La définition du sullogismos est strictement identique dans les Topiques et dans les Premiers Analytiques, alors qu'on admet généralement que, dans ce dernier traité, le terme désigne spécifiquement la structure formelle appelée aujourd'hui encore « syllogisme » . Le mot peut avoir le même sens d'un bout à l'autre de l'Organon et du corpus aristotélicien : il désigne le moment de la joute dialectique où l'interrogateur récapitule une section de la discussion et se montre en mesure d'imposer une conclusion à (...) laquelle son interlocuteur ne peut pas se dérober. À la suite de Hintikka (1993), on suggère que cette notion est issue des dialogues de Platon. C'est à partir de cette conception dialectique originelle que la théorie aristotélicienne de la rhétorique, d'une part, et la « syllogistique » formelle, de l'autre, ont pu se développer. The definition of a sullogismos in Aristotle's Topics and Prior Analytics is strictly identical, although it is generally admitted that in the latter treatise this word refers to the distinct deductive structure that we call "syllogism". This paper aims at showing that the word sullogismos may be given the same meaning throughout the Organon and throughout the Aristotelian corpus and that it refers to a characteristic move in the course of a dialectical debate, i.e. when the questioner, summing up a whole sequence of the previous discussion, shows that he is in a position to force upon his interlocutor a conclusion which the latter cannot escape. Following a suggestion made by Hintikka (1993), this paper shows that the notion most probably originates from Plato's dialogues, and uses it as a leading thread to show how the Aristotelian concept of rhetoric, on the one hand, and Aristotle's formal "syllogistic", on the other, may have grown out of this original dialectical core. (shrink)

Aristotle created logic and developed it to a level of great sophistication. There was nothing there before; and it took more than two millennia for something better to come around. The astonishment experienced by readers of the Prior Analytics, the most important of Aristotle's works that present the discipline, is comparable to that of an explorer discovering a cathedral in a desert. This article explains and evaluates some of Aristotle's views about propositions and syllogisms. The most important omission is the (...) difficult subject of syllogisms involving modalities. Aristotle distinguishes two relations of opposition that can obtain between propositions with the same subject- and predicate-expressions: contrariety and contradiction. In every canonical syllogism, one term is common to the two premises: it is called “middle term,” or simply “middle.” The remaining two terms of the premises are the only ones occurring in the conclusion: they are called “extreme terms,” or simply “extremes.”. (shrink)

In the present article we attempt to show that Aristotle's syllogistic is an underlying logiC which includes a natural deductive system and that it isn't an axiomatic theory as had previously been thought. We construct a mathematical model which reflects certain structural aspects of Aristotle's logic. We examine the relation of the model to the system of logic envisaged in scattered parts of Prior and Posterior Analytics. Our interpretation restores Aristotle's reputation as a logician of consummate imagination and skill. Several (...) attributions of shortcomings and logical errors to Aristotle are shown to be without merit. Aristotle's logic is found to be self-sufficient in several senses: his theory of deduction is logically sound in every detail. (His indirect deductions have been criticized, but incorrectly on our account.) Aristotle's logic presupposes no other logical concepts, not even those of propositional logic. The Aristotelian system is seen to be complete in the sense that every valid argument expressible in his system admits of a deduction within his deductive system: every semantically valid argument is deducible. (shrink)

Not until the early 1920’s was it possible to distinguish Aristotelian or traditional logic from Aristotle’s own ancient logic. We can now recognize many aspects of his logical investigations that are themselves modern, in the sense that modern logicians are making discoveries that Aristotle had already made or had anticipated. Here we gather five salient features of Aristotle’s logical investigations that reveal a striking philosophical modernity: 1) Aristotle took logic to be that part of epistemology used to establish knowledge of (...) logical consequence; 2) Prior Analytics is a metalogical treatise on the syllogistic deduction system; 3) Aristotle recognized the epistemic efficacy of certain elemental argument patterns, and he explicitly formulated them as rules of natural deduction in corresponding sentences; 4) Prior Analytics is a proof-theoretic treatise in which Aristotle describes a natural deduction system and demonstrates certain of the logical relationships among syllogistic deduction rules ; and finally, 5) Aristotle worked with a notion of substitution sufficient for distinguishing logical syntax and semantics. In this connection he also distinguished validity from deducibility sufficiently well to note the completeness of his logic. (shrink)

The Editor-in-Chief would like to thank the following colleagues who have helped maintain the standards ….

In this fast-paced, enlightening guide, Sharon M. Kaye takes us on a whistle-stop tour of medieval philosophy, revealing its astounding legacy to the discipline today.

This book presents the first study of the development of the theory of modal syllogistic in the Middle Ages.

Aristotelian causal theories incorporate some philosophically important features of the concept of cause, including necessity and essential character. The proposed formalization is restricted to one-place predicates and a finite domain of attributes (without individuals). Semantics is based on a labeled tree structure, with truth defined by means of tree paths. A relatively simple causal prefixing mechanism is defined, by means of which causes of propositions and reasoning with causes are made explicit. The distinction of causal and factual explanation are elaborated, (...) and examples of cyclic and convergent causation are given. Soundness and completeness proofs are sketched. (shrink)

This book claims that Aristotle followed an aspect theory of predication.

This book provides a detailed exposition of one of the most practical and popular methods of proving theorems in logic, called Natural Deduction. It is presented both historically and systematically. Also some combinations with other known proof methods are explored. The initial part of the book deals with Classical Logic, whereas the rest is concerned with systems for several forms of Modal Logics, one of the most important branches of modern logic, which has wide applicability.

By delving into the history and development of logic from its beginnings to the modern era, George Englebretsen rehabilitates term logic and demonstrates that an enhanced traditional logic remains a viable possibility. Taking inspiration from Fred Sommers' work, he creates an updated and fascinating version of term logic; one he believes to be just as legitimate as, and in ways superior to, the currently predominant mathematical logic.

a single life-span. Philosophers, then, do not see more or know more, and they do not see less or know less. They aim to see less detail and more of the abstract. Their details, if you like, are abstractions. Walking on God’s earth as a pedestrian, as a farmer working his fields or as a passer-by, one’s picture of one’s surroundings is every bit as intelligent as that of the pilot riding the sky. The views of the field are radically (...) different, however. One sees only a specific field and in all lively detail: the exact pattern of the land, or even the exact outline of a given leaf, grasshopper, grain of sand even. Acquaintance with minute detail is not without its price: details may stand in the way of conjuring the big picture. It may be difficult to compare whichever field one happens to be in with far off fields, with respect to their size or shape or any other quality. One may wish to inquire if far off fields were already planted, harvested, or even if they exist. A pedestrian may find it hard or even impossible to do so. The pedestrian view contains fine points that the pilot’s map never would, but it does not necessarily contain more information, for it lacks the general context. After all, there are only so many items that one can observe and account for at a single glance, a single map, a single book, a single life-span. (shrink)

The ancient Greeks were not only the founders of western philosophy, but the actual term "philosophy" is Greek in origin, most likely dating back to the late sixth century BC. Socrates, Plato, Aristotle, Pythagoras, Euclid, and Thales are but a few of the better-known philosophers of ancient Greece. During the amazingly fertile period running from roughly the middle of the first millennium BC to the middle of the first millennium AD, the world saw the rise of science, numerous schools of (...) thought, and—many believe—the birth of modern civilization. The Historical Dictionary of Ancient Greek Philosophy presents the history of Greek philosophy and the philosophers who made it famous. This is accomplished through a chronology, an introduction, a glossary, a bibliography, and hundreds of cross-referenced dictionary entries on important philosophers, concepts, issues, and events. (shrink)

CONSTITUÉ d'analyses et de réflexions sur les méthodes pratiquées aujourd'hui dans l'écriture de l'histoire de la philosophie, cet ouvrage vise à rendre compte de la différence des pratiques existant selon les traditions et à interroger l'existence d'une démarche historique spécifique au domaine de la philosophie. L'enjeu fondamental est donc de savoir s'il existe une historiographie propre à la philosophie. Les interrogations portent en particulier sur les questions des critères d'exactitude, de vérification, de crédibilité qui permettraient de distinguer et de décider (...) entre les interprétations. Si le travail de l'interprétation est infini, toujours à refaire, reprendre et corriger, cela n'implique nullement l'abandon des exigences qui fondent la pertinence historique. Une introduction indispensable à toute pratique de l'histoire de la philosophie. L'ouvrage comporte notamment des textes de : P. Aubenque (Paris IV), J. Biard (Tours), B. Bourgeois (Paris I), C. Coutel (Artois), Th. De Koninck (Laval, Québec), D. Deleule (Paris X), D. Garber (Chicago), P. Magnard (Paris IV), J.-M. Narbonne (Laval, Québec), E. Nuzzo (Salerne), John Rogers (Keele), J. B. Schneewind (Johns-Hopkins, Baltimore), Tom Sorell (Essex), J.-L. Vieillard-Baron (Poitiers), Y. C. Zarka (CNRS, Paris), mais aussi de F. P. Adorno (Salerne, CNRS), P. Caye (CNRS), P. Destrée (FNRS, Belgique), T. Gontier (CNRS), J.-B. Gourinat (CNRS), E. Picavet (Paris I), I. Radrizzani (Munich), C. Viano (CNRS), A. Vasiliu (CNRS). (shrink)

Philosophers have had an interest in language from the earliest times but the twentieth century, with its so-called 'linguistic turn' in philosophy, has seen a huge expansion of work focused specifically on language and its foundations. No branch of philosophy has been unaffected by this shift of emphasis. It is timely at the end of the century to review and assess the vast range of issues that have been developed and debated in this central area. The distinguished international contributors present (...) a clear, accessible guide to the fundamental questions raised by the philosophers about language. Contributions include Graeme Forbes on necessity, Susan Haack on deviant logics, Paul Horwich on truth, Charles Travis on Wittgenstein, L.J. Cohen on linguistic philosophy, Ruth Kempson on semantics and syntax and Christopher Hookway on ontology, to name but a few. A wide range of topics are covered from the metaphysics and ontology of language, language and mind, truth and meaning, to theories or reference, speech act theory, philosophy of logic and formal semantics. There are also articles on key figures from the twentieth century and earlier. Based on the foundation provided by the award-winning Encyclopedia of Language and Linguistics this single volume provides a collection of articles that will be an invaluable reference tool for all those interested in the area of philosophy of language, and also to those in cognitive science and psychology. All the articles have been thoroughly revised and updated. This volume gives a unique survey of topics that are at the very core of contemporary philosophy. (shrink)

In the great libraries of Europe and the United States, hidden in fading manuscripts on forgotten shelves, lie the works of medieval Hebrew logic. From the end of the twelfth century through the Renaissance, Jews wrote and translated commentaries and original compositions in Aristotelian logic. One can say without exaggeration that wherever Jews studied philosophy - Spain, France, Northern Africa, Germany, Palestine - they began their studies with logic. Yet with few exceptions, the manuscripts that were catalogued in the last (...) century have failed to arouse the interest of modem scholars. While the history of logic is now an established sub-discipline of the history of philosophy, the history of Hebrew logic is only in its infancy. The present work contains a translation and commentary of what is arguably the greatest work of Hebrew logic, the Sefer ha-Heqqesh ha-Yashar of Levi ben Gershom. Gersonides is well known today as a philosopher, astronomer, mathematician, and biblical exegete. But in the Middle Ages he was also famous for his prowess as a logician. The Correct Syllogism is his attempt to construct a theory of the syllogism that is free of what he considers to be the 'mistakes' of Aristotle, as interpreted by the Moslem commentator A verroes. It is an absorbing, challenging work, first written by Gersonides when he was merely thirty-one years old, then significantly revised by him. The translation presented here is of the revised version. (shrink)

While logical principles seem timeless, placeless, and eternal, their discovery is a story of personal accidents, political tragedies, and broad social change. If A, Then B begins with logic's emergence twenty-three centuries ago and tracks its expansion as a discipline ever since. -/- The book treats logic as more than a tale of individual abstraction; it sees logic as also being a result of politics, economics, technology, and geography, because all these factors helped to generate an audience for the discipline (...) from the start. The book thus relates developments in logical theory to the social history of different historical periods. -/- The book defends a number of controversial philosophical theses: (1) that rationally persuasive arguments must always proceed from premises that are initially more convincing than the conclusions to be proved (a position derived from Aristotle), (2) that intuitive logical judgments, though sometimes mistaken, can also count as certain knowledge, independent of the techniques used to construct formal logical systems, (3) that Wittgenstein was mistaken in thinking that philosophy was riddled with unintelligible language and that the real problems, instead, have been ambiguity and pretentious diction, and (4) that Nelson Goodman's argument to the effect that deductive logic can be "virtuously circular" is founded on a non sequitur. -/- . (shrink)

This is the first full assessment of British philosophy in the 19th century. Specially written essays by leading experts explore the work of the key thinkers of this remarkable period in intellectual history, covering logic and scientific method, metaphysics, religion, positivism, the impact of Darwin, and ethical, social, and political theory.

In this radical reinterpretation of Aristotle's Metaphysics, Walter E. Wehrle demonstrates that developmental theories of Aristotle are based on a faulty assumption: that the fifth chapter of Categories is an early theory of metaphysics that Aristotle later abandoned.

This Oxford Handbook covers the current state of the art in the philosophy of maths and logic in a comprehensive and accessible manner, giving the reader an overview of the major problems, positions, and battle lines. The 26 newly-commissioned chapters are by established experts in the field and contain both exposition and criticism as well as substantial development of their own positions. Select major positions are represented by two chapters - one supportive and one critical. The book includes a comprehensive (...) bibliography. (shrink)

This is a 1988 philosophical introduction to Aristotle, and Professor Lear starts where Aristotle himself starts. The first sentence of the Metaphysics states that all human beings by their nature desire to know. But what is it for us to be animated by this desire in this world? What is it for a creature to have a nature; what is our human nature; what must the world be like to be intelligible; and what must we be like to understand it (...) systematically? Through a consideration of these questions Professor Lear introduces us to the essence of Aristotle's philosophy and guides us through the central Aristotelian texts - selected from the Physics, Metaphysics, Ethics, Politics and from the biological and logical works. The book is written in a direct, lucid style which engages the reader with the themes in an active, participatory manner. (shrink)

Chapter 1 presents BS, a basic syllogistic system based on Aristotle's logic, in natural deduction form. Chapters 2 and 3 treat the metatheory of BS: consitency, soundness, independence, and completeness. Chapter 4 and 5 deal with syllogistic and, in turn, propositional and predicate logic, chapter 6 is on existential import, chapter 7 on subject and predicate and chapter 8 on classes. Chapter 9 adds negative variables to BS, and proves its soundness and completeness.

Aristotle’s Prior Analytics identifies deductions simpliciter with inferential necessity, so that a deduced conclusion is necessarily inferred from some premises. Modern logical reconstructions claim that inferential necessity in Aristotle corresponds to logical validity. However, this logical reconstruction fails on two accounts. First, logical validity does not highlight Aristotle’s distinction between inferential necessity and predicative necessity, meaning that the inferential necessity of a deduction is not of the same kind as the predicative necessity of a non‑deductive argument. Second, logical validity does (...) not explain the relevance of Aristotle’s distinction between complete and incomplete deductions. Logicians speak of complete deduction by adding the term “obvious” or “transparent” to logical validity, and then criticize Aristotle’s view for being unclear. However, Aristotle’s position is not confronted with this difficulty. There is nothing to add to inferential necessity, which already means complete deducibility, as opposed to incomplete deducibility, deemed to be potentially complete. Accordingly, the Prior Analytics reduces the incomplete deductions to the complete deductions in order to prove the potential, inferential necessity of the incomplete deductions. Logical validity would have been faithful to Aristotle’s text, if it had been possible to coin a notion of potential validity, distinct from both validity and invalidity. (shrink)

Much of the last fifty years of scholarship on Aristotle’s syllogistic suggests a conceptual framework under which the syllogistic is a logic, a system of inferential reasoning, only if it is not a theory or formal ontology, a system concerned with general features of the world. In this paper, I will argue that this a misleading interpretative framework. The syllogistic is something sui generis: by our lights, it is neither clearly a logic, nor clearly a theory, but rather exhibits certain (...) characteristic marks of logics and certain characteristic marks of theories. In what follows, I will present a debate between a theoretical and a logical interpretation of the syllogistic. The debate centers on the interpretation of syllogisms as either implications or inferences. But the significance of this question has been taken to concern the nature and subject-matter of the syllogistic, and how it ought to be represented by modern techniques. For one might think that, if syllogisms are implications, propositions with conditional form, then the syllogistic, in so far as it is a systematic taxonomy of syllogisms, is a theory or a body of knowledge concerned with general features of the world. Furthermore, if the syllogistic is a theory, then it ought to be represented by an axiomatic system, a system deriving propositional theorems from axioms. On the other hand, if syllogisms are inferences, then the syllogistic is a logic, a system of inferential reasoning. And furthermore, it ought to be represented as a natural deduction system, a system deriving valid arguments by means of intuitively valid inferences. I will argue that one can disentangle these questions—are syllogisms inferences or implications, is the syllogistic a logic or a theory, is the syllogistic a body of worldly knowledge or a system of inferential reasoning, and ought we to represent the syllogistic as a natural deduction system or an axiomatic system—and that we must if we are to have a historically accurate understanding of Aristotle. (shrink)

In 1934 a most singular event occurred. Two papers were published on a topic that had (apparently) never before been written about, the authors had never been in contact with one another, and they had (apparently) no common intellectual background that would otherwise account for their mutual interest in this topic.1 These two papers formed the basis for a movement in logic which is by now the most common way of teaching elementary logic by far, and indeed is perhaps all (...) that is known in any detail about logic by a number of philosophers (especially in North America). This manner of proceeding in logic is called ‘natural deduction’. And in its own way the instigation of this style of logical proof is as important to the history of logic as the discovery of resolution by Robinson in 1965, or the discovery of the logistical method by Frege in 1879, or even the discovery of the syllogistic by Aristotle in the fourth century BC. (shrink)

Polynomizing is a term that intends to describe the uses of polynomial-like representations as a reasoning strategy and as a tool for scientific heuristics. I show how proof-theory and semantics for classical and several non-classical logics can be approached from this perspective, and discuss the assessment of this prospect, in particular to recover certain ideas of George Boole in unifying logic, algebra and the differential calculus.

This presentation of Aristotle's natural deduction system supplements earlier presentations and gives more historical evidence. Some fine-tunings resulted from conversations with Timothy Smiley, Charles Kahn, Josiah Gould, John Kearns,John Glanvillle, and William Parry.The criticism of Aristotle's theory of propositions found at the end of this 1974 presentation was retracted in Corcoran's 2009 HPL article "Aristotle's demonstrative logic".