The Semantics of Propositions. Truth and Consequences
This chapter shows that the reader is familiar with the basics of the traditional theory of the syllogism and with the notation of standard first-order logic. It focuses on the semantics of propositions has investigated how content in the sense of extensional inclusion is used in the definition of truth-conditions and as a marker for syllogistic entailments. A valid entailment was universally acknowledged to be defined in terms of truth because a valid consequence is one that preserves truth. The distinction between distributive and non-distributive supposition was also held to apply to the predicates of categorical propositions because they too support valid descents and ascents to conjunctions and disjunctions of instances. The Logic’s semantic sense of distribution derives from medieval supposition theory. Supposition became a standard part of the “logic of terms” in the 13th century. Although logicians of the period differed on details, the elements that influence the Logic were widely taught.