This is a long-awaited new edition of one of the best known Oxford Logic Guides. The book gives an informal but thorough introduction to intuitionistic mathematics, leading the reader gently through the fundamental mathematical and philosophical concepts. The treatment of various topics has been completely revised for this second edition. Brouwer's proof of the Bar Theorem has been reworked, the account of valuation systems simplified, and the treatment of generalized Beth Trees and the completeness of intuitionistic first-order logic rewritten. Readers (...) are assumed to have some knowledge of classical formal logic and a general awareness of the history of intuitionism. (shrink)
Michael Dummett is a leading contemporary philosopher whose work on the logic and metaphysics of language has had a lasting influence on how these subjects are conceived and discussed. This volume contains some of the most provocative and widely discussed essays published in the last fifteen years, together with a number of unpublished or inaccessible writings. Essays included are: "What is a Theory of Meaning?," "What do I Know When I Know a Language?," "What Does the Appeal to Use Do (...) for the Theory of Meaning?," "Language and Truth," "Truth and Meaning," "Language and Communication," "The Source of the Concept of Truth," "Mood, Force, and Convention," "Frege and Husserl on Reference," "Realism," "Existence," "Does Quantification Involve Identity?," "Could there be Unicorns?," "Causal Loops," "Common Sense and Physics," "Testimony and Memory," "What is Mathematics About?," "Wittgenstein on Necessity: Some Reflections," and "Realism and Anti-Realism." Serving well as a companion to Dummett's other collections, the essays in this volume are not forbiddingly technical or specialized, and have relevance to many areas of analytic philosophy. (shrink)
The ideas of the German philosopher and mathematician Gottlob Frege lie at the root of the analytical movement in philosophy. Frege and Other Philosophers comprises all of Professor Dummett's published and previously unpublished essays on Frege, with the exception of those included in his Truth and Other Enigmas. In some of these essays he explores the relation of Frege's ideas to those of his predecessors and contemporaries. In others he considers critically some interpretations of Frege, and develops the argument for (...) a sound understanding of Frege's thought which he first delineated in The Interpretation of Frege's Philosophy. Several of the essays illustrate his contention that Frege's work remains the best starting point for the investigation of problems concerning truth, meaning, thought, and language, which are still among the most contentious issues in modern analytical philosophy. Any discussion of Frege's ideas is therefore also an exploration of fundamental and as yet unresolved issues of philosophy. (shrink)
Realism concerning a given subject-matter is characterised as a semantic doctrine with metaphysical consequences, namely as the adoption, for the relevant class of statements, of a truth-conditional theory of meaning resting upon the classical two-valued semantics. it is argued that any departure from classical semantics may, though will not necessarily, be seen as in conflict with some variety of realism. a sharp distinction is drawn between the rejection of realism and the acceptance of a reductionist thesis; though intimately related, neither (...) entails the other. realism is to be classified as "naive", "semi-naive" or "sophisticated": the first of these involves an all but unintelligible epistemological component. (shrink)
Philosophy is a discipline that makes no observations, conducts no experiments, and needs no input from experience. It is an armchair subject, requiring only thought. Yet that thought can advance knowledge in unexpected directions, not only through the discovery of new facts but also through the enhancement of what we already know. Philosophy can clarify our vision of the world and provide exciting ways to interpret it. Of course, philosophy's unified purpose hasn't kept the discipline from splintering into warring camps. (...) Departments all over the world are divided among analytical and continental schools, Heidegger, Hegel, and other major thinkers, challenging the growth of the discipline and obscuring its relevance and intent. Having spent decades teaching in American, Asian, African, and European universities, Michael Dummett has felt firsthand the fractured state of contemporary practice and the urgent need for reconciliation. Setting forth a proposal for renewal and reengagement, Dummett begins with the nature of philosophical inquiry as it has developed for centuries, especially its exceptional openness and perspective-which has, ironically, led to our present crisis. He discusses philosophy in relation to science, religion, morality, language, and meaning and recommends avenues for healing around a renewed investigation of mind, language, and thought. Employing his trademark frankness and accessibility, Dummett asks philosophers to resolve theoretical difference and reclaim the vital work of their practice. (shrink)
In this short, lucid, rich book, Sir Michael Dummett, perhaps the most eminent living British philosopher, sets out his views about some of the deepest questions in philosophy. The fundamental question of metaphysics is: what does reality consist of? Dummett puts forward his controversial view of reality as indeterminate: there may be no fact of the matter about whether an object does or does not have a given property.
Our model of time is the classical continuum of real numbers, and our model of other measurable quantities that change over time is that of functions defined on real numbers with real numbers as values. This model is not derived from reality or from our experience of it, but imposed on reality; and the fit is very imperfect. In classical mathematics, the value of a function for any real number as argument is independent of its value for any other argument: (...) the analogue is Hume's doctrine that events are loose and separate. This makes continuity in the change of any quantity a contingent law of physica, rather than a conceptual necessity. The article explores alternatives to this classical model. (shrink)
In this article the contemporary debate between realism and anti-realism in analytical philosophy is analyzed and discussed. It is claimed that the nature of the reference relation which holds between language and the world is central in this discussion which has both logical, semantical, and epistemological aspects. In a firstpart, A Tarski's (semantic) theory of truth is explained and it is shown how, amongst several theories of truth, Tarski's may be called a realist one. However, a Tarski-style semantics need not (...) lead to a realist theory of Truth and Reference, as is shown in a subsequent part. Here, H Putnam's views on these matters are discussed. It is shown how Putnam in the course of his intellectual history has changed his view from a realist to an anti-realist position. Putnam'sarguments show the importance of logical and metalogical issues in the debate. In a final part, Putnam's views are criticized and it is shown how a line of argument, analogous to Putnam's, may lead to a realist theory of meaning and reference. (shrink)