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)

This chapter contains sections titled: Philosophy Logic Science History Acknowledgments References.

Analytic philosophy is sometimes said to have particularly close connections to logic and to science, and no particularly interesting or close relation to its own history. It is argued here that although the connections to logic and science have been important in the development of analytic philosophy, these connections do not come close to characterizing the nature of analytic philosophy, either as a body of doctrines or as a philosophical method. We will do better to (...) understand analytic philosophy—and its relationship to continental philosophy—if we see it as a historically constructed collection of texts, which define its key problems and concerns. It is true, however, that analytic philosophy has paid little attention to the history of the subject. This is both its strength—since it allows for a distinctive kind of creativity—and its weakness—since ignoring history can encourage a philosophical variety of “normal science.”. (shrink)

This volume brings together new work on the logic and ontology of plurality and a range of recent articles exploring novel applications to natural language semantics. The contributions in this volume in particular investigate and extend new perspectives presented by plural logic and non-standard mereology and explore their applications to a range of natural language phenomena. Contributions by P. Aquaviva, A. Arapinis, M. Carrara, P. McKay, F. Moltmann, O. Linnebo, A. Oliver and T. Smiley, T. Scaltsas, P. Simons, (...) and B.-Y. Yi . (shrink)

This Element offers a new account of the philosophical significance of logical empiricism that relies on the past forty years of literature reassessing the project. It argues that while logical empiricism was committed to empiricism and did become tied to the trajectory of analytic philosophy, neither empiricism nor logical analysis per se was the deepest philosophical commitment of logical empiricism. That commitment was, rather, securing the scientific status of philosophy, bringing philosophy into a scientific conception of the (...) world. (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)

My purpose in this paper is to shed some light on two questions: In what sense is logic philosophical? And what is philosophical logic? I take these two questions as co-extensive: an answer to one of them is also (or can easily be converted into) an answer to the other. I approach the problem from three perspectives: a conceptual, a descriptive and a prescriptive perspective. In other words, I try to answer the following questions: (i) In what sense (...) can logic be taken as philosophical? (ii) In what sense has logic been taken as philosophical? (iii) In what sense should logic be taken as philosophical? To this end, I analyze excerpts from five works in which meanings are attributed to the expression “philosophical logic”. The meanings are then object of critical analysis: I try to assess which of these semantical alternatives do not hold up as satisfactory answers to (iii). The result of this analysis is then used as a starting point for my own answer to question (iii). (shrink)

Offering a collection of fifteen essays that deal with issues at the intersection of phenomenology, logic, and the philosophy of mathematics, this 2005 book is divided into three parts. Part I contains a general essay on Husserl's conception of science and logic, an essay of mathematics and transcendental phenomenology, and an essay on phenomenology and modern pure geometry. Part II is focused on Kurt Godel's interest in phenomenology. It explores Godel's ideas and also some work of Quine, (...) Penelope Maddy and Roger Penrose. Part III deals with elementary, constructive areas of mathematics. These are areas of mathematics that are closer to their origins in simple cognitive activities and in everyday experience. This part of the book contains essays on intuitionism, Hermann Weyl, the notion of constructive proof, Poincaré and Frege. (shrink)

_An in-depth look at the philosophical issues behind HBO's _Game of Thrones_ television series and the books that inspired it_ George R.R. Martin's _New York Times_ bestselling epic fantasy book series, A Song of Ice and Fire, and the HBO television show adapted from it, have earned critical acclaim and inspired fanatic devotion. This book delves into the many philosophical questions that arise in this complex, character-driven series, including: Is it right for a "good" king to usurp the throne of (...) a "bad" one and murder his family? How far should you go to protect your family and its secrets? In a fantasy universe with medieval mores and ethics, can female characters reflect modern feminist ideals? Timed for the premiere of the second season of the HBO _Game of Thrones_ series Gives new perspectives on the characters, storylines, and themes of _Game of Thrones_ Draws on great philosophers from ancient Greece to modern America to explore intriguing topics such as the strange creatures of Westeros, the incestuous relationship of Jaime and Cersei Lannister, and what the kings of Westeros can show us about virtue and honor as they play their game of thrones Essential reading for fans, _Game of Thrones and Philosophy_ will enrich your experience of your favorite medieval fantasy series. (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)

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 volume will be of particular interest to researchers working in the history, and in the philosophy, of logic and mathematics, and more generally, to ...

Peer Instruction is a simple and effective technique you can use to make lectures more interactive, more engaging, and more effective learning experiences. Although well known in science and mathematics, the technique appears to be little known in the humanities. In this paper, we explain how Peer Instruction can be applied in philosophy lectures. We report the results from our own experience of using Peer Instruction in undergraduate courses in philosophy, formal logic, and critical thinking. We have (...) consistently found it to be a highly effective method of improving the lecture experience for both students and the lecturer. (shrink)

onl y to discuss some claims concerning the relationship between mathematical logic and the philosophy of mathematics that repeatedly occur in his writings. Although I do not know to what extent they are representative of his present position, they correspond to widespread views of the logical community and so seem worth discussing anyhow. Such claims will be used as reference to make some remarks about the present state of relations between mathematical logic and the philosophy of (...) mathematics. (shrink)

1 Logic in philosophy The century that was Logic has played an important role in modern philosophy, especially, in alliances with philosophical schools such as the Vienna Circle, neopositivism, or formal language variants of analytical philosophy. The original impact was via the work of Frege, Russell, and other pioneers, backed up by the prestige of research into the foundations of mathematics, which was fast bringing to light those amazing insights that still impress us to-day. The (...) Golden Age of the 1930s deeply affected philosophy, and heartened the minority of philosophers with a formalanalytical bent. As Brand Blanshard writes in Reason and Analysis (1964) – I quote from memory here, to avoid the usual disappointment when re-reading an original text. (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.

As the title suggests, this is a book devoted not merely to logic; students will also examine the philosophical debates that led to the development of the field.

Available for the first time in 20 years, here are two important works from the 1920s by the best-known representative of the Vienna Circle.

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)

Jacques Derrida’s and Gilles Deleuze’s philosophies of justice share many similar features. For both, justice involves an overturning of law by extralegal means, made possible by an “undecidability” in the judgment-making process. To distinguish their conceptions of justice, we examine their implicit modes of non-classical reasoning with regard to “otherness,” building from Routley and Routley and Daniel Smith, to conclude that Derrida’s thinking on justice is at least paracomplete (or analetheic) while Deleuze’s is just paraconsistent (or dialetheic).

The Tractatus revolves around the connection between two central topics – the preconditions of symbolic representation and the nature of logic-cum-philosophy. Proper philosophy is an activity, namely of revealing the hidden structures that allow language to represent reality by way of logical analysis. At the same time the main purpose of such logical analysis consists in revealing metaphysical statements to be nonsensical. In the subsequent development of analytic philosophy, these two ideas parted company. The positive aim (...) of revealing the logical form of sentences resulted in a program closely associated with Davidson, namely a theory of meaning for natural languages that yields metaphysical corollaries. The negative aim of overcoming metaphysics ushered in the activity of dissolving conceptual confusions through conceptual rather than logical analysis, propelled by the later Wittgenstein. My presentation pursues these historical lines of influence. But the ultimate aim is a substantive one, namely to establish whether the two projects can be kept apart. With the later Wittgenstein, I criticize the claim that formal calculi constitute the hidden structure of natural languages. But I also contend that the hope of engaging in anti-metaphysical dialectic without relying on logico-conceptual analysis of some kind falls prey to a “myth of mere method”. (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)

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)

Originally written in 1956 and revised in 1972, this book explores the work of many of the most important thinkers of the 20th century, including Ayer, ...