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How are the figures of syllogisms determined by the position of the middle term?
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Ancient logic
Zeno's paradox, illustrated by Achilles' racing a tortoise.
In logic, the figure of a syllogism is determined by the specific arrangement of the middle term—the term that appears in both premises but not in the conclusion—within those premises. There are four figures, defined as follows:
- First Figure: The middle term is the subject of the major premise and the predicate of the minor premise.1
- Second Figure: The middle term is the predicate of both the major and minor premises.1
- Third Figure: The middle term is the subject of both the major and minor premises.1
- Fourth Figure: The middle term is the predicate of the major premise and the subject of the minor premise.1
While Aristotle explicitly identified the first three figures in his work, the fourth figure was recognized by later logicians as a distinct possibility for the placement of the middle term.2