will be less than that, but still cannot be less than the probability of the most probable disjunct.) So the cogency of the MBG argument will in the end depend on just how improbable the disjuncts are. And I hold that they are highly improbable, somewhere (I would estimate) around 0.1 each.

knowledge) that Jesus claimed to be divine is about 0.9, then the probability of [~(3a) & ~(3b) & ~(3c)], which is the proposition that the MBG arguer needs, is somewhere near 0.7, and the probability of (7) somewhere near.63.

In other words, there is a difference between these two probabilistic ways of arguing for a hypothesis H. Method A: Very probably P; P, therefore very probably Q; Q, therefore very probably R; R, therefore very probably H. Method B: Either P or Q or R or H; P is very probably false; R is very probably false; Q is very probably false; therefore H is very probably true. I say that the DPA applies only to arguments like Method A, not to arguments like method B.6 And Howard-Snyder seems to me to hold that the MGB argument must use something like Method A in establishing the probability of [~(3a) & ~(3b) & ~(3c)]. (See his formal statement of the probabilities on page 6 of his paper, where the previously arrived at value for “not lying” has to be multiplied in order to get the right value for “not institutionalizable,” and both have to be multiplied in order to get the right value for “not merely mistaken.”) I say, on the other hand, that the MBG argument is best understood as using something like Method B in establishing the probability of [~(3a) & ~(3b) & ~(3c)]. It is quite true that the MBG arguer needs a high probability

of the three conjuncts need have anything to do with the probabilities that we assign to the others. There is no need in this case to multiply probabilities.

Let me make the point in a slightly more formal way.7 If k is our

**background knowledge, let:**

Now given that P(d/k) = p(jd & ~b & ~ma & ~mi/k), Howard-Snyder claims that P(d/k) = P(jd/k) P(~b/jd & k) P(~ma/jd & k & ~b) P(~mi/jd & k & ~b & ~ma). But I deny that this is the correct way to read the MBG argument. In effect, I am using the following formula: P(d/k) = P(jd/k) P(~[b v ma v mi]/k & jd). Now suppose we read (3a), (3b), and (3c) of Howard-Snyder’s

**summary of the MBG argument as follows:**

Now since b, ma, and mi are exclusive (as noted, we can provide suitable definitions of the terms “mad,” “bad,” and “mistaken” which ensure that), and given my assumption that each of (3a), (3b), and (3c) has a probability of about 0.1, then the value of P(3a v 3b v 3c/k) will equal about 0.3.

0.3 = P(jd & ~d/k). Now both Howard-Snyder and I assume that the P(jd/k) is high, let’s say 0.9. Thus P(jd/k) = P(jd & d/k) + P(jd & ~d/k). So P(jd & d/k) = about 0.6. Accordingly, P(d/k) = about 0.6.8 I am not arguing that the dwindling probabilities objection is wholly irrelevant to the MBG argument. This is because undeniably there are four different probabilities at work in the argument, viz., the probabilities of (1), (4), (5), and (6). So Howard-Snyder is not off-base in raising the objection.

**Again, the MBG argument in essence says:**

So in the end you do have to multiply two probabilities, viz. the probability that (1) is true and the probability that [(3a) v (3b) v (3c)] is false.

But if the probabilities of these two sub-points are both high enough, then the probability of the conclusion will still be impressive.9 And this is just what I claim. Belief in (7) is rational because its probability is considerably greater than.5. In the light of the MBG argument, it is more probable than not (I actually believe it is much more probable than not) that Jesus was correct in claiming to be divine.

Snyder and I have supplied slightly different numbers for the probabilities of some of the propositions in question. As noted, I am inclined to assign a probability of about.9 to (1) and to each of ~(3a), ~(3b), and ~(3c). HowardSnyder gives a range of.7 -.9 for (1), and a range of.85 -.95 for ~(3a), ~(3b), and ~(3c). I do not wish to argue about that point; obviously, these are all estimates, and sensible people can sensibly disagree about such matters.

But there are two points where I do wish to differ. First, suppose that the probability that Howard-Snyder assigns to (7)—that is, between.43 and.77—is correct (and I do not agree that it is). Even if so (or so I would argue), that range is high enough that it can be rational to affirm (7), i.e., to believe in Christ’s divinity. Notice that the mid-point between.43 and.77 is.6, and I see no compelling to insist that we must suspend judgment on propositions that are this probable. Certainly we may suspend judgment in such cases; that certainly would be allowed, depending perhaps on other circumstances.10 But it does not seem sensible to hold that we must do so.

And of course that it is rational to believe (7) in the light of the MBG argument is all that I have been arguing for.

This leads directly to the second issue.11 I disagree with HowardSnyder’s claim that we can never justifiably believe that the final probability

probabilities assigned to it. That is, he argues that since we cannot justifiably be confident that the probability of (7) is greater than is arrived at when we work from the lowest estimate of each of the separate probabilities that precede it in the argument (which he computes as.43), “we should profess ignorance and suspend judgment.” This epistemic principle of HowardSnyder’s turns a slight difference in original probability estimate between the two of us (.9 versus.85-.95) into a truly significant difference in the end.

But surely this is misleading. The probability that we assign to a proposition represents our degree of uncertainty of the proposition’s truth.