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Form of argument that, in its most commonly discussed instances, has two categorical propositions as premises and one categorical proposition as conclusion. An example of a syllogism is the following argument: Every human is mortal (every M is P); every philosopher is human (every S is M); therefore, every philosopher is mortal (every S is P). Such arguments have exactly three terms (human, philosopher, mortal). Here, the argument is composed of three categorical (as opposed to hypothetical) propositions, it is therefore a categorical syllogism. In a categorical syllogism, the term that occurs in both premises but not in the conclusion (human) is the middle term; the predicate term in the conclusion is called the major term, the subject the minor term. The pattern in which the terms S, M, and P (minor, middle, major) are arranged is called the figure of the syllogism. In this example, the syllogism is in the first figure, since the major term appears as predicate in the first premise and the minor term as subject of the second.
This entry comes from Encyclopædia Britannica Concise. For the full entry on syllogism, visit Britannica.com.