The Logic of the Lewis Trilemma

—–Bilde: Ecce Homo, Antonio Ciseri (1871)—–

In his book Mere Christianity, C. S. Lewis writes the following:

I am trying here to prevent anyone saying the really foolish thing that people often say about Him: I’m ready to accept Jesus as a great moral teacher, but I don’t accept his claim to be God. That is the one thing we must not say. A man who was merely a man and said the sort of things Jesus said would not be a great moral teacher. He would either be a lunatic — on the level with the man who says he is a poached egg — or else he would be the Devil of Hell. You must make your choice. Either this man was, and is, the Son of God, or else a madman or something worse.

The argument Lewis presents here has become known as the “Lewis Trilemma” or “Lord, Liar, or Lunatic.” It is often thought of as an argument for the divinity of Jesus Christ. This, I think, is not quite right, or at least it doesn’t say enough. Lewis doesn’t seem to me to be arguing for the divinity of Jesus, full stop, but for the divinity of Jesus, given the view—call it Jesusianism—that Jesus was a wise and good man. Roughly, the thought seems to be that the historical facts leave us with only three possible hypotheses: that Jesus was telling the truth about his divinity, that he was deeply deluded, or that he was deeply morally depraved. Since only the first possibility is consistent with Jesus’s wisdom and goodness, so the argument goes, Jesusianism entails the divinity of Jesus.

The “Trilemma” has become popular among Christian apologists, who, however, generally use it in popular-level works which, for convenience and accessibility, pass over in silence many of its subtleties. Lewis’s original formulation, though it has all the rhetorical brilliance one expects from him (or rather, perhaps, for that very reason), is similarly “sloppy,” and leaves many key premises vague or implicit. This might lead the philosophically astute reader to dismiss the Trilemma as a bad argument, on the assumption that the formulation of it given by Lewis and later popular apologists are the best, most rigorous formulations of it that can be given.

This, I submit, is not so. What I want to do here is lay bare some of the logical structure of Lewis’s argument, with a view mainly to giving the best version of it rather than exegetical fidelity to Lewis’s formulation. I do not claim—or at any rate, I shall not argue very adamantly here—that my version of the argument is sound. My only ambition is to show that it is a good and interesting argument, worthy of serious debate, and for whose soundness a decent case can be made.

I begin by considering whether the “Trilemma” is really a trilemma at all, or whether there are additional possible hypotheses that Lewis has overlooked. I then argue that the probability calculus is the best way to go from there, and look at what light it can shed on how we should weigh the probabilities of the different hypotheses about who Jesus really was. Finally, I respond to some anticipated objections.

Trilemma, Quadrilemma, or Octolemma?

What do we mean when we call Lewis’s “Trilemma” a trilemma? Presumably that the choices laid before us—Lord, Liar, or Lunatic—are mutually exclusive and exhaustive; that we must choose at least and at most one of them.

The “trilemma” appears to involve a choice about the truth-values of three propositions: that Jesus claimed to be God incarnate (call it c), that Jesus believed he was God incarnate (call it b), and that Jesus was God incarnate (call it w). But as anyone who has made a truth table can tell you, this yields, not three (logical) possibilities, but eight:

c b w
T T T L1 (“Lord”)
T T F L2 (“Lunatic”)
T F T L3
T F F L4 (“Liar”)
F T T L5
F T F L6
F F T L7
F F F L8

As we can also see, though, most of the hypotheses that Lewis passes over are not very plausible. Consider L6, for example: If we hold that Jesus did not claim divinity, why think that he secretly had a false belief that he was divine? One of the skipped hypotheses, however, is at least one that has been proposed: L8, or the “Legend” hypothesis. Under that banner flies the view that Jesus did not exist at all (bracketing, for convenience, questions about the truth-values of assertions that contain non-referring proper names), as well as the view that he did exist, but was really a secular revolutionary, a pacifistic proto-hippie, or a Socratic sage whose alleged claim to divinity was a later invention of his followers. Thus, even if we want to consider only those possibilities that are at least somewhat plausible and not completely ad hoc, we are actually dealing with a quadrilemma rather than a trilemma. Apologists have duly dubbed the four-pronged revision of Lewis’s argument “Lord, Liar, Lunatic, or Legend.”

In any case, the core assumption of the argument seems to be that there is an inconsistency between accepting Jesusianism and denying the divinity of Jesus. However, charity and common sense militate against the view that Lewis and his intellectual progeny claim to have found a logical inconsistency here. After all, it is obviously very easy to tell a merely logically coherent story in which Jesusianism is true and Christianity is false, just as it is easy to tell a logically coherent story in which Jesus is a unicorn. Rather, Lewis can more charitably be interpreted as saying that L1—the “Lord” hypothesis—is, among the eight hypotheses, the only one that is both plausible (and, in particular, not ad hoc) and which does not render Jesusianism massively improbable.

It seems most fair and reasonable, therefore, to treat Lewis’s argument as a probabilistic one. If we want to formalize something like Lewis’s argument, our best bet is therefore the language of the probability calculus, to which we will now turn.

Does Jesusianism Render Christianity More Likely Than Not?

We are almost ready to give the argument itself. Before we do that, however, we must get two bits of formal housekeeping out of the way. Firstly, for readability I will adopt the convention that P(A) is high just in case P(A) > 0.5, low just in case P(A) < 0.5, and even just in case P(A) = 0.5. As should be readily apparent, these categories are mutually exhaustive and exclusive: P(A) must be either high, low, or even, and it cannot be more than one of them at once. Secondly, we must distinguish, e.g., between L4 and the proposition that Jesus was a deeply depraved liar. After all, a critic of the argument might want to dispute precisely the claim that Jesus’s being a liar follows from L4. Therefore, let L4 and L2 carry no implications about Jesus’s character by themselves. Instead, let us introduce two new hypotheses—“Liar” and “Lunatic”—which do carry implications about Jesus’s character (viz., respectively, that he was a liar and that he was a lunatic), but which, by themselves, make no claims about Jesus’s divinity or his own claims or beliefs about his divinity.

Here is the argument:

 

(1) If P(Liar v Lunatic|Jesusianism) is low, then P((c ∧ ¬b) v (b ∧ ¬w)|Jesusianism) is low.  (Premise)

(2) P(Liar v Lunatic|Jesusianism) is low.  (Premise)

(3) Therefore, P((c ∧ ¬b) v (b ∧ ¬w)|Jesusianism) is low.  (From 1 and 2)

(4) Therefore, P(L2 v L3 v L4 v L6|Jesusianism) is low. (From 3)

(5) Therefore, P(L1 v L5 v L7 v L8|Jesusianism) is high. (From 4)

(6) And P(L5 v L7 v L8|Jesusianism) is so low that P(L1 v L5 v L7 v L8|Jesusianism) remains high even if we subtract P(L5 v L7 v L8|Jesusianism) from it. (Premise)

(7) Therefore, P(L1|Jesusianism) is high.  (From 5 and 6)

 

It may be worth briefly explaining why (4), (5), and (7) do indeed follow. (The third premise follows by modus ponens, which I take it I don’t have to explain.) Readers who are familiar with the probability calculus (or willing to take the validity of my argument on faith) can safely skip the following paragraph. It is a theorem of the probability calculus that for any three propositions A, B, and C, if A and B are equivalent, then P(A|C) = P(B|C). Now, (c ∧ ¬b) v (b ∧ ¬w) is equivalent to L2 v L3 v L4 v L6. Therefore, P((c ∧ ¬b) v (b ∧ ¬w)|Jesusianism) = P(L2 v L3 v L4 v L6|Jesusianism). Therefore, if P((c ∧ ¬b) v (b ∧ ¬w)|Jesusianism) is low, so is P(L2 v L3 v L4 v L6|Jesusianism), so (4) follows. It is an axiom of the probability calculus (call it A1) that for any proposition A, P(A v ¬A) = 1. A bit of recursive grunt work thence leads us to the conclusion that the probability of the disjunction of all the L hypotheses is 1. Another axiom of the probability calculus (call it A2) is that for any two disjoint propositions, the probability of their disjunction is equal to the sum of their individual probabilities. Now, each L hypothesis is disjoint from every other L hypothesis. After all, if more than one L hypothesis were true, some contradiction or other would always follow, and it is a theorem of the probability calculus that every contradiction has a probability of 0. Therefore, P(L1 v … v L8) = P(L1) + … + P(L8) and P(L1 v … v L8|Jesusianism) = P(L1|Jesusianism) + … + P(L8|Jesusianism) = 1. This entails that P(L1 v L5 v L7 v L8|Jesusianism) = 1 – P(L2 v L3 v L4 v L6|Jesusianism). Consequently, if P(L2 v L3 v L4 v L6|Jesusianism) is low, P(L1 v L5 v L7 v L8|Jesusianism) is high, so (5) follows. Finally, by A2, P(L1 v L5 v L7 v L8|Jesusianism) = P(L1|Jesusianism) + P(L5 v L7 v L8|Jesusianism). Consequently, P(L1|Jesusianism) = P(L1 v L5 v L7 v L8|Jesusianism) – P(L5 v L7 v L8|Jesusianism). Consequently, if P(L1 v L5 v L7 v L8|Jesusianism) – P(L5 v L7 v L8|Jesusianism) > 0.5, then P(L1|Jesusianism) > 0.5, so (7) follows.

While the premises—(1), (2), and (6)—are debatable, I think they can all at least be shown to be reasonable. To that end, I will now show how one might begin to argue for them.

 

In defense of (1). One way to bring out the plausibility of this premise is to consider its contraposition:

 

(11) If P((c ∧ ¬b) v (b ∧ ¬w)|Jesusianism) is not low, nor is P(Liar v Lunatic|Jesusianism).

 

As a moment’s reflection will reveal, this is equivalent to

 

(12) If P((c ∧ ¬b) v (b ∧ ¬w)|Jesusianism) is equal to or greater than 0.5, then so is P(Liar v Lunatic|Jesusianism).

 

Let’s forget Jesus for a moment and consider the general pattern of inference instantiated by (12). Suppose you know with a non-negligible (indeed, at least an even) degree of certainty that I am going around and claiming to be God incarnate, though I do not in fact believe that I am. To be clear, my claims are not of the benign, New Agey “God is in all of us” sort: I claim to be alone in being God incarnate, and as such also alone in having the authority to forgive sins and save men from eternal hellfire. I gain some followers, many of whom throw away their lives—literally and figuratively—in my name, but I show no sign of backing down from my claims. How would—and should—that affect your opinion of my moral fiber? Wouldn’t it then, in the absence of very strong reasons to the contrary, be reasonable of you to assign a non-negligible (indeed, at least an even) probability to the proposition that I am a deeply depraved liar? To put it another way, doesn’t all the evidence for my lying about my divinity also count as evidence of my moral torpor?

The same holds, mutatis mutandis, for the case in which I am not lying about my divinity, but am earnestly and wrongly convinced of it: It seems reasonable to significantly downgrade one’s degree of belief in a person’s sanity as it becomes more likely that he is falsely but earnestly claiming to be God incarnate.

It is no good to object, as some may be tempted to do, that first-century Judaea was a different and more superstitious society than ours, so that claims to divinity should not necessarily be taken as evidence of moral or intellectual torpor in that social context, even given that it should so be taken in our social context. First-century Judeans—precisely because they were “superstitious”—took false claims to divinity far more seriously than even we do. Today, a false claim to divinity might at worst earn you a stay in prison or a mental hospital. Not nice, to be sure, but I’d still take it over death by torture.

In general, then, the idea is that a person’s tendency to lie about or mistakenly claim that he is God is correlated to the probability that he is either insane or evil. As a general rule, this seems obviously right. This doesn’t mean that there aren’t extraordinary cases where this rule does not hold. However, as always with rules of inference of the form “If A, then, all other things being equal, assume that B,” the burden of proof is on the critic who insists that all other things are not equal in this particular case; and I, for one, see no reason why all other things should not be equal in the case of Jesus.

 

In defense of (2). Much like (1), (2) instantiates a pattern of inference that seems obviously right: that it is—in the absence of reasons to the contrary—reasonable to infer from x’s being wise and good that x is probably neither a pathological and unrepentant liar nor a lunatic, and to draw this conclusion just is to assign a low probability to the disjunction “x is a liar or x is a lunatic.” I see no reasons to the contrary in the case of Jesus, and therefore conclude that this pattern of inference holds here too.

 

In defense of (6). For a start, P(L5 v L7) is obviously very, very low—probably virtually zero. The best thing that can be said about L5 and L7 is that they seem to be logically compatible with the evidence, just as is the hypothesis that Jesus was a loaf of bread. Further, I see no reason that Jesusianism should heighten their probability, but several ways in which one could argue that Jesusianism actually lowers their probability further. Thus, P(L5 v L7|Jesusianism) ≈2 0.

This leaves L8 with all the probabilistic heavy lifting. Now, if we hold to L8, it seems we must hold to one of two views: that Jesus did not exist at all, or that he existed but did not claim divinity. Call the first of these hypotheses L81, and the second L82. Obviously, L8 is equivalent to the disjunction of L81 and L82, so that P(L8|Jesusianism) = P(L81 v L82|Jesusianism). Since L81 andL82 are disjoint,P(L81 v L82|Jesusianism), in turn, is equal to P(L81|Jesusianism) + P(L82|Jesusianism). In order to determine P(L8|Jesusianism), we can therefore examine P(L81|Jesusianism) and P(L82|Jesusianism) individually.

So how likely are L81 and L82—and how likely are they on Jesusianism? It is worth noting, first, that the probability of L81 does not look very good to begin with. The non-existence of Jesus was entertained by serious scholars for a while and lives on in pop culture and among certain village atheists and conspiracy theorists, but almost all historians and Bible scholars now agree that Jesus existed. Consider, for example, the Wikipedia page “Christ myth theory,” whose sample of the theory’s present proponents is, as of this writing, almost completely limited to amateurs with anti-Christian axes to grind. But this is rendered academic by another point: If we believe that Jesus was a wise and good man—that is, if we accept Jesusianism—it plainly seems to follow deductively that Jesus existed. That Jesus existed is, of course, nothing but the negation of L81. Thus, since the negation of L81 is a deductive consequence of Jesusianism, P(L81|Jesusianism) = 0.

This leaves L82 virtually alone with the heavy lifting. That Jesus did indeed claim to be God—what L82 denies—is less commonly accepted than his existence, but again, scholarly opinion favors the view that he did—and for good reason. The earliest books of the New Testament are the epistles, which are thought to have been written as little as fifteen or twenty years after Jesus was crucified. It is clear from the epistles that belief in Jesus’s divinity—and belief that he openly proclaimed his divinity—was then already taken for granted in the Church. Many who personally experienced Jesus’s ministry would still have been alive at that time, and would have been at hand to deny these claims had they been false. And, considering the standing of the Church in pre-Constantinian Rome, they would have had much to gain by doing so. It is also notable that not a single early anti-Christian source (Porphyry’s Against the Christians, say) even suggests that Jesus did not claim divinity. But had there been even a slim possibility that Jesus did not make these claims, such sources would surely have raised it, considering what a devastating effect such a revelation would have had on the early Church.

Thus, it seems reasonable to say that we should say that P(L82) is low all on its own. And again, there is good reason to think that P(L82|Jesusianism) is lower still. Just think: Whence do we get the notion that Jesus claimed to be God? The Gospels, of course. Jesus’s claim to divinity (not to mention the truth of that claim) is utterly central to the Gospels: It is, ultimately, the reason they were written. Thus, if we deny that Jesus did claim to be God, this should occasion a more general skepticism about any beliefs we might have about him solely or exclusively on the grounds of the testimony of the Gospels. If the reason for this is not clear, have an analogy: If I found an ancient Roman text whose central contention was that Julius Caesar was a werewolf, it would be reckless of me to blithely accept any claim about Julius Caesar—even a claim that was at least logically compatible with Caesar’s non-werewolfhood—solely or mainly on the authority of that text. Now, we accept the propositions which are our grounds for declaring Jesus a wise and good man—that he did such and such good deeds, that he told such and such wise parables, and so on—solely or mainly on the grounds that they are found in the Gospels. Therefore, rejection of the claim that Jesus claimed divinity should occasion extremely strong skepticism about the Gospels in general, and therefore about our grounds for accepting Jesusianism (presuming that we do), and therefore also about Jesusianism itself. In a word, all evidence that Jesus did not claim divinity is also evidence that the Gospels are deeply unreliable, and all evidence that the Gospels are deeply unreliable is also evidence against Jesusianism.

In conclusion, poor L82—the only hypothesis we have considered whose value is not exactly or approximately equal to zero—is left with an awful lot of work which we seem within our rights to think it is incapable of doing. In other words, we seem within our rights to say that P(L1 v L5 v L7 v L8|Jesusianism) is all but equal to P(L1|Jesusianism) all on its own, and therefore that P(L1|Jesusianism) is high provided that P(L1 v L5 v L7 v L8|Jesusianism) is high.

Some Possible Counterarguments

I see three obvious counters to the argument outlined above. The first is to concede that Jesusianism is evidence for L1, but also insist that there is other, overriding counterevidence that should, all things considered, lead us to reject L1 even if we do accept Jesusianism. In other, more formal words, while P(L1|Jesusianism) may indeed be high, P(L1|k) (where k stands for all our background knowledge, excluding, for non-circularity, Jesusianism and any of the L-hypotheses if any of these are indeed known by us) is so exceedingly low that P(L1|Jesusianism ∧ k) also ends up low.

This, however, raises the question of what sort of background knowledge could so dramatically lower the probability of L1. One obvious answer is that naturalism is part of k, and that the probability of L1 on naturalism is extremely low, if not actually zero. That Christianity is most likely false given naturalism is hardly a shocking revelation. Indeed, I would argue that the falsehood of Christianity (and all other theistic religions) follows deductively from the truth of naturalism, so that P(L1|Naturalism) = 0. The controversial assumption here is that naturalism is part of our background knowledge. Now, I submit that, even if naturalism is at present a more reasonable hypothesis than non-naturalism (and I am not inclined to believe even this), it is not obvious that naturalism is part of our knowledge (not, at any rate, unless the many excellent contemporary philosophers who reject naturalism are to be excluded from this “we”). Anyhow, the burden of proof is on the naturalist here; if he wants to say that naturalism is part of our background knowledge, it is his job to show that it is, not our job to show that it isn’t.

The second counter is to deny that Jesus was, in fact, a wise and good man, thus mooting the conclusion. Strictly speaking, this counter is outside the scope of the present work, which sets out to show only that L1 is probable on Jesusianism, and not that it is probable, full stop. After all, and as mentioned, the second counter does not make that conclusion false; it simply makes it irrelevant to what we should actually believe and how we should actually live, much as is the probability of a proposition given (say) that unicorns exist. Still, let me say a very few words in defense of Jesusianism. Rejection of Jesusianism seems to me to have consequences that are deeper and more unpleasant than the Jesusian might appreciate. It is an historical fact that many of the moral beliefs we take for granted in the modern West—that all people are basically equal, that meekness and mildness are virtues, that the weak and downtrodden deserve help and compassion, and so on—are almost entirely products of Christianity, and hence, ultimately, of Jesus’s teachings. This is not to say, of course, that the Church—still less all its individual members—has always followed these teachings, but that is beside the point here. What I am concerned with here is not what the Church has done, but what the Church (or rather, Jesus) has taught. It is striking that, even in the modern, secularized West, most criticisms of the Church and its members boil down to the claim that they are not being true to the teachings of Jesus. Those who actually follow the teachings of Jesus—I mean people like Francis of Assisi or Dietrich Bonhoeffer—rarely come in for censure.

The third counter can take the form of a rhetorical question: “Couldn’t Jesus have been fundamentally mistaken without being either a liar or a lunatic?”3 This counter, unlike the first two, is not compatible with acceptance of all the premises. Instead, it seems to take aim at the second premise. At least two things can be said against it. The first is that, in a sense indeed he could, but that this is nowise incompatible with that possibility being less likely than not, which is what I have tried to establish. Is it possible, in a broad sense, that Jesus was wise, good, and mistaken about his own divinity? Yes, but this doesn’t make that possibility less likely than not. Unicorns could, in one sense, exist—but this doesn’t mean that the existence of unicorns is likely. The second is that it is misconceived to say that the argument is concerned with Jesus’s fundamental mistakenness as such, rather than with the nature of his fundamental mistakenness. I agree, of course, that it is possible to be fundamentally mistaken about lots of things—about which interpretation of quantum mechanics is correct, say, or about whether proper names refer directly or through Fregean senses—without being insane or morally contemptible. Other kinds of fundamental mistakenness, however, cannot get off so easily. Is it, for example, possible to be fundamentally mistaken about the morality of genocide without being deluded, brainwashed, or evil? I struggle to see that it is. This suggests that from fundamental mistakenness in areas of paramount existential importance—I mean primarily ethics and religion—it is indeed sometimes legitimate to deduce unflattering things about the character of the mistaken person. (This does not mean, of course, that a sane and decent person can’t be mistaken—even quite profoundly mistaken—about these subjects; it means only that, as the extent of the mistakenness increases, the probability that the mistaken person is sane and decent approaches 0. So, of course, does the probability that the mistaken person is not only sane and decent, but also wise and good; and it seems self-evident that the approach of this latter probability is far steeper.) And it was precisely these areas of paramount existential importance with which Jesus’s teachings were concerned.

In summary, it seems that a plausible case might be made that Jesusianism renders L1 more likely than not. Clearly, though, I have only scratched the surface of what could be said for and against my revamped version of Lewis’s argument.

Notes

[1] Thanks to Hans Robin Solberg, Dag Dramer, and Solveig Selseth for their invaluable editorial assistance, which they volunteered at very short notice.

[2] That is, it is approximately equal to.

[3] I owe this formulation to Jørgen Dyrstad.

2 Comments

  1. Interesting, thanks!

    A way to follow up on the third worry you adress is to ask what Christians are to say about people claiming to be on a special mission for other deities. Given that, say, the current incarnate Dalai Lama isn’t lunatic (or legend), is he a liar? That claims seems a bit harsh; whatever else you might say about him the guy seems well-meaning enough.

    Of course, one can point to other reasons for having more faith in Jesus than in these other religious figures, but given that these people are sane & sincere, and given that they are still dead wrong, the general form of the argument seems to be undermined.

  2. Hello, Georg! I hope all is well with our mutual friend in London.

    Your challenge is an interesting one. I think the way the Christian should respond to it is to question whether there are really any religious figures that both (a) are generally acknowledged to have been wise and good and (b) made claims about themselves which where as extraordinary as the claims Jesus made about himself (or, more precisely, which were such that they can be used as the basis for an argument analogous to the one Lewis gave). There are plenty of religious figures who satisfy one of these criteria, but I don’t think it’s obvious that there are any apart from Jesus who satisfy both. The Dalai Lama, for example, would arguably satisfy (a), but not (b); he is more comparable to the Pope than to Jesus. (This is not to deny that the wisdom and goodness of the Dalai Lama is evidence that he really is the reincarnation of the Buddha–only that the evidence is nowhere near as strong as it is in the case of Jesus.) On the other side, plenty of cult leaders and such satisfy (b), but not (a).

    (When talking about this, it is very important to see how mind-bendingly extraordinary Jesus’s self-understanding was. Jesus’s claims about himself are NOT analogous to those of, e.g., Abraham, Muhammad, or Siddharta Gautama, who come across as positively modest in comparison with Jesus. Unlike Jesus, none of these claimed to be more than mere humans, albeit humans who had received some special enlightenment or revelation.)

    It might still, though, be interesting to look at the principle of the thing: What should the Christian do, should there emerge a religious figure who did satisfy both (a) and (b), and who also made religious claims that were incompatible with those of Jesus? The natural answer is that he should try to break the tie by looking at other evidence for and against the figures’ competing claims. In the case of Jesus, I submit, there is a lot of evidence for his divinity other than Lewis’s argument, notably the considerable evidence for the historicity of his resurrection from the dead. (Ingvild Hellenes dives into some of this evidence in her excellent recent post on this very blog. To those who want to go deeper, I would also recommend Gary Habermas’s and William Lane Craig’s work on the Resurrection.)

    Also, it might not be a piece of cake to make an analogous argument even for a religious figure who does satisfy both (a) and (b). For while premises (1) and (2) do obviously analogize to anyone who satisfies these conditions, premise (6)–at least if one accepts them on the grounds I have given here–does not: It is grounded in some very specific historical facts about the life of Jesus, the early Church, and so on. In some cases where the historical facts are not as they are in the case of Jesus, a “Legend” hypothesis is a possibility.


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