Existential Assumptions for Aristotelian Logic

Abstract
This paper addresses the question of what existential assumptions are needed for the Aristotelian interpretation of the relationships between the four categorical propositions. The particular relationships in question are those unique to the Aristotelian logic, namely, contrariety, subcontrariety, subaltemation, conversion by limitation, and contraposition by limitation. The views of several recent authors of logic textbooks are surveyed. While most construe the Aristotelian logic as capable of being preserved by assuming that the subject class has a member, Irving Copi construes that logic as requiring that four assumptions about class membership be made. These are that the subject, predicate, complement of subject, and complement of predicate classes all have members. It is argued that only three assumptions about class membership are needed, viz., that subject, predicate, and complement of predicate classes have members
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    K. R. Popper (1946). Logic Without Assumptions. Proceedings of the Aristotelian Society 47:251 - 292.
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