The first systematic exposition of all the central topics in the philosophy of logic, Susan Haack's book has established an international reputation for its accessibility, clarity, conciseness, orderliness, and range as well as for its thorough scholarship and careful analyses. Haack discusses the scope and purpose of logic, validity, truth-functions, quantification and ontology, names, descriptions, truth, truth-bearers, the set-theoretical and semantic paradoxes, and modality. She also explores the motivations for a whole range of non-classical systems of (...) class='Hi'>logic, including many-valued logics, fuzzy logic, moddal and tense logics, and relevance logics. Persupposing only an elementary knowledge of formal logic, this book includes many useful summary tables and diagrams, as well as a helpful glossary of technical terms. Wide-ranging, informative, and eminently readable, this book has proven a valuable resource for generations of students and scholars in a variety of disciplines outside philosophy needing guidance on the philosophy of logic. (shrink)

Logical Atomism is a philosophy that sought to account for the world in all its various aspects by relating it to the structure of the language in which we articulate information. In _The Philosophy of Logical Atomism,_ Bertrand Russell, with input from his young student Ludwig Wittgenstein, developed the concept and argues for a reformed language based on pure logic. Despite Russell’s own future doubts surrounding the concept, this founding and definitive work in analytical philosophy by (...) one of the world’s most significant philosophers is a remarkable attempt to establish a novel way of thinking. (shrink)

A collection of interviews with influential theorists working in philosophy of logic. The questions: Why were you initially drawn to the philosophy of logic? What are your main contributions to the philosophy of logic? What is the proper role of philosophy of logic in relation to other disciplines, and to other branches of philosophy? What have been the most significant advances in the philosophy of logic? What are the most (...) important open problems in philosophy of logic, and what are the prospects for progress? Interviews with JC Beall, John Lane Bell, Johan van Benthem, Patricia A. Blanchette, Otávio Bueno, James Cargile, Mark Colyvan, Newton Carneiro Affonso da Costa, Pascal Engel, Susan Haack, Jaakko J. Hintikka, Dale Jacquette, Penelope Maddy, Lawrence S. Moss, Catarina Dutilh Novaes, Ahti-Veikko Pietarinen, Graham Priest, Stephen Read, Nicholas Rescher, Stewart Shapiro, Peter Simons, Timothy Williamson, Jan Woleński. (shrink)

THE PHILOSOPHY which I advocate is generally regarded as a species of realism, and accused of inconsistency because of the elements in it which seem contrary to that doctrine. For my part, I do not regard the issue between realists and their opponents as a funda- mental one; I could alter my view on this issue without changing my mind as to any of the doctrines upon which I wish to lay stress. I hold that logic is what (...) is fundamental in philosophy, and that schools should be characterized rather by their logic than by their metaphysic. My own logic is atomic, and it is this aspect upon which I should wish to lay stress. Therefore I prefer to describe my philosophy as "logical atomism," rather than as "realism," whether with or without some prefixed adjective. (shrink)

First published in 1971, Professor Putnam's essay concerns itself with the ontological problem in the philosophy of logic and mathematics - that is, the issue of whether the abstract entities spoken of in logic and mathematics really exist. He also deals with the question of whether or not reference to these abstract entities is really indispensible in logic and whether it is necessary in physical science in general.

First published in 1971, Professor Putnam's essay concerns itself with the ontological problem in the philosophy of logic and mathematics - that is, the issue of whether the abstract entities spoken of in logic and mathematics really exist. He also deals with the question of whether or not reference to these abstract entities is really indispensible in logic and whether it is necessary in physical science in general.

With his customary incisiveness, W. V. Quine presents logic as the product of two factors, truth and grammar-but argues against the doctrine that the logical truths are true because of grammar or language. Rather, in presenting a general theory of grammar and discussing the boundaries and possible extensions of logic, Quine argues that logic is not a mere matter of words.

This talk surveys a range of positions on the fundamental metaphysical and epistemological questions about elementary logic, for example, as a starting point: what is the subject matter of logic—what makes its truths true? how do we come to know the truths of logic? A taxonomy is approached by beginning from well-known schools of thought in the philosophy of mathematics—Logicism, Intuitionism, Formalism, Realism—and sketching roughly corresponding views in the philosophy of logic. Kant, Mill, Frege, (...) Wittgenstein, Carnap, Ayer, Quine, and Putnam are among the philosophers considered along the way. (shrink)

The volume deals with the history of logic, the question of the nature of logic, the relation of logic and mathematics, modal or alternative logics (many-valued, relevant, paraconsistent logics) and their relations, including translatability, to classical logic in the Fregean and Russellian sense, and, more generally, the aim or aims of philosophy of logic and mathematics. Also explored are several problems concerning the concept of definition, non-designating terms, the interdependence of quantifiers, and the idea (...) of an assertion sign. The contributions concerned with Wittgenstein's investigations into the philosophy of logic and mathematics pursue issues relating to logical necessity, the undeniability of the law of the excluded middle, and the source of self-evidence, often characterized in the literature as the "rule-following considerations". Additionally, they examine Wittgenstein's attitudes towards the very idea of set-theory as a possible foundation for arithmetic. The volume also includes a number of contributions on specific issues concerning Wittgenstein's views on moral and religious judgements. (shrink)

Metaphilosophy, Volume 53, Issue 2-3, Page 267-283, April 2022.

This book offers a comprehensive critical survey of issues of historical interpretation and evaluation in Bertrand Russell's 1918 logical atomism lectures and logical atomism itself. These lectures record the culmination of Russell's thought in response to discussions with Wittgenstein on the nature of judgement and philosophy of logic and with Moore and other philosophical realists about epistemology and ontological atomism, and to Whitehead and Russell’s novel extension of revolutionary nineteenth-century work in mathematics and logic. Russell's logical atomism (...) lectures have had a lasting impact on analytic philosophy and on Russell's contemporaries including Carnap, Ramsey, Stebbing, and Wittgenstein. Comprised of 14 original essays, this book will demonstrate how the direct and indirect influence of these lectures thus runs deep and wide. (shrink)

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. Key Features - 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 - 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. (shrink)

Logic in Buddhist Philosophy concerns the systematic study of anumāna (often translated as inference) as developed by Dignāga (480-540 c.e.) and Dharmakīti (600-660 c.e.). Buddhist logicians think of inference as an instrument of knowledge (pramāṇa) and, thus, logic is considered to constitute part of epistemology in the Buddhist tradition. According to the prevalent 20th and early 21st century ‘Western’ conception of logic, however, logical study is the formal study of arguments. If we understand the nature of (...) logic to be formal, it is difficult to see what bearing logic has on knowledge. In this paper, by weaving together the main threads of thought that are salient in Dignāga’s and Dharmakīti’s texts, I shall re-conceive the nature of logic in the context of epistemology and demarcate the logical part of epistemology which can be recognised as logic. I shall demonstrate that we can recognise the logical significance of inference as understood by Buddhist logicians despite the fact that its logical significance lies within the context of knowledge. (shrink)

Putnam, Hilary FPhilosophy of logic. Harper Essays in Philosophy. Harper Torchbooks, No. TB 1544. Harper & Row, Publishers, New York-London, 1971. v+76 pp. The author of this book has made highly regarded contributions to mathematics, to philosophy of logic and to philosophy of science, and in this book he brings his ideas in these three areas to bear on the traditional philosophic problem of materialism versus (objective) idealism. The book assumes that contemporary science (mathematical and (...) physical) is largely correct as far as it goes, or at least that it is rational to believe in it. The main thesis of the book is that consistent acceptance of contemporary science requires the acceptance of some sort of Platonistic idealism affirming the existence of abstract, non-temporal, non-material, non-mental entities (numbers,scientific laws, mathematical formulas, etc.). The author is thus in direct opposition to the extreme materialism which had dominated philosophy of science in the first three quarters of this century. the book can be especially recommended to the scientifically literate, general reader whose acquaintance with these areas is limited to the earlier literature of when it had been assumed that empiricistic materialism was the only philosophy compatible with a scientific outlook. To this group the book presents an eye-opening challenge fulfilling the author’s intention of “shaking up preconceptions and stimulating further discussion”. (shrink)

The paper addresses three main issues drawing on Husserl’s writings on logic. First, what gives the logical objects their objective status, given the fact that these are intimately connected with human mental processes? Second, if logical objects are objective then how is logical knowledge at all possible? The answer to this question leads to a transcendental foundation of formal logic. Third, how do the principles of logic apply to the real world? This question can be addressed by (...) positing a formal ontology. Against Russell and Whitehead, it has been pointed out that even if logical implication does not in any way depend on human mind, inference is definitely mind-dependent. But this thesis does not necessarily lead to psychologism, as has been pointed out by contemporary Indian logicians. Indian theories of inference deal with the question of truth and falsity but lack a formal ontology. Both pure logic and modern physics claim to be independent of human existence. This claim becomes evident in the conversation between Heisenberg and Tagore. Husserl had distinguished between logical grammar and logic of consequences. The notions of truth and falsity are relevant only in the context of logic of consequences. However, none of the well-known theories of truth, correspondence, coherence or pragmatic theory is free from defects. Following in the footprints of the Advaita Vedantins, it has been maintained that falsity is more fundamental than truth. In the process of cognitive history, a proposition is taken to be true, unless its falsity is proven. Hence the conclusion: since Philosophy is search for the truth, all Philosophy—infinitely—is a gradual rejection of all claims to truth and finally, destroys itself. (shrink)

This book explores the results of applying empirical methods to the philosophy of logic and mathematics. Much of the work that has earned experimental philosophy a prominent place in twenty-first century philosophy is concerned with ethics or epistemology. But, as this book shows, empirical methods are just as much at home in logic and the philosophy of mathematics. -/- Chapters demonstrate and discuss the applicability of a wide range of empirical methods including experiments, surveys, (...) interviews, and data-mining. Distinct themes emerge that reflect recent developments in the field, such as issues concerning the logic of conditionals and the role played by visual elements in some mathematical proofs. -/- Featuring leading figures from experimental philosophy and the fields of philosophy of logic and mathematics, this collection reveals that empirical work in these disciplines has been quietly thriving for some time and stresses the importance of collaboration between philosophers and researchers in mathematics education and mathematical cognition. (shrink)

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. Key Features - 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 - 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. (shrink)

This book addresses the hasty development of modern logic, especially its introducing and embracing various kinds of artificial languages and moving from the study of natural languages to that of artificial ones. This shift seemed extremely helpful and managed to elevate logic to a new level of rigor and clarity. However, the change that logic underwent in this way was in no way insignificant, and it is also far from an insignificant matter to determine to what extent (...) the "new logic" only engaged new and more powerful instruments to answer the questions posed by the "old" one, and to what extent it replaced these questions with new ones. Hence, this movement has generated brand new kinds of philosophical problems that have still not been dealt with systematically. Philosophy of Logical Systems addresses these new kinds of philosophical problems that are intertwined with the development of modern logic. Jaroslav Peregrin analyzes the rationale behind the introduction of the artificial languages of logic; classifies the various tools which were adopted to build such languages; gives an overview of the various kinds of languages introduced in the course of modern logic and the motifs of their employment; discusses what can actually be achieved by relocating the problems of logic from natural language into them; and reaches certain conclusions with respect to the possibilities and limitations of this "formal turn" of logic. This book is both an important scholarly contribution to the philosophy of logic and a systematic survey of the standard logical systems that were established during the short history of modern logic. (shrink)

In this historical article, Newton da Costa discusses Francisco Miró Quesada’s philosophical ideas about logic. He discusses the topics of reason, logic, and action in Miró Quesada’s work, and in the final section he offers his critical view. In particular, he disagrees with Miró Quesada’s stance on the historicity of reason, for whom “reason is essentially absolute”, whereas for da Costa it “is being constructed in the course of history”. Da Costa concludes by emphasizing the importance of Miró (...) Quesada’s theory of logic and reason, despite it still being incomplete. -/- Historical article by Newton da Costa, annotated and translated by J. C. Cifuentes and L. F. Bartolo Alegre. (shrink)

This work is divided into two parts. Part I contains sixteen critical es says by prominent philosophers and computer scientists. Their papers offer insightful, well-argued contemporary views of a broad range of topics that lie at the heart of philosophy in the second half of the twen tieth century: semantics and ontology, induction, the nature of prob ability, the foundations of science, scientific objectivity, the theory of naming, the logic of conditionals, simulation modeling, the relatiOn be tween minds (...) and machines, and the nature of rules that guide be havior. In this volume honoring Arthur W. Burks, the philosophical breadth of his work is thus manifested in the diverse aspects of that work chosen for discussion and development by the contributors to his Festschrift. Part II consists of a book-length essay by Burks in which he lays out his philosophy of logical mechanism while responding to the papers in Part I. In doing so, he provides a unified and coherent context for the range of problems raised in Part I, and he highlights interesting relationships among the topics that might otherwise have gone un noticed. Part II is followed by a bibliography of Burks's published works. (shrink)

This is the second edition of an important introduction to Leibniz's philosophy of logic and language first published in 1972. It takes issue with several traditional interpretations of Leibniz (by Russell amongst others) while revealing how Leibniz's thought is related to issues of great interest in current logical theory. For this new edition, the author has added new chapters on infinitesimals and conditionals as well as taking account of reviews of the first edition.

This volume collects together all of Russell's philosophical papers inspired by his work with Whitehead on Principia Mathematica.

First published in 1971, Professor Putnam's essay concerns itself with the ontological problem in the philosophy of logic and mathematics - that is, the issue of whether the abstract entities spoken of in logic and mathematics really exist. He also deals with the question of whether or not reference to these abstract entities is really indispensible in logic and whether it is necessary in physical science in general.

It is possible that some logician may not know that a and b exist, not know what they denote, and whether they are true or untrue. But virtually every logician will agree that the expression a ⊃ b cannot be true in a case in which a is true and b is false. Truth relationships thus understood — inasmuch as they are not specific to any particular field of science — are generally regarded as the proper concern of logic. (...) Only their study can uncover the typically human capacity to derive one piece of knowledge from another without referring back directly to objective reality. (shrink)

The polymathic Leibniz was surely one of the greatest and most enigmatic figures produced by the "century of genius." He is the only philosopher whom the renowned historian of the Prussian Academy of Sciences, Adolf von Harnack, would admit as a colleague to that august body, and Leibniz is universally admired by metaphysicians, theologians, advocates of cosmopolitanism and religious tolerance, students of international law, and, not the least, by philosophers of logic and language. Although efforts to canonize Leibniz as (...) the pure type of "harmonic synthesizer" have been under way for quite a long time, philosophers and historians are no longer so anxious as they once were to work out a synthetic unification of these and many other perspectives of Leibniz as was Mahnke, for instance, who characterized Leibniz’ philosophy as a synthesis of universal mathematics and individual metaphysics. (shrink)

For his contribution to the general series of Harper Essays in Philosophy, Hilary Putnam selects only one of several philosophical problems in the interrelated fields of logic and/or mathematics that have interested him, viz. the nominalism-realism issue: Are the "abstract entities" spoken of in these sciences, such as classes, number, functions from various kinds of things to real numbers, things that "really exist" or not? He is concerned to present a detailed argument for his own "qualified realism" rather (...) than a survey of current opinions. He argues persuasively that while a nominalist would like to eliminate all talk of logical classes such as S, M and P in favor of such circumlocutions as "The following schema turns out to be true no matter what words or phrases of the appropriate kind one may substitute for the letters S, M and P," etc., such descriptions avoid references to classes only by replacing them with equally nonphysical entities such as "all possible words, strings of letters, formalized languages," etc., and that the notion of truth or validity itself cannot be applied to physical objects or material inscriptions, but to what sentences mean or say, and the things they say are not physical. He rejects Quine's distinction that first order statements or arguments such as "All crows are black; all back things absorb light, therefore," etc., are logical truths, whereas "For all classes S, M and P, if all S is M and all M is P, then all S is P," are mathematical. This runs counter, he says, to the whole logical tradition. The natural intention of the logician in setting down first-order schemata is to assert implicitly their validity and that itself is a second-order assertion. All logic, therefore, including quantification theory, involves references to classes. This also highlights the difficulty of distinguishing between logic and mathematics in terms of first and second order logic, for if only the former is stipulated to be the proper domain of logic, then we must accept the awkward consequence that validity and implication turn out to be notions that belong to mathematics rather than logic. Since the nominalistic position presents the same problems for mathematics as for logic, Putnam sees no point in trying to draw any sharp distinction between the two, which explains his initial broad interpretation of logic as including all of pure mathematics and also the title of the book. To avoid some of the classical objections to a realistic interpretation of sets, he points up the distinction between a predicative and impredicative conception of set. Whereas the latter speaks of all sets of individuals as a well-defined totality, the former defines "set" only for a particular language N or a hierarchic series of languages, N, N', N", etc. in which it is still nonsensical to speak of "all sets" without qualification, though one can speak of "all" up to any given level in the series. While some form of set theory is necessary for all the sciences, both formal and physical, one can get along with predicative set theory. Putnam's basic argument for realism then comes down to this. Quantification over mathematical entities such as things, real numbers and functions is indispensable for logic, mathematics and the physical sciences and this commits one to accept the existence of such entities. In the final stages of the argument he examines and rejects the alternative options to realism, namely that realistic locutions about such entities represent logically deviant forms of speech, or that mathematical truths are "true by pure convention" or that such "entities" are useful fictions. In the closing paragraphs he indicates two other philosophical problems in logic that merit extensive discussion, namely the problem of equivalent constructions which is relevant to the question of whether mathematics needs "foundations" and the problem of whether we may not have to revise logical principles as we have geometrical ones on the grounds that in some sense logic may have empirical foundations.--A. B. W. (shrink)