Thinking outside the laws of thought

In ancient Greece, Aristotle took some important first steps towards systematizing types of arguments where reasoning is perfectly reliable. To give an example: If all philosophers are human and all humans are mortal, then all philosophers are mortal. Who could accept the two premises but not the conclusion? Aristotle's discovery was not that this or that particular argument is valid, but that certain kinds of argument are valid: no matter what words are substituted for 'philosophers', 'human' and 'mortal' in the argument above, we get a valid argument.

Since Aristotle, logicians have identified many more such laws of thought. In addition, the branch of mathematics concerned with probability has extended these laws with rules for how to reason using uncertain premises. One such rule is the conjunction rule which states that a statement of the form 'A and B' cannot be more probable than one of its parts. So, for example, if we know how probable 'It will be sunny', is we can correctly conclude that 'It will be sunny and birds will sing' is not more probable.

Our knowledge of correct reasoning has come a long way since ancient Greece and its fruits can be found throughout the sciences?from mathematics to the empirical sciences. But have logic and statistics also given us the principles whereby we actually reason? Unfortunately not. Research in cognitive psychology during the past thirty years has convincingly demonstrated that humans habitually break even the most basic of the laws of logic and statistics.

Suppose you meet Linda who is 31 years old, outspoken and very bright. As a student, she was deeply concerned with issues of discrimination and social justice. Now, what would you say is more probable, a) that she is a bank teller, or b) that she is a bank-teller who is also a feminist?

If you chose b) you are like most people tested in a classic study by Amos Tversky and Daniel Kahneman in the early 1980s. However, this response?a so-called conjunction fallacy?violates the conjunction rule. Sentence b) cannot be more probable than a). If Linda is a bank teller and a feminist then she is also a bank teller. So however unlikely this may be it cannot be more likely that she is both a bank teller and a feminist.

One response to these results might be to say that even though we violate statistical laws now and again, this does not mean that we are irrational in the strong sense that we violate the laws of logic. Surely we must respect the age-old syllogisms of Aristotle, the bedrock of certain reasoning? Not at all! As recent work by myself and psychologist James Hampton reveals, even these basic, deductive, forms of reasoning are frequently violated.

As illustration, consider something as mundane as sofas. First, do you agree that all sofas have backrests? Now consider uncomfortable handmade sofas. Do you think that all these have backrests as well?

If you answered 'yes' to the first question and 'no' to the second, then you have just violated a logical law very close to one of Aristotle's syllogisms. For if all uncomfortable handmade sofas are sofas?which they surely are?and all sofas have backrests, then all uncomfortable handmade sofas must have backrests too. See how close this example is to the syllogism 'if all philosophers are human and all humans are mortal, then all philosophers are mortal'. So the discovery that people actually often make this fallacy?the inverse conjunction fallacy? suggests that people are irrational in a very fundamental way.

Our research, which builds on an earlier study by Eldar Shafir and colleagues using social categories, found people exhibiting the inverse conjunction fallacy under many different conditions. It doesn't seem to matter whether the subject of discussion is sofas, other household artifacts, animals or fruit, or whether we speak of all sofas, every single sofa, or even 100% of the sofas. Even when the two relevant statements were placed next to each other and people were asked to say which they thought that was more likely, they were still liable to pick the more general statement.

The sofa-example in itself is of little importance, but the underlying irrationality it demonstrates can have disquieting consequences when it appears in our social interactions and behavior elsewhere. It can feed into social or racial prejudice by sustaining false general views in the face of counter examples.

It can be seen, for instance, when people maintain that, say, All Americans are bullies, even though they will deny that All Americans that they know are bullies. Such irrationality might also be undesirable in legislation or policy making since, if left unchecked, decisions about the general suitability of a law or policy for some group of people, might be based solely on the features of the most typical members of that group.

Taking another example, that people often make the inverse conjunction fallacy might have consequences for their perception of brands, since it implies that a brand might remain strong in spite of certain acknowledged exceptions. For instance, someone might maintain, say, that All Nike's products are of high quality even though they also deny that All Nike's basketball products are of high quality.

Potentially these studies will give us fundamental hints as to the processes behind our internal "veto power," and will help us understand the origin of disorders of voluntary action such as obsessive-compulsive disorders or attention deficit-hyperactivity disorder.

Why, then, do we so readily violate the laws of logic and statistics? Our explanation makes use of something called a prototype. A prototype is a mental representation that captures common features of the members of a category together with how important these features are for category membership. For instance, the prototype for 'sofa' might contain the features: is found in living rooms, has a backrest, has cushions etc. The fallacies arise when people base their judgments about truth and probability on such prototypes.

In the conjunction fallacy, people compare the mental representation they have of Linda with the prototypes corresponding to bank tellers and feminist bank tellers. Since there is greater similarity between Linda and the feminist bank teller prototype, people judge that it is more probable that Linda is both a bank teller and a feminist.

In the sofa example, people examine the prototypes corresponding to 'sofa' and 'uncomfortable handmade sofa' and assess the strength within each of the prototypes of the feature 'has a backrest'. According to a model developed by Hampton in the late 1980s, the importance of a feature for a complex concept tends to be the average of its importance for the parts. So, since sofas have backrests but neither uncomfortable things nor handmade things generally do, people will judge it more likely that all sofas have backrests than that all uncomfortable handmade sofas do.

Thus it is due to our reliance on similarity comparisons between prototypes?rather than on the relevant set relations?that we come to stray from the laws of logic and statistics. Since it turns out that we frequently rely on such comparisons it seems fair to conclude that Aristotle's assumption that man is a rational animal was wrong.

Martin Jönsson; Lund University. www.atomiumculture.eu