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Philip Johnson-Laird's How We Reason is a major contribution to the contemporary debate on the nature of reasoning. The author, who is widely known for his pioneering work in the experimental psychology of reasoning, in this book presents the theoretical framework of a life-long research project, which he labels a "model theory of mind". The book is also an application of the model theory to different areas of human reasoning: empirical beliefs, emotions, everyday reasoning, mental diseases, historical cases (such as the disaster of Chernobyl, the creativity of the Wright brothers in the invention of the first airplane, the notorious breaking of the Enigma code). In this review I will discuss the main point of Johnson-Laird's model theory, the idea that reasoning is essentially a process of possibilities.
In a nutshell, the theory says that reasoning involves the ability of thinking possible states of affair and what is common to them (chapter 3, see p. 39 in particular). More exactly, when we reason we represent the set of possible state of affairs of how the world could be. We do so by abstracting from the details of concrete pictures to form iconic representations, i.e. mental models whose architecture contains the common features of the different possible ways things can be arranged and combined. Johnson-Laird suggests us to think of these mental models as those an architect has in mind when he imagines the design of a future building.
Though, reasoning is not only about singular beliefs or propositions, rather it is primarily a dynamic process paradigmatically associated with the capacity of making inferences. Reasoning is "a set of processes that construct and evaluate implications among sets of propositions" (p.3). Inferences come in different guises, mainly - but not exclusively -- as deductions and inductions. Although the standard distinction between these two kinds of inferences is drawn in terms of generality and particularity (deductions are inferences from the general to the particular, inductions do the reverse), Johnson-Laird rejects this characterization to focus on a different aspect. The crucial distinction between deduction and induction is given by their effect on information: "The more possibilities that a proposition eliminates, the more information it contains" (p. 4). If we analyze the deductive process, we realize that the information that we draw in the conclusions already contained (though implicitly) in the premise. For instance, let's say that "a patient has chicken pox or she has measles" and assume in addition that "she doesn't have chicken pox". Therefore, she has measles. Here - the author argues -- "the conclusion adds no information to the premises, but makes explicit a proposition that holds in the one possibility consistent with them". (ibid.; see also chapter 10)
Inductions do the reserve work, afs their conclusions convey more information than those contained in the premises. If I see the well-known 99 white swans in a pond, I will infer that the next one will also be white; but this information goes beyond what was contained in the premise, which after all states that 99 swans swim in the pond. According to Johnson-Laird, inductions "rule out possibilities compatible with their premises", therefore they are ampliative of the information already in hand (ibid.; see also chapter 12). This way of characterizing the distinction between deductive and inductive inferences is not new, but the crucial focus here is not on the ampliative character of inductive knowledge. Rather, the attention is on the mental endowment that allows knowledge to become ampliative, that is in the the ability of reasoning in terms of possible outcomes. Clearly, an inference that does not exclude any of the possibilities given in the premise will restate all or part of the information already there; while an inference that goes beyond the information given in the premises, will exclude one of them (when I say that the next swan will be white, I'm excluding the possibility it could be black).
Rational persons are good reasoners, as they master the combination of all possibilities involved in inferences to hold valid conclusions. This is a difficult task, and often we merely think of being rational, while we are exposed to plain mistakes that strike us only when we become aware of them. The difficulty is inherent in the process of abstracting from the details to retain the common possibilities, since we often omit some of them. A good deal of the book is dedicated to explain how this can happen. At first, Johnson-Laird clears out the field from two competing theories: first, he rejects the thesis that we do not reason at all, but just react to problem-solving situations by giving responses predetermined by our phylogenetic endowments. Second, he criticizes at length the idea that these mistakes are a matter of logical failures. In fact, we cannot identify rational capacities solely with logical competence. Not only reasoners can be rational without any previous logical expertise, but the occurrence of systematic errors in reasoning is also common among logical experts.
Johnson-Laird proposes to concentrate rather on the ability of grasping the force of counterexamples, whose role can be fully appreciated only within the model theory of mind (chapter 16).
Take, for instance, the well-known selection task experiment:
"We have to select evidence to find out whether a general claim about four cards is true or false:
If a card has a 'A' on one side then it has a '2' on this other side.
The four cards are laid out in front of us: A, B, 2, and 3, and we know that each of them has a letter on one side and a number on the other side. Given this task, we tend to select A card and perhaps the 2 card. We fail to see the relevance of the 3 card. But, if this card has a A on its other side, the general claim is false… To anyone who has studied logic, the error of omission in the selection task is puzzling". (pp. 14-15).
The author argues that the mistake is not due to the lack of formal-logical competence, because it suffices to change the content of the experiment leaving the structure intact to notice striking effects on the performance of the subjects involved (p. 15). This does not mean that logic does not have any role in reasoning: we can and should reason out of logic when we can, and we can learn from logic. But, logic lacks the constitutive role in reasoning that logicians and philosophers often attribute to it. Logic cannot be the foundation of a psychology of reasoning.
However, if we lack logic as a constituent of a psychological theory of reasoning, what shall this constituent be? We have remarked above that the model theory of reasoning conceives of models as possibilities and combinations of possibilities. The answer is based on this crucial idea.
To explain this, Johnson-Laird discusses several examples. For brevity, I will concentrate only on cases of deductive conclusions. Here is one:
If the patient has pimple-shaped spots, then she has chicken pox
The patient has pimple-shaped spots.
When we understand the first premise, we realize that is compatible with at least two possibilities. One possibility is that the patient has pimple-shaped spots and chicken pox, and the other possibility is that the patient doesn't have pimple-shaped spots. But, we also grasp that the second premise rules out this latter possibility. Only the first possibility remains, and so it follows that the patient has chicken pox…..We have made a deduction not using the logical form of the premises, but using their contents to imagine possibilities (p. 16; emphasis added).
The crucial aspect of example is that the possibilities that we envisage are mental models that represent possible ways things can be. The best way to picture the content of a mental model about a possible state of affairs is by using Venn diagrams (see chapter 20):
Let 'p' and 'q' stand respectively for 'the patient has pimpled-shaped spots', and 'the patient has chicken pox'. The red area represents the possibilities in which the conditional is true: either the the patient has the spots and she has chicken pox (the intersection in the middle), or just she has chicken pox (the remaining red part). The white area stands for the case the conditional is false (the case when the consequent is false). If we add the second premise, which states that the antecedent is true in this particular inference, we obtain the following diagram:
Here we represent the conclusion of the inference: given that 'p' obtains, 'q' follows. By looking at the Venn's diagram we have an intuitive iconic representation that expresses better than the truth-tables what are the possibilities involved and which of them are excluded as we add more premises. Of course, the more possibilities reasoners have to deal with, the more likely is for them to make mistakes. If we have embedded conditionals (say, conditionals that contain under conditionals) the circles representing the possibilities would grow exponentially, and the common intersections would became smaller. However, this simple diagrammatic representation already highlights two difficulties that experiments have found common in subjects.
First, if people overlook one or more possibilities, their conclusions will correspond to just some of the possibilities compatible with the premises. In our case, people tend to hold the conditional true only in the case where both p and q are true, that is to identify the central intersection in the figure as the only case in which the conditional is true.
Second, notice that the material conditional "if p then q" is equivalent to the disjunction "not-p or q" (the truth-table is identical). When we consider the two possibilities in a disjunction, we find prima facie difficult to grasp what it means. For one thing, the disjunction can be either inclusive or exclusive. In this case it is exclusive, but this conclusion is not immediately clear if we reason in terms of a purely logical notation. When conditionals of this sort appear as premises of inferences such as in Modus Ponens, the blurry nature of the disjunction is often a source of error, and empirical evidence confirm these predictions (see chapter 2, in particular pp. 40-44).
Notwithstanding the efforts of constructing a logic of thought on the basis of purely formal notation, the diagrammatic representation enables us to represent the possible combinations at hand, and to clarify cases of vagueness. Logical notation comes later, when we express those models as propositions.
The book discusses at length these and other puzzles. Whoever is interested in a detailed account of how visual, iconic, and model representations can do a better work than formal rules in explaining reasoning, would find Part III (chapter 10 on If-clauses) and Part VII (where the role of diagrams is discussed) particularly interesting.
Before concluding, I would like to make some brief remarks on this point: for all those who have familiarity with the debate over the normative role of logic, it will not be surprised to hear that logic is not a grammar of the mind. But one can object to the author's position by arguing that the difficulty in understanding the role of logic in reasoning is due to the representationalist framework of the model theory of mind, not to logic itself. Within this framework, the distinction between form and content of a proposition is assumed at the outset. Classical logic relies upon this distinction to study models of inferences whose validity depends only on the form of the inference, not on the content of propositions.
In contrast with this view, one can think of a different kind of inferences, that are valid quite independently of the logical constants that appear therein. For instance, the inference from "London is South of York" to "York is North of London" is valid although no logical vocabulary appears in the inferential step. These are called material inferences, which are valid in virtue of the content of the terms and propositions they contain. This idea, originally due to Wittgenstein and later refined by Wilfrid Sellars, conceives of the form of inferences as the explicit counterpart of particular inferences already taken as valid by a community of speakers. Here the representationalist view is turned upside down and representations are rather explained in terms of the practice of making inference. Surprisingly as it might be, this view meets the desiderata of the model theory: first, it starts out with inferential practices, so it captures the dynamic aspect of reasoning crucial to Johnson-Laird. Second, it takes content as an ingredient of validity. Third, it recognizes a role to counterexamples and underlies the fallibilist conception of rationality defended in the book: inferentialist approaches admit that what was treated as a valid inference in the past can be later discovered unwarranted in the light of new scientific evidence. Surely enough, pre-Galilean scientists believed in the inference from "The Sun revolves around the Earth" to "Earth is at the center of the Solar system", which was later disproved. But, the fact that inferences of this sort are wrong is not an argument against logic as such. Rather it shows that a more critical approach to the given tradition can elicit logical models that explain conceptual change and the complexity of natural language without debunking logic from its role in reasoning.
However, whether or not one is skeptical that cognitive science is able to explain away the logical nature of reasoning, in reading How We Reason readers will remain impressed by the breath and depth of Johnson-Laird's analysis. The empirical evidence that supports his endeavor is convincing, and the clear prose makes this book a guide for students and teachers in any course in epistemology, rationality, and scientific reasoning.
© 2010 Daniele Santoro
Daniele Santoro, Research Fellow, Luiss University - Rome