Logical Consequence

Abstract

This article presents an outline of the history of logical consequence. The first part considers the material transmitted to the Early Middle Ages from Antiquity in order to show how thinking about consequence and, in particular, about the conditional proposition became the central project of early twelfth-century logic. The section part summarizes the extraordinary development by Peter Abelard of a unified relevantistic theory of the conditional and argument on the basis of Boethius's confused accounts of the hypothetical syllogism and topical inference. The third part examines a period of crisis and its resolution late in the twelfth century in favor of the medieval version of the classical account of logical consequence. It also looks at William of Ockham's rejection of this pair of consequence relations in favor of a contrast between what he calls material and formal consequences in which relevance as a semantical requirement no longer has a place.

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