The Boundary Stones of Thought

An Essay in the Philosophy of Logic

Author: Ian Rumfitt

Publisher: Oxford University Press, USA

ISBN: 0198733631

Category: Philosophy

Page: 345

View: 1057

Classical logic has been attacked by adherents of rival, anti-realist logical systems: Ian Rumfitt comes to its defence. He considers the nature of logic, and how to arbitrate between different logics. He argues that classical logic may dispense with the principle of bivalence, and may thus be liberated from the dead hand of classical semantics.

The Boundary Stones of Thought

An Essay in the Philosophy of Logic

Author: Ian Rumfitt

Publisher: OUP Oxford

ISBN: 019105335X

Category: Philosophy

Page: 320

View: 4096

The Boundary Stones of Thought seeks to defend classical logic from a number of attacks of a broadly anti-realist character. Ian Rumfitt is sympathetic to many of the premisses underlying these attacks. Indeed, he regards some of them as effective challenges to certain principles of classical semantics, notably the Principle of Bivalence. He argues, though, that they are ineffective against classical logic itself. The book starts by considering the general problem of how conflicts over logical laws may be rationally discussed and adjudicated. This leads to a consideration of the nature of logic: Rumfitt identifies the particular features that mark out logical consequence from other consequence relations, and he advances a new argument for the ancient thesis that there is a modal element in the notion of logical consequence. He develops a theory of that modal element in terms of perhaps incomplete possibilities, rather than fully determinate possible worlds. Some prima facie powerful arguments against the validity of certain classical logical laws are then analysed in the light of this account of logic. Throughout, care is taken to separate lines of anti-classical argument that, although distinct, are often run together or confused. The analysis yields, as by-products, semantic theories for a number of problematical areas of discourse. These areas include our talk about sub-atomic particles, about the infinite, about infinitesimals, about sets, and vague discourse. Rumfitt concludes by defending his stance of accepting classical logic while rejecting Bivalence, against Aristotle's argument that a classical logician is committed to Bivalence. The ultimate aim is to liberate classical logic from the dead hand of classical semantics.

The Metaphysics of Logic

Author: Penelope Rush

Publisher: Cambridge University Press

ISBN: 1107039649

Category: Mathematics

Page: 278

View: 9932

This wide-ranging collection of essays explores the nature of logic and the key issues and debates in the metaphysics of logic.

The Logical Structure of the World

And, Pseudoproblems in Philosophy

Author: Rudolf Carnap

Publisher: Open Court Publishing

ISBN: 9780812695236

Category: Philosophy

Page: 364

View: 1506

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. In The Logical Structure of the World, Carnap adopts the position of "methodological solipsism" and shows that it is possible to describe the world from the immediate data of experience. In his Pseudoproblems in Philosophy, he asserts that many philosophical problems are meaningless.

Truth, Meaning, Justification, and Reality

Themes from Dummett

Author: Michael Frauchiger

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3110459132

Category: Philosophy

Page: 260

View: 337

This collection concentrates on vital themes from Michael Dummett, one of the most influential and creative analytic philosophers of our time. The contributors, who include some of Dummett's distinguished former students, critically reflect on various concerns of Dummett's ground-breaking work in philosophy of language, metaphysics, and philosophy of mathematics and logic. The essays direct towards aspects of Dummett's pioneering work in the history of analytical philosophy, particularly his interpretations of the works of Frege and of Wittgenstein, which in conjunction with Dummett's own highly original ideas on truth and meaning have shaped decisive contemporary debates concerning notably the distinction between realism and anti-realism. Further, the volume includes a cheerfully serious excursion into popular philosophy by Dummett himself and reveals less known facets of Dummett's many-sided work and activities such as his political philosophy of immigration and asylum, and beyond that, his untiring and warm-hearted campaign for racial justice and humanity. Contributors: Michael Dummett, Eva Picardi, Crispin Wright, Timothy Williamson, Ian Rumfitt, Daniel Isaacson, Dag Prawitz, Dale Jacquette, Alex Burri, Michael Frauchiger.

The Oxford Handbook of Truth

Author: Michael Glanzberg

Publisher: Oxford University Press

ISBN: 0191502669

Category: Philosophy

Page: 800

View: 8614

Truth is one of the central concepts in philosophy, and has been a perennial subject of study. Michael Glanzberg has brought together 36 leading experts from around the world to produce the definitive guide to philosophical issues to do with truth. They consider how the concept of truth has been understood from antiquity to the present day, surveying major debates about truth during the emergence of analytic philosophy. They offer critical assessments of the standard theories of truth, including the coherence, correspondence, identity, and pragmatist theories. They explore the role of truth in metaphysics, with lively discussion of truthmakers, proposition, determinacy, objectivity, deflationism, fictionalism, relativism, and pluralism. Finally the handbook explores broader applications of truth in philosophy, including ethics, science, and mathematics, and reviews formal work on truth and its application to semantic paradox. This Oxford Handbook will be an invaluable resource across all areas of philosophy.

The Universal Computer

The Road from Leibniz to Turing, Third Edition

Author: Martin Davis

Publisher: CRC Press

ISBN: 1351384813

Category: Mathematics

Page: 222

View: 9432

The breathtakingly rapid pace of change in computing makes it easy to overlook the pioneers who began it all. Written by Martin Davis, respected logician and researcher in the theory of computation, The Universal Computer: The Road from Leibniz to Turing explores the fascinating lives, ideas, and discoveries of seven remarkable mathematicians. It tells the stories of the unsung heroes of the computer age – the logicians.

Meanings and Other Things

Author: Gary Ostertag

Publisher: Oxford University Press

ISBN: 0199684936

Category:

Page: 560

View: 3124

Stephen Schiffer's writing has been central to analytic philosophy of language and mind since the 1970s. In 1972 his book Meaning launched an important research program into Gricean, or intention-based, approaches to linguistic meaning, which would come to dominate much subsequent theorizing about language. A sea change occurred in 1987 with the publication of Remnants of Meaning. Schiffer here repudiated the project initiated by Meaning, arguing that the theory of public-language meaning it described and the account of mental representation it required were based on false presuppositions. The ramifications here were far reaching and set the agenda for discussions in the philosophy of language and mind for a generation. In 2003, The Things We Mean initiated a more positive program, but one informed by the negative results of Remnants. Things also reflected the broadening of Schiffer's concerns, which now extended to metaphysics, metaethics, and the skeptical paradoxes. In Meanings and Other Things fourteen leading philosophers explore central themes in Schiffer's writings. Topics range from theories of meaning to moral cognitivism, the nature of paradox, and the problem of vagueness. The volume also contains a comprehensive introduction that describes the evolution of Schiffer's thought, and closes with Schiffer's replies to his critics, extended essays that bring us up to date on Schiffer's current thinking on the themes that have defined not only his career, but philosophy of language as it is now practised.

Art and Morality

Essays in the Spirit of George Santayana

Author: Morris Grossman

Publisher: Oxford University Press

ISBN: 0823257223

Category: PHILOSOPHY

Page: 315

View: 7477

The guiding theme of these essays by aesthetician, musician, and Santayana scholar Morris Grossman is the importance of preserving the tension between what can be unified and what is disorganized, random, and miscellaneous. Grossman described this as the tension between art and morality: Art arrests a sense of change and yields moments of unguarded enjoyment and peace; but soon, shifting circumstances compel evaluation, decision, and action. According to Grossman, the best art preserves the tension between the aesthetic consummation of experience and the press of morality understood as the business of navigating conflicts, making choices, and meeting needs. This concern was intimately related to his reading of George Santayana. The best philosophy, like the best art, preserves the tension between what can be ordered and what resists assimilation, and Grossman read Santayana as exemplifying this virtue in his embrace of multiple perspectives. Other scholars have noted the multiplicity or irony in Santayana's work, but Grossman was unique in taking such a style to be a substantive part of Santayana's philosophizing.

Philosophical Grammar

Author: Ludwig Wittgenstein

Publisher: Univ of California Press

ISBN: 9780520245020

Category: Language Arts & Disciplines

Page: 495

View: 8355

Wittgenstein wrote this book during 1932-1934 - the period just before he began to dictate the Blue Book. In Part I he discusses the notions of "proposition," "sense," "language," "grammar"; what "saying something" is, what distinguishes signs form random marks or noises. Must we start with "primary" signs which need no explanation? In what sense have we a general concept of proposition or of language? The phrases "family of cases" and "family similarities," which the Investigations use, are here; and comparison brings out what is special in the later development. But although it is close to the Investigations at some points, and to the Philosophische Bemerkungen at others, the Philosophical Grammar is an independent work and discusses much that is not in either of them. It is Wittgenstein's fullest treatment of logic and mathematics in their connection with his later understanding of "proposition," "sign," and "system." In Part II he writes on logical inference and generality - criticizing views of Frege and Russell and earlier views of his own, developing his conception of "law of a series" and of " ... and so on"--Leading to his discussion of mathematics, which fills two fifths of the volume: the ideas of "foundations of mathematics," of cardinal numbers, of mathematical proof, and especially of inductive or recursive proofs (with reference to Skolem), which he treats to a depth and extent beyond anything he said of them elsewhere.

The Problems of Philosophy

Author: Bertrand Russell

Publisher: Courier Corporation

ISBN: 048612116X

Category: Philosophy

Page: 128

View: 9048

Accessible, thought-provoking study by Nobel Prize-winner considers distinction between appearance and reality, existence and nature of matter, idealism, inductive logic, intuitive knowledge, many other stimulating subjects.

Proofs and Refutations

The Logic of Mathematical Discovery

Author: Imre Lakatos

Publisher: Cambridge University Press

ISBN: 1316425339

Category: Science

Page: N.A

View: 864

Imre Lakatos's Proofs and Refutations is an enduring classic, which has never lost its relevance. Taking the form of a dialogue between a teacher and some students, the book considers various solutions to mathematical problems and, in the process, raises important questions about the nature of mathematical discovery and methodology. Lakatos shows that mathematics grows through a process of improvement by attempts at proofs and critiques of these attempts, and his work continues to inspire mathematicians and philosophers aspiring to develop a philosophy of mathematics that accounts for both the static and the dynamic complexity of mathematical practice. With a specially commissioned Preface written by Paolo Mancosu, this book has been revived for a new generation of readers.

Kant and the Claims of Taste

Author: Paul Guyer

Publisher: Cambridge University Press

ISBN: 9780521576024

Category: Philosophy

Page: 424

View: 9354

The book offers a detailed account of Kant's views on judgments of taste, aesthetic pleasure, imagination and many other topics.

Vagueness and Thought

Author: Andrew Bacon

Publisher: Oxford University Press

ISBN: 0198712065

Category: Philosophy

Page: 368

View: 1407

Vagueness is the study of concepts that admit borderline cases. The epistemology of vagueness concerns attitudes we should have towards propositions we know to be borderline. On this basis Andrew Bacon develops a new theory of vagueness in which vagueness is fundamentally a property of propositions, explicated in terms of its role in thought.

Plato's Camera

How the Physical Brain Captures a Landscape of Abstract Universals

Author: Paul M. Churchland

Publisher: MIT Press

ISBN: 0262300826

Category: Philosophy

Page: 304

View: 8076

In Plato's Camera, eminent philosopher Paul Churchland offers a novel account of how the brain constructs a representation -- or "takes a picture" -- of the universe's timeless categorical and dynamical structure. This construction process, which begins at birth, yields the enduring background conceptual framework with which we will interpret our sensory experience for the rest of our lives. But, as even Plato knew, to make singular perceptual judgments requires that we possess an antecedent framework of abstract categories to which any perceived particular can be relevantly assimilated. How that background framework is assembled in the first place is the motivating mystery, and the primary target, of Churchland's book. Unexpectedly, this neurobiologically grounded account of human cognition also provides a systematic story of how such low-level epistemological activities are integrated within an enveloping framework of linguistic structures and regulatory mechanisms at the social level. As Churchland illustrates, this integration of cognitive mechanisms at several levels has launched the human race on an epistemological adventure denied to all other terrestrial creatures.

The Interpretation of Cultures

Author: Clifford Geertz

Publisher: Basic Books

ISBN: 0465093566

Category: Social Science

Page: 576

View: 616

In The Interpretation of Cultures, the most original anthropologist of his generation moved far beyond the traditional confines of his discipline to develop an important new concept of culture. This groundbreaking book, winner of the 1974 Sorokin Award of the American Sociological Association, helped define for an entire generation of anthropologists what their field is ultimately about.