History and Philosophy of Modern Mathematics

Author: William Aspray,Philip Kitcher
Publisher: U of Minnesota Press
ISBN: 9780816615674
Category: Mathematics
Page: 386
View: 9220
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.

Italian Studies in the Philosophy of Science

Author: Maria Luisa Dalla Chiara
Publisher: Springer Science & Business Media
ISBN: 9789027707352
Category: Science
Page: 529
View: 6475
The impressive record of Italian philosophical research since the end of Fascism thirty-two years ago is shown in many fields: esthetics, social and" personal ethics, history and sociology of philosophy, and magnificently, perhaps above all, in logic, foundations of mathematics and the philosophY, methodology, and intellectual history ofthe empirical sciences. To our pleasure, Maria Luisa Dalla Chiara of the University of Florence gladly agreed to assemble a 'sampler' of recent Italian logical and analytical work on the philosophical foundations of mathematics and physics, along with a number of historical studies of epistemological and mathematical concepts. The twenty-five essays that form this volume will, we expect, encourage English-reading philosophers and scientists to seek further works by these authors and by their teachers, colleagues, and students; and, we hope, to look for those other Italian currents of thought in the philosophy of science for which points of departure are not wholly analytic, and which also deserve study and recognition in the world wide philosophical community. Of course, Italy has long been related to that world community in scien titlc matters.

Russell's Unknown Logicism

A Study in the History and Philosophy of Mathematics
Author: Sebastien Gandon
Publisher: Palgrave Macmillan
ISBN: 0230576990
Category: Mathematics
Page: 263
View: 3519
One hundred years ago, Russell and Whitehead published their epoch-making Principia Mathematica (PM), which was initially conceived as the second volume of Russell's Principles of Mathematics (PoM) that had appeared ten years before. No other works can be credited to have had such an impact on the development of logic and on philosophy in the twentieth century. However, until now, scholars only focused on the first parts of the books – that is, on Russell's and Whitehead's theory of logic, set-theory and arithmetic. Sebastien Gandon aims at reversing the perspective. His goal is to give a picture of Russell's logicism based on a detailed reading of the developments dealing with advanced mathematics - namely projective geometry and the theory of quantity. This book is not only the first study ever made of the 'later' portions of PoM and PM, it also shows how this shift of perspective compels us to change our view of the logicist program taken as a whole.

(Lebedev to Zworykin).

Author: Roy Porter
Publisher: N.A
ISBN: 9780195216653
Page: 598
View: 640

Continuity and Change in the Development of Russell’s Philosophy

Author: P.J. Hager
Publisher: Springer Science & Business Media
ISBN: 9401108447
Category: Philosophy
Page: 200
View: 4701
The general view of Russell's work amongst philosophers has been that repeat edly, during his long and distinguished career, crucial changes of mind on fun damental points were significant enough to cause him to successively adopt a diversity of radically new philosophical positions. Thus Russell is seen to have embraced and then abandoned, amongst others, neo-Hegelianism, Platonic re alism, phenomenalism and logical atomism, before settling finally on a form of neutral monism that philosophers have generally found to be incredible. This view of Russell is captured in C. D. Broad's famous remark that "Mr. Russell pro duces a different system of philosophy every few years . . . " (Muirhead, 1924: 79). Reflecting this picture of Russell continually changing his position, books and papers on Russell's philosophy have typically belonged to one of two kinds. Either they have concentrated on particular periods of his thought that are taken to be especially significant, or, accepting the view of his successive conversion to dis tinctly different philosophical positions, they have provided some account of each of these supposedly disconnected periods of his thought. While much good work has been done on Russell's philosophy, this framework has had its limitations, the main one being that it conceals the basic continuity behind his thought.

Studies in Whitehead’s Philosophy

Author: Edward G. Ballard,Alan B. Brinkley,Ramona T. Cormier,Harold N. Lee,Stephen C. Pepper,Andrew J. Reck,Robert C. Whittemore
Publisher: Springer Science & Business Media
ISBN: 9401181357
Category: Science
Page: 114
View: 2480

Whitehead’s Philosophy of Science and Metaphysics

An Introduction to His Thought
Author: W. Mays
Publisher: Springer Science & Business Media
ISBN: 9401010854
Category: Philosophy
Page: 152
View: 6850

The New Century

Bergsonism, Phenomenology and Responses to Modern Science
Author: Keith Ansell-Pearson,Alan D. Schrift
Publisher: Routledge
ISBN: 131754692X
Category: Philosophy
Page: 456
View: 9669
This volume covers the period between the 1890s and 1930s, a period that witnessed revolutions in the arts and society which set the agenda for the rest of the century. In philosophy, the period saw the birth of analytic philosophy, the development of new programmes and new modes of inquiry, the emergence of phenomenology as a new rigorous science, the birth of Freudian psychoanalysis, and the maturing of the discipline of sociology. This period saw the most influential work of a remarkable series of thinkers who reviewed, evaluated and transformed 19th-century thought. A generation of thinkers - among them, Henri Bergson, Emile Durkheim, Sigmund Freud, Martin Heidegger, Edmund Husserl, Karl Jaspers, Max Scheler, and Ludwig Wittgenstein - completed the disenchantment of the world and sought a new re-enchantment.

Kant and Philosophy of Science Today:

Author: Michela Massimi
Publisher: Cambridge University Press
ISBN: 9780521748513
Category: Philosophy
Page: 204
View: 5046
There has been an increasing interest in Kant and philosophy of science in the past twenty years. Through reconstructing Kantian legacies in the development of nineteenth and twentieth century physics and mathematics, this volume explores what relevance Kant's philosophy has in current debates in philosophy of science, mathematics and physics.

The Blackwell Guide to the Philosophy of Science

Author: Peter Machamer,Michael Silberstein
Publisher: John Wiley & Sons
ISBN: 0470756527
Category: Science
Page: 360
View: 1205
This volume presentsa definitive introduction to the core areas of philosophy of science.

Tool and Object

A History and Philosophy of Category Theory
Author: Ralph Krömer
Publisher: Springer Science & Business Media
ISBN: 3764375248
Category: Mathematics
Page: 367
View: 994
Category theory is a general mathematical theory of structures and of structures of structures. It occupied a central position in contemporary mathematics as well as computer science. This book describes the history of category theory whereby illuminating its symbiotic relationship to algebraic topology, homological algebra, algebraic geometry and mathematical logic and elaboratively develops the connections with the epistemological significance.

Proceedings of the Boston Colloquium for the Philosophy of Science 1964/1966

In Memory of Norwood Russell Hanson
Author: Robert S. Cohen,Marx W. Wartofsky
Publisher: Springer Science & Business Media
ISBN: 9401035083
Category: Science
Page: 489
View: 7007
This third volume of Boston Studies in the Philosophy of Science contains papers which are based upon Colloquia from 1964 to 1966. In most cases, they have been substantially modified subsequent to presentation and discussion. Once again we publish work which goes beyond technical analysis of scientific theories and explanations in order to include philo sophical reflections upon the history of science and also upon the still problematic interactions between metaphysics and science. The philo sophical history of scientific ideas has increasingly been recognized as part of the philosophy of science, and likewise the cultural context of the genesis of such ideas. There is no school or attitude to be taken as de fining the scope or criteria of our Colloquium, and so we seek to under stand both analytic and historical aspects of science. This volume, as the previous two, constitutes a substantial part of our final report to the U. S. National Science Foundation, which has continued its support of the Boston Colloquium for the Philosophy of Science by a grant to Boston University. That report will be concluded by a subse quent volume of these Studies. It is a pleasure to record our thanks to the Foundation for its confidence and funds. We dedicate this book to the memory of Norwood Russell Hanson. During this academic year of 1966-67, this beloved and distinguished American philosopher participated in our Colloquium, and he did so before.

What Place for the A Priori?

Author: Michael J. Shaffer,Michael L. Veber
Publisher: Open Court
ISBN: 0812697413
Category: Philosophy
Page: 384
View: 9574
This book deals with questions about the nature of a priori knowledge and its relation to empirical knowledge. Until the twentieth century, it was more or less taken for granted that there was such a thing as a priori knowledge, that is, knowledge whose source is in reason and reflection rather than sensory experience. With a few notable exceptions, philosophers believed that mathematics, logic and philosophy were all a priori. Although the seeds of doubt were planted earlier on, by the early twentieth century, philosophers were widely skeptical of the idea that there was any nontrivial existence of a priori knowledge. By the mid to late twentieth century, it became fashionable to doubt the existence of any kind of a priori knowledge at all. Since many think that philosophy is an a priori discipline if it is any kind of discipline at all, the questions about a priori knowledge are fundamental to our understanding of philosophy itself.

New Essays on Leibniz Reception

In Science and Philosophy of Science 1800-2000
Author: Ralph Krömer,Yannick Chin-Drian
Publisher: Springer Science & Business Media
ISBN: 3034605048
Category: Mathematics
Page: 278
View: 3248
This book is a collection of essays on the reception of Leibniz’s thinking in the sciences and in the philosophy of science in the 19th and 20th centuries. Authors studied include C.F. Gauss, Georg Cantor, Kurd Lasswitz, Bertrand Russell, Ernst Cassirer, Louis Couturat, Hans Reichenbach, Hermann Weyl, Kurt Gödel and Gregory Chaitin. In addition, we consider concepts and problems central to Leibniz’s thought and that of the later authors: the continuum, space, identity, number, the infinite and the infinitely small, the projects of a universal language, a calculus of logic, a mathesis universalis etc. The book brings together two fields of research in the history of philosophy and of science (research on Leibniz, and the research concerned with some major developments in the 19th and 20th centuries); it describes how Leibniz’s thought appears in the works of these authors, in order to better understand Leibniz’s influence on contemporary science and philosophy; but it also assesses that reception critically, confronting it in particular with the current state of Leibniz research and with the various editions of his work.

Bolzano's Philosophy and the Emergence of Modern Mathematics

Author: Paul Rusnock
Publisher: Rodopi
ISBN: 9789042015012
Category: Philosophy
Page: 218
View: 9342

A Companion to the Philosophy of Time

Author: Adrian Bardon,Heather Dyke
Publisher: John Wiley & Sons
ISBN: 1118522052
Category: Philosophy
Page: 600
View: 8499
A Companion to the Philosophy of Time presents thebroadest treatment of this subject yet; 32 specially commissionedarticles - written by an international line-up of experts –provide an unparalleled reference work for students and specialistsalike in this exciting field. The most comprehensive reference work on the philosophy of timecurrently available The first collection to tackle the historical development ofthe philosophy of time in addition to covering contemporarywork Provides a tripartite approach in its organization, coveringhistory of the philosophy of time, time as a feature of thephysical world, and time as a feature of experience Includes contributions from both distinguished,well-established scholars and rising stars in the field

Studies in the Scientific and Mathematical Philosophy of Charles S. Peirce

Author: Carolyn Eisele
Publisher: Mouton De Gruyter
Category: Mathematics
Page: 386
View: 2074

Routledge History of Philosophy Volume IX

Philosophy of the English-Speaking World in the Twentieth Century 1: Science, Logic and Mathematics
Author: S. G. Shanker
Publisher: Routledge
ISBN: 1134393369
Category: Philosophy
Page: 504
View: 1129
Volume 9 of the Routledge History of Philosophy surveys ten key topics in the philosophy of science, logic and mathematics in the twentieth century. Each of the essays is written by one of the world's leading experts in that field. Among the topics covered are the philosophy of logic, of mathematics and of Gottlob Frege; Ludwig Wittgenstein's Tractatus; a survey of logical positivism; the philosophy of physics and of science; probability theory, cybernetics and an essay on the mechanist/vitalist debates. The volume also contains a helpful chronology to the major scientific and philosophical events in the twentieth century. It also provides an extensive glossary of technical terms in the notes on major figures in these fields.

Standards of Philosophical Rationality

Traditions and Modern Times
Author: Zbigniew Drozdowicz
Publisher: LIT Verlag Münster
ISBN: 364390388X
Category: Religion
Page: 144
View: 2715
This book focuses on the standards of philosophical rationality, corresponding to a philosophy that aspires to be more than the wisdom that stems from and addresses everyday human needs. It is a search for standards that would, as it were, show the way to philosophical wisdom for anyone who is willing and able to assess it. One of the problems is that people have had a different understanding of the basic concept of rationality, which is the rationale. (Series: Development in Humanities - Vol. 1)

Mathematics and the Roots of Postmodern Thought

Author: Vladimir Tasic
Publisher: Oxford University Press
ISBN: 9780195349955
Category: Mathematics
Page: 200
View: 414
This is a charming and insightful contribution to an understanding of the "Science Wars" between postmodernist humanism and science, driving toward a resolution of the mutual misunderstanding that has driven the controversy. It traces the root of postmodern theory to a debate on the foundations of mathematics early in the 20th century, then compares developments in mathematics to what took place in the arts and humanities, discussing issues as diverse as literary theory, arts, and artificial intelligence. This is a straightforward, easily understood presentation of what can be difficult theoretical concepts It demonstrates that a pattern of misreading mathematics can be seen both on the part of science and on the part of postmodern thinking. This is a humorous, playful yet deeply serious look at the intellectual foundations of mathematics for those in the humanities and the perfect critical introduction to the bases of modernism and postmodernism for those in the sciences.