This volume pays homage to the historian of logic Angel d’Ors (1951-2012), by bringing together a set of studies that together illuminate the complex historical development of logic and semantics. Two main traditions, Aristotelian and terminist, are showcased to demonstrate the changes and confrontations that constitute this history, and a number of different authors and texts, from the Boethian reception of Aristotle to the post-medieval terminism, are discussed. Special topics dealt with include the medieval reception of ancient logic; technical tools for the medieval analysis of language; the medieval theory of consequence; the medieval practice of disputation and sophisms; and the post-medieval refinement of the terminist tools. Contributors are E.J. Ashworth, Allan Bäck, María Cerezo, Sten Ebbesen, José Miguel Gambra, C.H. Kneepkens, Kalvin Normore, Angel d’Ors, Paloma Pérez-Ilzarbe, Stephen Read, Joke Spruyt, Luisa Valente, and Mikko Yrjönsuuri. These articles were also published in Vivarium, Volume 53, Nos. 2-4 (2015).

This book sets out for the first time in English and in the terms of modern logic the semantics of the Port Royal Logic (La Logique ou l’Art de penser, 1662-1685) of Antoine Arnauld and Pierre Nicole, perhaps the most influential logic book in the 17th and 18th centuries. Its goal is to explain how the Logic reworks the foundation of pre-Cartesian logic so as to make it compatible with Descartes’ metaphysics. The Logic’s authors forged a new theory of reference based on the medieval notion of objective being, which is essentially the modern notion of intentional content. Indeed, the book’s central aim is to detail how the Logic reoriented semantics so that it centered on the notion of intentional content. This content, which the Logic calls comprehension, consists of an idea’s defining modes. Mechanisms are defined in terms of comprehension that rework earlier explanations of central notions like conceptual inclusion, signification, abstraction, idea restriction, sensation, and most importantly within the Logic’s metatheory, the concept of idea-extension, which is a new technical concept coined by the Logic. Although Descartes is famous for rejecting "Aristotelianism," he says virtually nothing about technical concepts in logic. His followers fill the gap. By putting to use the doctrine of objective being, which had been a relatively minor part of medieval logic, they preserve more central semantic doctrines, especially a correspondence theory of truth. A recurring theme of the book is the degree to which the Logic hews to medieval theory. This interpretation is at odds with what has become a standard reading among French scholars according to which this 16th-century work should be understood as rejecting earlier logic along with Aristotelian metaphysics, and as putting in its place structures more like those of 19th-century class theory.

Logical form has always been a prime concern for philosophers belonging to the analytic tradition. For at least one century, the study of logical form has been widely adopted as a method of investigation, relying on its capacity to reveal the structure of thoughts or the constitution of facts. This book focuses on the very idea of logical form, which is directly relevant to any principled reflection on that method. Its central thesis is that there is no such thing as a correct answer to the question of what is logical form: two significantly different notions of logical form are needed to fulfill two major theoretical roles that pertain respectively to logic and to semantics. This thesis has a negative and a positive side. The negative side is that a deeply rooted presumption about logical form turns out to be overly optimistic: there is no unique notion of logical form that can play both roles. The positive side is that the distinction between two notions of logical form, once properly spelled out, sheds light on some fundamental issues concerning the relation between logic and language.

This collection of new essays presents cutting-edge research on the semantic conception of logic, the invariance criteria of logicality, grammaticality, and logical truth. Contributors explore the history of the semantic tradition, starting with Tarski, and its historical applications, while central criticisms of the tradition, and especially the use of invariance criteria to explain logicality, are revisited by the original participants in that debate. Other essays discuss more recent criticism of the approach, and researchers from mathematics and linguistics weigh in on the role of the semantic tradition in their disciplines. This book will be invaluable to philosophers and logicians alike.

Although philosophical semantics has become both a discipline in its own right and the source of the analytic techniques used in the rest of philosophy, its foundations have themselves been problematic. To provide a unified account of the field, John L. Pollock discusses issues including the nature of possible worlds, modalities, counterfactuals, and causation. Originally published in 1985. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Brimming with visual examples of concepts, derivation rules, and proof strategies, this introductory text is ideal for students with no previous experience in logic. Symbolic Logic: Syntax, Semantics, and Proof introduces students to the fundamental concepts, techniques, and topics involved in deductive reasoning. Agler guides students through the basics of symbolic logic by explaining the essentials of two classical systems, propositional and predicate logic. Students will learn translation both from formal language into English and from English into formal language; how to use truth trees and truth tables to test propositions for logical properties; and how to construct and strategically use derivation rules in proofs. This text makes this often confounding topic much more accessible with step-by-step example proofs, chapter glossaries of key terms, hundreds of homework problems and solutions for practice, and suggested further readings.

The book provides a historical (with an outline of the history of the concept of truth from antiquity to our time) and systematic exposition of the semantic theory of truth formulated by Alfred Tarski in the 1930s. This theory became famous very soon and inspired logicians and philosophers. It has two different, but interconnected aspects: formal-logical and philosophical. The book deals with both, but it is intended mostly as a philosophical monograph. It explains Tarski’s motivation and presents discussions about his ideas (pro and contra) as well as points out various applications of the semantic theory of truth to philosophical problems (truth-criteria, realism and anti-realism, future contingents or the concept of correspondence between language and reality).

Originally published in 1990. A common complaint of philosophers, and men in general, has been that women are illogical. On the other hand, rationality, defined as the ability to follow logical argument, is often claimed to be a defining characteristic of man. Andrea Nye undermines assumptions such as: logic is unitary, logic is independent of concrete human relations, 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, imperial administrators, church officials, or scientists. She relates logical techniques, such as logical division, syllogisms, and truth functions, to ways in which those with power speak to and about those subject to them. She shows, in the specific historical settings of Ancient and Hellenistic Greece, medieval Europe, and Germany between the World Wars, how logicians reworked language so that dialogue and reciprocity are impossible and one speaker is forced to accept the words of another. In the personal, as well as confrontative style of her readings, Nye points the way to another power in the words of women that might break into and challenge rational discourses that have structured Western thought and practice.

The papers presented in this volume examine topics of central interest in contemporary philosophy of logic. They include reflections on the nature of logic and its relevance for philosophy today, and explore in depth developments in informal logic and the relation of informal to symbolic logic, mathematical metatheory and the limiting metatheorems, modal logic, many-valued logic, relevance and paraconsistent logic, free logics, extensional v. intensional logics, the logic of fiction, epistemic logic, formal logical and semantic paradoxes, the concept of truth, the formal theory of entailment, objectual and substitutional interpretation of the quantifiers, infinity and domain constraints, the Löwenheim-Skolem theorem and Skolem paradox, vagueness, modal realism v. actualism, counterfactuals and the logic of causation, applications of logic and mathematics to the physical sciences, logically possible worlds and counterpart semantics, and the legacy of Hilbert's program and logicism. The handbook is meant to be both a compendium of new work in symbolic logic and an authoritative resource for students and researchers, a book to be consulted for specific information about recent developments in logic and to be read with pleasure for its technical acumen and philosophical insights.- Written by leading logicians and philosophers- Comprehensive authoritative coverage of all major areas of contemporary research in symbolic logic- Clear, in-depth expositions of technical detail- Progressive organization from general considerations to informal to symbolic logic to nonclassical logics- Presents current work in symbolic logic within a unified framework- Accessible to students, engaging for experts and professionals- Insightful philosophical discussions of all aspects of logic- Useful bibliographies in every chapter