A common reaction to Hegel’s suggestion that we collapse Kant’s distinction between form and content is that, since such a move would also deprive us of any way of distinguishing the merely logical from the real possibility of our concepts, it is incoherent and ought to be rejected. It is true that these two distinctions are intimately related in Kant, such that if one goes, the other does as well. But it is less obvious that giving them up as Kant (...) conceives them is as incoherent a proposal as many of Hegel’s critics think. It has been the point of a recent account of Hegel’s idealism to demonstrate that his critique of Kant’s dichotomy between form and content or concept and intuition does not commit him to the view that human cognition is materially creative of its content in the manner of a God-like or intuitive intellect—does not, in other words, signify a return to a pre-Critical metaphysics. This is the interpretative stance I adopt here as well, in hope of giving defenders of Kant reasons for taking Hegel more seriously. (shrink)

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)

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.

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)

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.

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)

Philosophy of Logic: 5 Questions is a collection of interviews with some of the world's most influential and prominent scholars working on 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, OtAvio 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 Wole ski ". (shrink)

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.

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.

1 Meaning and Truth Objection to propositions Propositions as information Diffuseness of empirical meaning Propositions dismissed Truth and semantic ascent Tokens and eternal sentences 2 Grammar Grammar by recursion Categories Immanence and transcendence Grammarian's goal reexamined Logical grammar Redundant devices Names and functors Lexicon, particle, and name Criterion of lexicon Time, events, adverbs Attitudes and modality 3 Truth Truth and satisfaction Satisfaction by sequences Tarski's definition of truth Paradox in the object language Resolution in set theory 4 Logical Truth In (...) terms of structure In terms of substitution In terms of models Adequacy of substituteon In terms of proof In terms of grammar 5 The Scope of Logic Affinities of identity Identity reduced Set theory Set theory in sheep's clothing Logic in wolf's clothing Scope of the virtual theory Simulated class quantification Other simulated quantification Annexes 6 Deviant Login Change of logic, change of subject Logic in translation Law of excluded middle Debate about the dichotomy Intuitionism Branched quantifiers Substitutional quantification Its strength 7 The Ground of Logical Truth The semblance of a theory An untenable dualism The place of logic For Further Reading Index. (shrink)

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)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:The Philosophy of the Commentators, 200–600 AD: A Sourcebook. Vol. I, Psychology (with Ethics and Religion)James WilberdingRichard Sorabji. The Philosophy of the Commentators, 200–600 AD: A Sourcebook. Vol. I, Psychology (with Ethics and Religion). Pp. xv + 430. Vol. II, Physics. Pp. xix + 401. Vol. III, Logic and Metaphysics Pp. xvii + 394. Ithaca, New York: Cornell University Press, 2005. Paper, $39.50, each volume.Interest (...) in the Greek commentators continues to grow, thanks in large part to Richard Sorabji, who has done more than anyone else to reestablish them as at once faithful and original philosophers who remain relevant even to modern students of philosophy. The Sourcebook makes the commentators still more accessible by providing an introductory tool for the systematic exploration of their thought.Each volume contains a 30-page introduction consisting of roughly six sections: an explanation of the aims of the Sourcebook (1–5), a brief introduction to the commentators (5–12), a survey of issues relating to Neoplatonism (12–14) and the compatibility of Platonic and Aristotelian philosophy (14–19), a section entitled "The commentators and Christianity" (19–25), which is largely devoted to offering renewed support for Sorabji's suggestion from Aristotle Transformed (Cornell 1990) regarding the content of Ammonius's concession to the Christian patriarch in the 490s, and, finally, a short, volume-specific section designed to survey some of the innovations and disagreements in the respective subjects (25–28/29/30). Each volume is divided into between 18 and 28 topics, which are subdivided into as many as 26 subtopics (on average 5–6), and these subtopics are often further divided into as many as 8 subsections (on average roughly 4 subsections for every 10 subtopics). Nearly all subtopics and subsections contain introductions (typically one or two paragraphs, occasionally longer) as well as some interspersed annotations that together serve two functions: they review some of the relevant background passages—mostly from Plato and Aristotle, but also from the Presocratic and Hellenistic schools—and they introduce and summarize the passages contained in the Sourcebook by surveying some of the issues raised by the passages that follow. Both the introductions and the annotations are kept brief, since Sorabji's aim is to explain the relevant concepts "only so far as necessary for a first understanding" (4). The passages themselves are mostly drawn from surviving Greek as well as Latin texts of the commentators—a group that features Plotinus, Porphyry, and Proclus (see 4)—but also includes a handful of passages preserved only in Hebrew and Arabic. For example, included in the subtopic devoted to the status of nature (Physics 1[b]) is an English translation of a passage from Themistius preserved only in Averroes' Metaphysics. Over one hundred scholars contributed translations, though Sorabji emphasizes that in the interests of greater harmony he reworked them so that "the final versions are rather based on the work of the translators" (xvii). Often, Sorabji also refers to additional passages containing like-minded or opposing views not included in the Sourcebook, as well as cross-references to other passages in the Sourcebook. In most cases he provides a helpful selection of secondary literature on the subject. [End Page 470]There are some striking differences between the Sourcebook and two comparable introductory collections, Long and Sedley (LS), and Kirk, Raven, and Schofield (KRS), which might offer the clearest picture of the nature and objectives of the Sourcebook. The foremost of these is the very task of introducing periods in which the amount of surviving material is so different. Whereas of Hellenistic and especially of Pre-Socratic philosophy we have in large part only fragments, of the commentators we possess thousands of pages of Greek text. This means that the Sourcebook is the result of a long process of selection and systematization that ultimately captures only a fraction of the available material. Far from being a shortcoming, this belongs to the very nature of framing an introduction to such an extensive body of literature and would become problematic only if Sorabji wished to establish a canon of the philosophically significant texts of the period. He explicitly rejects such an aim, however (5). The Sourcebook also... (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)

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 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)

This chapter contains sections titled: Introduction Logical Consequence Logical Pluralism Applications of Logic Conclusion References.

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)