(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)

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.

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)

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.

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 ...

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)

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)

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)

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 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)

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)

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)

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

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)

“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 topics is a theory of argumentation based upon topoi or in Latin loci. The medieval logicians used works by Aristotle and Boethius as their sources for this doctrine, but they developed it in a rather original way. The topics became a higher-level analysis of arguments which are non-valid from a purely formal point of view, but where it is none the less legitimate to infer the conclusion from the premiss. In this connection the topics give rise to a (...) number of discussions about the form and the matter of arguments. Further the topic contribute to the elaboration of the important doctrine of the second intentions, i.e. higher-level concepts of the particular things. In some respects the topics may be said to form a link between formal and informal logic. The topics vanished as a part of logic at the end of the Middle Ages, perhaps because the medieval logicians never got rid of Boethius' claim to have compiled a complete list of the loci, which was an unlucky one. The topics does not have an exact parallel in modern formal logic, but some reflections on non-formal argumentation by recent authors contain certain resemblances to it. (shrink)

This work is essentially a history of the scholastic conception of dialectica from Garlandus Compotista to William Ockham, with an eye to rendering intelligible the puzzling nature of late medieval treatises on logical obligations. Such treatises seem to countenance violations of fundamental and indisputable logical rules, for example, that a disjunction is false if both of its disjuncts are false. In large part to explain this apparent surd development in medieval logic, Eleonore Stump has collected into a (...) single volume twelve separately published essays. Together they form an interesting and convincing argument. (shrink)

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)

This book presents the very latest research on the medieval use of sophisms in logical and grammatical investigation by twenty-three of the leading experts in Europe and beyond. Important insights into the genre of sophismatic treatises have been gained only very recently, and the organisation of the European Symposium on this topic in 1990 led to a concentration of research and evaluation of insights. The papers are divided into three groups: one covers textual study and analysis of the role (...) of sophisms in the medieval curriculum; another deals with grammatical sophisms; and the third covers particular logical sophisms, from 'Man is the worthiest of creatures' and problems in the theory of reference to the Liar paradox and the work of William of Ockham. (shrink)

This paper seeks to articulate the relationship between medieval logic and theology. Reviewing modern scholarship, we find that the purpose of medieval logic, when it is even inquired about, has proven difficult to articulate without reference to theology. This prompts reflection on the metaphors of logic as a “tool” and a “game”: a tool is not merely instrumental, insofar as it can have its own intrinsic goods and can shape and be shaped by that which (...) it serves; likewise a game, with its own intrinsic goods, may yet contribute to extrinsic goods as well. After reviewing some distinctive ways in which theology shaped developments of medieval logic, this paper summarizes key examples from the work of Thomas Aquinas where medieval logic shaped the articulation of, and is therefore crucial to a proper understanding of, theological arguments and claims. The conclusion suggests implications for future philosophical and theological work. (shrink)