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Rationality and the Wason Selection Task: a Logical Account∗

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Rationality and the Wason Selection Task: a Logical Account∗ Rationality and the Wason Selection Task: A logical Account∗ Abstract The main goal of the paper is to investigate the relation between indicative conditionals and rationality. We will do this by consider- ing several interpretations of a very well-known example of reasoning involving conditionals, that is the Wason selection task, and showing how those interpretations have different bearings on the notion of ra- tionality. In particular, in the first part of the paper, after having briefly presented the selection task, we will take a look at two prag- matic responses to the challenge posed by the task, through Wason’s notion of confirmation bias and Grice’s theory of conversational im- plicature. The second part will introduce Adams’ probabilistic view of indicative conditionals and will give reasons for preferring his account to those aforementioned. The conclusion will evaluate the question of human rationality in the light of the new standpoint acquired. Duca Simone University of Bristol 1 The Question There is a venerable (philosophical) tradition which describes human beings as rational creatures. Famously, Aristotle said “Man is a rational animal”. It may be added that it is so unless we are very tired or angry or drunk, but generally we agree with that idea. However, during the last 40 years, ∗This work benefitted from the support of the European Science Foundation and the Arts and Humanities Research Council. 109 various psychologists have suggested the existence of much deeper problems than the above-mentioned exceptions. They pointed out that, given certain circumstances, people systematically fail to apply simple rules of (classical) logical inference. At this point, we could legitimately ask ourselves a very basic question. Let’s call it The Question: “Are people irrational?”. 2 The Plan In the first part of this paper, we shall present where the psychologists’ worries about human rationality originated from, namely the Wason Selection Task or ‘The Task’, as we shall call it. Actually, we will see that, according to “traditional”cognitive psychology, The Task provided sufficient grounds to give a positive answer to The Question. The second part of the paper will take a broader perspective and will show that, in answering The Question, the interpretation of a certain type of conditional sentence, that is indicative conditionals, is crucially relevant1. Firstly, we will take a brief look at a pragmatic defense of rationality through Wason’s notion of confirmation bias and Grice’s theory of conversational implicature. Secondly, we will introduce Adams’ probabilistic view of indicative conditionals and will give reasons for preferring his account to those aforementioned. The Conclusion will evaluate The Question in the light of the new standpoint acquired. In particular, all interpretations that we will be mentioning favour a negative answer to The Question, but Adams’, in virtue of its higher generality, seems to grasp the very essence of the problem. 1Conditional sentences are traditionally classified in two main groups: indicative and subjunctive conditionals or counterfactuals. An example of the first kind is If Brutus didn’t kill Caesar, then someone else did. The corresponding counterfactual would be If Brutus hadn’t kill Caesar, then someone else would have. In general, indicative conditionals are of the form did/did, while counterfactuals has the had/would have form. Most importantly, we would tend to accept the former example, but not the latter. In fact, we would say that If Brutus hadn’t kill Caesar, then someone else would have is false, because, contrary to what the counterfactual seems to express, there is no necessity in the fact that Caesar was murdered. 110 3 The Task Once a friend of mine came to me and said “I want to challenge your reasoning skills”and produced four cards. Each card had a number on one side and a letter on the other. Two cards were showing their number-side and the other two their letter-side. The cards were showing something like the following string: A, K, 2, 7. The Task was to determine which card/s should one turn in order to verify the following conditional sentence or ‘rule’: If there is vowel on one side of the card, then there is an even number on the other. The Task, which was originally developed by the English psychologist Peter Wason, was meant to show that the majority of people do not reason consistently with the principles of classical logic, therefore the psychologists’ worries. But let us be more precise, starting with spelling out how The Task actually works. As a start, we can formalise the rule in the following straightforward way: p q, where p stands for There is a vowel on one side, q stands for There is an⊃ even number on the other and ‘ ’ represents the material implication of classical logic. In this way, the⊃ string p, p, q, q (where means “not”) would represent the previous arrangement¬ ¬ of the cards.¬ Let’s now take a look at a typical distribution of results regarding The Task (see Figure 1 below). It’s interesting to note that, after 40 years and innumerable iterations of the experiment, the distributions is still found to be the same. Now, anyone who has some acquaintance with propositional logic should be quite startled by the data. In fact, the results show that only a small percentage of the participants choose the right cards, namely p and q. At this point, it should be pointed out that, in the last few decades the¬ study of human reasoning had been dominated by roughly two tendencies. On the one hand, some researchers (such as Wason himself) considered classical logic as the ultimate criterion for rationality, possibly out of ignorance of 111 Card/s selected # Persons (%) p, q 46 p 33 p, q, not-q 7 p, not-q 4 Other combinations 10 Figure 1: A typical outcome regarding the Wason selection task (Wason & Johnson-Laird, 1972) the alternatives; on the other, some others (such as Herbert Simon and Gerd Gigerenzer) were too quick in abandoning logic altogether. Having said this, it seems clear why cognitive psychology tended to interpret the previous data as undermining the idea that humans are rational. Nonetheless, the psychologists’ reaction is justified only in case “If. then. ” is interpreted correctly as the classical Material Implication. Furthermore, classical logic cannot capture the notion of uncertainty, which is an essential feature of reasoning. Two questions may then arise: Does classical logic yield the best criterion of validity of inferential reasoning? What if we interpret “If. then. ” differently? In this paper, we shall deal with the latter question. In particular, we will explore the idea that different interpretations may be able to give a better account of The Task outcome and, consequently, cast some light on the notion of rationality. However, let us conclude our analysis of The Task first. We said that the correct answer to The Task was choosing p and q. Why? The key is given by the classical rule of inference called Contraposition¬ , that is p q ∴ q p and the corresponding axiom (p q) ( q p). Contraposition⊃ ¬ tells⊃¬ us that any argument with p q as⊃ premise≡ ¬ and⊃¬ q p as conclusion is valid. Now, one way to make clear⊃ how this is relevant¬ ⊃ for¬ solving The Task is saying that Material Implication puts a ‘condition’ on its antecedent. This means that, when we consider p q, we should pick the card p, since that’s the relevant one. On the other hand,⊃ if we consider the logically equivalent q p, the antecedent is q; therefore, we should choose the corresponding¬ ⊃¬ card. Doing so, we have¬ enough information on both components of the rule. This reasoning guarantees that, on our particular formulation of The Task, the correct answer consists in choosing A and 7. Another way to put this would be to look at another equivalence. 112 In fact, we know that the material conditional p q is also equivalent to (p q). This means that the conditional is false⊃ when both p and q are the¬ ∧ case.¬ Consequently, we should choose A and 7 to check for the falsity¬ of the rule. So far, so good. It should now be clear how we should reason in order to give the right answer. However, we still have not explained of why the majority of people choose also irrelevant cards, notably q. The next two sections will be partly concerned with this problem. 4 Wason and Grice A first attempt to explain why people generally perform The Task poorly came from Wason himself. Its basic idea is what in psychology and cognitive science is called Confirmation Bias. Roughly, this is a tendency to interpret new information in order to confirm one’s preconceptions, avoiding information and interpretations which contradict prior beliefs. Wason was among the first to investigate this phenomenon. His experiment consisted in presenting his subjects the following numerical series: 2, 4, 6, and telling them that the triple conforms to a particular rule. The participants were then asked to discover the rule by generating their own triples and use the feedback they received from the experimenter. Every time the subject generated a triple, the experimenter would indicate whether the triple conformed to the rule. Finally, once they were sure of the correctness of their hypothesized rule, the participants were asked to announce the rule. The outcome of the experiment showed that, in spite of the fact that the rule was simply “Any ascending sequence”, the subjects often announced rules that were far more complex than the correct one. More interestingly, the subjects seemed to test only “positive” examples, that is triples that subjects believed would conform to their rule and confirm their hypothesis.
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