The study of reasoning is very important because it pertains to the heart of the question of whether people think logically and rationally. Do people follow the basic rules of logic when they make inferences? Some researchers highlight the flaws of human reasoning and its irrationality; others stress the enormous flexibility and rationality of human reasoning.
Reasoning can be distinguished in inductive reasoning and deductive reasoning. Inductive reasoning refers to moving from the specific to the general, for example, “You can find the whole of nature within one flower.” Studying the details of a flower can lead to general hypotheses and rules about nature. This is an inductive approach. On the other hand, deductive reasoning means taking a general rule or theory and making inferences about a specific example.
Deductive reasoning has been widely studied using propositions in the form of “If… then” statements and using deductive arguments, also called syllogisms. Let us take the following example for a proposition: “If A, and B, but not C at the same time of E, then F in order to avoid G.” This example is quite abstract. An example of this proposition is, “If you have a car (A) which runs on diesel (B), but not a car which runs on regular gasoline (C), when you want to start the car (E), then you have to wait a bit and let it glow before you start (F), otherwise you damage the motor (G).”
An example for a syllogism is the following: “All cats love sausages. Fluffy is a cat. Therefore, Fluffy loves sausages.” The syllogism consists of two arguments, also called premises, and one conclusion. According to rules of logic, if the premises are true, the conclusion is also true. In our example, the two premises are true; therefore, the conclusion is also true. The presented syllogism only consists of two premises. Syllogisms become difficult, however, when they consist of many premises, when they include the quantifier “some” instead of “all,” or when one premise is negated.
Several theoretical approaches have been developed that try to explain how people deal with syllogisms, that is, what cognitive processes occur when people solve syllogisms. A first approach, according to Sternberg, for example, distinguishes several components: encoding the information presented, mentally representing the meaning of the words in the premises, and controlling one’s own mental processes. A second approach, following Braine, for example, stresses the mental rules or inferences people use to draw conclusions. People might not be aware of these rules. These rules are often implicit like the rules of grammar we use to build sentences. A third approach, developed by Johnson-Laird, understands deductive reasoning as the building of mental models. Similar to understanding language by constructing mental models, people construct mental models when they read premises and draw conclusions. Recent neuropsychological studies of Goel and colleagues find initial support for the mental models approach. However, one might see these approaches not as mutually exclusive or contradictory, but as complementing one another.
In the context of cognitive development, the ability of deductive reasoning starts with the concrete operational stage (labeled by Jean Piaget) at around the age of 6 or 7 years. One prerequisite for deductive reasoning is the ability of the child to build groups and hierarchies of groups on different levels of abstraction, for example, the ability to know and differentiate dogs from cats and birds, and in greater complexity, differentiating German shepherds from poodles and bulldogs. This ability allows children to categorize objects correctly using necessary and sufficient criteria. Children at the preoperational stage of cognitive development, however, classify objects if they merely look similar (e.g., for them a carp and a whale are both fish). Although children in the preoperational stage can classify objects, children in the concrete operational stage are able to do this with more complexity and sophistication.
In the earlier years of childhood, some mistakes of deductive reasoning can be evident and observed. Many children, for example, overgeneralize and label every animal they see as “dog.” The implicit argument might be the following: “All objects that move, that have two eyes, two ears, a nose, and four legs are dogs. This concrete object that moves in the park has two eyes, two ears, a nose, and four legs. Therefore, it is a dog.” However, the object might not be a dog, but a sheep or a cat. In most cases, when the child then says “dog” and it is not a dog, other persons present might correct the child and help the child to differentiate and further refine his or her schemata.
Another error in deductive reasoning is undergeneralization. A child might call only one specific brand of cereal, Cheerios, for instance, as “cereal” and not apply the category “cereal” to all other brands. The implicit argument might be the following: “This food which is round, small, and has a whole in the middle is cereal. This food is flat. Therefore, it is not cereal.” It is common knowledge to most adults that Cheerios and corn flakes are both cereal. However, the child only labels the Cheerios as cereal. In both examples regarding overgeneralization and undergeneralization, the mistake lies in the first premise, that is, that all objects that have two eyes, two ears, a nose, four legs, and move are dogs; and that only Cheerios are cereal. The child is not yet able to distinguish appropriately between groups and is not able to differentiate between levels of abstraction.
One way to help children improve their deductive reasoning is visualization, for example, using Venndiagrams. Venn-diagrams are geometric figures (e.g., circles or rectangles) that show similarities by overlapping figures. When drawing a Venn diagram about dogs and German shepherds, it becomes visually quite obvious that the group of dogs is bigger and more encompassing than the group of German shepherds and that the group of German shepherds is all included and a part of the group of dogs.
The ability of deductive and inductive reasoning acquired during the concrete operational stage is further developed during the stage of formal operational thinking. The abstract quality of formal operational thinking helps adolescents step back from the concrete content and judge the validity of the inferences. Let us consider the following syllogism: “All scorpions are mammals. Mammals are warm blooded. Therefore, scorpions are warm blooded.” One might say this conclusion is true; another one might say this conclusion is not true. And both answers are right! The conclusion is logically correct and valid just following the abstract rules of logic and temporarily assuming the truth of the premises. However, the content of the first premise is untrue. In reality, scorpions are not mammals. Therefore, considering world knowledge about scorpions and mammals, people might think this is nonsense, and therefore might choose the answer “not true.” Similarly, one might abstract from the content of the two previous examples on dogs and cereals and only judge the logical validity of the conclusions.
Premises conflicting with world knowledge are one difficulty in working with syllogisms. We already mentioned that syllogisms with negated premises or abstract formulated syllogisms are more difficult then syllogisms that are not negated and concrete. There are still other factors that influence the accuracy of solving syllogisms. Researchers such as Luria, Scribner, and Cole presented syllogisms to people from different educational backgrounds in different cultures in Africa, America, and Asia. In all cultures, participants who have a formal education, attend school, or have gone to school were able to solve syllogisms better than participants who did not go to school. Participants without formal school education gave correct answers in about 50% of the cases, which is not better than chance. This result does not necessarily mean that people who go to school think more rationally than those who do not go to school. They might just be more familiar with such kinds of problems. Looking not just at right or wrong answers, but at the kinds of answers and justifications of participants without formal school education, shows their way of thinking. In one study, Scribner presented the following syllogism: “All children like candy. Mary is a child. Does Mary like candy?” Someone without formal education might answer: “How would I know if Mary likes candy. I don’t even know her!” or “Who is Mary?” These answers show that participants without formal school education interpret the syllogisms personally, using their world knowledge. They often refused to accept initial premises that contradicted their own experiences and they refused to treat general premises as truly general. It seems like they were not able or willing to stay within the problem boundaries. Interestingly, they could solve syllogisms easily that referred to familiar content.
To summarize, deductive reasoning is the ability to draw specific conclusions from general information. It is a key ability that children start acquiring in the concrete operational stage and that adolescents and adults further develop in the formal operational stage. Prerequisites for deductive reasoning are elaborated mental concepts on different levels of abstraction, as well as certain rules of inference. Research shows that in most cultures, formal schooling as well as familiarity with the material presented facilitate success on formal reasoning tasks.
References:
- Braine, M. D. S. (1978). On the relation between the natural logic of reasoning and standard logic. Psychological Review,85, 1–21.
- Cole, , & Scribner, S. (1974). Culture and thought: Apsychological introduction. New York: Wiley.
- Deductive and inductive arguments. (n.d.). Retrieved from http://webpages.shepherd.edu/maustin/rhetoric/deductiv.htm
- Goel, V., & Dolan, J. (2001). Functional neuroanatomy of three-term relational reasoning. Neuropsychologia, 39,901–909.
- Luria, A. (1976). Cognitive development: Its cultural and social foundation (L. Solotaroff, Trans.). Cambridge, MA: Harvard University Press.
- Johnson-Laird, P. (1983). Mental models. Cambridge, MA: Harvard University
- Sternberg, R. J. (1977). Component processes in analogical reasoning. Psychological Review, 84, 353–378.
- Van Dyke, F. (n.d.). A visual approach to deductive reasoning.Retrieved from http://illuminations.nctm.org/lessonplans/9-12/reasoning/