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How do the premises and conclusion function in an Aristotelian syllogism?
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Ancient logic
Zeno's paradox, illustrated by Achilles' racing a tortoise.
In an Aristotelian syllogism, the premises and conclusion function as a structured deduction where the conclusion follows of necessity from the stated premises. Each component is a categorical proposition consisting of terms that function as subjects or predicates.123
The roles of these terms are defined by their position in the conclusion:
- Major Term: The predicate of the conclusion. The premise containing this term is the major premise.23
- Minor Term: The subject of the conclusion. The premise containing this term is the minor premise.23
- Middle Term: A third term that appears in both premises but is absent from the conclusion. It serves as the link that relates the major and minor terms to one another.23
By relating the major and minor terms to the middle term in the premises, the syllogism establishes a necessary relationship between them in the conclusion. Aristotle identified various figures and moods based on how these terms are arranged, determining which patterns constitute valid logical inferences.2435