Syllogism

Logical and reasoning tasks are typically classified as either deductive or inductive. In deductive reasoning, if the premises are true and a valid rule of inference is used, the conclusion must be true. In inductive reasoning, in contrast, the conclusion can be false even if the premises are true. In many cases, deductive reasoning also involves moving from general principles to specific conclusions, while inductive reasoning involves moving from specific examples to general conclusions.

Cognitive psychologists study deductive reasoning by examining how people reason using syllogisms, logical arguments comprising a major and a minor premise that lead to a conclusion. The premises are assumed to be true; the validity of the conclusion depends upon whether a proper rule of inference is used. The classic example of deduction is:

All men are mortal.

Socrates is a man. Socrates is a mortal.

A more modern example of deduction might be:

All dinosaurs are animals. All animals are in zoos. All dinosaurs are in zoos.

The conclusion is valid but is not true, because one of the premises (all animals are in zoos) is not true. Broadly speaking, truth refers to content (that is, applicability of the conclusion to the real world), and validity refers to form (that is, whether the conclusion is drawn logically). It is thus possible to have a valid argument that is nevertheless untrue. Even if a valid rule of inference is applied and a valid conclusion is drawn, the conclusion may not be true. If a valid conclusion has been drawn from true premises, however, the argument is called "sound."

With inductive reasoning, the validity of the conclusion is less certain. The classic example of induction is:

Every crow I have seen in my life up to this time has been black.

All crows are black.

Other examples of induction include a child who begins to say "goed" (from "go") instead of "went," a detective piecing together evidence at the scene of a crime, and a stock analyst who, after observing that prices have fallen during the past two Septembers, urges clients to sell in August. In all these cases, a conclusion is drawn based on evidence observed prior to the conclusion. There remains the possibility, however, that additional evidence may render the conclusion incorrect. It does not matter how many positive instances (for example, black crows, September stock declines) have been observed; if one counterexample can be found (a white crow, a September stock rise), the conclusion is incorrect.

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