Proofs and Refutations is essential reading for all those interested in the methodology, the philosophy and the history of mathematics. Much of the book takes the form of a discussion between a teacher and his students. They propose various solutions to some mathematical problems and investigate the strengths and weaknesses of these solutions. Their discussion (which mirrors certain real developments in the history of mathematics) raises some philosophical problems and some problems about the nature of mathematical discovery or creativity. Imre (...) Lakatos is concerned throughout to combat the classical picture of mathematical development as a steady accumulation of established truths. He shows that mathematics grows instead through a richer, more dramatic process of the successive improvement of creative hypotheses by attempts to 'prove' them and by criticism of these attempts: the logic of proofs and refutations. (shrink)

Das Ziel: Konstitutionssystem der Begriffe Das Ziel der vorliegenden Untersuchungen ist die Aufstellung eines erkenntnismäßig-logischen Systems der ...

First published in 1949 expressly to introduce logical positivism to English speakers. Reichenbach, with Rudolph Carnap, founded logical positivism, a form of epistemofogy that privileged scientific over metaphysical truths.

This early work by Robin G. Collingwood was originally published in 1939 and we are now republishing it with a brand new introductory biography. 'An Autobiography' is the story of Collingwood's personal and academic life. Robin George Collingwood was born on 22nd February 1889, in Cartmel, England. He was the son of author, artist, and academic, W. G. Collingwood. He was greatly influenced by the Italian Idealists Croce, Gentile, and Guido de Ruggiero. Another important influence was his father, a professor (...) of fine art and a student of Ruskin. He published many works of philosophy, such as Speculum Mentis (1924), An Essay on Philosophic Method (1933), and An Essay on Metaphysics (1940). (shrink)

2014 Reprint of 1945 Edition. Full facsimile of the original edition, not reproduced with Optical Recognition Software. The first part deals with Greek cosmology and is the longest, the most elaborate and, on the whole, the liveliest part of a book which never deviates into dullness. The dominant thought in Greek cosmology, Collingwood holds, was the microcosm-macrocosm analogy, nature being the substance of something ensouled where "soul" meant the self-moving. Part II is "The Renaissance View of Nature ." Collingwood describes (...) the rise and decline of the deists' view of Nature as a machine designed by the Great Contriver who, having turned it out, watches it go. Part III, "The Modern View of Nature," deals with very recent or contemporary philosophy and science, discerning in it a radical evolutionism first in biology and later in cosmology. Remains to this day a classic text in the history of ideas. (shrink)

This paper discusses the connection between the actual history of mathematics and Lakatos's philosophy of mathematics, in three parts. The first points to studies by Lakatos and others which support his conception of mathematics and its history. In the second I suggest that the apparent poverty of Lakatosian examples may be due to the way in which the history of mathematics is usually written. The third part argues that Lakatos is right to hold philosophy accountable to history, even if Lakatos's (...) own view of mathematics fails that test. (shrink)

Alexandre Koyré a réuni trois ans avant sa mort (1964) ces Etudes d'histoire de la pensée philosophique. On retrouve ici la curiosité inlassable de l'auteur des Etudes newtoniennes, qui nous livre une histoire de la pensée philosophique de Zénon à Martin Heidegger, de Spinoza à Condorcet et à Louis de Bonald. L'auteur aborde à la fois les questions sur le vide et l'espace infini au XIVe siècle, celles sur le temps d'après la Logique d'Iéna, dont la doctrine inspirera la phénoménologie (...) de Husserl, de Heidegger et de Sartre, et d'autres sur la langue et la terminologie hégéliennes. (shrink)

This book argues against the view that mathematical knowledge is a priori,contending that mathematics is an empirical science and develops historically,just as ...

The Idea of History is the best-known book of the great Oxford philosopher, historian, and archaeologist R.G. Collingwood. It was originally published posthumously in 1946, having been mainly reconstructed from Collingwood's manuscripts, many of which are now lost. For this revised edition, Collingwood's most important lectures on the philosophy of history are published here for the first time. These texts have been prepared by Jan van der Dussen from manuscripts that have only recently become available. The lectures contain Collingwood's first (...) comprehensive statement of his philosophy of history; they are therefore essential for a full understanding of his thought, and in particular for a correct interpretation of The Idea of History itself. Van der Dussen contributes a substantial introduction in which he explains the background to this new edition and surveys the scholarship of the last fifty years. (shrink)

History and Philosophy of Modern Mathematics was first published in 1988. Minnesota Archive Editions uses digital technology to make long-unavailable books once again accessible, and are published unaltered from the original University of Minnesota Press editions. The fourteen essays in this volume build on the pioneering effort of Garrett Birkhoff, professor of mathematics at Harvard University, who in 1974 organized a conference of mathematicians and historians of modern mathematics to examine how the two disciplines approach the history of mathematics. In (...) History and Philosophy of Modern Mathematics, William Aspray and Philip Kitcher bring together distinguished scholars from mathematics, history, and philosophy to assess the current state of the field. Their essays, which grow out of a 1985 conference at the University of Minnesota, develop the basic premise that mathematical thought needs to be studied from an interdisciplinary perspective. The opening essays study issues arising within logic and the foundations of mathematics, a traditional area of interest to historians and philosophers. The second section examines issues in the history of mathematics within the framework of established historical periods and questions. Next come case studies that illustrate the power of an interdisciplinary approach to the study of mathematics. The collection closes with a look at mathematics from a sociohistorical perspective, including the way institutions affect what constitutes mathematical knowledge. (shrink)

Descartes has often been called the 'father of modern philosophy'. His attempts to find foundations for knowledge, and to reconcile the existence of the soul with the emerging science of his time, are among the most influential and widely studied in the history of philosophy. This is a classic and challenging introduction to Descartes by one of the most distinguished modern philosophers. Bernard Williams not only analyzes Descartes' project of founding knowledge on certainty, but uncovers the philosophical motives for his (...) search. With acute insight, he demonstrates how Descartes' _Meditations _are not merely a description but the very enactment of philosophical thought and discovery. Williams covers all of the key areas of Descartes' thought, including God, the will, the possibility of knowledge, and the mind and its place in nature. He also makes profound contributions to the theory of knowledge, metaphysics and philosophy generally. With a new foreword by John Cottingham. (shrink)

Descartes has often been called the 'father of modern philosophy'. His attempts to find foundations for knowledge, and to reconcile the existence of the soul with the emerging science of his time, are among the most influential and widely studied in the history of philosophy. This is a classic and challenging introduction to Descartes by one of the most distinguished modern philosophers. Bernard Williams not only analyzes Descartes' project of founding knowledge on certainty, but uncovers the philosophical motives for his (...) search. With acute insight, he demonstrates how Descartes' _Meditations _are not merely a description but the very enactment of philosophical thought and discovery. Williams covers all of the key areas of Descartes' thought, including God, the will, the possibility of knowledge, and the mind and its place in nature. He also makes profound contributions to the theory of knowledge, metaphysics and philosophy generally. With a new foreword by John Cottingham. (shrink)

This book draws its inspiration from Hilbert, Wittgenstein, Cavaillès and Lakatos and is designed to reconfigure contemporary philosophy of mathematics by making the growth of knowledge rather than its foundations central to the study of mathematical rationality, and by analyzing the notion of growth in historical as well as logical terms. Not a mere compendium of opinions, it is organised in dialogical forms, with each philosophical thesis answered by one or more historical case studies designed to support, complicate or question (...) it. The first part of the book examines the role of scientific theory and empirical fact in the growth of mathematical knowledge. The second examines the role of abstraction, analysis and axiomatization. The third raises the question of whether the growth of mathematical knowledge constitutes progress, and how progress may be understood. Readership: Students and scholars concerned with the history and philosophy of mathematics and the formal sciences. (shrink)

Presents general information about meteorology, weather, and climate and includes more than thirty activities to help study these topics, including making a ...

Includes bibliographical references and index. isbn 0-226-97861-3 (alk. paper) — isbn 0-226-97862-1 (pbk. : alk. paper) 1. Science — Philosophy. 2. Science — History. 3. Progress. I. Title. Q175 .Z25 2004 501 — dc2i 200301 1970 ...

Philosophy written in English is overwhelmingly analytic philosophy, and the techniques and predilections of analytic philosophy are not only unhistorical but anti-historical, and hostile to textual commentary. Analytic usually aspires to a very high degree of clarity and precision of formulation and argument, and it often seeks to be informed by, and consistent with, current natural science. In an earlier era, analytic philosophy aimed at agreement with ordinary linguistic intuitions or common sense beliefs, or both. All of these aspects of (...) the subject sit uneasily with the use of historical texts for philosophical illumination. In this book, ten distinguished philosophers explore the tensions between, and the possibilities of reconciling, analytic philosophy and history of philosophy. Contributors: M. R. Ayers, John Cottingham, Daniel Garber, Gary Hatfield, Anthony Kenny, Steven Nadler, G. A. J. Rogers, Tom Sorell, Catherine Wilson, Yves Charles Zarka. (shrink)

_Lakatos: An Introduction_ provides a thorough overview of both Lakatos's thought and his place in twentieth century philosophy. It is an essential and insightful read for students and anyone interested in the philosophy of science.

In this book, which is both a philosophical and historiographical study, the author investigates the fallibility and the rationality of mathematics by means of rational reconstructions of developments in mathematics. The initial chapters are devoted to a critical discussion of Lakatos' philosophy of mathematics. In the remaining chapters several episodes in the history of mathematics are discussed, such as the appearance of deduction in Greek mathematics and the transition from Eighteenth-Century to Nineteenth-Century analysis. The author aims at developing a notion (...) of mathematical rationality that agrees with the historical facts. A modified version of Lakatos' methodology is proposed. The resulting constructions show that mathematical knowledge is fallible, but that its fallibility is remarkably weak. (shrink)

In this ambitious study, David Corfield attacks the widely held view that it is the nature of mathematical knowledge which has shaped the way in which mathematics is treated philosophically and claims that contingent factors have brought us to the present thematically limited discipline. Illustrating his discussion with a wealth of examples, he sets out a variety of approaches to new thinking about the philosophy of mathematics, ranging from an exploration of whether computers producing mathematical proofs or conjectures are doing (...) real mathematics, to the use of analogy, the prospects for a Bayesian confirmation theory, the notion of a mathematical research programme and the ways in which new concepts are justified. His inspiring book challenges both philosophers and mathematicians to develop the broadest and richest philosophical resources for work in their disciplines and points clearly to the ways in which this can be done. (shrink)

In this ambitious study, David Corfield attacks the widely held view that it is the nature of mathematical knowledge which has shaped the way in which mathematics is treated philosophically, and claims that contingent factors have brought us to the present thematically limited discipline. Illustrating his discussion with a wealth of examples, he sets out a variety of new ways to think philosophically about mathematics, ranging from an exploration of whether computers producing mathematical proofs or conjectures are doing real mathematics, (...) to the use of analogy, the prospects for a Bayesian confirmation theory, the notion of a mathematical research programme, and the ways in which new concepts are justified. His highly original book challenges both philosophers and mathematicians to develop the broadest and richest philosophical resources for work in their disciplines, and points clearly to the ways in which this can be done. (shrink)