In arithmetic, if only because many of its methods and concepts originated in India, it has been the tradition to reason less strictly than in geometry, ...

This highly acclaimed book is a major contribution to the philosophy of language as well as a systematic interpretation of Frege, indisputably the father of ...

A collection of all but two of the author's philosophical essays and lectures originally published or presented before August 1976.

§ i. After deserting for a time the old Euclidean standards of rigour, mathematics is now returning to them, and even making efforts to go beyond them. ...

This is a critical examination of the astonishing progress made in the philosophical study of the properties of the natural numbers from the 1880s to the 1930s. Reassessing the brilliant innovations of Frege, Russell, Wittgenstein, and others, which transformed philosophy as well as our understanding of mathematics, Michael Potter places arithmetic at the interface between experience, language, thought, and the world.

In this work Dummett discusses, section by section, Frege's masterpiece The Foundations of Arithmetic and Frege's treatment of real numbers in the second volume ...

1. Naturalism Naturalism, it has been said, is the distinctive development in philosophy over the last thirty years. There has been a naturalistic turn away from the a priori methods of traditional philosophy to a conception of philosophy as continuous with natural science. The doctrine has been extensively discussed and has won considerable following in the USA. This is, on the whole, not true of Britain and continental Europe, where the pragmatist tradition never took root, and the temptations of scientism (...) in philosophy were less alluring. Contemporary American naturalism originates in the writings of Quine, the metaphysician of twentieth-century science. With extraordinary panache, he painted a largescale picture of human nature, of language and of the web of belief. I believe that in almost every major respect, it is, like the picture painted by Descartes, the great metaphysician of seventeenth-century science, mistaken. But it evidently appeals to the spirit of the times. So it is worthy of critical examination and careful refutation. I shall argue that the naturalistic turn is a cul-de-sac – a turn that is to be passed by if we are to keep to the highroad of good sense. Naturalism, like so many of Quine’s doctrines, was propounded in response to Carnap. As Quine understood matters, Carnap had been persuaded by Russell’s Our Knowledge of the External World that it is the task of philosophy to demonstrate that our knowledge of the external world is a logical construction out of, and hence can be reduced to, elementary experiences. Quine rejected the reductionism of Carnap’s Logischer Aufbau, and found the idealist basis uncongenial to his own dogmatic realist behaviourism, inspired by Watson and later reinforced by Skinner. The rejection of reductionism and ‘unregenerate realism’, Quine averred, were the sources of his naturalism (FME 72). What exactly was this? We can distinguish in Quine between three different but inter-related programmes for future philosophy: epistemological, ontological and philosophical naturalism. Naturalized epistemology is to displace traditional epistemology, transforming the investigation into ‘an enterprise within natural science’ (NNK 68) – a psychological enterprise of investigating how the ‘input’ of radiation, etc., impinging on the nerve endings of human beings can ‘ultimately’ result in an ‘output’ of our theoretical descriptions of the external world.. (shrink)

Carnap's position on mathematical truth in The Logical Syntax of Language has been attacked from two sides: Kreisel argues that it is formalistic but should not be, and Friedman argues that it is not formalistic but needs to be. In this paper I argue that the Carnap of Syntax does not eliminate our ordinary notion of mathematical truth in favour of a formal analogue; so Carnap's notion of mathematical truth is not formalistic. I further argue that there is no conflict (...) between Carnap's use of informal notions and his principle of tolerance; so Carnap's definition of mathematical truth need not be formalistic. CiteULike Connotea Del.icio.us What's this? (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)

This work is the long awaited sequel to the author’s classic Frege: Philosophy of Language. But it is not exactly what the author originally planned. He tells us that when he resumed work on the book in the summer of 1989, after a long interruption, he decided to start afresh. The resulting work followed a different plan from the original drafts. The reader does not know what was lost by their abandonment, but clearly much was gained: The present work may (...) be the most compactly organized of Dummett’s philosophical books, and its value as commentary on Frege is enhanced by its being organized as a study of Die Grundlagen der Arithmetik and selected parts of Grundgesetze. Moreover, since Dummett has been thinking and writing about Frege for forty years, we have a single, mature chronological stage of his thought. (shrink)