A Short History of Logic by William Ritchie Sorley, first published in 1911, is a rare manuscript, the original residing in one of the great libraries of the world. This book is a reproduction of that original, which has been scanned and cleaned by state-of-the-art publishing tools for better readability and enhanced appreciation. Restoration Editors' mission is to bring long out of print manuscripts back to life. Some smudges, annotations or unclear text may still exist, due to permanent (...) damage to the original work. We believe the literary significance of the text justifies offering this reproduction, allowing a new generation to appreciate it. (shrink)

This chapter contains sections titled: A Timeline of Medieval Logicians A Guide to the Literature.

History of Logic and Semantics offers a collection of studies on the development of the Aristotelian and terminist approaches to language, from the Boethian reception of Aristotle to the post-medieval terminism. These articles were also published in Vivarium, Volume 53, Nos. 2-4.

From the start the better logicians found much to take exception to in Prantl. Peirce, for example, describes him as "a writer of little judgment and over-rated learning, whose useful history of logic is full of blunders, misappreciations, and insensate theories, and whose own Billingsgate justifies almost any tone toward him". As is indicated in this comment, Prantl attempted to judge and assess the value of the logical achievements that he made the object of his study. However, he (...) himself had little logical acumen. If not justified, this is to some extent excused by Heinrich Scholz, the first comprehensive historian of logic after Prantl. In his Abriß der Geschichte der Logik, which first appeared in 1931 and has now been translated, he maintains that no trustworthy conception of the history of logic was possible until modern and mathematical logic provided a precise criterion for formal logic. In particular he maintains that logic in the course of its history has assumed different Gestalten, which must be distinguished if sense is to be made of it. He is especially concerned to distinguish formal logic, whether in its ancient Aristotelian or its modern mathematical Gestalt, from its non-formal extensions into psychology, epistemology, and metaphysics. It is certainly true that the rise of mathematical logic has also witnessed a renewed interest in the history of logic. Scholars using the means provided by modern analysis have found much in the past of great logical interest, which had previously been dismissed as worthless extravagance. The logic of the Stoics and of the 14th-century scholastics are prime examples. (shrink)

AbstractŁukasiewicz introduced a new methodological approach to the history of logic. It consists of the use of modern formal logic in the research of the history of logic. Although he was not the first to use formal logic in his historical research, Łukasiewicz was the first who used it consistently and formulated it as a requirement for a historian of logic. The aim of this paper is to present Łukasiewicz's contribution and the (...) class='Hi'>history of its formulation. In addition, the paper will present its reception. There are two main themes in Łukasiewicz’s work on the history of logic. He discussed Stoic logic and Aristotle’s syllogistic. The second part of the paper focuses on current reception of Łukasiewicz’s contribution and on the question of whether there is a difference between knowledge about his contribution to Stoic logic and to Aristotle’s syllogistic, given that it has been hypothesised that Łukasiewicz’s contribution is currently more known among Aristotelian scholars than among those who focus on Stoic logic. Based on the papers that have appeared in the last five years at Web of Science and Scopus this hypothesis has not been confirmed. (shrink)

Inductive Logic is number ten in the 11-volume Handbook of the History of Logic. While there are many examples were a science split from philosophy and became autonomous (such as physics with Newton and biology with Darwin), and while there are, perhaps, topics that are of exclusively philosophical interest, inductive logic — as this handbook attests — is a research field where philosophers and scientists fruitfully and constructively interact. This handbook covers the rich history of (...) scientific turning points in Inductive Logic, including probability theory and decision theory. Written by leading researchers in the field, both this volume and the Handbook as a whole are definitive reference tools for senior undergraduates, graduate students and researchers in the history of logic, the history of philosophy, and any discipline, such as mathematics, computer science, cognitive psychology, and artificial intelligence, for whom the historical background of his or her work is a salient consideration. (shrink)

Greek, Indian and Arabic Logic marks the initial appearance of the multi-volume Handbook of the History of Logic. Additional volumes will be published when ready, rather than in strict chronological order. Soon to appear are The Rise of Modern Logic: From Leibniz to Frege. Also in preparation are Logic From Russell to Gödel, The Emergence of Classical Logic, Logic and the Modalities in the Twentieth Century, and The Many-Valued and Non-Monotonic Turn in (...) class='Hi'>Logic. Further volumes will follow, including Mediaeval and Renaissance Logic and Logic: A History of its Central. In designing the Handbook of the History of Logic, the Editors have taken the view that the history of logic holds more than an antiquarian interest, and that a knowledge of logic's rich and sophisticated development is, in various respects, relevant to the research programmes of the present day. Ancient logic is no exception. The present volume attests to the distant origins of some of modern logic's most important features, such as can be found in the claim by the authors of the chapter on Aristotle's early logic that, from its infancy, the theory of the syllogism is an example of an intuitionistic, non-monotonic, relevantly paraconsistent logic. Similarly, in addition to its comparative earliness, what is striking about the best of the Megarian and Stoic traditions is their sophistication and originality. Logic is an indispensably important pivot of the Western intellectual tradition. But, as the chapters on Indian and Arabic logic make clear, logic's parentage extends more widely than any direct line from the Greek city states. It is hardly surprising, therefore, that for centuries logic has been an unfetteredly international enterprise, whose research programmes reach to every corner of the learned world. Like its companion volumes, Greek, Indian and Arabic Logic is the result of a design that gives to its distinguished authors as much space as would be needed to produce highly authoritative chapters, rich in detail and interpretative reach. The aim of the Editors is to have placed before the relevant intellectual communities a research tool of indispensable value. Together with the other volumes, Greek, Indian and Arabic Logic, will be essential reading for everyone with a curiosity about logic's long development, especially researchers, graduate and senior undergraduate students in logic in all its forms, argumentation theory, AI and computer science, cognitive psychology and neuroscience, linguistics, forensics, philosophy and the history of philosophy, and the history of ideas. (shrink)

The passionate and staunch defence of logic of the controversial thinker Ibn Ḥazm, Abū Muḥammad ʿAlī b. Aḥmad b. Saʿīd of Córdoba (384-456/994-1064), had lasting consequences in the Islamic world. Indeed, his book Facilitating the Understanding of the Rules of Logic and Introduction Thereto, with Common Expressions and Juristic Examples (Kitāb al-Taqrīb li-ḥadd al-manṭiq wa-l-mudkhal ilayhi bi-l-alfāẓ al-ʿāmmiyya wa-l-amthila al-fiqhiyya), composed in 1025-1029, was well known and discussed during and after his time; and it paved the way for (...) the studies of his compatriots Ibn Bājjah (d. 1138), Ibn Ṭufayl (1185), and Ibn Rushd (1198), who each gave demonstrative reasoning a privileged place within the methods of attaining knowledge. Unfortunately, as too often in the history of science, Ibn Ḥazm’s innovative perspectives and contributions in logic have been overlooked or considered with an attitude of contempt. On the one hand, his work has been seen, at best, as promulgating the benefits of studying Aristotle’s logic, so that his contribution is assessed as more didactical than conceptual. And on the other hand, those who do examine his innovations often consider them to be mistaken. As indicated by Chejne (1984, p. 2) contempt towards the logical work of Ibn Ḥazm was also present in its reception by the Eastern philosophers who accused him of deviating from Aristotelian logic and of dabbling in things beyond his capability. However, a reassessment of his work on logic has since begun, by delving into the ways the thinker of Córdoba studied the links between deontic and modal qualification of propositions. In this context Lameer’s (2013) paper on the logical sources of Ibn Ḥazm is worth mentioning; the author (p. 417, footnote 1) observes that, although, strictly speaking, it was al-Fārābī who first drew the parallelism between deontic and modal concepts, it was Ibn Ḥazm who developed it and worked it out in a more precise manner. A primary aim of this paper is to help fill some of these gaps by stressing the role of the work of Ibn Ḥazm in developing a notion of deontic necessity deeply rooted in legal normativity, and in explicitly discussing the transference between deontic and modal concepts. According to our view; the basic units of Islamic deontic logic are what we might call, indulging in terminological anachronism, heteronomous imperatives. As it turns out, the heteronomy of imperatives within Islamic legal systems contrasts with those of the purely moral realm, which seem to be closer to an autonomous conception of moral law. There it concurs again with Leibniz’s proposal to define obligatory as “what is necessary for a good person to do”. In the present paper, we will focus on the heteronomous imperatives of legal systems rather than on the imperatives of the purely moral realm. In this context, the work of Ibn Ḥazm extends the parallelism between the necessity of events and that of human actions stressed by his predecessors. According to our understanding, Ibn Ḥazm’s parallelism can be rendered explicit formally by means of a conditional (or hypothetical) structure shared by both deontic and modal propositions. Moreover, this structure makes apparent that this parallelism displays an underlying system of “degrees”. Indeed, while in the domain of events, given some conditions, it makes sense to distinguish between an event that is more likely to happen than another. Ibn Ḥazm speaks of near and distant possibility (such as the higher degree of likelihood of rain, given the condensation of clouds in December, and its lower degree, when the condensation occurs in summer); and, in the domain of actions, the Islamic notion of weighting actions determines degrees of virtue (or of legal and moral value). So whereas the degree of virtue of performing a forbidden act as determined by the distribution of sanction and reward is 0, we obtain the same value by pondering the likelihood of an impossible event to take place. Furthermore, as discussed in section II.3.2, the system of values at work in the parallelism can be seen as opening the way to a more direct correspondence. Thus, while in the realm of nature, likelihood of occurrence of an event is dependent upon the conditions specific to the occurrence of that event; while, in the realm of jurisprudence, likelihood of performing an action is dependent upon the distribution of reward and sanction specific to that action (being that, given the choice to perform or not perform a given action, those that will be rewarded are more likely to be performed than those that are not). According to this perspective, the point of the parallelism is that both deontic and modal qualifications measure the degree of an action or event to become actual; that is – indulging once more in anachronism (but this time from the Leibnizian background) – the degree measures how feasible (facile) an action or event may be. This suggests that Ibn Ḥazm’s perspectives already herald the links to probability and possibility explored by Leibniz six centuries later – see for example Leibniz’s (1671, A VI, I, p. 424-26) use of probability in the context of conditional right. Nevertheless, it also shows a crucial difference to the approach developed in the Elementa Jura Naturalis: whereas Leibniz’s studies seek to define what is to be just or virtuous, the logical system of deontic imperatives within Islamic jurisprudence presupposes that what is to be virtuous has already been settled. Determining what is to be virtuous is not achieved by logical reasoning within the system of legal jurisprudence, but by delving into the higher objectives of the Sharīʿa. While developing our point, we will delve into the logical structure of the heteronomous imperatives. This distinguishes our contribution from the existing literature, such as the papers of Chejne (1984), Lameer (2014), and Guerrero (1997, 2010, 2014), which do not provide a logical analysis of the deontic concepts put into work by Ibn Ḥazm. The true antecedent to the present paper is the work of Farid Zidani (2007, 2015), who, so far as we know, was the first to undertake such a task. Some of our own developments and general epistemological thoughts go beyond Ibn Ḥazm’s framework and motivations; mainly those contained in sections II.3.2 and IV. However, according to our view, these reflections suggest that Ibn Ḥazm’s approach has the substance for a broader and deeper exploration of the logic of norms. The paper is structured as follows:I.Ibn Ḥazm’s Logic of Heteronomous Imperatives. After presenting some extracts of the relevant text, we proceed by providing a formal reconstruction of the five forms of deontic modalities. II. A Landmark in the History of the Logical Analysis of Norms. Duties and Modalities. In this section, we study the transferences from deontic to modal necessity and possibility. We briefly compare the deontic system of Islamic Jurisprudence with that of Leibniz.III. Leibniz and Hypothetical Imperatives in Law.IV. Beyond Ibn Ḥazm: Conclusions and the Work Ahead. We will conclude the paper by discussing briefly some conceptual points that distinguish the logic of heteronomous imperatives from contemporary deontic logic. Our final words will discuss deontic-modal parallelism in the context of Ibn Ḥazm’s rejection of reasoning by conjecture and what we call “the internalization of nature.”. (shrink)

Ayda Ignez Arruda was a key figure in the development of the Brazilian school of Paraconsistent logic and the first person to write a historical survey of the field. Despite her importa...

The book is a collection of the author¿s selected works in the philosophy and history of logic and mathematics. Papers in Part I include both general surveys of contemporary philosophy of mathematics as well as studies devoted to specialized topics, like Cantor's philosophy of set theory, the Church thesis and its epistemological status, the history of the philosophical background of the concept of number, the structuralist epistemology of mathematics and the phenomenological philosophy of mathematics. Part II contains (...) essays in the history of logic and mathematics. They address such issues as the philosophical background of the development of symbolism in mathematical logic, Giuseppe Peano and his role in the creation of contemporary logical symbolism, Emil L. Post's works in mathematical logic and recursion theory, the formalist school in the foundations of mathematics and the algebra of logic in England in the 19th century. The history of mathematics and logic in Poland is also considered. This volume is of interest to historians and philosophers of science and mathematics as well as to logicians and mathematicians interested in the philosophy and history of their fields. (shrink)

Aristotle was the first thinker to devise a logical system. He drew upon the emphasis on universal definition found in Socrates, the use of reductio ad absurdum in Zeno of Elea, claims about propositional structure and negation in Parmenides and Plato, and the body of argumentative techniques found in legal reasoning and geometrical proof. Yet the theory presented in Aristotle’s five treatises known as the Organon—the Categories, the De interpretatione, the Prior Analytics, the Posterior Analytics, and the Sophistical Refutations—goes far (...) beyond any of these. (shrink)

This short note reviews briefly the history of logic in the last 100 years or so, discussing the rise of “classical” logic, and then of non-classical logic. The role of logic in contemporary departments of mathematics, computer science, and philosophy is then discussed. A few final words address the question of where logic might be going.

This volume brings together the studies by the late Gabriel Nuchelmans (1922-96) on the history of logic and semantics from the 12th to the 17th century. They exemplify his conviction that the study of problems of modern analytical philosophy can help in understanding the authors of earlier centuries - and that the study of earlier solutions can stimulate modern discussions. The first articles deal with medieval theories of the proposition and predication; the final section is concerned with Renaissance (...) philosophy, from Lorenzo Valla to Locke. (shrink)

The author offers some interesting suggestions for the rewriting of the history of logic which modern developments in symbolic logic demand. He divides the history into two parts, the first dealing with what is called the Aristotelian core of logic and the improvements made on that core within a basically classical tradition, and the second, with the tradition of improvements inspired by Leibniz' idea of mathematical logic. The book is brief and much less of (...) a comprehensive history than a prolegomena.--R. H. K. (shrink)

The editors of the Handbook of the History of Logic adopted various strategies of narration in particular volumes of the entire work. Presentations are sometimes o...

Excerpt from A History of Formal Logic In this edition of the most considerable history Of formal logic yet published, the Opportunity has Of course been taken to make some adjustments seen to be necessary in the original, with the author's full concurrence. Only in 36, however, has the numeration of cited passages been altered owing to the introduction of new matter. Those changes are as follows. About the Publisher Forgotten Books publishes hundreds of thousands of (...) rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works. (shrink)

The volume contains twenty essays devoted to the philosophy of mathematics and the history of logic. They have been divided into four parts: general philosophical problems of mathematics, Hilbert's program vs. the incompleteness phenomenon, philosophy of mathematics in Poland, mathematical logic in Poland. Among considered problems are: epistemology of mathematics, the meaning of the axiomatic method, existence of mathematical objects, distinction between proof and truth, undefinability of truth, Goedel's theorems and computer science, philosophy of mathematics in Polish (...) mathematical and logical schools, beginnings of mathematical logic in Poland, contribution of Polish logicians to recursion theory. (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)

It must be acknowledged that the essays presented here do not constitute a systematic account of any sort but represent occasional forays. Some deal with matters that happened to evoke Rescher's interest, others grew out of a chance encounter with a text he deemed to be of particular value. Throughout, challenges of the work itself more than compensated the author's efforts. Logic has always been of crucially important concern to philosophers. Rescher's own involvement with the history of (...) class='Hi'>logic goes back to his work on Leibniz in the 1950's (represented by Chapter 8 of the present book). Thereafter, during the 1960's he devoted considerable effort to the contributions of the medieval logicians of the Arabic-using world (here represented in Chapters 2-6). Moreover, Rescher have from time to time returned to the area to look at some aspects of the more recent scene, as Chapters 8-9 illustrate. In some instances the present essays have been overtaken by subsequent events-events which in fact helped to promote. This is true in particular in chapter 6's work on Arabic work regarding temporal modalities, which was instrumental in evoking the important contributions of Tony Street of Cambridge University. (shrink)

Convinced that logic has a history and that its history always manages to surprise the philosophers, Claude Imbert has devoted much of her work to the study of the Stoic school and of the late-nineteenth-century German logician Gottlob Frege. In the fifth chapter of her book Pour une histoire de la logique, she examines the trajectory of Frege's awareness of what his new logic entails, in particular the way it subverts the project of Kant.

Convinced that logic has a history and that its history always manages to surprise the philosophers, Claude Imbert has devoted much of her work to the study of the Stoic school and of the late-nineteenth-century German logician Gottlob Frege. In the fifth chapter of her book Pour une histoire de la logique, she examines the trajectory of Frege's awareness of what his new logic entails, in particular the way it subverts the project of Kant.

Convinced that logic has a history and that its history always manages to surprise the philosophers, Claude Imbert has devoted much of her work to the study of the Stoic school and of the late-nineteenth-century German logician Gottlob Frege. In the fifth chapter of her book Pour une histoire de la logique, she examines the trajectory of Frege's awareness of what his new logic entails, in particular the way it subverts the project of Kant.

Logical positivism is often characterized as a set of naive doctrines on meaning, method, and metaphysics. In recent decades, however, historians have dismissed this view as a gross misinterpretation. This new scholarship raises a number of questions. When did the standard reading emerge? Why did it become so popular? And how could commentators have been so wrong? This essay reconstructs the history of a “caricature” and rejects the hypothesis that it was developed by ill-informed Anglophone scholars who failed to (...) appreciate the subtleties of European scientific philosophy. It argues that the received view has a more complicated history and was frequently promoted by the European positivists themselves. The essay shows that the view has roots in both American and European scientific philosophy and emerged as a result of the complex interplay between the two communities in the years before the intellectual migration. (shrink)

The book is a collection of the author’s selected works in the philosophy and history of logic and mathematics. Papers in Part I include both general surveys of contemporary philosophy of mathematics as well as studies devoted to specialized topics, like Cantor's philosophy of set theory, the Church thesis and its epistemological status, the history of the philosophical background of the concept of number, the structuralist epistemology of mathematics and the phenomenological philosophy of mathematics. Part II contains (...) essays in the history of logic and mathematics. They address such issues as the philosophical background of the development of symbolism in mathematical logic, Giuseppe Peano and his role in the creation of contemporary logical symbolism, Emil L. Post's works in mathematical logic and recursion theory, the formalist school in the foundations of mathematics and the algebra of logic in England in the 19th century. The history of mathematics and logic in Poland is also considered.This volume is of interest to historians and philosophers of science and mathematics as well as to logicians and mathematicians interested in the philosophy and history of their fields. (shrink)

The History of Philosophical and Formal Logic introduces ideas and thinkers central to the development of philosophical and formal logic. From its Aristotelian origins to the present-day arguments, logic is broken down into four main time periods: Antiquity and the Middle Ages The early modern period High modern period Early 20th century Each new time frame begins with an introductory overview highlighting themes and points of importance. Chapters discuss the significance and reception of influential works and (...) look at historical arguments in the context of contemporary debates. To support independent study, comprehensive lists of primary and secondary reading are included at the end of chapters, along with exercises and discussion questions. By clearly presenting and explaining the changes to logic across the history of philosophy, The History of Philosophical and Formal Logic constructs an easy-to-follow narrative. This is an ideal starting point for students looking to understand the historical development of logic. (shrink)

Is logic masculine? Is women's lack of interest in the "hard core" philosophical disciplines of formal logic and semantics symptomatic of an inadequacy linked to sex? Is the failure of women to excel in pure mathematics and mathematical science a function of their inability to think rationally? Andrea Nye undermines the assumptions that inform these questions, assumptions such as: logic is unitary, logic is independenet of concrete human relations, and logic transcends historical circumstances as well (...) as gender. In a series of studies of the logics of historical figures--Parmenides, Plato, Aristotle, Zeno, Abelard, Ockham, and Frege--she traces the changing interrelationships between logical innovation and oppressive speech strategies, showing that logic is not transcendent truth but abstract forms of language spoken by men, whether Greek ruling citizens, or scientists. (shrink)

Comme tout hommage posthume réussi, le livre que nous recensons souffre de ce douloureux paradoxe : celui dont on honore la mémoire aurait adoré le lire. Il s’agit également de l’un des très rares hommages posthumes dont la liste des contributeurs comprend le nom du défunt lui-même. Joli pied de nez qu’aurait sans aucun doute apprécié l’apparemment très austère Angel d’Ors (1951-2012). Les quelque treize contributions réunies par Paloma Pérez-Ilzarbe et María Cerezo sont parfaitement représen...

This is a "revised, updated and enlarged translation" of the second edition of the single volume Romanian work Istoria Logicii published by Editura Didactica, Bucharest, 1975.