With William of Ockham and John Buridan, Walter Burley is often listed as one of the most significant logicians of the medieval period. Nevertheless, Burley’s contributions to medieval logic have received notably less attention than those of either Ockham or Buridan. To help rectify this situation, the author here provides a comprehensive examination of Burley’s account of consequences, first recounting Burley’s enumeration, organization, and division of consequences, with particular attention to the shift from natural and accidental to formal and material consequence, and then locating Burley’s contribution to the theory of consequences in the context of fourteenth-century work on the subject, detailing its relation to the earliest treatises on consequences, then to Ockham and Buridan.
William of Ockham and John Buridan provide different accounts of the distinction between formal and material consequences. Some consequences – in particular, enthymemes – that Ockham would classify as formal would be classified as material by Buridan. This paper explains this taxonomical discrepancy. It identifies the root of the discrepancy not in a difference between Ockham’s and Buridan’s notions of propositional hylomorphism but rather in Ockham’s endorsement of relational characterizations of consequences.
This paper summarizes medieval definitions and divisions of consequences and explains the import of the medieval development of the theory of consequence for logic today. It then introduces the various contributions to this special issue of Vivarium on consequences in medieval logic.
This paper offers an analysis of Marsilius of Inghen’s definition of consequentia and of his treatment of logical validity as presented in the first book of his treatise on Consequentiae. Comparing Marsilius of Inghen’s, John Buridan’s, and Albert of Saxony’s theories, the author argues that Marsilius’ account is based on a conception of consequence as a relation of entailment among propositions rather than as a type of conditional sentence and, thus, moves the discussion away from the sentential level. Therefore, Marsilius’ theory represents an original and important contribution to fourteenth-century discussions on consequences.
In medieval theories of consequence, we encounter several criteria of validity. One of these is known as the containment criterion: a consequence is valid when the consequent is contained or understood in the antecedent. The containment criterion was formulated most frequently in the thirteenth and fourteenth centuries, but it can be found in earlier writings as well. In The Tradition of the Topics in the Middle Ages, N.J. Green-Pedersen claimed that this criterion originated with Boethius. In this article, the author shows that a notion of containment is indeed present in Boethius, but is not used to define or describe the relation between antecedent and consequent, i.e., the relation of consequence, as Green-Pedersen asserted. The author then offers two interpretations of the notion of containment that are present in Boethius – a metaphysical and a semantic interpretation – and shows how these relate to the containment criterion.
The history of thinking about consequences in the Middle Ages divides into three periods. During the first of these, from the eleventh to the middle of the twelfth century, and the second, from then until the beginning of the fourteenth century, the notion of natural consequence played a crucial role in logic, metaphysics, and theology. The first part of this paper traces the development of the theory of natural consequence in Abaelard’s work as the conditional of a connexive logic with an equivalent connexive disjunction and the crisis precipitated by the discovery of inconsistency in this system. The second part considers the accounts of natural consequence given in the thirteenth century as a special case of the standard modal definition of consequence, one for which the principle ex impossibili quidlibet does not hold, in logics in which disjunction is understood extensionally.
The problem of universals is one of the main philosophical issues. In this book the author reconstructs the history of the problem considering a selection of medieval representative texts and authors. The source of medieval and postmedieval debate is identified in the Socratic-Platonic survey on the definition of concepts. In the
Categories, Aristotle discusses important topics concerning the relations that exist between logical terms. In particular he establishes a kind of predication principle: categorial terms have a certain predication relation if (and only if) some facts expressed by ordinary sentences hold. The
Categories also because of their particular disciplinary status, halfway between logic and metaphysics, leave a number of questions open. Among these questions, a particularly intriguing one is Porphyry’s riddle: are there genera and species? And, if there are such things, what are they like?