The Enigma of Reason: A New Theory of Human Understanding

by Dan Sperber

  The Adventure of the Stolen Diamond and the Missing Premise

  Contrary to received wisdom, sound syllogisms (and other sound formal deductions) do not provide compelling arguments in ordinary reasoning. We illustrate why not with a new Sherlock Holmes adventure.

  A telegram is brought to Sherlock Holmes. He reads it, turns, and addresses his friend Dr. Watson:

  Holmes: The butler didn’t steal the diamond. So, it is the gardener who did.

  Watson, trusting Holmes’s powers of deduction, might be convinced.

  According to the standard logicist view, however, Holmes failed to express a proper deductive argument. Note that he used an argumentative device, “so,” but no logical terms. At best, his statement is an enthymeme, that is, a truncated version of a true logical argument. If so, Holmes could have been more explicit:

  Holmes: Either the butler stole the diamond or the gardener did [first premise]. The butler didn’t [second premise]. So the gardener stole the diamond [conclusion].

  This logical version with the logical terms “or” and “not” corresponds to a disjunctive syllogism:

  Premises: 1. P or Q

  2. not P

  Conclusion: Q

  Such a syllogism is said to be valid. When the premises of a valid syllogism are true, the syllogism is said to be not only valid but sound: the conclusion of a sound syllogism is necessarily true. Perhaps Watson recognized the full syllogism that Holmes had expressed in a truncated form and was convinced not just by his trust in Holmes’s logical acumen but by the actual logic of the argument.

  Does, however, a syllogism that you know to be sound provide you, by itself, with a sufficient argument in favor of its conclusion? It is a common mistake to think so.

  Suppose the telegram Holmes has just received is from the chief of police and reads: “The diamond was stolen by the gardener.” Holmes, who until then had no idea who might have stolen the diamond, rightly accepts this as a fact, but rather than just report it to Watson, he decides to convey the information in syllogistic form. He might say the following, speaking truly:

  Holmes: Either the pope stole the diamond or the gardener did. The pope didn’t. So the gardener stole the diamond.

  Holmes’s pseudo-argument is blatantly circular, and Watson should easily recognize this: since the pope was never considered a possible culprit, Holmes’s only plausible ground for asserting the first premise of the argument (“Either the pope stole the diamond or the gardener did”) is that he already knew that the gardener stole the diamond and could have said so directly. Sure, the syllogism is sound, but Watson would recognize it not as a genuine argument but as a somewhat quirky way for Holmes to assert what he knew independently. Watson’s reason to accept that the gardener stole the diamond would, in that case, have nothing to do with the logical soundness of Holmes’s pseudoargument and everything to do with his trust in Holmes.

  In the same circumstances, a disingenuous Holmes could have been just as logical and strictly truthful but nevertheless misleading. He could have spoken as follows:

  Holmes: Either the butler stole the diamond or the gardener did. The butler didn’t. So the gardener stole the diamond.

  Replacing the pope with the butler doesn’t change a bit the logic of the syllogism, nor does it alter its soundness, but it is likely that this time Watson would mistake it for a genuine argument, a reason to accept its conclusion. Why? Because, unlike the pope, the butler might have been suspected, and Holmes might have deduced that the gardener stole the diamond from information that the butler didn’t. Watson could think that Holmes had produced not only a sound syllogism but also a genuine argument.

  More generally, for any fact you happen to know, you can always construct a sound syllogism that has this fact as its conclusion and that suggests that you came to know this fact thanks to your powers of deduction. Such a syllogism, however, doesn’t give any genuine support to its conclusion. For a syllogism to serve as a bona fide argument in support of its conclusion, there must be good, noncircular reasons to accept its premises. This is not a logical requirement. From a logical point of view, circularity isn’t a problem. Noncircularity, on the other hand, is a requirement of good reasoning. Hence, when a full syllogism is presented on its own as an argument, the argument itself is incomplete; it carries an implicit premise. It implies that there are good, noncircular reasons to accept the explicit premises and, as a consequence, the conclusion.

  The common wisdom is that most arguments ordinarily used in conversation are, in fact, truncated syllogism (which they sometimes are, but much less often than is generally assumed). What we have just shown is that arguments consisting just of a syllogism, even a fully explicit one, are themselves truncated arguments: they implicitly convey that their premises are not just true but provide genuine reasons to accept the conclusion. There goes the alleged systematic superiority of explicitly laid-out syllogisms over informal statements of reasons: both, in fact, provide incomplete arguments.

  In Reasoning, Logic Is a Heuristic Tool

  Syllogisms are not better arguments for inquisitive or argumentative reasoning. They are an altogether different kind of thing.7 Syllogisms (and deductions generally) are abstract formal or semiformal structures that make explicit a relationship of logical consequence between premises and conclusion. They may be used for a variety of purposes, but in themselves, they don’t do anything. The arguments used in reasoning, on the other hand, are not defined by their structure, which is quite variable, but by what they do, namely, provide reasoners with reasons to come to some conclusion.

  It is a commonplace that merely recognizing a syllogism as valid is not a reason to accept its conclusion. We have shown, moreover, why recognizing a syllogism as sound isn’t a sufficient reason to accept its conclusion either. Only if you have independent reasons to accept its premises may a sound syllogism give you a reason to accept its conclusion. What the syllogism does, in such a case, is help you see how the reasons in favor of the premises are also reasons in favor of the conclusion.

  What if you take a given syllogism to be sound and you do have good noncircular reasons to accept the premises? Shouldn’t you, in this case, accept the conclusion? The answer is again no. What you have now is a reason either to accept the conclusion or to change your mind about at least one of the premises. This is far from being a mere theoretical possibility or a rarity. Actually, a common use of syllogisms in reasoning is to bring people to revise their beliefs by showing them that these beliefs entail consequences that they have strong independent reasons to reject.

  A reductio ad absurdum, as this form of argumentation is called, consists in arguing against a claim by showing that it leads to an absurdity, or at least to a manifest falsehood.8 Suppose that Watson answered Holmes’s apparent demonstration that the gardener was the thief by informing him, “My dear Holmes, your syllogism is, as usual, impeccable but your conclusion cannot be true: the gardener had a heart attack and died the day before the diamond was stolen; I happen to be the doctor who signed the death certificate!” Watson’s testimony would override the words of the chief of police. The very logicality of the syllogism would then force Holmes to reject at least one of its two premises: perhaps the thief was neither the butler nor the gardener but someone else, or else the thief must have been the butler after all.

  Most ordinary inquiries and arguments are about empirical facts. They involve premises that, even when we accept them as true, are less than certain and admit of exceptions. A conclusion derived from such premises inherits their precariousness. A syllogism with premises that are not strictly true is not a strict proof. As a result, having a good or even a compelling reason to reject the conclusion of a syllogism should cause one to reconsider the premises—to reconsider them, yes, but not necessarily to reject them completely. What may happen rather is that a premise, rather than being simply rejected, is recognized to have exceptions.

  To illustrate, we adapt the case of Mary having an ess
ay to write (which Ruth Byrne used to argue that modus ponens deductions can be “suppressed,” as we saw in Chapter 1).

  Tang and Julia are Mary’s flat mates. They wonder whether she will be back in time for dinner:

  Tang: Well, if Mary has an essay to write, she stays late in the library.

  Julia: Actually, she does have an essay to write. Let’s not wait for her!

  So they prepare the dinner, set the table, and open the wine, and then, just as they are about to sit down, Mary arrives.

  Julia: We thought you had an essay to write and you would stay late in the library.

  Mary: I do have an essay to write, and if the library had remained open, I would have stayed there.

  Tang: A glass of wine?

  Tang’s and Julia’s initial statements provided the two premises of a conditional syllogism, the conclusion of which was that Mary would stay late in the library (and hence not be back in time for dinner). They both initially accepted this conclusion but then, obviously, had to reject it when Mary appeared. Mary’s explanation, however, showed that their premises had been credible, and their reasoning sensible; the problem was just that the circumstances were not quite normal.

  A statement like Tang’s, “If Mary has an essay to write, she stays late in the library,” was not intended or understood to express a necessary truth or an undisputable empirical fact. Like most such statements in ordinary life, it expressed high probability in normal conditions—but then, conditions are not always normal. Tang had no need to qualify his statement by saying something like “probably” or “in normal conditions”; this is how Julia would have understood it anyhow. Mary’s unexpected return shows that the two premises of the syllogism were not a sufficient condition to accept its conclusion—not because one of them was false, but because one of them admitted of exceptions, as do most of our ordinary life generalizations.

  So, it turns out, reasons to reject the conclusion of a syllogism do not even force you to reject any of its premise; they might just make you more aware of the in-normal-conditions (also called “ceteris paribus”) character of at least one of the premises.

  How to account for all this? One might deny that “if” and other connectives such as “and” and “or” have the logical sense classically attributed to them. Perhaps their sense is based on a nonmonotonic logic; perhaps it is probabilistic. These are semantic solutions: they consist in revising our understanding of the sense of words. There is, however, another way to go. The philosopher Paul Grice argued for an alternative, pragmatic solution that would explain what is happening with logical connectives (and, actually, with words and utterances in general) by focusing less on what words mean and more on what speakers mean when they use these words. He thought that the classical semantics of logical connectives could be preserved and that apparent counterexamples could be explained in pragmatic terms. (Of course, the semantic and the pragmatic approaches are not incompatible; on the contrary, in a full account, they should be integrated).9

  Here we make a brief remark on the pragmatics of connectives and of syllogisms generally. Grice’s insights have been developed in modern pragmatics and in particular in relevance theory. A basic idea of relevance theory is that the linguistic sense of words and sentences is used not to encode what the speaker means but merely to indicate it—indicate it in a precise way but with room for interpretation.

  A tourist asks a Parisian a question:

  Tourist: How far is the Eiffel Tower?

  Parisian: It is near.

  In the Parisian’s answer, the word “near” may convey “within a short walking distance” if the tourist who is asking is on foot, and “within short driving distance” if the tourist is in a car. The word “near,” of course, has a linguistic sense, but this sense is not identical to the meaning the speaker intends to convey; rather, this sense makes it possible to infer what the speaker means, given the context.

  A word such as “near” has a vague sense that must be made more precise in context. But what about words, such as “straight,” that have a precise sense? These too serve as a starting point for inferring the speaker’s meaning:

  Tourist (standing in front of the American Church on the Quai d’Orsay): What is the way to the Eiffel Tower?

  Parisian: Keep walking straight ahead. You can’t miss it.

  Actually the Quai d’Orsay is not a straight street. It follows the curves of the river Seine. Were the tourist to follow the advice literally and to keep walking straight ahead, she would end up in the river. In the context, however, “straight” conveys that she should stay on the same street, even if this makes for a curved rather than a straight trajectory. Here, the word “straight” is used loosely. So words can be used to indicate a meaning that is narrower or looser than the sense linguistically encoded.10

  Logical connectives (as well as quantifiers and modals) behave like ordinary words. They don’t encode the communicator’s intended meaning but merely indicate it. Take the case of “or.” The sense of “or” is such that a statement of the form “P or Q” is true if one of the two disjuncts (P, Q) is true. So, for instance, if the gardener stole the diamond, then Holmes speaks truly when he says, “Either the butler stole the diamond or the gardener did.” But, as we pointed out, Holmes would be typically understood to mean not only what his utterance literally and explicitly means but also implicitly that he has some reasons to assert the disjunction other than just knowing that one of the disjuncts (that the gardener stole the diamond, in this case) is true. Typically, a “P or Q” statement conveys a greater confidence in the disjunction itself than in each of the disjuncts. Thus, in most ordinary contexts, the word “or” conveys more than the logical sense it encodes.

  “Or” can also be used to convey less than its logical sense. Imagine the following dialogue:

  Police chief: Either the butler stole the diamond or the gardener did.

  Holmes: Are we sure? Either the butler stole the diamond or the gardener did, or some other member of the household did, or another inhabitant of the village, or of the county, or of the country.

  If it turned out that the thief wasn’t even an inhabitant of the country but just a visitor from abroad, it wouldn’t make much sense to say that Holmes had been wrong. He is clearly using a multiple disjunction (“… or … or … or …”) to express a kind of implicit meaning that utterances with “or” typically convey: that each of the individual propositions connected by “or” is in doubt, and he is doing so without committing to the truth of the whole disjunction itself. He is, in other terms, expressing both more and less than the literal sense of his utterance.

  Other logical connectives such as “and” and “if” (as well as quantifiers such as “some” or “all”) can be used to convey not (or not just) their literal meaning but some meaning inferred in context. For instance, it is well known that an “If P, then Q” statement can be intended and understood not only to convey that P is a sufficient condition for Q (which corresponds to the literal sense of “if”) but also to convey that P is a necessary and sufficient condition for Q (corresponding to “if and only if”) or that P is a necessary condition for Q (corresponding to “only if”). When interlocutors use “if” in such nonliteral ways, they are not violating any rule of logic or of semantics. They are just making a normal use of language. Logical connectives, it turns out, can be used in the same way as discourse markers such as “therefore” and “but” to suggest implications that should be derived in the context even though they are not entailed by the literal meaning of the utterance.

  It might have been tempting to view verbal expressions of logical relationships as similar to verbal expression of arithmetic relationships (as in “A hundred and thirty-five euros divided by five equals twenty-seven euros”). Whether they are done with written digits and special symbols or with words, arithmetic operations obey strict rules of construction and interpretation. Even when they are performed verbally, arithmetic operations are not interpreted on
the basis of pragmatic consideration; number words and words such as “divided” and “equal” are used literally.

  Unlike verbal arithmetic, which uses words to pursue its own business according to its own rules, argumentation is not logical business borrowing verbal tools; it fits seamlessly in the fabric of ordinary verbal exchanges. In no way does it depart from usual expressive and interpretive linguistic practices.

  Statements with logical connectives (or other logical devices), and even sequences of such statements that more or less correspond to syllogisms, are just part of normal language use. They are used by speakers to convey a meaning that cannot be just decoded but that is intended to be pragmatically interpreted. Not only the words used but also the force with which premises and conclusions are being put forward are open to interpretation. They may be intended as categorical or as tentative assertions, hedged by an implicit “in normal conditions.”

  When you argue, you do not stop using language in the normal way, nor does your audience refrain from interpreting your statements using the same pragmatic capacities they use all the time. In argumentation, ordinary forms of expression and interpretation are not overridden by alleged “rules of reasoning” that might be compared to rules of arithmetic. Rules of arithmetic are taught and are not contested. There is no agreement, on the other hand, on the content and very existence of rules of reasoning. What is sometimes taught as rules of reasoning is either elementary logic or questionable advice for would-be good thinking or good argumentation (such as lists of fallacies to avoid, which are themselves fallacious).11

  We have been focusing on argumentation, but what about reasoning done “in one’s head”? Such individual reasoning, we would argue, is a normal use of silent inner speech.12 The pragmatics of inner speech have not been properly studied. Given, however, that much inner speech rehearses or anticipates conversations with others, the pragmatics involved are probably not that different from the pragmatics of public speech. When we speak to ourselves, we use words loosely or metaphorically as often as we do in public speech. Our assertions are just as likely to be hedged or qualified with an implicit “probably” or “in normal conditions.” There is no reason to assume that when we reason in our head, we follow logical rules that we typically ignore in public argumentation.