Categorical syllogism

Categorical statements affirm or deny a predicate of all or some members of a subject class. Two premises contain three terms; the middle term occurs in both premises and connects the other two, which appear in the conclusion.

For illustration: all mammals are animals; all whales are mammals; therefore all whales are animals. “Mammals” is the middle term. This biological example illustrates the structure rather than reproducing an example from Aristotle.

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If every B is A and every C is B, every C must be A. Changing the arrangement or the quantity and quality of the premises may remove that necessity; Aristotle examines both successful and unsuccessful patterns.

All whales being animals and all horses being animals does not imply that all horses are whales. A shared broader class alone does not establish the required relationship between the two narrower classes.

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Aristotle treats demonstration as a kind of syllogism rather than identifying every syllogism with scientific proof. The truth, origin and explanatory standing of the premises require further investigation.

Checking a consequence therefore does not replace checking its premises. An inference may preserve a formal connection while starting from error, and a coincidentally true conclusion does not establish a reliable pattern.

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