Thinking and Reasoning

Transcription

1 Syllogistic Reasoning Thinking and Reasoning Syllogistic Reasoning Erol ÖZÇELİK The other key type of deductive reasoning is syllogistic reasoning, which is based on the use of syllogisms. Syllogisms are deductive arguments that involve drawing conclusions from two premises (Maxwell, 2005; Rips, 1994, 1999). All syllogisms comprise a major premise, a minor premise, and a conclusion. Major premise: All humans are mortal. Minor premise: All Greeks are humans. Conclusion: All Greeks are mortal. Four kinds of premises Atmosphere bias theory (Begg & Denny, 1969; Woodworth & Sells, 1935) All humans are mortal. No humans are perfect. Some humans are healthy. Some humans are healthy. Universal affirmative Universal negative Particular affirmative Particular negative 1. If there is at least one negative in the premises, people will prefer a negative solution. 2. If there is at least one particular in the premises, people will prefer a particular solution. For example, if one of the premises is No pilots are children, people will prefer a solution that has the word no in it. Nonetheless, the theory does not account very well for large numbers of responses 1

2 Research findings on syllogistic reasoning In general, people tend to be slower and make more errors when one or more premises are quantified by some or when one or more premises are negative. A syllogism presented in the order A-B, B-C (for example, Some red books are astronomy books. All astronomy books are large. ) is much easier to work with than one presented in the order or B-A, C-B (Johnson-Laird, 1975). A mental model is an internal representation of information that corresponds analogously with whatever is being represented (see Johnson-Laird, 1983) People reason by constructing models Conclusions drawn by inspecting models An attempt is made to construct alternative models that will falsify the conclusion. In other words, there is a search for counterexamples to the conclusion. If no alternative models refute, draw inference as valid conclusion Consider these premises: All the squares are striped. Some of the striped objects have bold borders. When the participant is asked to judge the following conclusion, Some of the squares have bold borders. The participant inspects their mental model and sees that, indeed, the conclusion is true in that model. Consider these premises: Some of the scientists are parents. All of the parents are drivers. When the participant is asked to judge the following conclusion, Some of the scientists are drivers. 2

3 Premises The lamp is on the right of the pad. The book is on the left of the pad. The clock is in front of the book. The vase is in front of the lamp. Conclusion The clock is to the left of the vase. Mental models book pad lamp clock vase The construction of mental models involves the limited processing resources of working memory The greater the number of models needed in reasoning through the problem, the more likely errors are to occur ( Johnson- Laird, Byrne, & Tabossi, 1989; Johnson-Laird & Steedman, 1978). People make errors in reasoning because they overlook some of the ways in which the premises might be true. For example, a participant imagines Figure 10.3a as a realization of the premises and overlooks the possibility of Figure 10.3b. The principle of truth Application in real life Individuals minimise the load on working memory by tending to construct mental models that represent explicitly only what is true, and not what is false. A problem in the Chernobyl disaster was that, for several hours, engineers failed to consider the possibility that the reactor was no longer intact 3

4 Belief bias (Evans et al., 1983) Belief bias All democrats support free speach All dictators are not democrats Therefore, all dictators donot support free speech Invalid, but believable Tendency to endorse arguments whose conclusions you believe, regardless of whether they are valid or not. Making illogical (invalid) conclusions that conform with prior beliefs. Application in real life People can easily apply modus ponens arguments, but not modus tollens arguments. Many people do not recognize the logical fallacies of denying the antecedent or affirming the consequent, at least as these fallacies are applied to abstract reasoning problems (Braine & O Brien, 1991; O Brien, 2004; Rips, 1988,1994). Application in real life: Informal syllogistic reasoning Susan: We are planning to go out tonight to a new club on the river. Would you like to go with us? Steve: I ve been to a couple of those clubs before, and I didn t like them. They were noisy, hot, and expensive. All those clubs on the river are wastes of money. If I think a place is a waste of money, I won t go to it. Will Steve go to the new club? 4

5 Application in real life: Informal syllogistic reasoning If I had mozzarella cheese, it would be in the refrigerator. There is no mozzarella cheese in the refrigerator. Therefore, I have no mozzarella cheese ). Modus Tollens If P, then Q Not Q Not P Dual-Process Theories of Reasoning There are two systems involved in reasoning, which means that there is more than one way to respond to a reasoning problem. Mistakes can occur if output from the wrong system is used as the basis for responding. Any task that demands logical thinking activates a fast intuitive system which relies on general heuristics, including taking into account context and similarity to previous problems (System 1); and a slower, more analytical system that is sensitive to rules (System 2). System 1 makes quick judgments based on a relatively superficial analysis of the situation, so it does not carry out precise and detailed reasoning processes. System 2 works more slowly but more precisely, using explicit reasoning processes to work through a problem on a step-by-step basis. 5