Aristotle’s Notion of Deduction

Aristotle’s notion of deduction (syllogism) differs from the conception of logical consequence in classical logic in two essential features, which are required by Aristotle’s definition of syllogism and are incorporated into his formalisation of deduction: in addition to the standard necessary truth-preservation, Aristotle requires relevance of premises for the conclusion and non-repetition of premises in the conclusion. These requirements, together with Aristotle’s conception of simple propositions, lead to the result that valid deductive steps (syllogisms) must have very specific forms, namely the well-known syllogistic shape. All other kinds of deduction lacking this shape, such as “syllogisms based on a hypothesis”, can be considered “syllogisms” only in a relative sense: they are based on an assumption of the existence of genuine syllogistic deductions in the syllogistic shape. Aristotle’s demands should cover all kinds of deduction: all valid deduction must be relevant and non-repetitive. This brings Aristotle’s definition much closer to the intuition associated with the notion of logical consequence.