ABSTRACT
An investigation into existence presuppositions and ecthesis, Aristotle’s rule “setting out” the species presumed by universal affirmatives, in the context of Corcoran and Smiley’s natural deduction theory for the syllogictic as generalized by the author. It is shown that ecthesis is a discharge rule that functions in syllogistic semantics in much the way that disjunction-elimination and existential instantiation function in first-order logic, that ecthesis is stronger than the perfect syllogisms and may replace them in the natural deduction system, and that if the requirement that the subject stand for a non-empty set is added to the truth-conditions of affirmative propositions, it need not be required that every term in every interpretation stands for a non-empty set.
