We describe the earliest occurrences of the Liar Paradox in the Arabic tradition. e early Mutakallimūn claim the Liar Sentence is both true and false; they also associate the Liar with problems concerning plural subjects, which is somewhat puzzling. Abharī (1200-1265) ascribes an unsatisfiable truth condition to the Liar Sentence—as he puts it, its being true is the conjunction of its being true and false—and so concludes that the sentence is not true. Tūsī (1201-1274) argues that self-referential sentences, like the (...) Liar, are not truth-apt, and defends this claim by appealing to a correspondence theory of truth. Translations of the texts are provided as an appendix. (shrink)

Josse Clichtove represents a turning point in the history of disputation, for he combines one of the earliest accounts of the doctrinal disputation with one of the latest accounts of the obligational disputation. This paper describes the nature and significance of the theories that he offered. Particular attention is paid to the doctrines of truth, necessity and possibility which lie behind his doctrines; and also to the light which his work throws on the aims and nature of an obligational disputation.

HISTORICAL INTRODUCTION Although many of the details of the development of logic in the Middle Ages remain to be filled in, it is well known that between ...

I examine the treatment of metaphor by medieval logicians and how it stemmed from their reception of classical texts in logic, grammar, and rhetoric. I consider the relation of the word 'metaphor' to the notions of translatio and transumptio, and show that it is not always synonymous with these. I also show that in the context of commentaries on the Sophistical Refutations metaphor was subsumed under equivocation. In turn, it was linked with the notion of analogy not so much in (...) the Greek sense of a similarity between two proportions or relations as in the new medieval sense of being said secundum prius et posterius. Whether or not analogy could be reduced to metaphor, or the reverse, depended on the controversial issue of the number of acts of imposition needed to produce an equivocal term. A spectrum of views is canvassed, including those found in the logic commentaries of John Duns Scotus. (shrink)

INTRODUCTION The main purpose of this work is to provide an English translation of and commentary on a recently published Arabic text dealing with conditional propositions and syllogisms. The text is that of Avicenna (Abu 'All ibn Sina, ...

"On Reduplication is a study of the logical properties of reduplicative propositions, that is, of propositions having qualifications, like 'Christ "qua God is a ...

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 ...

Epistemic logic is one of the most exciting areas in medieval philosophy. Neglected almost entirely after the end of the Middle Ages, it has been rediscovered by philosophers of the twentieth century. Epistemic Logic in the Later Middle Ages provides the first comprehensive study of the subject. Ivan Boh explores the contrast between epistemic and alethic conceptions of consequence, the general epistemic rules of consequence, the search for conditions of knowing contingent propositions, the problems of substitutivity in intentional contexts, the (...) considerations of epistemic/doxastic iterated modalities, and the problems of composite and divided senses in authors ranging from Abelard to Frachantian. Boh concludes with a comparison between medieval endeavors and the epistemic logic of our own times. Written in a clear and readable style with minimal symbolic apparatus, this book employs modern symbolism and conceptual frameworks, and complements the studies of the syntacticand semantic dimensions of medieval logic. (shrink)

The notion of 'symbol' in Eriugena's writing is far from clear. It has an ambiguous semantic connection with other terms such as 'signification', 'figure', 'allegory', 'veil', 'agalma', 'form', 'shadow', 'mystery' and so on. This paper aims to explore into the origins of such a semantic ambiguity, already present in the texts of the pseudo-Dionysian corpus which Eriugena translated and commented upon. In the probable Neoplatonic sources of this corpus, the Greek term symbolon shares some aspects of its meaning with other (...) words inherited from the ancient tradition, such as synthēma , eikōn , homoiotēs. Some of them, such as eikōn and homoiotēs, belong to the field of images and are associated with linguistic semantics in the Neoplatonic commentaries not only to Plato but also to Aristotle's logical works. Among the late ancient Neoplatonists, particular attention is paid to Proclus and to his use of the term agalma. In fact, the textual history of this word seems to be a privileged perspective from which to reconstruct the Neoplatonic semantic blending of symbol and image, as well as the main role played by linguistic issues in this conflation. (shrink)

In the history of medieval semantics, supposition theory is important especially in the twelfth and thirteenth centuries. In this theory the emphasis is on the term, whose properties one tries to determine. In the fourteenth century the focus is on the proposition, of which a term having supposition is a part. The idea is to analyse propositions in order to determine their truth (probare). The Speculum puerorum written by Richard Billingham was the standard textbook for this approach. It was very (...) influential in Europe. The theory of the probatio propositionis was meant to solve problems both in (empirically oriented) scientific propositions such as used by the Oxford Calculators, and theological propositions, especially those about the Trinity. The book is original, concise, but not clear in every respect. Studying medieval commentaries may help us to understand Richard's book. In the present paper three commentaries are presented. The commentators discussed problems about the status of Richard's book, and about its doctrine: what is the relation between probatio and truth, what is the relation between probatio and supposition, what exactly are mediate and immediate terms (e.g.is the pronoun 'this' mediate or immediate?). The commentators sometimes criticize Richard. For example, one of them argues, against Billingham, that the verb 'can' ampliates its subject term and is therefore mediate. (shrink)

These are two of only three medieval treatises known to the editors explicitly devoted to discussion of concepts. That is not to deny that other works treat extensively of concepts among other matters.

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)

William of Ockham discussed the fallacy of amphiboly twice in his writings. The first treatment was in his Expositio super libros Elenchorum, where he simply presents Aristotle’s treatment, updates it with some Latin examples, and tells us it is not too important, since we do not often run into cases of ambiguity of thiskind. Later, in his Summa logicae, however, he extends his treatment appreciably. He here includes under ambiguous statements philosophical and theological sentences which are improperly stated. Led by (...) Aristotle, Augustine and Anselm, Ockham finds that in their writings they give us instances of improper statements which need to be restated properly before they can be evaluated as true or false. These leads provide for Ockham a key to unlocking the teaching treasures of the Ancients. (shrink)

This book examines the medieval tradition of Aristotelian logic from two perspectives.

This article is currently available as a free download on ingentaconnect.

Walter Burley (1275-c.1344) and John Wyclif (1328-1384) follow two clearly stated doctrinal options: on the one hand, they are realists and, on the other, they defend a correspondence theory of truth that involves specific correlates for true propositions, in short: truth-makers. Both characteristics are interdependent: such a conception of truth requires a certain kind of ontology. This study shows that a) in their explanation of what it means for a proposition to be true, Burley and Wyclif both develop what we (...) could call a theory of intentionality in order to explain the relation that must obtain between the human mind and the truth-makers, and b) that their explanations reach back to Augustine, more precisely to his theory of ocular vision as exposed in the De trinitate IX as well as to his conception of ideas found in the Quaestio de ideis. (shrink)

"At the end of the fourteenth century there were roughly three categories of work available to those studying logic. The first category is that of commentaries on Aristotle's 'Organon'. The most comprehensive of these focussed either on the books of the Logica Vetus, which included Porphyry's Isagoge along with the Categories and De Interpretatione; or on the books of the Logica Nova, the remaining works of the 'Organon' which had become known to the West only during the twelfth century. In (...) addition there were, of course, numerous commentaries on individual books of the.. (shrink)

"Abelard composed four works on logic: (1) Introductiones Parvulorum, which consists of short glosses on Porphyry Eisagoge and Aristotle Categories and De Interpretatione; (2) Logica Ingredientibus (so called because ingredientibus is the first word of its text), which consists of longer glosses on the texts covered by the previous work together with Boethius' De Differentiis Topicis and was probably written while Abelard was teaching in Paris before 1120; (3) Logica Nostrorum Petitioni (so called because nostrorum petitioni are the first words (...) of its text), which consists of longer glosses on the Eisagoge and may date from the time of his teaching at the hermitage of the Paraclete; (4) Dialectica, which has the form of an independent work about the subjects covered by Boethius' logical writings and Victorinus' treatise De Definitionibus and seems to contain materials from different periods of Abelard's life but probably did not reach its final form until a late date, perhaps the time of his stay at Cluny shortly before his death. Of these the second and the fourth are the most valuable. The Dialectica indeed, though based, like that of Garland, chiefly on the works of Boethius and written with the prolixity which was all too common among medieval authors, is an original composition of great importance for the development of logic. Abelard's mind was the keenest (though not in all respects the most admirable) that had been devoted to the subject for more than a thousand years, and he approached his task with the belief that it was still possible to make discoveries: 'Non enim tanta fuit antiquorum scriptorum perfectio ut non et nostro doctrina indigeat studio, nec tantum in nobis mortalibus scientia potest crescere ut non ultra possit augmentum recipere.' (1) The Dialectica survives in a single manuscript which lacks the opening sections. Excerpts from it were published by Victor Cousin in 1836 in his Ouvrages inédits d' Abelard. But unfortunately the text was not printed in full until 1956, and before that date it was therefore not possible to appreciate the magnitude of Abelard's contribution to the doctrines we regard as characteristically medieval.. (shrink)

"With Abelard, the term 'copula' enters into western thought. In fact, although widely attested, the use of the term 'copula' in reference to Aristotle's work is totally anachronistic. (1) What led to this term? In his Dialectica, Abelard was mainly concerned with the way syllogisms can be construed. The interest of the copula was in fact derivative from this main concern. As Kneale and Kneale (The development of logic, 1962: 206) put it, 'it is clear that for his [Aristotle's] theory (...) of syllogism he assumes in every general proposition two terms of the same kind, that is to say, each capable of being a subject and each capable of being a predicate'. Thus, since the only linguistic entities that can play these two roles are nouns (in modern terms, noun phrases), it is easy to understand why the copula became central. Abelard pursued the Aristotelian theory by emphasizing the role of be as the element that can turn a noun into a predicate in a syllogism rather than as the element that provides the sentence with a time specification (see Dialectica: 161). It is this conceptual shift that underlies the invention of the term 'copula', which is cast on the Latin copulare meaning 'to link'. For example, in sentences like a man is a mammal and Socrates is a man the copula allows the noun phrase a man to play the role of the subject, in the first, and that of the predicate, in the second. Clearly, in such a framework the assumption that the copula can be interpreted as a predicate meaning 'existence'. (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)

Each inhabitant of our world Gilbert calls (following Boethius) an id quod est or subsistens. Its main constituents are the subsistentiae (or the subsistent's id quo which is sometimes taken collectively to stand for ea quibus) and these are accompanied by the 'accidents', quantity and quality. The subsistent owes its status (or transitory condition) to a collection of inferior members of the Aristotelian class of accidents, which to Gilbert's mind are rather 'accessories' or 'attachments from without' (extrinsecus affixa). (...) The term 'substantia' is used both to stand for substance and substantial form (subsistentia), i.e., that by which something is subsistent (or 'is a substance'). The collection of subsistentiae (substantial forms) or the forma totius is called natura. However, 'natura' is also used to stand for either just one subsistentia or all the forms found in a subsistens even including its 'accidental' forms (quantity and quality). The inclusion of all kinds of accidents (including those inferior ones that make up a thing's status) is seldom found in the intension of the word 'natura'. One of the key notions featuring in Gilbert's ontology is esse aliquid. 'To be a-something' has a threefold import. First, it means 'to be only some thing', and to miss perfection. Second, it has the positive sense of 'being a something', i.e. 'being determinate and well-delineated', not indefinite, not formless that is. Third, 'to be a something' implies concreteness, corporealness and singularity. (shrink)

IT is well known that the art of logic (logica or diale(c)tica) knew a remarkable flourishing period during the twelfth century. In the first half of the century its main centres in Paris were: the School of Notre DameI, of St. Victor2, of the Petit Pont3 and of Mont Ste Geneviève4. The present paper aims to offer some new evidence from the manuscripts on the teaching of logic as given in the School of Mont Ste.

v. 1. On the twelfth century theories of fallacy.--v. 2. The origin and early development of the theory of supposition.

Francesco Patrizi da Cherso's Discussiones peripateticae (1581) are one of the most comprehensive analyses of the whole of Aristotelian philosophy to be published before Werner Jaeger's Aristoteles. The main thrust of the argument in the Discussiones is that whatever Aristotle had said that was true was not new, and that whatever he had said that was new was not true. The article shows how Patrizi proves this with respect to the Organon, and deals with the implications for the history af (...) ancient philosophy in general implied by his stance. (shrink)

The paper investigates the propriety of applying the form versus matter distinction to arguments and to logic in general. Its main point is that many of the currently pervasive views on form and matter with respect to logic rest on several substantive and even contentious assumptions which are nevertheless uncritically accepted. Indeed, many of the issues raised by the application of this distinction to arguments seem to be related to a questionable combination of different presuppositions and expectations; this holds in (...) particular of the vexed issue of demarcating the class of logical constants. I begin with a characterization of currently widespread views on form and matter in logic, which I refer to as ‘logical hylomorphism as we know it’—LHAWKI, for short—and argue that the hylomorphism underlying LHAWKI is mereological. Next, I sketch an overview of the historical developments leading from Aristotelian, non-mereological metaphysical hylomorphism to mereological logical hylomorphism (LHAWKI). I conclude with a reassessment of the prospects for the combination of hylomorphism and logic, arguing in particular that LHAWKI is not the only and certainly not the most suitable version of logical hylomorphism. In particular, this implies that the project of demarcating the class of logical constants as a means to define the scope and nature of logic rests on highly problematic assumptions. (shrink)

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 thesis is on the history and philosophy of logic and semantics. Logic can be described as the ‘science of reasoning’, as it deals primarily with correct patterns of reasoning. However, logic as a discipline has undergone dramatic changes in the last two centuries: while for ancient and medieval philosophers it belonged essentially to the realm of language studies, it has currently become a sub-branch of mathematics. This thesis attempts to establish a dialogue between the modern and the medieval traditions (...) in logic, by means of ‘translations’ of the medieval logical theories into the modern framework of symbolic logic, i.e. formalizations. One of its conclusions is that, when properly understood within their own framework, the interest of medieval logical theories for modern investigations go beyond mere historical interest, but that a thorough conceptual analysis of such theories must be undertaken in order to avoid conceptual misprojections. While such translations of medieval into modern logic have been attempted before, the approach presented here is innovative in that attention is paid to the similarities as well as to the dissimilarities between the two traditions, and to what can be learned from the medieval masters for modern investigations in logic and semantics. (shrink)

On the basis of passages from John Buridan's Summula Suppositionibus and Sophismata, E. Karger has reconstructed what could be called the ?Buridanian theory of inferential relations between doubly quantified propositions?, presented in her 1993 article ?A theory of immediate inference contained in Buridan's logic?. In the reconstruction, she focused on the syntactical elements of Buridan's theory of modes of personal supposition to extract patterns of formally valid inferences between members of a certain class of basic categorical propositions. The present study (...) aims at offering semantic corroboration?a proof of soundness?to the inferential relations syntactically identified by E. Karger, by means of the analysis of Buridan's semantic definitions of the modes of personal supposition. The semantic analysis is done with the help of some modern logical concepts, in particular that of the model. In effect, the relations of inference syntactically established are shown to hold also from a semantic point of view, which means thus that this fragment of Buridan's logic can be said to be sound. (shrink)

Aristotle in the central chapters of his Sophistical Refutations gives advice on how to counter unfair argumentation by similar means, all the while taking account not only of the adversary's arguments in themselves, but also of his philosophical commitments and state of mind, as well as the impression produced on the audience. This has offended commentators, and made most of them, medieval and modern alike, pass lightly over the relevant passages. A commentary that received the last touch in the very (...) early 13th century is more perceptive because, it is argued, the commentator had lived in a 12th-century environment of competing Parisian schools that was in important respects similar to the one of Aristotle's Athens. (shrink)

This study contains three parts. The first tries to follow the spread of the study of the Prior Analytics in the first two centuries during which it was at all studied in Western Europe, providing in this connection a non-exhaustive list of extant commentaries. Part II points to a certain overlap between commentaries on the Prior Analytics and works from the genre of sophismata . Part III lists the questions discussed in a students' compendium from about the 1240s and in (...) six commentaries per modum quaestionis from the 1270s through the 1290s. (shrink)

Clashes between bits of non-homogeneous theories inherited from antiquity were an important factor in the formation of medieval theories in logic and grammar, but the traditional categories of Aristotelianism, Stoicism and Neoplatonism are not quite adequate to describe the situation. Neoplatonism is almost irrelevant in logic and grammar, while there might be reasons to introduce a new category, LAS = Late Ancient Standard, with two branches: (1) logical LAS = Aristotle + Boethius, and (2) grammatical LAS = Stoics &c. (...) → Apollonius → Priscian. (shrink)

The Greek under the Latin and the Latin under the Greek -- Greek-Latin philosophical interaction -- The odyssey of semantics from the Stoa to Buridan -- The Chimera's diary -- Where were the stoics in the late Middle Ages? -- Theories of language in the Hellenistic age and in the twelfth and thirteenth centuries -- Late-ancient ancestors of medieval philosophical commentaries -- Boethius on Aristotle -- Boethius on the metaphysics of words -- Western and Byzantine approaches to logic -- Greek (...) and Latin medieval logic -- Philoponus, Alexander, and the origins of medieval logic -- Analyzing syllogisms or anonymus Aurelianensis III, the (presumably) earliest extant Latin commentary on the prior analytics, and its Greek model -- Fragments of Alexander's commentaries on Analytica posteriora and Sophistici elenchi. (shrink)

v. 1. The Greek tradition -- v. 2. Greek texts and fragments of the Latin translation of "Alexander's" commentary -- v. 3. Appendices, Danish summary, indices.

The principle that a necessarily false proposition implies any proposition, and that a necessarily true proposition is implied by any proposition, was apparently first propounded in twelfth century Latin logic, and came to be widely, though not universally, accepted in the fourteenth century. These principles seem never to have been accepted, or even seriously entertained, by Arabic logicians. In the present study, I explore some thirteenth century Arabic discussions of conditionals with impossible antecedents. The Persian-born scholar Afdal al-Dīn al-Kh najī (...) (d.1248) suggested the novel idea that two contradictory propositions may follow from the same impossible antecedent, and closely related to this point, he suggested that if an antecedent implies a consequent, then it will do so no matter how it is strengthened. These ideas led him, and those who followed him, to reject what has come to be known as 'Aristotle's thesis' that no proposition is implied by its own negation. Even these suggestions were widely resisted. Particularly influential were the counter-arguments of Na īr al-Dīn al-T ī (d.1274). (shrink)

La première fois que SECUNDUM PLACITUM se présente chez Boèce, c'est dans sa traduction de la définition aristotélienne du nom du Peri Herméneias (I6 a I9): "Ovoμα μν oüv στ φων σημαντιΧ Χατ συνΧην...Ι qu'il rend: NOMEN ERGO EST VOX SIGNIFICATIVA SECUNDUM PLACITUM. L'expression y est le substitut de Χατ συνν qu'on interprète en général comme signifiant «par convention». En interprétant SECUNDUM PLACITUM de la même manière, on a l'avantage de faire correspondre parfaitement l'expression latine au sens usuel du terme (...) grec. En a-t-on le droit? Ici surgissent deux problèmes connexes: Quel est le sens exact de Χατ συνΧην, quel est celui de SECUNDUM PLACITUM? Commençons par le premier. (shrink)

In his major work, the Periphyseon, the ninth century Latin philosopher John Scottus Eriugena gives, with the help of what he calls "dialectic", a rational analysis of reality. According to him, dialectic is a science which pertains both to language and reality. Eriugena grounds this position in a realist ontological exegesis of the Aristotelian categories, which are conceived as categories of being. His interpretation tends to transform logical patterns, such as Porphyry's Tree or the doctrine of the categories, into a (...) structure which is both ontological and logical, and to use them as tools for the analysis of the sensible world. The combination of dialectic interpreted as a science of being, capable of expressing truths about the sensible world as well as about discourse, with an ontological interpretation of logical concepts allows Eriugena to develop his metaphysical theory, a strong realism. Eriugena not only supports a theological realism (of divine ideas), but also, and principally, an ontological realism, the assertion of the immanent existence of forms. Eriugena claims that genera and species really subsist in the individuals: they are completely and simultaneously present in each of the entities which belong to them. (shrink)

In this essay I argue that Albert would reject the need for a separate fourth mode of common personal supposition, and that his view of merely confused supposition has not been fully explicated by modern scholars. I first examine the various examples of conjunct descent given by modern scholars from his Perutilis logica , and show that Albert clearly adopts it in resolving the sophistic examples involved. Second, I explicate the view of merely confused supposition that Albert defends in his (...) Sophismata , and then attempt to answer the question: which view of merely confused supposition was his final view, the view articulated in the Perutilis logica or the view in the Sophismata ? I conclude that based upon his Sophismata view of merely confused supposition, Albert came to realize the logical strength his revised theory of personal supposition afforded, and consequently, that he is one of the earliest 14th-century logicians to adopt conjunct terminal descent to resolve various sophisms, a move which gave his theory of personal supposition a logical symmetry having two sorts of propositional descents to singulars, and two sorts of terminal descents to singulars. (shrink)