Against Logical Form

Psychologica Belgica 2010, 50-3&4, 193-221. DOI: http://dx.doi.org/10.5334/pb-50-3-4-193 Against logical form P.N. Johnson-Laird Princeton University, New Jersey, USA This research was supported in part by a grant from the National Science Foundation SES 0844851 to study deductive and probabilistic reasoning. The author is grateful to Geoffrey Goodwin, Sangeet Khemlani, Niklas Kunze, and Max Lotstein, for their critical readings of an earlier draft, and to Monica Bucciarelli, Ruth Byrne, Vittorio Girotto, Paolo Legrenzi, Juan Madruga, Walter Schaeken, and Walter Schroyens, for help and encouragement over the years. The paper is dedicated to André Vandierendonck, a stalwart investigator of mental models. Abstract An old view in logic going back to Aristotle is that an inference is valid in virtue of its logical form. Many psychologists have adopted the same point of view about human reasoning: the first step is to recover the logical form of an inference, and the second step is to apply rules of inference that match these forms in order to prove that the conclusion follows from the premises. The present paper argues against this idea. The logical form of an inference transcends the grammatical forms of the sentences used to express it, because logical form also depends on context. Context is not readily expressed in additional premises. And the recovery of logical form leads ineluctably to the need for infinitely many axioms to capture the logical properties of relations. An alternative theory is that reasoning depends on mental models, and this theory obviates the need to recover logical form. Introduction Reasoning in daily life depends on the ability to grasp that a set of propositions implies a conclusion. Nearly everyone grasps, for example, that these premises: The government subsidized the bank or the bank went broke. In fact, the bank didn’t go broke. imply that the government subsidized the bank. That is, naïve individuals realize that if the premises are true then the conclusion must be true too. ————— P.N. Johnson-Laird, Professor P.N. Johnson-Laird, Department of Psychology, Princeton University, New Jersey 08540, USA, E-mail: 194 AGAINST LOGICAL FORM The term naïve here refers to individuals who have not explicitly mastered logic; it does not impugn their intelligence. Plenty of intelligent people have never learned logic, and yet they reason well (Stanovich, 1999). However, the claim that naïve individuals can make deductions is controversial, because some logicians and some psychologists argue to the contrary (e.g., Oaksford & Chater, 2007). These arguments, however, make it much harder to understand how human beings were able to devise logic and mathematics if they were incapable of deductive reasoning beforehand. In the mid-1970’s when experimental psychologists began to propose theories about the mental processes of reasoning, they converged on a fundamental idea. Its intellectual god-father was Jean Piaget, and the idea was that naïve individuals construct an unconscious logical calculus that enables them to reason. Piaget used this idea to try to explain how infants developed into adults who could master logic and mathematics (e.g., Inhelder & Piaget, 1958). According to more recent proponents of this idea, this calculus contains formal rules of inference, such as: A or B. Not B. Therefore, A. where the values of the variables A and B can be any propositions whatsoever. The first step in an inference is accordingly to establish the logical form of the premises, and the second step is to match these forms to corresponding formal rules of inference that allow an inference to be made. Further rules may then be applicable until the chain of inferences yields a proof of the required conclusion. For the inference above about the bank, both of these steps are straightforward. The logical form of the premises matches the preceding formal rule. It delivers the conclusion, A, to which the reasoning system restores the rightful contents: The government subsidized the bank The formal hypothesis about the mental processes of reasoning is longstanding, plausible, influential. Nearly all cognitive scientists, including philosophers (e.g., Pollock, 1989), linguists (e.g., Sperber and Wilson, 1986), artificial intelligencers (e.g., Cherniak, 1986), and students of automated theorem-proving (e.g., Bledsoe, 1977; Wos, 1988) concurred with it at first. Likewise, psychologists saw their job as to find out which sort of logic, and which sort of formalization, human reasoners relied on. They made many proposals about these matters (e.g., Osherson, 1974-6; Johnson-Laird, 1975; Braine, 1978; Rips, 1983, 1994; Macnamara, 1986; Braine & O’Brien, 1998). JOHNSON-LAIRD 195 The story of psychological studies of reasoning since that happy time can be construed as a move away from this idea of mental logic. André Vandierendonck has played an important part in this story. He showed how reasoning about spatial and temporal relations depends, not on formal rules, but on mental models (Vandierendonck & De Vooght, 1996), which can be annotated with symbols to represent indeterminacies (e.g., Vandierendonck, Dierckx, & De Vooght, 2004), and which are affected both by the constraints of working memory (e.g., Vandierendonck & De Vooght, 1997; Duyck, Vandierendonck, & De Vooght, 2003) and by reasoners’ strategies (e.g., Dierckx, Vandierendonck, & Pandelaere, 2003). And so my aim in this chapter – as a way of thanking André both for his research and for his kindness to me – is to consider a major weakness in the hypothesis of mental logic, one that has nagged away at me for years. It is the principle that the first step in using mental logic is the recovery of the logical form of the premises. My argument is that logical form, and therefore formal rules of inference, are unlikely to play any significant role in the mental processes underlying reasoning in daily life. There is no reason why they should do so. Logic captures the implications among sentences, usually expressed in a formalized language. In contrast, reasoning is the mental process of drawing conclusions from sets of propositions, usually expressed in natural language. Hence, logic may tell us no more about reasoning than bookkeeping tells us about why people spend their money. Indeed, few logicians these days argue that logic should be a basis for psychological theory (see Harman, 1986). The present article is not a critique of logic. What it does criticize, however, is the doctrine that logic provides the basis for human reasoning. It does not argue that everyday propositions lack a logical form, but merely that the task of recovering it is extraordinarily difficult and probably unnecessary. If this criticism is correct, does it follow that psychologists should dispense with logic? Not at all. There is much that students of reasoning can learn from logic, including which implications among sentences are valid. The m (...truncated)