Some of the most influential and best-known experiments in the reasoning literature are on what is known as conditional reasoning, namely, reasoning that employs the“if . . . then . . .” construction. What has emerged from extensive research into conditional reasoning is that people are generally not very adept at mastering conditionals. Most of us are very bad at applying some basic rules of inference governing the conditional. We have particular difficulties with the rule of modus tollens outlined earlier. Moreover, we regularly commit fallacious inferences involving the conditional– fallacies such as the fallacy of affirming the consequent.
To affirm the consequent is to conclude A from a conditional if A then B and its consequent B. We can compare the two forms of inference side by side:
The two forms of inference are superficially very similar– but in the case of affirming the consequent, as is not the case with modus tollens, it is possible to have true premises and a false conclusion. Valid Invalid If A then B If A then B Not B B ___ ___ Not-A A
Exercise 4.6 Give an example that shows affirming the consequent to be fallacious.
The most developed studies of conditional reasoning are inspired by the so-called Wason selection task. Let us start with a typical version of the basic task that inspired the whole research program. Subjects were shown the four cards illustrated inFigure 4.6and told that each card has a letter on one side and a number on the other. Half of each card was obscured and the subjects were asked which cards they would have to turn over to determine whether the following conditional is true or false: If a card has a vowel on one side then it has an even number on the other.
It is obvious that the E card will have to be turned over. Since the card has a vowel on one side, the conditional will certainly be false if it has an odd number on the other side. Most subjects get this correct. It is fairly clear that the second card does not need to be turned over, and relatively few subjects think that it does need to be turned over. The problems arise with the two numbered cards.
Reflection shows (or should show!) that the 4 card does not need to be turned over, because the conditional would not be disconfirmed by finding a consonant on the other side. The conditional is perfectly compatible with there being cards that have a conson- ant on one side and an even number on the other. The 5 card, however, does need to be turned over, because the conditional will have to be rejected if it has a vowel on the other side (this would be a situation in which we have a card with a vowel on one side, but no even number on the other). Unfortunately, very few people see that the 5 card needs to be turned over, while the vast majority of subjects think that the 4 card needs to be turned over. This result is pretty robust, as you will find out if you try it on friends and family.
So what is going wrong here? It could be that the experimental subjects, and indeed the rest of us more generally, are reasoning in perfectly domain-general ways, but simply employing the wrong domain-general inferential rules. On this interpretation, instead of applying the domain-general rule of modus tollens we all have an unfortunate tendency to apply the equally domain-general, but hopelessly unreliable, principle of affirming the consequent.
However, one of the most interesting aspects of the literature spawned by the Wason selection task is the powerful evidence it provides that this may well not be the right way to think about the psychology of reasoning. It turns out that performance on the selection task varies drastically according to how the task is formulated. There are“real- world” ways of framing the selection task on which the degree of error is drastically
E C 4
5
Figure 4.6 A version of the Wason selection task. Subjects are asked which cards they would have to turn over in order to determine whether the following conditional is true or false: If a card has a vowel on one side then it has an even number on the other.
diminished. One striking set of results emerged from a variant of the selection task carried out by Richard Griggs and Jerome Cox. They transformed the selection task from what many would describe as a formal test of conditional reasoning to a problem-solving task of a sort familiar to most of the experimental subjects.
Griggs and Cox preserved the abstract structure of the selection task, asking subjects which cards would have to be turned over in order to verify a conditional. But the conditional was a conditional about drinking age, rather than about vowels and even numbers. Subjects were asked to evaluate the conditional: If a person is drinking beer, then that person must be over 19 years of age(which was, apparently, the law at the time in Florida). They were presented with the cards shown inFigure 4.7and told that the cards show the names of drinks on one side and ages on the other. Before making their choice subjects were told to imagine that they were police officers checking whether any illegal drinking was going on in a bar.
The correct answers (as in the standard version of the selection task we have already considered) are that the BEER card and the 16 card need to be turned over. On this version of the selection task subjects overwhelmingly came up with the correct answers, and relatively few suggested that the third card would need to be turned over. What is particularly interesting is the subsequent discovery that if the story about the police officers is omitted, performance reverts to a level comparable to that on the original selection task.
The finding that performance on the selection task can be improved by framing the task in such a way that what is being checked is a condition that has to do with permissions, entitlements, and/or prohibitions has proved very robust. The fact that we are good at reasoning with so-called deontic conditionals (conditionals that express rules, prohibitions, entitlements, and agreements) has suggested to many theorists that we have a domain-specific competence for reasoning involving deontic conditionals. This competence does not carry over to conditional reasoning in other domains (which explains why we are generally not very good at the abstract form of the selection task).