Many historical and philosophical studies treat infinity as an exclusively quantitative notion, whose proper domain of application is mathematics and physics. The main aim of this paper is to disentangle, by critically examining, three notions of infinity in the early modern period, and to argue that one—but only one—of them is quantitative. One of these non-quantitative notions concerns being or reality, while the other concerns a particular iterative property of an aggregate. These three notions will emerge through examination of three (...) central figures in the period: Locke, Descartes, and Leibniz. (shrink)

A “conceptual spaces” approach is used to formalize Aristotle’s main intuitions about time and change, and other ideas about temporal points of view. That approach has been used in earlier studies about points of view. Properties of entities are represented by locations in multidimensional conceptual spaces; and concepts of entities are identified with subsets or regions of conceptual spaces. The dimensions of the spaces, called “determinables”, are qualities in a very general sense. A temporal element is introduced by adding a (...) time variable to state functions that map entities into conceptual spaces. That way, states may have some permanency or stability around time instances. Following Aristotle’s intuitions, changes and events will not be necessarily instant phenomena, instead they could be processual and interval dependent. Change is defined relatively to the interval during which the change is taking place. Time intervals themselves are taken to represent points of view. To have a point of view is to look at the world as it is in the selected interval. Many important concepts are relativized to intervals, for instance change, events, identity, ontology, potentiality, etc. The definition of points of view as intervals allows to compare points of view in relation to all these concepts. The conceptual space approach has an immediate semantic and structural character, but it is tempting to develop also logics to describe them. A formal language is introduced to show how this could be done. (shrink)

The studies that make up this book were written and brought together to honor the memory of Jan Pinborg. His unexpected death in 1982 at the age of forty-five shocked and saddened students of medieval philosophy everywhere and left them with a keen sense of disappoint ment. In his fifteen-year career Jan Pinborg had done so much for our field with his more than ninety books, editions, articles, and reviews and had done it all so well that we recognized him (...) as a leader and counted on many more years of his scholarship, his help, and his friendship. To be missed so sorely by his international colleagues in an academic field is a mark of Jan's achievement, but only of one aspect of it, for historians of philosophy are not the only scholars who have reacted in this way to Jan's death. In his decade and a half of intense productivity he also acquired the same sort of special status among historians of linguistics, whose volume of essays in his memory is being G. L. Bursill-Hall almost simultane published under the editorship of ously with this one. Sten Ebbesen, Jan's student, colleague, and successor as Director of the Institute of Medieval Greek and Latin Philology at the University of Copenhagen, has earned the gratitude of all of us by memorializing Jan 1 in various biographical sketches, one of which is accompanied by a 2 complete bibliography of his publications. (shrink)

This book investigates Aristotle’s views on abstraction and explores how he uses it. In this work, the author follows Aristotle in focusing on the scientific detail first and then approaches the metaphysical claims, and so creates a reconstructed theory that explains many puzzles of Aristotle’s thought. Understanding the details of his theory of relations and abstraction further illuminates his theory of universals. Some of the features of Aristotle’s theory of abstraction developed in this book include: abstraction is a relation; perception (...) and knowledge are types of abstraction; the objects generated by abstractions are relata which can serve as subjects in their own right, whereupon they can appear as items in other categories. The author goes on to look at how Aristotle distinguishes the concrete from the abstract paronym, how induction is a type of abstraction which typically moves from the perceived individuals to universals and how Aristotle’s metaphysical vocabulary is "relational.’ Beyond those features, this work also looks at how of universals, accidents, forms, causes and potentialities have being only as abstract aspects of individual substances. An individual substance is identical to its essence; the essence has universal features but is the singularity making the individual substance what it is. These theories are expounded within this book. One main attraction in working out the details of Aristotle’s views on abstraction lies in understanding his metaphysics of universals as abstract objects. This work reclaims past ground as the main philosophical tradition of abstraction has been ignored in recent times. It gives a modern version of the medieval doctrine of the threefold distinction of essence, made famous by the Islamic philosopher, Avicenna. (shrink)

Thomas Bradwardine (d. 1349) was an English philosopher, logician, and theologian of some note; but though recent scholarship has revived an interest in much of his work, little attention has been paid to an early treatise he wrote on the topic of future contingents, entitled De futuris contingentibus. In this thesis I aim to address this deficit, arguing in particular that the treatise makes original use of the divine power distinction to resolve the apparent conflict between God’s foreknowledge on the (...) one hand, and human free will on the other. Bradwardine argues that God’s foreknowledge operates in accord with God’s ordained power, and so relative to God’s ordained power, our actions are indeed compelled; however, because of Bradwardine’s appeal to the distinction in power, he is able to maintain that our actions remain free relative to God’s absolute power, and are thus free, absolutely speaking. This solution is, I argue, unique to Bradwardine, although it seems to be abandoned in his later writing. Bradwardine’s approach to the problem is heavily influenced by three figures in particular — Boethius, Anselm of Canterbury, and John Duns Scotus — each of whose solutions I discuss in some detail. Furthermore, Bradwardine explicitly places his own solution in opposition to that of William Ockham, and so I give substantial attention to examining Ockham’s position. But while I agree with Bradwardine’s assessment that Ockham’s position undermines God’s foreknowledge in ways that should be untenable to someone of 14th-century Christian commitments, I argue that Bradwardine’s solution amounts to an equally untenable determinism. An appendix contains excerpts from my own English translation of the De futuris contingentibus (the first into any modern language), in parallel with the original Latin. (shrink)