![]() ![]() Both the development of systematic treatises on consequence and the application of hylomorphic language to consequences first take place in the later middle ages, culminating in the work of the Parisian arts master John Buridan. The accompanying growth of hylomorphism, and particularly mereological hylomorphism, in thinking about consequence. The division of consequences into natural and accidental, and the later replacement of this division by that into formal and material varieties. The development of the concept of consequence, first as a replacement for the framework of Aristotle’s Topics, then as a broader category under which syllogistic, too, was subsumed. This paper contributes to an explanation of how a sea change in logic from the later 13th to the early 14th century relates to certain metaphysical debates during the same period. The result was a thoroughly systematic and extensive treatment of logical theory and logical consequence which repays investigation. Buridan developed a general theory embracing the assertoric syllogism, the modal syllogism and syllogisms with oblique terms. Aristotle’s notion of syllogistic consequence was subsumed under the treatment of formal consequence. In Oxford, in contrast, formal consequence included analytic consequences such as ‘If it’s a man, then it’s an animal’. In Buridan and his followers in Paris, formal consequence was that preserved under uniform substitution. Both schools distinguished formal from material consequence, but in very different ways. By the fourteenth century, two main lines of thought had developed, one at Oxford, the other at Paris. ![]() Among their own theories developed to explain Aristotle’s theories of valid and invalid reasoning was a theory of consequence, of what arguments were valid, and why. The recovery of Aristotle’s logic during the twelfth century was a great stimulus to medieval thinkers. The final chapter concludes: highlighting the characteristic marks of medieval and modern approaches to consequences relative to each other summarizing the various developments that led to the adoption of the account of formal consequence epitomized in Buridan's work and suggesting prospects for recovering the most promising aspects of the medieval treatments of the topic. Chapter five introduces Walter Burley's thinking about consequences, examining: Burley's division and enumeration of consequences his distinction between principal and derivative rules licensing good consequences the relation of the division of consequences into formal and material varieties to Burley's preferred division between natural and accidental consequences the relation Burley's work bears to Buridan, to the Boethian reception of Aristotle's Topics, and to the earliest treatises on consequences. I show that Ockham's divided modalities are not fully assimilable to narrow-scope propositions of classical modal logic formalize Ockham's account in an extension of first-order modal logic with restricted quantification and provide a complete account of relations between two-term divided modal propositions on Ockham's account. ![]() Chapter four examines the account of divided modal consequence in William of Ockham. I show that Pseudo-Scotus' account is dependent on that of Buridan, and therefore most post-date it. Chapter three examines the account of formal consequence in Pseudo-Scotus. The second chapter provides a detailed contrast of Buridan's account of formal consequence with those of Tarski, on the one hand, and later classical logic, on the other. After this, I introduce the account of formal consequence advanced by John Buridan, the medieval predecessor to the semantic account advocated by Tarski and his followers. Chapter one introduces the reader to the dominant philosophical approaches to formal consequence from the turn of the twentieth century to today. In this dissertation, I trace the roots of this concept in medieval logic from Pseudo-Scotus and John Buridan back to the earliest treatises on consequences, and provide translations of the three earliest known treatises on consequences - two anonymous, a third by Walter Burley. The concept of formal consequence is at the heart of logic today, and by extension, plays an important role in such diverse areas as mathematics, computing, philosophy, and linguistics. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |