prosleptic syllogism

logic

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July 13, 2026

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A prosyllogism is a syllogism whose conclusion serves as a premise for a subsequent syllogism. This concept is part of the broader field of logic, which studies the principles of valid reasoning.1

Theophrastus of Eresus, a successor to Aristotle, developed a theory of inferences involving propositions he termed "prosleptic propositions." These propositions were understood to implicitly contain a third, indefinite term. Inferences using these propositions were called prosleptic syllogisms. Theophrastus categorized these into three figures based on the position of this implicit middle term. While some prosleptic propositions are equivalent to categorical propositions, others are not, indicating their unique role in logical reasoning.23

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history of logic
Theophrastus of Eresus
…inferences involving them were termed prosleptic syllogisms. Greek proslepsis can mean “something taken in addition,” and Theophrastus claimed that propositions like these implicitly contain a third, indefinite term, in addition to the two definite terms (“α” and “γ” in the example).
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…inferences involving them were termed prosleptic syllogisms. Greek proslepsis can mean “something taken in addition,” and Theophrastus claimed that propositions like these implicitly contain a third, indefinite term, in addition to the two definite terms (“α” and “γ” in the example).
Read More