The logic of where and while in the 13th and 14th centuries.

Medieval analyses of molecular propositions include many non-truthfunctional connectives in addition to the standard modern binary connectives (conjunction, disjunction, and conditional). Two types of non-truthfunctional molecular propositions considered by a number of 13th- and 14th-century authors are temporal and local propositions, which combine atomic propositions with ‘while’ and ‘where’. Despite modern interest in the historical roots of temporal and tense logic, medieval analyses of ‘while’ propositions are rarely discussed in modern literature, and analyses of ‘where’ propositions are almost completely overlooked. In this paper we introduce 13th- and 14th-century views on temporal and local propositions, and connect the medieval theories with modern temporal and spatial counterparts

The Logic of Where and While in the 13th and 14th Centuries

Medieval analyses of molecular propositions include many non-truthfunctional connectives in addition to the standard modern binary connectives (conjunction, disjunction, and conditional). Two types of non-truthfunctional molecular propositions considered by a number of 13th- and 14th-century authors are temporal and local propositions, which combine atomic propositions with ‘while’ and ‘where’. Despite modern interest in the historical roots of temporal and tense logic, medieval analyses of ‘while’ propositions are rarely discussed in modern literature, and analyses of ‘where’ propositions are almost completely overlooked. In this paper we introduce 13th- and 14th-century views on temporal and local propositions, and connect the medieval theories with modern temporal and spatial counterparts

Medieval Theories on the Conceivability of the Impossible: a Survey of Impossible Positio in Ars Obligatoria during the 13th-14th Centuries

During the 13th century, several logicians in the Latin medieval tradition showed a special interest in the nature of impossibility, and in the different kinds or ‘degrees’ of impossibility that could be distinguished. This discussion resulted in an analysis of the modal concept with a finesse of grain unprecedented in earlier modal accounts. Of the several divisions of the term ‘impossible’ that were offered, one became particularly relevant in connection with the debate on ars obligatoria and positio impossibilis: the distinction between ‘intelligible’ and ‘unintelligible’ impossibilities. In this article, I consider some 13th-century tracts on obligations that provide an account of the relation betweenimpossibility and intelligibility and discuss the inferential principles that are permissible when we reason from an impossible – but intelligible – premise. I also explore the way in which the 13th-century reflection on this topic survives, in a revised form, in some early 14th-century accounts of positio, namely, those of William of Ockham, Roger Swineshead and Thomas Bradwardine

The case for post-scholasticism as an internal period indicator in Medieval philosophy

This article responds to a critical research challenge in Medieval philosophy scholarship regarding the internal periodisation of the register. By arguing the case for ‘post-scholasticism’ as an internal period indicator (1349–1464, the era between the deaths of William of Ockham and Nicholas of Cusa), defined as ‘the transformation of high scholasticism on the basis of a selective departure thereof’, the article specifies a predisposition in the majority of introductions to and commentaries in Medieval philosophy to proceed straight from 1349 to 1464, understating 115 years of pertinent Medieval philosophical discourse. It is argued that in the modern account of Medieval philosophy, this understatement is manifested in either a predating of Renaissance philosophy to close the gap between 1349 and 1464 as far as possible or in proceeding straight from 1349 to Renaissance philosophy. The article presents five unique philosophical themes from this delicate period, indicating that ‘post-scholasticism’ was indeed a productive period in late Medieval philosophy, which should not be bypassed as an inconsequential entrance to Renaissance philosophy. The period 1349–1464 should accordingly be appreciated for its idiosyncratic contributions to the history of ideas in the late-14th and early-15th centuries, with reference to the political intensification of the via moderna, the pivotal separation of philosophy and theology and the resulting independence of the natural sciences, in res critique of institutions, transforming pragmatics and the rise of philosophical materialism. Contribution: This article contributes to methodological development in Medieval philosophy by responding to a critical research challenge regarding the internal periodisation of the later Middle Ages. Arguing the case for ‘post-scholasticism’ as an internal period indicator (1349 to 1464 in Medieval philosophy, the article presents unique philosophical themes from the period, indicating that it was a productive stage in late Medieval philosophy which should not be bypassed as an inconsequential entrance to Renaissance philosophy

Nominalism and the Via Moderna in Luther's Theological Work

Luther’s adoption of the theology of the via moderna (also called the Nominalists) varied during the late medieval period. This school of thought had developed during the 15th century mainly as a method for interpreting Aristotle and relied on certain 14th-century authorities, such as William of Ockham, John Buridan, Gregory of Rimini, and Peter of Ailly among others. Luther studied philosophy according to the via moderna in Erfurt, where his teachers Jodocus Trutfetter and Bartholomaeus Arnoldi of Usingen represented a position that tolerated the Thomist and Scotist views. The school also featured a specific kind of theology based on its interpretation of Aristotle. Among the most influential theologians in the German via moderna was Gabriel Biel in Tübingen, whose theology was crucial for Luther’s understanding of the school’s positions. Besides Ockham, whom Biel mentioned as his main authority in his Sentences commentary, Biel adopted the positions of several other authors, even outside the common authorities of the via moderna. Other influential theologians and philosophers affiliated with the via moderna were John Mair in Paris and John Eck in Ingolstadt. Later both became adversaries of Luther and the Lutherans, as did Luther’s former teacher Usingen. The University of Wittenberg did not support the via moderna at all. Thomist and Scotist forms of the via antiqua were predominant among its academics, including the later Reformer Andreas Bodenstein of Karlstadt. During his early years as a student in Erfurt, Luther remained largely among the camp of the via moderna. Soon after moving to Wittenberg, Luther developed his criticism of Aristotle and late medieval theology, where his main target was Biel’s theology, especially his doctrine of grace. However, during those years Luther retained much of his early education, including an interpretation of Aristotle in which he adopted several of Ockham’s ideas. During his later years, Luther made use of terminological tools of the via moderna, even when opposing some of its theological positions.Peer reviewe

Obligations, Sophisms and Insolubles

The focus of the paper is a sophism based on the proposition ‘This is Socrates’ found in a short treatise on obligational casus attributed to William Heytesbury. First, the background to the puzzle in Walter Burley’s traditional account of obligations (the responsio antiqua), and the objections and revisions made by Richard Kilvington and Roger Swyneshed, are presented. All six types of obligations described by Burley are outlined, including sit verum, the type used in the sophism. Kilvington and Swyneshed disliked the dynamic nature of the responsio antiqua, and Kilvington proposed a revision to the rules for irrelevant propositions. This allowed him to use a form of reasoning, the “disputational meta-argument”, which is incompatible with Burley’s rules. Heytesbury explicitly rejected Kilvington’s revision and the associated meta-argument. Swyneshed also revised Burley’s account of obligations, formulating the so-called responsio nova, characterised by the apparently surprising thesis that a conjunction can be denied both of whose conjuncts are granted. On closer inspection, however, his account is found to be less radical than first appears

Why Don't Mediaeval Logicians Ever Tell Us What They’re Doing? Or, What Is This, A Conspiracy?

Earlier version of this paper were read at the conference "Looking Back, Looking Forward: Philosophy, Its History and Future: A Conference to Celebrate the Centenary of the Doctoral Program at the University of Toronto," October 25, 1997; to the Medieval Studies Institute (Indiana University), September 27, 1999; and to the Purdue Philosophy Colloquium, November 2, 2000.A talk highlighting four examples of a peculiar problem facing historians of late medieval logic and semantic theory. While we often know a great deal about the mechanics and details of many of the theories during this period, we too often don't know exactly what the theories were about! The talk discusses four examples of this: (a) the theory of "obligationes," (b) "exposition" or "exponibles," (c) "proofs of propositions," and (d) the theory of "supposition.

William of Occam

It is now that the second period of the Middle Ages sets in. It is known as the Age of Revival. The Age of Revival begins with the opening of the eleventh century and ends with the discovery of the New World. During all this time civilization was making slow but sure advances; social order was gradually triumphing over feudal anarchy, and governments were becoming more regular. The last part of the period especially was marked by a great intellectual revival, a movement known as the Renaissance, or ‘New Birth\u27, by improvements, inventions, and discoveries which greatly stirred men\u27s minds and awakened them as from a sleep