This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain (...) in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

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.

This dissertation is a comparative study of Aristotelian and Chinese logic. I briefly overview the reports of difficulties in understanding that derives from cultural differences. I claim that these difficulties not only result from the fact that concepts in each language fail to match properly, but also from the fact that the logical spaces themselves are structured differently. Aristotelian logic is based on the structure of a classificatory system---a hierarchical structure of names for kinds of things (...) organized into genera/species. Chinese logic is based on a Chinese binary system---a yin-yang structure of associative relations. ;I discuss the difficulties of translating the first three chapters of Matthew Lipman's Harry Stottlemeier's Discovery---one of a series of novels used in the Philosophy for Children Project---into Chinese. These chapters discuss the logical relations constituting the Aristotelian Square of Opposition. I find that most translation problems result from the fact that the logical structures of these two languages fail to match. ;I report my research on the responses of American and Chinese school children to reading chapter one of Harry Stottlemeier's Discovery , one in the original English version and the other in Chinese. The study of discussions among older children offers evidence for my claim that logical spaces of Western and Chinese thinking are structured differently, but the study of discussions among younger children gives a hope that there is a chance for there to be communication between the two very different ways of thinking. ;The conclusion is that Aristotelian logic and Chinese logic have two very different objectives, and as a consequence, different patterns for constructing logical relations. These two patterns represent two thinking models. The former is like a tree. It represents a finite number of things according to a presumed order. The latter is like a net; from any point on the net, one can link to any number of related points in an ever-changing world. The possibility of a mutually beneficial rapprochement between Chinese and Aristotelian logic depends on whether we can lay out a way for each side to understand the other in a common discourse. (shrink)

When we hear the word logic, we tend to think of arguments, premises and conclusions, claims and evidence for claims. But this is only half of it. Arguments are made of words, and words are symbols or signs of concepts, the building blocks of human thought. The study of the concept, the most fundamental aspect of logic, was once an essential part of liberal education, and to aid in its recovery is the goal of this book. This is (...) a must-have for any introductory logic course. (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)

A new theoretical approach to Aristotelian Logic based on three axioms has been recently introduced. This formalization of the theory allowed for the unification of its uncommunicated traditional branches, thus restoring the theoretical unity of AL. In this brief paper, the applicability of the three AL axioms to Propositional Logic is explored. First, it is shown how the AL axioms can be applied to some simple PL arguments in a straightforward manner. Second, the development of a proof (...) method for PL inspired by the AL axioms is presented. This method mimics the underlying mechanics of the proof method from AL, and offers a complementary alternative to proof methods such as truth trees. (shrink)

Proceedings of an international research and development conference, Tuscon, Arizona, October 1985. One hundred and twenty-eight papers are presented in this hefty volume.

John Corcoran and George Boger. Aristotelian logic and Euclidean geometry. Bulletin of Symbolic Logic. 20 (2014) 131. -/- By an Aristotelian logic we mean any system of direct and indirect deductions, chains of reasoning linking conclusions to premises—complete syllogisms, to use Aristotle’s phrase—1) intended to show that their conclusions follow logically from their respective premises and 2) resembling those in Aristotle’s Prior Analytics. Such systems presuppose existence of cases where it is not obvious that the (...) conclusion follows from the premises: there must be something deductions can show. Corcoran calls a proposition that follows from given premises a hidden consequence of those premises if it is not obvious that the proposition follows from those premises. By a Euclidean geometry we mean an extended discourse beginning with basic premises—axioms, postulates, definitions—1) treating a universe of geometrical figures and 2) resembling Euclid’s Elements. There were Euclidean geometries before Euclid (fl. 300 BCE), even before Aristotle (384–322 BCE). Bochenski, Lukasiewicz, Patzig and others never new this or if they did they found it inconvenient to mention. Euclid shows no awareness of Aristotle. It is obvious today—as it should have been obvious in Euclid’s time, if anyone knew both—that Aristotle’s logic was insufficient for Euclid’s geometry: few if any geometrical theorems can be deduced from Euclid’s premises by means of Aristotle’s deductions. Aristotle’s writings don’t say whether his logic is sufficient for Euclidean geometry. But, there is not even one fully-presented example. However, Aristotle’s writings do make clear that he endorsed the goal of a sufficient system. Nevertheless, incredible as this is today, many logicians after Aristotle claimed that Aristotelian logics are sufficient for Euclidean geometries. This paper reviews and analyses such claims by Mill, Boole, De Morgan, Russell, Poincaré, and others. It also examines early contrary statements by Hintikka, Mueller, Smith, and others. Special attention is given to the argumentations pro or con and especially to their logical, epistemic, and ontological presuppositions. What methodology is necessary or sufficient to show that a given logic is adequate or inadequate to serve as the underlying logi of a given science. (shrink)

Stewart Shapiro and Alan Weir have argued that a crucial part of the demonstration of Frege's Theorem (specifically, that Hume's Principle implies that there are infinitely many objects) fails if the Neo-logicist cannot assume the existence of the empty property, i.e., is restricted to so-called Aristotelian Logic. Nevertheless, even in the context of Aristotelian Logic, Hume's Principle implies much of the content of Peano Arithmetic. In addition, their results do not constitute an objection to Neo-logicism so (...) much as a clarification regarding the view of logic that the Neo-logicist must take. (shrink)

Philosophy in the medieval Latin West before 1200 is often thought to have been dominated by Platonism. The articles in this volume question this view, by cataloguing, describing and investigating the tradition of Aristotelian logic during this period, examining its influence on authors usually placed within the Aristotelian tradition (Eriugena, Anselm, Gilbert of Poitiers), and also looking at some of the characteristics of early medieval Platonism. Abelard, the most brilliant logician of the age, is the main subject (...) of three articles, and the book concludes with two more general discussions about how and why medieval philosophy should be studied. (shrink)

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

Originally published in 1938. This compact treatise is a complete treatment of Aristotle’s logic as containing negative terms. It begins with defining Aristotelian logic as a subject-predicate logic confining itself to the four forms of categorical proposition known as the A, E, I and O forms. It assigns conventional meanings to these categorical forms such that subalternation holds. It continues to discuss the development of the logic since the time of its founder and address traditional (...) logic as it existed in the twentieth century. The primary consideration of the book is the inclusion of negative terms - obversion, contraposition etc. – within traditional logic by addressing three questions, of systematization, the rules, and the interpretation. (shrink)

Originally published in 1938. This compact treatise is a complete treatment of Aristotle’s logic as containing negative terms. It begins with defining Aristotelian logic as a subject-predicate logic confining itself to the four forms of categorical proposition known as the _A, E, I _and_ O_ forms. It assigns conventional meanings to these categorical forms such that subalternation holds. It continues to discuss the development of the logic since the time of its founder and address traditional (...) logic as it existed in the twentieth century. The primary consideration of the book is the inclusion of negative terms - obversion, contraposition etc. – within traditional logic by addressing three questions, of systematization, the rules, and the interpretation. (shrink)

Although most natural law ethical theories recognize moral absolutes, there is not much agreement even among natural law theorists about how to identify them. The author argues that in order to understand and determine the morality (or immorality) of a human action, it must be considered in relation to the organized system of human practices within which it is performed. Such an approach, he argues, is to be found in the natural law theory of Thomas Aquinas, especially once it is (...) recognized that the logical structure of Aquinas's ethical theory is basically that of an Aristotelian science. In order to depict this structure and to explain how it bears upon the analysis of action, the author investigates a number of issues that have attracted the attention of Thomistic and Aristotelian scholarship. He examines the nature of practical reason, its relationship with theoretical reason, the derivation of lower from higher ethical principles, the incommensurability of human goods, the relationship between will and intellect, and the principle of double effect. The book will be useful to students and scholars interested in ethics, especially from an Aristotelian and/or Thomistic perspective. One appendix reproduces the Leonine text of the De malo (question 6), with facing English translation. Another appendix provides facing Latin text and English translation of the Summa Theologiae I-II (question 94, article 2). ABOUT THE AUTHOR: Kevin L. Flannery, S.J., author of many works on the history of logic--particularly Aristotelian logic--is dean of the faculty of philosophy and professor of the history of ancient philosophy at the Pontifical Gregorian University in Rome. PRAISE FOR THE BOOK: ""I know of no more careful and detailed study of Thomas's principle that the realms of theoretical and practical rationality are parallel. This principle is indeed central to an understanding of Thomas Aquinas's ethical thought, and Father Flannery examines its ramifications most perspicaciously. His book constitutes a valuable and important addition to the Thomistic literature. Father Flannery's writing is lucid, if not always extremely engaging, and his arguments are well supported by references to, and quotations from, the Aristotelian and Thomistic texts upon which they are based.""--The Medieval Review ""It would be hard to overstate the importance of this book at the present juncture of Thomistic studies.""--Ralph McInerny, University of Notre Dame ""... of interest and of great value mostly to specialists in Aquinas's ethics or moral theory more generally. Flannery presents complex matters clearly, and his explanations of the logical presuppositions of Aquinas's moral thought are always illuminating.""--Jean Porter, Theological Studies ""This is a significant work that belongs on the bookshelf of any serious student of Aquinas.... An important contribution to Thomistic studies.""--Irish Theological Quarterly ""This scholastic text will particularly appeal to thinkers interested in Aristotelian mathematics and logic and their practical integration into Thomistic natural law ethics. However, all natural law scholars must address the questions of context and method raised by Flannery's insights and his careful, precise textual analyses."" -- Beverly Whelton, Review of Metaphysics. (shrink)

The paper uses the theory of generalized quantifiers to discuss existential import and its implications for Aristotelian logic, namely the square of opposition, conversions and the assertoric syllogistic, as well as for more recent generalizations to intermediate quantifiers like “most”. While this is a systematic discussion of the semantic background one should assume in order to obtain the inferences and oppositions Aristotle proposed, it also sheds some light on the interpretation of his writings. Moreover by applying tools from (...) modern formal semantics to the investigation of classical Aristotelian logic and its extensions, we combine different approaches to the logic of quantification. We will present variants of quantifiers that are associated to the four corners of the square of opposition with and without existential import and discuss their role for the logical square, conversions and the syllogistic. It will turn out that there is no way to ascribe existential import that validates all inferences and relations which one is willing to hold in Aristotelian logic. Two options, however, provide reasonable results. Existential import should either be ascribed only to affirmative statements or only be ascribed to universal quantification. The former option is preferable for a mere reconstruction of the classical Aristotelian logic while the latter option is more attractive if Aristotelian logic is generalized to intermediate quantifiers. (shrink)

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

This book shows otherwise. John Martin rehabilitates Neoplatonism, founded by Plotinus and brought into Christianity by St. Augustine.

The rediscovery of Aristotle’s works on syllogisms in the Latin world, especially the Sophistici Elenchi and then the Prior Analytics, gave rise to sophisticated views on the nature of syllogistic form and syllogistic matter in the thirteenth century. It led to debates on the ontology of the syllogism as studied in the Prior Analytics, i.e. the syllogism made of letters and the four logical constants a/e/i/o, with deep consequences on the definition of logic as a universal method for all (...) sciences and as a science itself. (shrink)

This is a textbook on traditional deductive logic, designed for a one semester course. Topics such as definition and the informal fallacies take the scope of the book somewhat beyond the boundaries of formal logic. Although the subjects covered in this book are for the most part topics standard in Aristotelian textbooks, the detail of the analysis exceeds the standard treatment. The book is divided into five main parts. The first part deals with the basic concepts of (...) logic, and the second part specifically examines the basic concepts of Aristotelian logic. Part 1 introduces the reader to the notions of argument and of validity. A valid argument is an argument whose conclusion follows necessarily from its premises, whereas a deductive argument is an argument that claims to be valid. (shrink)

Some of the outstanding masters of Kurdish historical schools (Medresê) are usually and rightly seen as belonging to the Aristotelian tradition. In this introductory study I briefly present some manuscripts of Kurdish glosses on Aristotelian logical texts, and show that the Aristotelian logical tradition, as inherited from early Islamic philosophers, also formed an important strand in Kurdish schools. Kurdish students' peculiar approach to Aristotelian logic affected the way in which Categories, De Interpretatione and Isagoge were (...) studied in Kurdish schools from the fifteenth century onwards. (shrink)

Syllogism is a form of logical argument allowing one to deduce a consistent conclusion based on a pair of premises having a common term. Although Aristotle was the first to conceive and develop this way of reasoning, he left open a lot of conceptual space for further modifications, improvements and systematizations with regards to his original syllogistic theory. From its creation until modern times, syllogism has remained a powerful and compelling device of deduction and argument, used by a variety of (...) figures and assuming a variety of forms throughout history. The Aftermath of Syllogism investigates the key developments in the history of this peculiar pattern of inference, from Avicenna to Hegel. Taking as its focus the longue durée of development between the Middle Ages and the nineteenth century, this book looks at the huge reworking scientific syllogism underwent over the centuries, as some of the finest philosophical minds brought it to an unprecedented height of logical sharpness and sophistication. Bringing together a group of major international experts in the Aristotelian tradition, The Aftermath of Syllogism provides a detailed, up to date and critical evaluation of the history of syllogistic deduction. (shrink)

I want to pull together some well-known facts which, when taken together, provide us with a plausible, and I think persuasive, argument that Aristotle's logic is inconsistent. We cannot, of course, hope to show that it is formally inconsistent since he does not present us with a fully worked-out formal system. On the other hand, we do have Lukasiewicz's formal version of Aristotelian logic which he proves consistent. (edited).

The controversy which has raged between those who accept Aristotelian Logic and those who reject it, seems to continue. It is, I believe, advisable to consider the arguments on both sides. Modern Logicians for the most part insist that Aristotelian Logic breaks down, i.e. it is not true for all meanings of the terms. On the other hand there are those who insist on the validity of Aristotelian Logic claiming that those values for which (...) it fails are not permissible values. But there is one who stands almost entirely alone in his position—namely Professor H. B. Smith—who maintains that Aristotelian Logic breaks down because and only because its interpretation into Boolean terms has been accomplished by means of a definition that is not forced upon us and which, since it gives up desirable principles, is to be rejected. (shrink)

Considers the literary genres in which logical texts were written in the post-classical period. Articles describe the kinds of texts that were written and the implications for educational practices, as well as the continuities and developments between one language culture and another.".

This paper addresses the question of what existential assumptions are needed for the Aristotelian interpretation of the relationships between the four categorical propositions. The particular relationships in question are those unique to the Aristotelian logic, namely, contrariety, subcontrariety, subaltemation, conversion by limitation, and contraposition by limitation. The views of several recent authors of logic textbooks are surveyed. While most construe the Aristotelian logic as capable of being preserved by assuming that the subject class has (...) a member, Irving Copi construes that logic as requiring that four assumptions about class membership be made. These are that the subject, predicate, complement of subject, and complement of predicate classes all have members. It is argued that only three assumptions about class membership are needed, viz., that subject, predicate, and complement of predicate classes have members. (shrink)

We want to show that Aristotle’s general conception of syllogism includes as its essential part the logical concept of necessity, which can be understood in a causal way. This logical conception of causality is more general then the conception of the causality in the Aristotelian theory of proof (“demonstrative syllogism”), which contains the causal account of knowledge and science outside formal logic. Aristotle’s syllogistic is described in a purely intensional way, without recourse to a set-theoretical formal semantics. It (...) is shown that the conclusion of a syllogism is justified by the accumulation of logical causes applied during the reasoning process. It is also indicated that logical principles as well as the logical concept of causality have a fundamental ontological role in Aristotle’s “first philosophy”. (shrink)