Boethius, the Roman philosopher, was executed for treason and pilloried by modern scholars for misinterpreting Aristotle to the West. This book examines his semantics and logic, attempting to clear his name and lend him new credence.

The prologue of the Sophistici elenchi is as close an Aristotelian text gets to dealing with language as a subject matter in its own right, only in reverse. Language and its features bear consideration to the extent that they account for some major predicaments discursive reasoning is prone to, both as a separate and as a common endeavour. That being said, the linguistic pitfalls that trick us into thinking that whatever is the case for words and word-compounds is (...) also the case for the things and facts linguistic items stand for reveal as much about good linguistic habits and sound argumentation as they themselves are revealed by the principles and rules our argumentation goes by. In this connection, Aristotle resorted to a curious (or not so curious) analogy between words and counters which played a major role in explaining why language is such a powerful source of illusion and deception. As it happens, Aristotle accounting analogy is a case in point for showcasing the level of sophistication medieval Latin literature on fallacies achieved as early as the first half of the twelfth century. As a matter of fact, Western commentators managed to build compelling cases both in favour of and against the understanding that was to become and still is the standard story – which, of course, speaks volumes about their exegetical proficiency and technical expertise. On the one hand, trusting implicitly Boethius’ translation and well aware of his views on disputational hazards as opposed to computational reliability, they usually understood Aristotle’s comparison as if it was an analogy in name only. On the other hand, despite Boethius’ translation put them at a considerable disadvantage, Latin commentators were able to construe Aristotle’s analogy as bringing together two sets of symbolic variables (words and counters) that are neither entirely free nor entirely bound – which expose them to subtle but critical shifts in value and meaning. (shrink)

This book recounts the remarkable history of efforts by significant medieval thinkers to accommodate the ontology of the Trinity within the framework of Aristotelian logic and ontology. These efforts were remarkable because they pushed creatively beyond the boundaries of existing thought while trying to strike a balance between the Church's traditional teachings and theoretical rigor in a context of institutional politics. In some cases, good theology, good philosophy, and good politics turned out to be three different things. The principal (...) thinkers discussed are Augustine, Boethius, Abélard, Gilbert of Poitiers, Bonaventure, Aquinas, Scotus, and Ockham. The aspects of Trinitarian doctrine dealt with are primarily internal ontological questions about the Trinity. The approach draws on history of theology and philosophy, as well as on the modern formal disciplines of set-theoretic semantics and formal ontology. Augustine inaugurated the project of constructing models of the Trinity in language drawn from Platonic and Aristotelian philosophy, especially the conceptual framework of Aristotle's Categories. He used the Aristotelian notions of substance and relation to set up a model whose aim was not so much to demystify the Trinity as to demonstrate the logical consistency of maintaining that there is one and only one God at the same time as maintaining that there are three distinct persons, each of whom is God. Standing against this tradition are various heretical accounts of the Trinity. The book also analyzes these traditions, using the same techniques. All these accounts of the Trinity are evaluated relative to the three constraints under which they were formed, bearing in mind that the constraints on philosophical theorizing are not limited to internal consistency but also take note of explanatory power. Besides analyzing and evaluating individual accounts of the Trinity, the book provides a novel framework within which different theories can be compared. (shrink)

Since Aristotle and the Stoa, there has been a clash, worsened by modern predicate logic, between logically defined operator meanings and natural intuitions. Pragmatics has tried to neutralize the clash by an appeal to the Gricean conversational maxims. The present study argues that the pragmatic attempt has been unsuccessful. The “softness” of the Gricean explanation fails to do justice to the robustness of the intuitions concerned, leaving the relation between the principles evoked and the observed facts opaque. Moreover, (...) there are cases where the Gricean maxims fail to apply. A more adequate solution consists in the devising of a sound natural logic, part of the innate cognitive equipment of mankind. This account has proved successful in conjunction with a postulated cognitive mechanism in virtue of which the universe of discourse is stepwise and recursively restricted, so that the negation selects different complements according to the degree of restrictedness of Un. This mechanism explains not only the discrepancies between natural logical intuitions and known logical systems; it also accounts for certain systematic lexicalization gaps in the languages of the world. Finally, it is shown how stepwise restriction of Un produces the ontogenesis of natural predicate logic, while at the same time resolving the intuitive clashes with established logical systems that the Gricean maxims sought to explain. (shrink)

We present probabilistic approaches to check the validity of selected connexive principles within the setting of coherence. Connexive logics emerged from the intuition that conditionals of the form If ∼A, then A, should not hold, since the conditional’s antecedent ∼A contradicts its consequent A. Our approach covers this intuition by observing that for an event A the only coherent probability assessment on the conditional event A|~A is p(A|~A)=0 . Moreover, connexive logics aim to capture the intuition that conditionals should express (...) some “connection” between the antecedent and the consequent or, in terms of inferences, validity should require some connection between the premise set and the conclusion. This intuition is covered by a number of principles, a selection of which we analyze in our contribution. We present two approaches to connexivity within coherence-based probability logic. Specifically, we analyze connections between antecedents and consequents firstly, in terms of probabilistic constraints on conditional events (in the sense of defaults, or negated defaults) and secondly, in terms of constraints on compounds of conditionals and iterated conditionals. After developing different notions of negations and notions of validity, we analyze the following connexive principles within both approaches: Aristotle’s Theses, Aristotle’s Second Thesis, Abelard’s First Principle and selected versions of Boethius’ Theses. We conclude by remarking that coherence-based probability logic offers a rich language to investigate the validity of various connexive principles. (shrink)

In Ciceronis Topica and De topicis differentiis are Boethius's two treatises on Topics. Together these two works present Boethius's theory of the art of discovering arguments, a theory that was highly influential in the history of medieval logic. Eleonore Stump here presents the first English language translation of In Ciceronis Topica, Boethius's extended commentary on Cicero's Topica. To supplement her translation, Professor Stump has provided an introduction that supplies essential information about In Ciceronis Topica, (...) class='Hi'>Boethius's life, and the tradition of dialectic; her detailed notes explore the many philosophical problems in Boethius's text. A significant contribution to the history of Western intellectual life in its own right, Boethius's ''In Ciceronis Topica makes an excellent companion to Professor Stump's earlier work, Boethius's De topicis differentiis. (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)

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)

The Consolations of Philosophy by Boethius, whose English translators include King Alfred, Geoffrey Chaucer, and Queen Elizabeth I, ranks among the most remarkable books to be written by a prisoner awaiting the execution of a tyrannical death sentence. Its interpretation is bound up with his other writings on mathematics and music, on Aristotelian and propositional logic, and on central themes of Christian dogma. -/- Chadwick begins by tracing the career of Boethius, a Roman rising to high office (...) under the Gothic King Theoderic the Great, and suggests that his death may be seen as a cruel by-product of Byzantine ambitions to restore Roman imperial rule after its elimination in the West in AD 476. Subsequent chapters examine in detail his educational programme in the liberal arts designed to avert a threatened collapse of culture and his ambition to translate into Latin everything he could find on Plato and Aristotle. -/- Boethius has been called `last of the Romans, first of the scholastics'. This book is the first major study in English of a writer who was of critical importance in the history of thought. (shrink)

We propose a new modal logic endowed with a simple deductive system to interpret Aristotle's theory of the modal syllogism. While being inspired by standard propositional modal logic, it is also a logic of terms that admits a (sound) extensional semantics involving possible states-of-affairs in a given world. Applied to the analysis of Aristotle's modal syllogistic as found in the Prior Analytics A8-22, it sheds light on various fine-grained distinctions which when made allow us to (...) clarify some ambiguities and obtain a completely consistent system and prove all of the modal syllogisms considered valid by Aristotle. This logic allows us also to make a connection with the axioms of modern propositional modal logic and to perceive to what extent these are implicit in Aristotle's reasoning. Further work will involve addressing the question of the completeness of this logic (or variants thereof) together with an extension of the logic to include a calculus of relations (for instance the relational syllogistic treated in Galen's Introduction to Logic) which Slomkowsky has argued is already found in the Topics. (shrink)

This book comprises two long chapters. The first chapter, entitled “The China syndrome, logical form, translation,” is a treatise on linguistic relativism with specific reference to Chinese language. It is not directly related to the title of the book, “Aristotle in China,” except by what it calls “the Aristotelian principle” implied in the “guidance and constraint hypothesis” of linguistic relativism. The writing of this chapter is motivated as a critical response to Angus Graham’s Disputers of the Tao, characterized (...) by Robert Wardy as adhering itself to the “ guidance and constraints hypothesis,” which means that the linguistic structure of a particular language is either guiding or giving constraint to a certain way of philosophical thinking. Chapter 1 traces this position back to B. Worf’s Language, Thought and Reality, which, on the basis of the Hopi language, propounds something similar to the guidance and constraint hypothesis. Then it shows the historical connection of this position to Levi-Bruhl’s Mentalité primitive and Von Humbolt’s monograph Lettre à M. Abel-Rémusat sur la nature des formes grammaticales en générale, et sur le genie de la langue chinois en particulier. For Robert Wardy, this hypothesis could be found also in philosophy of language, for example in Quine’s notion of “radical translation” and Davidson’s critique of it. It is also extended to sinology as in the case of French sinologists such as Granet and Gernet, who were under the influence of Humboldt’s legacy. (shrink)

In this paper, we discuss the syllogisms from both fronts : Aristotle and Boethius. We mainly focus on the differences with respect to categorical and hypothetical syllogisms in Aristotle and Boethius. Regarding Aristotle’s works on logic, it is not unusual to claim that Aristotle extensively worked on categorical syllogisms. In Prior Analytics, Aristotle gave proofs for many valid moods. However we cannot find a similar treatment for hypothetical syllogism in his works. Thus, (...) it might be a reason for his students to improve Aristotle’s theory of syllogisms by filling the gaps in hypothetical syllogisms. As Boethius already emphasized in the Book I of De Hypotheticis Syllogismis, the Peripatetic School only initiated the start. The remaining and detailed treatise was due to Boethius himself. The impression we got from Boethius’s and Aristotle’s works on syllogisms is that the categorical syllogism is almost entirely developed by Aristotle himself, whereas the extensive and the detailed study of the hypothetical syllogism was carried out by Boethius, although he was not the first figure in the history who gave concise expositions on hypothetical syllogism. Boethius’s translations of syllogisms in medieval era were the primer resource and textbook for Aristotelian logic during the early Medieval ages. Therefore, the scholars of those times had no other chance but to work from Boethius’s commentaries. So, the evident properties of Aristotelian figures were not then visible. Boethius wrote several textbooks in logic. A detailed investigation might yield significant information on Boethius’s logic compared with the influence of Aristotle on Boethius. (shrink)

This paper investigates the implicative conditional, a connective intended to describe the logical behavior of an empirically defined class of natural language conditionals, also named implicative conditionals, which excludes concessive and some other conditionals. The implicative conditional strengthens the strict conditional with the possibility of the antecedent and of the contradictory of the consequent. $${p\Rightarrow q}$$ p ⇒ q is thus defined as $${\lnot } \Diamond {(p \wedge \lnot q) \wedge } \Diamond {p \wedge } \Diamond {\lnot q}$$ ¬ (...) ◊ ( p ∧ ¬ q ) ∧ ◊ p ∧ ◊ ¬ q. We explore the logical properties of this conditional in a reflexive normal Kripke semantics, provide an axiomatic system and prove it to be sound and complete for our semantics. The implicative conditional validates transitivity and contraposition, which we take to be integral parts of reasoning and communication. But it only validates restricted versions of strengthening the antecedent, right weakening, simplification, and rational monotonicity. Apparent counterexamples to some of these properties are explained as due to contextual factors. Finally, the implicative conditional avoids the paradoxes of material and strict implication, and validates some connexive principles such as Aristotle’s theses and weak Boethius’ thesis, as well as some highly entrenched principles of conditionals, such as conjunction of consequents, disjunction of antecedents, modus ponens, cautious monotonicity and cut. (shrink)

Boethius, “the first of the scholastics,” had an influence on the Latin Middle Ages that is difficult to overestimate. His translations of and commentaries on Aristotle’s philosophical and logical works were the main conduit between the Greek classical culture and the early Middle Ages. His two commentaries on Aristotle’s Peri Hermenias (“On Interpretation”), the longer of which is translated in the present two volumes (the first covering Books 1–3 and the second Books 4–6), were particularly influential. Unfortunately, (...) those seeking to understand this aspect of Boethius will find little to encourage them here. Aquinas is mentioned once (on the book jacket), and Augustine only a few times. About other .. (shrink)

Boethius was a Roman senator who rose to high office under the Gothic king Theoderic the Great. He translated into Latin all he knew of Plato and Aristotle, and was profoundly interested in the issues of theology and philosophy. The Consolations were written while he awaited the execution of a tyrannical death sentence. The Consolations of Philosophy have been translated into English by King Alfred, Geoffrey Chaucer, and Queen Elizabeth I. This scholarly study by Henry Chadwick, the first (...) this century since the War, has stimulated new interest in these remarkable works. (shrink)

This interdisciplinary study offers an interpretation of the major logical, philosophical/theological and poetic writings of Boethius, Abelard and Alan of Lille. The author examines their theories of language and the ways in which they explore how words illuminate things, how the mind comprehends God and how the individual reaches beatitude.

The first part of the book examines language as a tool of logic, and deals with Alfarabi's analysis of the meanings of various terms as they are used in logic and philosophy.

The thirteenth-century logician Lambert of Auxerre was well known for his Summa Lamberti, or simply Logica, written in the mid-1250s, which became an authoritative textbook on logic in the Western tradition. Our knowledge of medieval logic comes in great part from Lambert's Logica and three other texts: William of Sherwood's Introductiones in logicam, Peter of Spain's Tractatus, and Roger Bacon's Summulae dialectics. Of the four, Lambert's work is the best example of question-summas that proceed principally by asking and (...) answering questions on the subject matter. Thomas S. Maloney's translation of Logica, the only complete translation of this work in any language, is a milestone in the study of medieval logic. More than simply a translation, Maloney's project is a critical, comprehensive study of Lambert's logic situated in the context of his contemporaries and predecessors. As such, it offers a wealth of annotation and commentary. The lengthy introduction and extensive notes to the text explain the origin, theoretical context, and intricacies of the text and its doctrines. Maloney also addresses the disputed issues of authorship, date, and place of publication of the Summa Lamberti and makes available to the English-only audience the French, German, and Italian secondary sources--all translated--that are needed to enter the discussion. "Thomas S. Maloney fully commands the primary and secondary sources necessary to elucidate Lambert's Logica. An expert on Roger Bacon's philosophy, he demonstrates a rare proficiency in medieval Latin and scholastic logic. His references to sources from the ancient (Aristotle and Boethius) and medieval worlds are apposite, perspicuous, and useful. The volume's presentation with an appropriate introduction and commentary in the endnotes will no doubt establish it as an indispensable resource for scholars in the twenty-first century." --Alan Perreiah, University of Kentucky. (shrink)

Presenting the first book-length study in English of Aristotle's Sophistical Refutations, this work takes a fresh look at this seminal text on false reasoning.

Due to the importance of Aristotle’s Peri Hermeneias in Medieval Arabic and Latin, I took this text as a relatively shared script that is interpreted by Al-Farabi and Aquinas.

One of the singularities of Latin exegesis of Aristotle’s Sophistici elenchi, is that it arbitrarily brought together two families of fallacies, the «figure of speech» and the «accident», despite the fact that they are on either side of the divide between sophisms related to expression and sophisms independent of expression, a divide that lays at the heart of Aristotle’s taxonomy of sophistic arguments. What is behind this surprising identification? The talk is meant to show that it actually originates (...) from a curious mistake in Boethius’ translation of Aristotle’s Sophistici elenchi, 22, 178b 36-37 which radically transformed the nature of the argument at stake. While it was originally an example of the fallacies related to the «figure of speech», Boethius’ translation wrongly brings about two arguments instead of one, both related to the «accident». This explains why authors from the Latin tradition came to think that fallacies of «figure of speech» were linked to fallacies of «accident» closely enough to ask whether they actually fell outside expression, even though it does not at first glance appear that such a possibility was allowed or even suggested by Aristotle’s text. This odd question illustrates some of the remarkable features of the medieval archive and how some of its most peculiar problems came to be. It specifically allows us to reconstruct the mechanisms through which a minor disturbance in the letter of the text leads to a whole new way of organising its exegetical material. (shrink)

"The twelve chapters of this volume all began their existence as contributions to workshops held between 2009 and 2011 by a Danish-Swedish research network called The Aristotelian Tradition: The reception of Aristotle's works on logic and metaphysics in the Middle Ages, headquartered in Gothenburg and funded by the Bank of Sweden Tercentenary Foundation. Most of them were written by members of the network, some by invited speakers. While the volume amply illustrates the set of scholarly approaches characteristic of (...) the "Copenhagen School of Medieval Philosophy" (notably a strong philological foundation and an interest in ancient as well as medieval and Greek as well as Latin texts), its thematic diversity reflects the network's breadth of interests. What unites the chapters in this respect is simply a concern with different historical manifestations of Aristotelian thought on logical and metaphysical matters. The volume includes studies of texts by, among others, Apuleius, Boethius, Anonymus Aurelianensis III, Michael of Ephesus, Averroes, Anonymus Cantabrigiensis, Nicholas of Paris, Robert Kilwardby, Anonymus O, Thomas Aquinas, William of Ockham, and Francisco Suárez, relating to themes and passages in Aristotle's Categories, On Interpretation, Prior Analytics 1, Posterior Analytics 1, Sophistical Refutations and Metaphysics A and Z. The last two chapters consist of a new edition, with English translation and commentary, of the first part of a fiercely anti-Aristotelian work, which has been described as the starting-point for Renaissance Platonism and Aristotelianism alike: George Gemistos Plethon's On Aristotle's Departures from Plato."--. (shrink)

The Introduction to philosophy written by Porphyry at the end of the second century AD is the most successful work of its kind ever to have been published. It was translated into most respectable languages, and for a millennium and a half every student of philosophy read it as his first text in the subject. Porphyry's aim was modest: he intended to explain the meaning of five terms, 'genus', 'species', 'difference', 'property', and 'accident' - terms which he took to be (...) important to Aristotelian logic and metaphysics, and hence to philosophy in general. Thus in principle the Introduction is simple and elementary. In fact, there are sometimes difficulties and doubts on the surface of the text - and beneath the surface there are frequent depths or profundities. The work raises, directly or indirectly, a number of perennial philosophical questions. In addition, the Introduction became, in Boethius's Latin translation, the point of reference for one of the longest-lasting of philosophical disputes - the dispute over the status of 'universals'.This book contains a new English translation of the Introduction, preceded by a study of the life and works of Porphyry, the purpose and nature of the Introduction, and the history of the text. It is accompanied by a discursive commentary the primary aim of which is to analyse and assess the philosophical theses and arguments which the Introduction puts forward. The twentieth century turned away from Aristotelian logic, and the Introduction lost its position on the syllabus. Barnes does not argue that it should be put back in its old place; but his commentary - the first to be published in English, and the fullest to be published for a century - suggests that there is blood in the old man yet. CLARENDON LATER ANCIENT PHILOSOPHERSGeneral Editors: Jonathan Barnes and A. A. Long This series, which is modelled on the familiar Clarendon Aristotle and Clarendon Plato series, is designed to encourage philosophers and students of philosophy to explore the fertile terrain of later ancient philosophy. The texts range in date from the first century BC to the fifth century AD, and will cover all the parts and all the schools of philosophy. Each volume contains a substantial introduction, an English translation, and a critical commentary on the philosophical claims and arguments of the text. The translations aim primarily at accuracy and fidelity; but they are also readable and accompanied by notes on textual problems that affect the philosophical interpretation. No knowledge of Greek or Latin is assumed. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Aristotle on False Reasoning: Language and the World in the Sophistical RefutationsMarina Berzins McCoyAristotle on False Reasoning: Language and the World in the Sophistical Refutations. Scott Schreiber. Albany: SUNY Press, 2003. pp. 240. $68.50, hardcover; $22.95, paperback.Scott Schreiber's Aristotle on False Reasoning is the first full-length English commentary on Aristotle's Sophistical Refutations in the last century. Aristotle's Sophistical Refutations is a text (...) that has received relatively little attention in the last century of scholarship, despite a revival of interest in other aspects of Aristotle's work concerned with the nature of good argument and rhetoric. (The 1995 French translation and commentary by Loius-Andre Dorion is a notable exception.) Schreiber finds the primary reason [End Page 92] for inattention to this text to lie in the tendency of contemporary Anglo-American philosophy to resolve problems in reasoning through linguistic clarification (xiv). Aristotle's claim that some errors are due to language while others lie outside the realm of linguistic error is not one to which contemporary analytic philosophy has been particularly sympathetic. The Sophistical Refutations has been neglected in light of contemporary logic. Schreiber's book attempts to return to Aristotle's project on his own philosophical terms, in order to better understand why Aristotle classified errors in reasoning as he did. Schreiber's approach is to examine each of the twelve types of false reasoning that Aristotle lays out in the Sophistical Refutations, with particular attention to Aristotle's examples, in order to understand the principles behind the overall system.Schreiber argues that Aristotle had good reason for separating errors due to language from those outside of language: Aristotle's classification of error is tied to his notion of the resolution of false arguments. To understand how to resolve a sophistical argument, we must first understand how it could have been believed to be true. Since Aristotle's aim in the Sophistical Refutations is to show why certain sorts of arguments are deceptive to some who hear them, his method of explaining errors is less a pure examination of their logical errors than of how such erroneous arguments can deceive. Aristotle is concerned with two types of problems with sophistical argument: first, why such an argument is false; and second, why it might appear to be true. Schreiber shows that most commentators have not given sufficient attention to the second of these concerns in their attempts to understand Aristotle's taxonomy. As Schreiber puts it, "Examples of false reasoning are unified into groups and differentiated into subgroups not by the nature of the confusions that they engender but by the different ways that confusion is cleared up" (54). False reasoning is due not only to mistakes in logic, but also to mistaken beliefs about language and reality. Careful examination of Aristotle's thinking allows us to see the importance of beliefs about the world in good and bad argument.For the most part, Schreiber's examinations of Aristotle's examples are lucid and helpful in understanding both the particular example at hand as well as the general picture of Aristotle's classifications. Schreiber continually returns to the importance of Aristotle's own view of language and argument in contrast to the approaches of contemporary linguistics and logic. For example, while some twentieth-century scholars have attempted to explain Aristotle's distinction between homonymy and amphiboly in terms of the contemporary distinction between semantics and syntax, [End Page 93] Aristotle seems to distinguish the two according to whether a general predicate signifies many particulars regardless of context, or in a propositional context (31). In the end, Schreiber does not think that the categories of homonymy and amphiboly can be completely distinct, even on Aristotle's own grounds, but still finds the categories useful. Schreiber is also careful to provide criticism of Aristotle's categories when warranted, both defending Aristotle against his contemporary critics when he thinks they have misunderstood him, and pointing out genuine weaknesses in Aristotle's arguments.Schreiber's book is clearly intended as a response to the contemporary Anglo-American reading of Aristotle. Much of the book assumes at least some familiarity with the ways in... (shrink)

'De syllogismis' is the fifth treatise of John Buridan's 'Summulae dialecticae', a textbook he wrote for his logic course in the Faculty of Arts at the University of Paris. 'De syllogismis' contains material related to Aristotle's Analytica Priora and Boethius's 'De hypotheticis syllogismis'. The textbook discusses inferences involving not only propositions de inesse, but also propositions featuring oblique, reduplicative and infinite terms. Buridan displays a keen interest in modal inferences and inferences involving propositional attitudes. Buridan's De syllogismis (...) continues along the lines of his nominalist conception of the relations between mind, language and reality. (shrink)

To date no investigation has sought to interpret key themes in Aristotle’s writings on metaphysics, e.g., substance, potentiality, actuality, proximate cause, etc., within the context of a temporal logic or logic of events. Essentially, what follows is a programmatic effort to interpret aspects of Aristotle’s insights in Book Lambda of the Metaphysics in terms of recent advances in the development of a temporal logic, while being attentive to the sense of the original text as far (...) as possible. The significance of such an enterprise lies in unearthing and clarifying conceptual interconnections in Aristotle’s metaphysical writings which would be difficult to fathom through other means. This project, however exploratory in its present form, seems feasible partly because of the fact that at numerous points in Aristotle’s thesis process metaphors from the study of biology are strikingly evident. Also, there is additional justification for the suggested analysis in that his work involves repeated references to the “lived” activity of one’s inquiring into the nature of things. Thus a view of Aristotle’s pronouncements which presupposes a logic of events, where events are analysed pragmatically, i.e., in terms of a language-user and the extension of whatever is claimed to have occurred, is not alien to the mode of expression with which he presents his views. (shrink)

This book explores the reaction of tenth-century Arab philosopher Abu Nasr Alfarabi to the logical works of Aristotle. From numerous short treatises the author develops a systematic and comprehensive topical survey of Alfara bi's logical writings. The book is divided into two major parts: language as a tool of logic and logic as a tool with which to analyze language. The first five chapters deal with Alfarabi's analysis of the meanings of various terms as they (...) are used in logic and philosophy. Alfarabi refutes the Arab grammarians who claimed that Arab logicians were building a language within a language and shows that the philosophical meanings of terms are in fact their most original and essential meanings. The final chapter deals with Alfarabi's analysis of certain aspects of the Arabic language and demonstrates that Arabic, like any natural language, conforms to universal logical structures of which natural languages are only a concrete expression. (shrink)

Geach's account of the Aristotelian logic of categorical sentences supplemented the views shared by Frege, Russell, Quine and others. I argue that this particular predicate logic approach and Geach's points apply to only one variety of natural language categorical sentences. For example, it takes the universal categorical as a universal conditional “If anything is a man, then it is mortal”. A different natural language form can and should be invoked: “Every man is a mortal.” Employing special (...) restricted quantifiers in a version of predicate logic, we justify a full square of opposition and the rules of quality and quantity that Geach rejected. (shrink)

RésuméDans cet article, je soutiens qu'Aristote utilise une approche de la logique que l'on retrouve chez les praticiens de la logique informelle d'aujourd’hui. Même si sa position est complexe, Aristote privilégie des interprétations intensionnelles plutôt qu'extensionnelles de sa logique syllogistique. Il n'utilise pas les fonctions de vérité, mais adopte une version de la sémantique qui accentue le rôle du langage naturel qui ouvre, pour ainsi dire, une fenêtre sur la réalité métaphysique. Le mouvement de la logique informelle fut, en grande (...) partie, une initiative canadienne représentée par des auteurs bien connus tels Johnson, Blair, Govier et plusieurs autres. (shrink)

Aristotle (384-322 BC) was an ancient Greek philosopher, pupil of Plato, and tutor of Alexander the Great. His works span the topics of biology, metaphysics, mind, logic, language, science, epistemology, ethics, and politics. Aristotle held that there are many divine beings, but a supremely divine being is the first cause of the universe and the goodness of all other beings. This divine being plays a fundamental explanatory role in Aristotle’s thought.

Examines Boethius's translations of logical texts by Aristotle and Porphyry, and his commentaries on them. It sets out Boethius's interpretation of the Aristotelian Categories, his response to the Problem of Universals, his semantics, and his first answer to the problem of free will and divine prescience. It argues that Boethius made an important decision to go against the trend of logical commentary in his period and return to Porphyry's strongly Aristotelian approach.

The paper studies the relation between systems of modal logic and systems of consequential implication, a non-material form of implication satisfying "Aristotle's Thesis" (p does not imply not p) and "Weak Boethius' Thesis" (if p implies q, then p does not imply not q). Definitions are given of consequential implication in terms of modal operators and of modal operators in terms of consequential implication. The modal equivalent of "Strong Boethius' Thesis" (that p implies q implies that (...) p does not imply not q) is identified. (shrink)

In this paper an algebraic system of the new type is proposed (namely, a vectorial lattice). This algebraic system is a lattice for the language of Aristotle’s syllogistic and as well as a lattice for the language of Vasiľév’s syllogistic. A lattice for the language of Aristotle’s syllogistic is called a vectorial lattice on cap-semilattice and a lattice for the language of Vasiľév’s syllogistic is called a vectorial lattice on closure cap-semilattice. These constructions are (...) introduced for the first time. (shrink)

In this paper I present the text, a translation, and a commentary of a long anonymous scholium to Aristotle’s Analytics which is a Greek parallel to Boethius’ De Hypotheticis Syllogismis, but has so far not been recognized as such. The scholium discusses hypothetical syllogisms of the types modus ponens and modus tollens and hypothetical syllogisms constructed from three conditionals (‘wholly hypothetical syllogisms’). It is Peripatetic, and not Stoic, in its theoretical approach as well as its terminology. There are (...) several elements of early Peripatetic hypothetical syllogistic preserved in it, and there is a large number of close parallels to Boethius’ De Hypotheticis Syllogismis which we find in no other source. It is very likely that there was a Greek source from which both the scholium and large parts of Boethius’ De Hypotheticis Syllogismis are ultimately derived. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Philosophy and Rhetoric 36.2 (2003) 168-172 [Access article in PDF] Logic and the Art of Memory: The Quest for a Universal Language. Paolo Rossi. Trans. Stephen Clucas. Chicago: University of Chicago Press, 2000. Pp. xxviii + 333. $32.00 cloth. Of the traditional five canons of rhetoric—inventio, dispositio, elocutio, memoria, and actio—the most circuitous and fascinating history belongs to memoria. From its propulsion of Homeric lore to its (...) grounding of rhetorical invention to its exile under print culture to its recent revival in public memory studies, the promiscuous and perplexing history of memory in the West may be one of the least appreciated, and perhaps least understood, elements of rhetorical and intellectual history. The publication in 1966 of Frances Yates's highly praised The Art of Memory drew the attention of contemporary scholars to the importance of mnemotechnics to the culture of late medieval and early modern Europe. 1 Yates persuasively argued that the art of memory is an integral element of European intellectual history, one that can enrich our understanding of everything from Dominican theology to Shakespearian theater. However, six years earlier, in 1960, the Italian intellectual historian Paolo Rossi published in Italian an important precursor to Yates's work entitled Clavis Universalis: Arti Della Memoria e Logica Combinatoria da Lullo a Leibniz. The book traces the encyclopaedic and mnemotechnical traditions from Aristotle through Cicero and Raymond Lull and into the early-modern period, arguing that the art of memory provides an important antecedent to the advent of method in seventeenth-century philosophy, especially in the works of Bacon, Descartes, and Leibniz. Yates, in her preface to The Art of Memory, acknowledges her debt to Rossi's work, and now this work has been made available in English translation. Stephen Clucas's translation, under the title Logic and the Art of Memory, will no doubt stimulate and supplement research into the mnemotechnical tradition in the English-speaking world, and perhaps lead us to reconsider the relationship between philosophy and rhetoric.Rossi argues that the neglect of the mnemotechnical tradition in its Ciceronian and Lullian strands has distorted our understanding of the "new" science and philosophy of the seventeenth-century, which is often interpreted as constituting, in a Kuhnian sense, a drastic paradigm shift from a [End Page 168] Renaissance worldview that still retained occult elements. Rossi places the work of Bacon, Descartes, and Leibniz within the historical strand of the logico-encyclopaedic and mnemotechnical traditions, suggesting that these figures culminate late medieval and early modern intellectual and cultural ambitions as much as they give rise to new ones. Rossi makes his argument by providing a history of mnemotechnics from Aristotle into the fifteenth century in chapter one; by examining the fascination with encyclopaedism, combinatoria, and memory in the sixteenth century in chapters two and three; by investigating the role of artificial memory in the works of key intellectual figures in the late sixteenth and seventeenth centuries in chapters four through six; and by tracing the impulse toward universal knowledge and its connection to mnemotechnics among seventeenth-century Cartesians, Baconians, and in the work of Leibniz, in chapters seven and eight.Chapter one, after showing the pervasiveness of Renaissance mnemotechnical literature, surveys its classical and medieval antecedents in philosophy and rhetoric. Rossi argues that Aristotle's De memoria et reminiscentia, Cicero's De oratore, Quintilian's De institutione oratoria, the Rhetorica ad Herennium, and the works of Albertus Magnus and Thomas Aquinas were each important to the mnemotechnical tradition into the seventeenth century. Fourteenth- and fifteenth-century treatises on the ars memorativa and the ars predicandi, drawing on these classical and medieval theories, emphasize the importance of memory places (loci), images (imagines), and order or arrangement (dispositio) in mnemotechnics. Additionally, they intimately link the memory to the imagination, stressing the importance of exciting and stimulating the imagination in memorization. The Italian Pietro da Ravenna, for example, attributed the might of his memory to, in his own words, turning "the images of the most beautiful virgins into memory places" (22). Such imaginative mnemonic techniques were considered to... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Aristotle on False Reasoning: Language and the World in the Sophistical RefutationsMarina Berzins McCoyAristotle on False Reasoning: Language and the World in the Sophistical Refutations. Scott Schreiber. Albany: SUNY Press, 2003. pp. 240. $68.50, hardcover; $22.95, paperback.Scott Schreiber's Aristotle on False Reasoning is the first full-length English commentary on Aristotle's Sophistical Refutations in the last century. Aristotle's Sophistical Refutations is a text (...) that has received relatively little attention in the last century of scholarship, despite a revival of interest in other aspects of Aristotle's work concerned with the nature of good argument and rhetoric. (The 1995 French translation and commentary by Loius-Andre Dorion is a notable exception.) Schreiber finds the primary reason [End Page 92] for inattention to this text to lie in the tendency of contemporary Anglo-American philosophy to resolve problems in reasoning through linguistic clarification (xiv). Aristotle's claim that some errors are due to language while others lie outside the realm of linguistic error is not one to which contemporary analytic philosophy has been particularly sympathetic. The Sophistical Refutations has been neglected in light of contemporary logic. Schreiber's book attempts to return to Aristotle's project on his own philosophical terms, in order to better understand why Aristotle classified errors in reasoning as he did. Schreiber's approach is to examine each of the twelve types of false reasoning that Aristotle lays out in the Sophistical Refutations, with particular attention to Aristotle's examples, in order to understand the principles behind the overall system.Schreiber argues that Aristotle had good reason for separating errors due to language from those outside of language: Aristotle's classification of error is tied to his notion of the resolution of false arguments. To understand how to resolve a sophistical argument, we must first understand how it could have been believed to be true. Since Aristotle's aim in the Sophistical Refutations is to show why certain sorts of arguments are deceptive to some who hear them, his method of explaining errors is less a pure examination of their logical errors than of how such erroneous arguments can deceive. Aristotle is concerned with two types of problems with sophistical argument: first, why such an argument is false; and second, why it might appear to be true. Schreiber shows that most commentators have not given sufficient attention to the second of these concerns in their attempts to understand Aristotle's taxonomy. As Schreiber puts it, "Examples of false reasoning are unified into groups and differentiated into subgroups not by the nature of the confusions that they engender but by the different ways that confusion is cleared up" (54). False reasoning is due not only to mistakes in logic, but also to mistaken beliefs about language and reality. Careful examination of Aristotle's thinking allows us to see the importance of beliefs about the world in good and bad argument.For the most part, Schreiber's examinations of Aristotle's examples are lucid and helpful in understanding both the particular example at hand as well as the general picture of Aristotle's classifications. Schreiber continually returns to the importance of Aristotle's own view of language and argument in contrast to the approaches of contemporary linguistics and logic. For example, while some twentieth-century scholars have attempted to explain Aristotle's distinction between homonymy and amphiboly in terms of the contemporary distinction between semantics and syntax, [End Page 93] Aristotle seems to distinguish the two according to whether a general predicate signifies many particulars regardless of context, or in a propositional context (31). In the end, Schreiber does not think that the categories of homonymy and amphiboly can be completely distinct, even on Aristotle's own grounds, but still finds the categories useful. Schreiber is also careful to provide criticism of Aristotle's categories when warranted, both defending Aristotle against his contemporary critics when he thinks they have misunderstood him, and pointing out genuine weaknesses in Aristotle's arguments.Schreiber's book is clearly intended as a response to the contemporary Anglo-American reading of Aristotle. Much of the book assumes at least some familiarity with the ways in... (shrink)

1. "The map of logic." Comparatively recently, Kant's words to the effect that in the two thousand years since Aristotle logic had made "not a single step forward and, all things considered, it seems to be a fully finished and completed discipline" used to be quoted widely and not unsympathetically. Today, however, there are works about logic in which the listing of logical disciplines runs into the dozens. In this regard the attempt by the American logician (...) N. Rescher to compile a diagram or "map of logic," in which the list of the branches of logic takes up several pages, is noteworthy. Also characteristic is the following statement by one of the major modern representatives of mathematical logic, S. Kleene: "Since the discovery of non-Euclidean geometries by Lobachevsky and Bolyai , it has become clear that different systems of geometries are conceptually equally possible…. Identically, there are different logics.". (shrink)

According to Plutarch, the theory of psychological disharmony relies on the Platonic music harmony. When Plato refers to music harmony, he means the kind of harmony where the concept of God is the source through which all beings emanate. The mental passions define the quality of human character and consequently develop the social man. As far as the Aristotelian ethical theory is concerned, morality does not condemn the passions, because it has a clear ontological and anthropological basis. The Stoics stress (...) that a trait of the human soul is sociality, and that happens because all human beings are under the law of sympathy and constitute a whole. At medieval times, Boethius portrays the middle age social conditions which also resemble with our postmodern societies. (shrink)

In previous articles, it has been shown that the deductive system developed by Aristotle in his "second logic" is a natural deduction system and not an axiomatic system as previously had been thought. It was also stated that Aristotle's logic is self-sufficient in two senses: First, that it presupposed no other logical concepts, not even those of propositional logic; second, that it is (strongly) complete in the sense that every valid argument expressible in the (...) class='Hi'>language of the system is deducible by means of a formal deduction in the system. Review of the system makes the first point obvious. The purpose of the present article is to prove the second. Strong completeness is demonstrated for the Aristotelian system. (shrink)

This volume includes twelve studies by international specialists on Aristotle and his commentators. Among the topics treated are Aristotle's political philosophy and metaphysics, the ancient and Byzantine commentators' scholia on Aristotle's logic, philosophy of language and psychology as well as studies of broader scope on developmentalism in ancient philosophy and the importance of studying Late Antiquity.

Since the first chapter of this book presents an intro duction to the present state of game-theoretical semantics (GTS), there is no point in giving a briefer survey here. Instead, it may be helpful to indicate what this volume attempts to do. The first chapter gives a short intro duction to GTS and a survey of what is has accomplished. Chapter 2 puts the enterprise of GTS into new philo sophical perspective by relating its basic ideas to Kant's phi losophy (...) of mathematics, space, and time. Chapters 3-6 are samples of GTS's accomplishments in understanding different kinds of semantical phenomena, mostly in natural languages. Beyond presenting results, some of these chapters also have other aims. Chapter 3 relates GTS to an interesting line of logical and foundational studies - the so-called functional interpretations - while chapter 4 leads to certain important methodological theses. Chapter 7 marks an application of GTS in a more philo sophical direction by criticizing the Frege-Russell thesis that words like "is" are multiply ambiguous. This leads in turn to a criticism of recent logical languages (logical notation), which since Frege have been based on the ambi guity thesis, and also to certain methodological sug gestions. In chapter 8, GTS is shown to have important implications for our understanding of Aristotle's doctrine of categories, while chapter 9 continues my earlier criticism of Chomsky's generative approach to linguistic theorizing. (shrink)

The Oxford Handbook of Aristotle reflects the lively international character of Aristotelian studies, drawing contributors from the United Kingdom, the United States, Germany, France, Switzerland, Italy, Canada, and Japan; it also, appropriately, includes a preponderance of authors from the University of Oxford, which has been a center of Aristotelian studies for many centuries. The volume equally reflects the broad range of activity Aristotelian studies comprise today: such activity ranges from the primarily textual and philological to the application of broadly (...) Aristotelian themes to contemporary problems irrespective of their narrow textual fidelity. In between these extremes one finds the core of Aristotelian scholarship as it is practiced today, and as it is primarily represented in this Handbook: textual exegesis and criticism. Even within this more limited core activity, one witnesses a rich range of pursuits, with some scholars seeking primarily to understand Aristotle in his own philosophical milieu and others seeking rather to place him into direct conversation with contemporary philosophers and their present-day concerns. No one of these enterprises exhausts the field. On the contrary, one of the most welcome and enlivening features of the contemporary Aristotelian scene is precisely the cross-fertilization these mutually beneficial and complementary activities offer one another. The volume, prefaced with an introduction to Aristotle's life and works by the editor, covers the main areas of Aristotelian philosophy and intellectual enquiry: ethics, metaphysics, politics, logic, language, psychology, rhetoric, poetics, theology, physical and biological investigation, and philosophical method. It also, and distinctively, looks both backwards and forwards: two chapters recount Aristotle's treatment of earlier philosophers, who proved formative to his own orientations and methods, and another three chapters chart the long afterlife of Aristotle's philosophy, in Late Antiquity, in the Islamic World, and in the Latin West. (shrink)