(Appeared in: J. Bernard-J. Kelemen: Zeichen, Denken, Praxis , Institut fur Sozio-Semiotische Studien: Vienna, 1990, pp. 249-267. To print the published version, click here.).

This book presents novel formalizations of three of the most important medieval logical theories: supposition, consequence and obligations. In an additional fourth part, an in-depth analysis of the concept of formalization is presented - a crucial concept in the current logical panorama, which as such receives surprisingly little attention.Although formalizations of medieval logical theories have been proposed earlier in the literature, the formalizations presented here are all based on innovative vantage points: supposition theories as algorithmic hermeneutics, theories of (...) consequence analyzed with tools borrowed from model-theory and two-dimensional semantics, and obligations as logical games. For this reason, this is perhaps the first time that these medieval logical theories are made fully accessible to the modern philosopher and logician who wishes to obtain a better grasp of them, but who has always been held back by the lack of appropriate ‘translations' into modern terms.Moreover, the book offers a reflection on the very nature of logic, a reflection that is prompted by the comparisons between medieval and modern logic, their similarities and dissimilarities. It is thus a contribution not only to the history of logic, but also to the philosophy of logic, the philosophy of language and semantics.The analysis of medieval logic is also relevant for the modern philosopher and logician in that, being the unifying methodology used across all disciplines at that time, logic really provided unity to science. It thus presents a unified model of scientific investigation, where logic plays the aggregating role. (shrink)

This chapter deals with medieval logic from the time when it first had full resources for systematic creative contributions onward. It focuses on the era when the ancient heritage was available and medieval logic was able to add something substantial to it, even to surpass it in some respects. The chapter explains that characterization such as this cannot be adequately expressed with years or by conventional period denominations; however, it is hoped that the grounds for drawing (...) boundaries will become clearer during the course of the story. (shrink)

PART ONE ELEMENTS OF SCHOLASTIC LOGIC I THE LEGACY OF SCHOLASTIC LOGIC "\ T 7E MAY safely describe the initial scholastic contri- VV bution to logical ...

Terence Parsons presents a new study of the development and continuing value of medieval logic, which expanded Aristotle's basic principles of logic in important ways. Parsons argues that the resulting system is as rich as contemporary first-order symbolic logic.

The overarching aim of this excellent book is to demonstrate the common ground between medieval logic and logical theories of the twentieth century by analyzing some important medieval approaches to three important topics in medieval logic and then showing that in each case, once we determine what is really going on in the medieval theory, it can be formalized in such a way as to show how it resembles one or more developments in twentieth-century (...) logical theory. Analysis in terms of modern logical theory has a lot to offer the study of medieval logical theories, the author claims, and twentieth-century theory can learn some interesting lessons from examining its medieval counterparts. Much of the material in these specific discussions has been presented in earlier versions in the author's published articles. "The Philosophy of Formalization" , however, is new. English translations are used in the text, though the Latin is supplied in the footnotes. (shrink)

This volume, the first dedicated and comprehensive companion to medieval logic, covers both the Latin and the Arabic traditions, and shows that they were in fact sister traditions, which both arose against the background of a Hellenistic heritage and which influenced one another over the centuries. A series of chapters by both established and younger scholars covers the whole period including early and late developments, and offers new insights into this extremely rich period in the history of (...) class='Hi'>logic. The volume is divided into two parts, 'Periods and Traditions' and 'Themes', allowing readers to engage with the subject from both historical and more systematic perspectives. It will be a must-read for students and scholars of medieval philosophy, the history of logic, and the history of ideas. (shrink)

Though Arthur Prior is now best known for his founding of modern temporal logic and hybrid logic, much of his early philosophical career was devoted to history of logic and historical logic. This interest laid the foundations for both of his ground-breaking innovations in the 1950s and 1960s. Because of the important rôle played by Prior's research in ancient and medieval logic in his development of temporal and hybrid logic, any student of Prior, (...) temporal logic, or hybrid logic should be familiar with the medieval logicians and their work. In this article we give an overview of Prior's work in ancient and medieval logic. (shrink)

_ Source: _Volume 56, Issue 3-4, pp 201 - 221 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.

An awareness of the wide scope of medieval logic and the role it played in university education at all levels, together with the way it was used in writings on both science and theology, is crucial for the historian of medieval thought. The growth of this awareness since the mid-twentieth century is shown by the ongoing expansion of editorial work, together with the discussion of the logic actually found in such prominent authors as Aquinas and Scotus. (...) It has gone hand in hand with the use of developments in modern logic. First came the realization that medieval logic extended beyond basic Aristotelian syllogistic, and could be related to modern developments in propositional and quantificational logic in... (shrink)

“The expression ‘free logic’ is an abbreviation for the phrase ‘free of existence assumptions with respect to its terms, general and singular’.”1 Classical quantification theory is not a free logic in this sense, as its standard formulations commonly assume that every singular term in every model is assigned a referent, an element of the universe of discourse. Indeed, since singular terms include not only singular constants, but also variables2, standard quantification theory may be regarded as involving even the (...) assumption of the existence of the values of its variables, in accordance with Quine’s famous dictum: “to be is to be the value of a variable”. (shrink)

The paper discusses in how far medieval logic can appropriately be characterized as a formal science. In this respect, the special mediecal approach to logic as a scientia sermocinalis is examined as well as its main doctrines, namely the theories of supposition and of consequences, and the famous characterization of logic as an ars artium or scientia scientiarum. It is pointed out that medieval logic is not devoted to the setting up of formal systems (...) or any metalogical analysis of formal structures. Logic in the medieval sense of the discipline is necessarily connected with semantical aspects of natural language. Accordingly, we are confronted with a discipline going far beyond the formal structures of discourse. The classification of medieval logic as a formal science is appropriate only under selected perspectives. (shrink)

Introduction Since my work in medieval logic has concentrated on dialectic. I have tried to trace scholastic treatments of dialectic to discussions of it in ...

The very first dedicated, comprehensive companion to medieval logic, covering both the Latin and Arabic sister traditions.

Medieval logicians advanced far beyond the logic of Aristotle, and this book shows how far that advance took them in two central areas. Broadie focuses upon the work of some of the great figures of the fourteenth century, including Walter Burley, William Ockham, John Buridan, Albert of Saxony, and Paul of Venice, and deals with their theories of truth conditions and validity conditions. He reveals how much of what seems characteristically twentieth-century logic was familiar long ago. Broadie (...) has extensively revised his text for this second edition, while preserving the character of the first. There are now fuller accounts of supposition, of intentional contexts, and of medieval syllogistic, and the conclusion has been substantially expanded. (shrink)

One of the founding myths of analytic philosophy is that the predicate logic that was developed in the late 19th century was far more powerful than its predecessors. This ambitious book argues on the contrary that medieval philosophers developed "a system of logic that is similar to the predicate calculus in richness and power" – or that, as Parsons put it in his presidential address to the APA, "the core of medieval logic is as accurate (...) and as expressive as the core of contemporary logic.". (shrink)

While for a long time the study of medieval logic focused on editorial projects and reconstructions of central medieval doctrines such as the theories of signification, supposition, consequences, and obligations, nowadays the spectrum of analysis has broadened and is increasingly informed by modern logical research, whose perspective is then applied to medieval logic. Promoting this tendency, logicians and researchers concerned with semantics in the Gesellschaft für Philosophie des Mittelalters und der Renaissance (GPMR) founded a working (...) group bringing together medieval logic and modern applied logic. The present volume is a seminal document of these interests and activities. It analyzes theories in medieval logic which are useful for solving questions of recent logic and explains crucial parts of medieval logic, philosophy, and theology by applying techniques of present-day logic. (shrink)

Is medieval logic formal? And if yes, in what sense? There are striking affinities between medieval and contemporary theories of language. Authors from the two periods share formal ambitions and maintain complex, and at time uneasy, relations with natural language. However, modern scholars became careful not to overlook the specificities of theories developed more than five hundred years apart, in particular with respect to their 'formal' character. In 1972, Alfonso Maieru noted that the efforts of medieval (...) logicians to identify logical structures in language which are formal enough to become objects of scientific consideration. He also stressed that the language investigated is a historical one, Latin, so that one can legitimately wonder to which extent... one is allowed to speak of 'formal logic' in the middle ages. In other words, medieval logic is characterized by a tension between 'formalist ambitions' and constraints proper to natural language. Today, our knowledge of the field has considerably expanded, calling for a new assessment of the question. (shrink)

"The role of logic in the Middle Ages. Regarding the role of logic within the framework of arts and sciences during the Middle Ages, we have to distinguish two related aspects, one institutional and the other scientific. As to the first aspect, we have to remember that the medieval educational system was based on the seven liberal arts, which were divided into the trivium, i.e., three arts of language, and the quadrivium, i.e., four mathematical arts. The so-called (...) trivial arts were grammar, rhetoric, and logic, and during a period of several centuries virtually every educated person, at least every university graduate, received a training in these matters, especially in logic. Students in the medieval faculty of arts probably spent more time studying logic than any other discipline. This first -- institutional -- aspect concerning the role of logic is explained by the second -- scientific -- aspect. The trivial disciplines provided techniques of analysis and a technical vocabulary that permeate philosophical, scientific and theological writings. Logic, as mentioned before, was referred to and was generally regarded as the art of arts and the science of sciences. The increasing cultural dominance of the universities with their obligatory disputationes and their hierarchy of examinations on the one hand and the outstanding status of logic on the other were corresponding features of the educational world of the 13th century. The core of the logic curriculum from the 12th century onwards was provided by the logical works of Aristotle. These represented the material for the study of types of predication, the analysis of simple propositions or statements (2) and their relations of inference and equivalence, the analysis of modal propositions, of the structure and the types of the syllogism, dialectical topics, fallacies and scientific reasoning as based on the demonstrative syllogism. Medieval logicians, however, realized that there were other, non-Aristotelian, approaches to logical subjects, questions and methods that could be investigated.. (shrink)

Central topics in medieval logic are here treated in a way that is congenial to the modern reader, without compromising historical reliability. The achievements of medieval logic are made available to a wider philosophical public then the medievalists themselves. The three genres of logica moderna arising in a later Middle Ages are covered: obligations, insolubles and consequences - the first time these have been treated in such a unified way. The articles on obligations look at the (...) role of logical consistence in medieval disputation techniques. Those on insolubles concentrate on medieval solutions to the Liar Paradox. There is also a systematic account of how medieval authors described the logical content of an inference, and how they thought that the validity of an inference could be guaranteed. (shrink)