by Dan Sperber
Couldn’t all the evidence showing that ordinary reasoning isn’t governed by the rules of classical logic suggest that it is governed by another kind of logic or by a probabilistic system of inference? Classical deductive logic is “monotonic.” This means that if some conclusion logically follows from some initial set of premises, it also follows from any larger set of premises that includes the initial set. As the example of Mary having an essay to write well illustrates, ordinary human reasoning is not monotonic. Not only in daily life but also in scientific, technical, medical, or legal reasoning, conclusions are typically tentative. They may be revised or retracted in the light of new considerations (such as Mary showing up in time for dinner after all). In fact, monotonic inference is, at best, of very limited use for a real-life cognitive system.
In early experimental psychology of reasoning, the nonmonotonic character of ordinary reasoning had been largely ignored or idealized away. In many recent approaches to reasoning, on the contrary, it has been given a central role. Some scholars, such as the cognitive scientist Keith Stenning and the logician Michiel van Lambalgen, aim to replace classical logic with a “nonmonotonic logic” that would provide better insight into the way people actually reason. Others, such as psychologists Mike Oaksford and Nick Chater, argue that reasoning is best viewed not as a logical but as a probabilistic—and more specifically Bayesian—form of thinking.13
The project of replacing standard logic with nonmonotonic logic or of replacing logic altogether with probabilities shares a basic presupposition with the traditional approach: that the study of inference must be based on a general and formal understanding of norms of good inference. We are not convinced. We have argued for an evolutionary and modularist view of inferential processes. Every inferential module aims at providing a specific kind of cognitive benefit, and at doing so in a cost-effective way. In this perspective, investigating a given module is a matter of relating its particular procedures to its particular function. The function of the reason module, in particular, is much more specific than that of optimizing knowledge and decision making in general. Investigating general norms of inference, while interesting from a philosophical or from a machine intelligence point of view, may not tell us that much about any specific inference module. It may tell us little, in particular, about the reason module (just as a general theory of locomotion would be of limited use in understanding how bats fly or snakes crawl).
While we doubt that recent nonmonotonic or probabilistic approaches provide the key to understanding reasoning proper, we of course agree with the critics of classical logic that it fails to provide a plausible norm for human inference. Shouldn’t we then also agree that classical logic is altogether irrelevant to the study of reasoning? Well, no. Let us venture a limited defense of classical logic, one that defenders of classical logic may not be too happy about. Logic can be used not just as a norm or as a procedure but also as a heuristic tool that clarifies questions and suggests answers. This, we claim, is a main role that logic plays in reasoning. Of course, this goes against the standard view that the function of logic is precisely to overcome the limitations of heuristic thinking.
If syllogisms can be interpreted with some freedom and according to the context, if, even when they are logically sound, they don’t necessarily compel rational reasoners to accept their conclusion, what good do they do? What is the point of using them at all? The answer we want to suggest is that they often highlight reasons to accept a conclusion that is not immediately intuitive or to reject a conclusion that is. The very schematism of syllogisms (and deductive relationships generally) tends to exaggerate the degree of logical dependence among our assumptions. In particular, it dramatizes mere incoherencies (where two or more ideas might each give reasons to reject the others) as straight inconsistencies or logical contradictions. Just as exaggerating contours in a picture helps recognition and just as leaving out details in a narrative helps one follow the story, leaving out hedges and ignoring exceptions help focus on reasons that may lead to adopting or rejecting a conclusion. Incoherencies are often hard to detect and to reflect upon. Dressing them up as logical inconsistencies makes them salient targets for the reason module.14
Reasoning itself, as we have described it, involves higher-order intuitions about how lower-order intuitions may support some conclusion. True, in principle, the higher-order intuitions might be just about logically relevant properties of reasons and conclusions and might ignore other aspects of their content, but why should they be? This, anyhow, is not what happens. When reasoning about a given issue, higher-order intuitions are about various properties of lower-order intuitions, whether “logical” or not, that are relevant to their value as reasons. Higher-order intuitions in reasoning are metacognitive rather than just “metalogical.” Reasoning is based on rich and varied intuitions about intuitions.
Take the kind of reasoning that would classically be represented by means of a disjunctive syllogism with a main premise of the form “P or Q.” Depending, so to speak, on the P and the Q involved—depending, that is, on content properties that from a standard logicist point of view shouldn’t be taken into account—higher-order intuitions may be developed in different directions.
You are reasoning about the location of a book you need and have the intuition that the book must be either in the study or in the living room. You have been searching for it in the study, but so far without success. You decide to look for it in the living room. Of course, if asked to explain why you are now moving to the living room, you might articulate your answer in syllogistic form: “I thought that the book is either in the study or in the living room. It is not in the study; hence it must be in the living room.” This would make it sound as if all that was involved was a bit of logic. In fact, your reasoning is more attuned to the particulars of the case. In your mind, you are not ruling out the possibility that you might have missed the book in the study; it is just that the more you looked and failed to find it, the more this became an intuitive reason to conclude that it must be in the living room (or else that you were mistaken in your initial intuition that it had to be in one of these two rooms). The way your reasoning proceeds is sensitive to the fact that a book cannot be in the two rooms at the same time, to the fact that in both rooms there is so much clutter that you might miss it, and to the fact that your initial intuition about the possible location of the book is based on less-than-certain memory. Even when you express it as a syllogism, you expect your audience to take this as just a schematic rendering of your thinking and to use their own richer intuitions to understand and evaluate your reasons.
Take now a different example, where the schematism is the same but the relevant intuitions quite different. Seeing Molly frown, you intuit that she must be upset about something that occurred yesterday or worried about something that might occur. Which is it? She tells you that what occurred yesterday didn’t upset her and you assume that she is sincere. You conclude that she is probably worried. Your initial intuition that Molly might be upset or worried didn’t quite exclude that she might be both. Her sincerely saying that she was not upset didn’t rule out that she might be upset without realizing it. Your intuitive reasons favor, then, a somewhat tentative conclusion: you tend to believe that she is worried rather than upset, or at least more worried than upset. Suppose now that you tell Ramon, a common friend, “Molly is worried!” and he answers, “I think she is just upset about what happened yesterday.” You might then argue in syllogistic form: “Looking at Molly’s face, you cannot tell whether she is upset or worried; she says, however, that she is not upset, not about yesterday, not about anything, and she is manifestly sincere; hence she must be worried.” Again, this would schematize your reasoning, but in so doing, it would present Ramon with a clear challenge and with reasons to revise his beliefs and either to conclude just that Molly is worried or to view things in a more nuanced way, as you do yourself.
In argumentative reasoning in particular, the use of logical relatio
nship plays a heuristic role for one’s audience. It helps challenge them to examine and enrich or revise their beliefs or else to defend them with arguments in their turn. Thanks in part to its logical garb, argumentation, if not always convincing, is at least quite generally challenging.
More generally, however, reasoning is not the use of logic (or of any similar formal system) to derive conclusions. But what, then, is the method of reasoning (if there is one)?
Is There a Method for Reasoning?
Reasoning, as we have described it so far, is rather limited. Humans reason when they are trying to convince others or when others are trying to convince them. Solitary reasoning occurs, it seems, in anticipation or rehashing of discussions with others and perhaps also when one finds oneself holding incompatible ideas and engages in a kind of discussion with oneself. Just as with justifications, the production of arguments proceeds by means of backward inference, from a favored conclusion to reasons that would support it.
Surely, something must be missing in this picture: one is often prompted to reason not by a clash of ideas (with others or within oneself) but by self-addressed questions. Moreover, isn’t the point of such individual, inquisitive reasoning to discover the right answer to a question of one’s own rather than to confirm an already favored conclusion?
There are indeed questions that we can and do approach on our own, without any bias, any hunch in favor of this or that answer, and that we are able to answer by reasoning forward, from premises to conclusion. These, however, tend to be special kinds of questions that are approached with ad hoc reasoning methods rather than with everybody’s everyday reasoning dispositions. The simplest examples of such questions are found in games or puzzles devised to entertain, teach, or test people.
Figure 15. A Sudoku grid.
Take the game of Sudoku (see the example in Figure 15). It is played on a square grid of eighty-one cells, some already containing a digit at the beginning of the game, the others blank.
The task is to find the digit that each of the blank cells should contain, knowing that every digit between 1 and 9 must occur once and only once in every vertical column, every horizontal row, and every three-by-three box indicated by thick lines.
Sudoku players approach the task in an impartial manner. They have no a priori hunch and no stake whatsoever in any particular solution. They know that in every grid there is one and only one right solution for each and every cell, and the players’ goal is to find them all. That much is clear. What is less clear is how the players proceed.
In the simplest cases, it is possible to find the digit that goes in a given cell by means of a simple elimination method until only one possibility is left. Which digit, for instance, should go in the central (grayed in the figure) cell? Looking at the grid, you find reasons to eliminate digit 1 (it already occurs in both the horizontal and the vertical rows that contain the grayed square), digits 2 and 3 (they already occur in the three-by-three box), and so on with all nine digits except 5, which therefore must be the digit that goes in this central cell. Sudoku is a perfect illustration of Sherlock Holmes’s famous maxim, “When you have eliminated the impossible, whatever remains, however improbable, must be the truth” (and of the very limited usefulness of “thinking like Sherlock Holmes”).
The elimination method we just illustrated may help players find a few missing digits, but it will not help them fill the whole grid. To fully solve a Sudoku puzzle, even a simple one, players must use more complex methods. The real challenge for psychologists, however, is not so much to understand how players apply methods they have been taught but how some of them at least discover useful methods on their own.15 After all, the reasoning involved in discovering these methods is much more impressive than that involved in solving a puzzle once you know what method to apply.
How do ordinary Sudoku players discover new methods? We argued that in general, when people reason, they start from an intuitive bias or a hunch in favor of a given conclusion and look for reasons in its favor through backward inference. While this is not the way players use methods to solve a Sudoku puzzle, it is, we suggest, the way players discover these very methods in the first place (when they don’t learn them from others). Merely understanding the rules of Sudoku makes the use of the simple elimination method we have described fairly intuitive. Practice familiarizes players with various subtle regularities of Sudoku grids and provides them with intuitive insight into more and more elaborate methods for which successful applications provide confirming reasons.
The discovery of effective Sudoku methods may well be, then, yet another instance of basic biased reasoning: a search for reasons in favor of an initial intuition—not, in this case, an intuition about the digit that goes in a given cell, but a higher-order intuition about the kind of considerations that may allow the player to narrow down the range of possible digits for every cell. If we are right, this means that people do not use a general higher-order explicit method to discover the various, more specific, explicit methods needed to solve a Sudoku puzzle.
Sudoku puzzles are problems that, with practice and explicit methods, people can solve. Does this generalize to reasoning problems across domains? Can one, with the right method, effectively answer questions of any kind? The short answer is no.
Humans are, it is true, capable of applying methods that they have been taught or that they have discovered on their own to do a great variety of things: solve a Sudoku puzzle, construct a Lego castle, find a word in an alphabetic dictionary, buy from a vending machine, bake a cake, convert Roman into Arabic numerals, learn the basic moves of tap dancing, find solutions to arithmetic or geometric problems, or use databases to answer queries about, say, legal precedents, life expectancy, or the yield of equities. This ability to understand and apply step-by-step methods is a hugely important aspect of human psychology. It plays a major role in the development and transmission of cultural skills, including specialized problem-solving skills. The psychologist Keith Stanovich has argued that the ease with which people acquire and apply such methods (or “mindware”) correlates with individual differences in rationality.16 Still, reasoning doesn’t consist in applying such methods, and in general, it doesn’t need them. Applying these methods is no more quintessential reasoning than military marching is quintessential walking.
Most of the questions that people encounter in their daily life or in the pursuit of their longer-term interests cannot, in any case, be answered by following instructions. Every year, new psychological counseling books offer to instruct you on how to reason better in business, love, friendship, and games, promising to do much better than last year’s books that made the same promises. While they may at times include some sensible advice, all these books come short of delivering on their promises. Achieving such desirable results involves understanding a great many aspects of the world around us, and knowing which to take into account and which to ignore in any given situation; it involves identifying and tackling an endless variety of issues along the way; there are no adequate instructions for reasoning effectively about most real life problems.
What differentiates Sudoku puzzles from most issues on which we might reason is that they are perfectly well-defined. The wider context is not relevant, the evidence is all here, there is one and only one correct solution, and any incorrect solution leads to clear inconsistencies. In psychology, such problems with a definite and recognizable solution and some effective methods to discover it have often been studied under the label of “problem solving” rather than “reasoning.” Solving such problems when the right method is not known typically involves some reasoning but also trial-and-error tinkering and task-specific forms of insight.
Many games and many serious problems in mathematics, logic, programming, or technology involve problem solving in this sense. Scientist, technicians, and laypersons have discovered and developed methods to address problems that can be solved in such a way. Some of these methods have become cultural success stories because of thei
r practical applications, scientific relevance, intellectual elegance, or appeal as leisure activities.
To psychologists of reasoning, problems and puzzles that can be solved in clear and effective ways, especially problems devised on purpose by experimentalists such as the Wason selection task, may seem to provide optimal material for experimental investigation. The temptation has been to assume not only that some of these problems are easy and fun to experiment with but also that they provide crucial evidence on the basic mechanisms of reasoning. Such narrowly circumscribed tasks are, however, special cases among the quite diverse challenges that reasoning helps us confront. Problem solving involves some reasoning, but most reasoning doesn’t even resemble problem solving in the narrow sense in which psychologists use the phrase.
When people reason on moral, social, political, or philosophical questions, they rarely if ever come to universal agreement. They may each think that there is a true answer to these general questions, an answer that every competent reasoner should recognize. They may think that people who disagree with them are, if not in bad faith, then irrational. But how rational is it to think that only you and the people who agree with you are rational? Much more plausible is the conclusion that reasoning, however good, however rational, does not reliably secure convergence of ideas.
