Syllogistic Reasoning and Categorical Syllogisms: Analytical Essay
In addition to conditional reasoning, 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.
Categorical syllogism comprise of two premises and a conclusion. the premises state something about the category memberships of the terms. In fact, each term represents all, none, or some of the members of a particular class or category.
As with other syllogisms, each premise contains two terms. One of them must be the middle term, common to both premises. The first and the second terms in each premise are linked through the categorical membership of the terms. That is, one term is a member of the class indicated by the other term. However the premises are worded, they state that some (or all or none) of the members of the category of the first term are (or are not) members of the category of the second term. To determine whether the conclusion follows logically from the premises, the reasoner must determine the category memberships of the terms.
Logicians often use circle diagrams to illustrate class membership. The conclusion for this syllogism does in fact follow logically from the premises. This is shown in the circle diagram in this figure by Strenberg & Strenberg (2011):
However, the conclusion is false because the premises are false. For the preceding categorical syllogism, the subject is cognitive psychologists, the middle term is pianists, and the predicate is athletes. In both premises, we asserted that all members of the category of the first term were members of the category of the second term.
There are four kinds of premises (See also in the table below by Sternberg & Sternberg,2011)
In categorical syllogisms, in particular, we cannot draw logically valid conclusions from categorical syllogisms with two particular premises or with two negative premises.
Based on these premises, one cannot conclude even that some cognitive psychologists are smart. The left-handed people who are smart might not be the same left-handed people who are cognitive psychologists. We just don’t know. Consider a negative example:
We cannot conclude anything one way or the other about whether students eat pizza based on these two negative premises. As you may have guessed, people appear to have more difficulty (work more slowly and make more errors) when trying to deduce conclusions based on one or more particular premises or negative premises (Strenberg & Strenberg, 2011).
How do people solve syllogisms? Many theories have been proposed as to how people solve categorical syllogisms. One of the earliest theories was the atmosphere bias (Begg & Denny, 1969; Woodworth & Sells, 1935). There are two basic ideas of this theory:
Other researchers focused attention on the conversion of premises (Chapman & Chapman, 1959). Here, the terms of a given premise are reversed. People sometimes believe that the reversed form of the premise is just as valid as the original form. The idea is that people tend to convert statements like “If A, then B” into “If B, then A.” They do not realize that the statements are not equivalent. These errors are made by children and adults alike (Markovits, 2004).
A more widely accepted theory is based on the notion that people solve syllogisms by using a semantic (meaning-based) process based on mental models (Ball & Quayle, 2009; Espino et al., 2005; Johnson-Laird & Savary, 1999; Johnson-Laird & Steedman, 1978). This view of reasoning as involving semantic processes based on mental models may be contrasted with rule-based (“syntactic”) processes, such as those characterized by formal logic (Strenberg & Strenberg, 2011).
A mental model is an internal representation of information that corresponds analogously with whatever is being represented (see Johnson-Laird, 1983). Some mental models are more likely to lead to a deductively valid conclusion than are others. In particular, some mental models may not be effective in disconfirming an invalid conclusion (Strenberg & Strenberg, 2011).
For example, in the Johnson-Laird study, participants were asked to describe their conclusions and their mental models for the syllogism, “All of the artists are beekeepers. Some of the beekeepers are clever. Are all artists clever?”
One participant said, “I thought of all the little . . . artists in the room and imagined they all had beekeeper’s hats on” (Johnson-Laird & Steedman, 1978, p. 77). The figure below by Strenberg & Strenberg (2011), shows two different mental models for this syllogism.
As the figure shows, the choice of a mental model may affect the reasoner’s ability to reach a valid deductive conclusion. Because some models are better than others for solving some syllogisms, a person is more likely to reach a deductively valid conclusion by using more than one mental model (Strenberg & Strenberg, 2011).
In the figure, the mental model shown in (a) may lead to the deductively invalid conclusion that some artists are clever.
By observing the alternative model in (b), we can see an alternative view of the syllogism. It shows that the conclusion that some artists are clever may not be deduced on the basis of this information alone. Specifically, perhaps the beekeepers who are clever are not the same as the beekeepers who are artists.
The difficulty of many problems of deductive reasoning relates to the number of mental models needed for adequately representing the premises of the deductive argument (Johnson-Laird, Byrne, & Schaeken, 1992). Arguments that entail only one mental model may be solved quickly and accurately.
However, to infer accurate conclusions based on arguments that may be represented by multiple alternative models is much harder (Strenberg & Strenberg, 2011). Such inferences place great demands on working memory (Gilhooly, 2004).
In these cases, the individual must simultaneously hold in working memory each of the various models (Strenberg & Strenberg, 2011). Only in this way can he or she reach or evaluate a conclusion. Thus, limitations of working-memory capacity may underlie at least some of the errors observed in human deductive reasoning (Johnson-Laird, Byrne, & Schaeken, 1992).
In two experiments, the role of working memory was studied in syllogistic reasoning (Gilhooly et al., 1993). In the first, syllogisms were simply presented either orally or visually. Oral presentation used a higher load on working memory because participants had to remember the premises. In the visual presentation condition, participants could just only look at the premises. As predicted, performance was lower in the oral-presentation condition. In a second experiment, participants needed to solve syllogisms while at the same time performing another task. Either the task drew on working-memory resources or it did not. The researchers found that the task that drew on working-memory resources interfere with syllogistic reasoning.
Other factors also may contribute to the ease of forming appropriate mental models. People seem to solve logical problems more accurately and more easily when the terms have high imagery value (Clement & Falmagne, 1986).
In deductive reasoning, as in many other cognitive processes, we engage in many heuristic shortcuts. These shortcuts sometimes lead to inaccurate conclusions. In addition to these shortcuts, we often are influenced by biases that distort the outcomes of our reasoning (Strenberg & Strenberg, 2011).
Heuristics in syllogistic reasoning include overextension errors. In these errors, we overextend the use of strategies that work in some syllogisms to syllogisms in which the strategies fail us (Strenberg & Strenberg, 2011).
For example, although reversals work well with universal negatives, they do not work with other kinds of premises. We also experience foreclosure effects when we fail to consider all the possibilities before reaching a conclusion. In addition, premise-phrasing effects may influence our deductive reasoning (Strenberg & Strenberg, 2011). For example, the sequence of terms or the use of particular qualifiers or negative phrasing. Premise-phrasing effects may lead us to leap to a conclusion without adequately reflecting on the deductive validity of the syllogism.
Biases that affect deductive reasoning generally relate to the content of the premises and the believability of the conclusion. They also reflect the tendency toward confirmation bias. In confirmation bias, we seek confirmation rather than disconfirmation of what we already believe. Suppose the content of the premises and a conclusion seem to be true. In such cases, reasoners tend to believe in the validity of the conclusion, even when the logic is flawed (Evans, Barston, & Pollard, 1983).
Confirmation bias can be detrimental and even dangerous in some circumstances (Strenberg & Strenberg, 2011). For instance, in an emergency room, if a doctor assumes that a patient has condition X, the doctor may interpret the set of symptoms as supporting the diagnosis without fully considering all alternative interpretations (Pines, 2005). This shortcut can result in inappropriate diagnosis and treatment, which can be extremely dangerous.
Other circumstances where the effects of confirmation bias can be observed are in police investigations, paranormal beliefs, and stereotyping behaviour (Ask & Granhag, 2005; Biernat & Ma, 2005; Lawrence & Peters, 2004). To a lesser extent, people also show the opposite tendency to disconfirm the validity of the conclusion when the conclusion or the content of the premises contradicts the reasoner’s existing beliefs (Evans, Barston, & Pollard, 1983; Janis & Frick, 1943).
To enhance our deductive reasoning, we may try to avoid heuristics and biases that distort our reasoning (Strenberg & Strenberg, 2011). We also may engage in practices that facilitate reasoning.
For example, we may take longer to reach or to evaluate conclusions. Effective reasoners also consider more alternative conclusions than do poor reasoners (Galotti, Baron, & Sabini, 1986). In addition, training and practice seem to increase performance on reasoning tasks. The benefits of training tend to be strong when the training relates to pragmatic reasoning schemas (Cheng et al., 1986) or to such fields as law and medicine (Lehman, Lempert, & Nisbett, 1987). The benefits are weaker for abstract logical problems divorced from our everyday life (see Holland et al., 1986; Holyoak & Nisbett, 1988).
One factor that affects syllogistic reasoning is mood or emotions. When people are in a sad mood, they tend to pay more attention to details (Schwarz & Skurnik, 2003). People tend to do better in syllogistic reasoning tasks when they are in a sad mood than when they are in a happy mood (Fiedler, 1988; Melton, 1995). People in a neutral mood tend to show performance in between the two extremes.
From: Cognitive Psychology 6th Edition by Sternberg & Sternberg, 2011
Even without training, you can improve your own deductive reasoning through developing strategies to avoid making errors. For example, an unscrupulous politician might state, “We know that some suspicious-looking people are illegal aliens. We also know that some illegal aliens are terrorists. Therefore, we can be sure that some of those people whom we think are suspicious are terrorists, and that they are out to destroy our country!” The politician’s syllogistic reasoning is wrong. If some A are B and some B are C, it is not necessarily the case that any A are C. This is obvious when you realize that some men are happy people and some happy people are women, but this does not imply that some men are women.
Make sure you are using the proper strategies in solving syllogisms. Remember that reversals only work with universal negatives. Sometimes translating abstract terms to concrete ones (e.g., the letter C to cows) can help. Also, take the time to consider contrary examples and create more mental models. The more mental models you use for a given set of premises, the more confident you can be that if your conclusion is not valid, it will be disconfirmed. Thus, the use of multiple mental models increases the likelihood of avoiding errors.
The use of multiple mental models also helps you to avoid the tendency to engage in confirmation bias. Circle diagrams also can be helpful in solving deductive-reasoning problems.
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