History and Philosophy of Modern Mathematics

Author: William Aspray,Philip Kitcher
Publisher: U of Minnesota Press
ISBN: 9780816615674
Category: Mathematics
Page: 386
View: 9868
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.

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: 7441
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.

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: 6677
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.

Italian Studies in the Philosophy of Science

Author: Maria Luisa Dalla Chiara
Publisher: Springer Science & Business Media
ISBN: 9789027707352
Category: Science
Page: 529
View: 3616
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.

Philosophy and Geometry

Theoretical and Historical Issues
Author: L. Magnani
Publisher: Springer Science & Business Media
ISBN: 9401096228
Category: Science
Page: 256
View: 7439
Philosophers have studied geometry since ancient times. Geometrical knowledge has often played the role of a laboratory for the philosopher's conceptual experiments dedicated to the ideation of powerful theories of knowledge. Lorenzo Magnani's new book Philosophy and Geometry illustrates the rich intrigue of this fascinating story of human knowledge, providing a new analysis of the ideas of many scholars (including Plato, Proclus, Kant, and Poincaré), and discussing conventionalist and neopositivist perspectives and the problem of the origins of geometry. The book also ties together the concerns of philosophers of science and cognitive scientists, showing, for example, the connections between geometrical reasoning and cognition as well as the results of recent logical and computational models of geometrical reasoning. All the topics are dealt with using a novel combination of both historical and contemporary perspectives. Philosophy and Geometry is a valuable contribution to the renaissance of research in the field.

(Lebedev to Zworykin).

Author: Roy Porter
Publisher: N.A
ISBN: 9780195216653
Page: 598
View: 3451

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: 6969
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.

Brazilian Studies in Philosophy and History of Science

An account of recent works
Author: Décio Krause,Antonio Videira
Publisher: Springer Science & Business Media
ISBN: 9048194229
Category: Science
Page: 354
View: 4511
This volume, The Brazilian Studies in the Philosophy and History of Science, is the first attempt to present to a general audience, works from Brazil on this subject. The included papers are original, covering a remarkable number of relevant topics of philosophy of science, logic and on the history of science. The Brazilian community has increased in the last years in quantity and in quality of the works, most of them being published in respectable international journals on the subject. The chapters of this volume are forwarded by a general introduction, which aims to sketch not only the contents of the chapters, but it is conceived as a historical and conceptual guide to the development of the field in Brazil. The introduction intends to be useful to the reader, and not only to the specialist, helping them to evaluate the increase in production of this country within the international context.

Creating Modern Probability

Its Mathematics, Physics and Philosophy in Historical Perspective
Author: Jan von Plato
Publisher: Cambridge University Press
ISBN: 9780521597357
Category: Mathematics
Page: 323
View: 7489
In this book the author charts the history and development of modern probability theory.

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: 1161

Discourse on a New Method

Reinvigorating the Marriage of History and Philosophy of Science
Author: Mary Domski,Michael Dickson
Publisher: Open Court
ISBN: 0812697227
Category: Philosophy
Page: 928
View: 5746
Addressing a wide range of topics, from Newton to Post-Kuhnian philosophy of science, these essays critically examine themes that have been central to the influential work of philosopher Michael Friedman. Special focus is given to Friedman's revealing study of both history of science and philosophy in his work on Kant, Newton, Einstein, and other major figures. This interaction of history and philosophy is the subject of the editors' "manifesto" and serves to both explain and promote the essential ties between two disciplines usually regarded as unrelated.

The Kantian Legacy in Nineteenth-century Science

Author: Michael Friedman,Alfred Nordmann
Publisher: MIT Press
ISBN: 0262062542
Category: Philosophy
Page: 370
View: 5109
Historians of philosophy, science, and mathematics explore the influence of Kant'sphilosophy on the evolution of modern scientific thought.

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: 6090
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.

An Essay on the Foundations of Geometry

Author: Bertrand Russell
Publisher: Cosimo, Inc.
ISBN: 1602063095
Category: Mathematics
Page: 220
View: 9912
Bertrand Russell was a prolific writer, revolutionizing philosophy and doing extensive work in the study of logic. This, his first book on mathematics, was originally published in 1897 and later rejected by the author himself because it was unable to support Einstein's work in physics. This evolution makes An Essay on the Foundations of Geometry invaluable in understanding the progression of Russell's philosophical thinking. Despite his rejection of it, Essays continues to be a great work in logic and history, providing readers with an explanation for how Euclidean geometry was replaced by more advanced forms of math. British philosopher and mathematician BERTRAND ARTHUR WILLIAM RUSSELL (1872-1970) won the Nobel Prize for Literature in 1950. Among his many works are Why I Am Not a Christian (1927), Power: A New Social Analysis (1938), and My Philosophical Development (1959).

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: 7440

Philosophy of Science: The Key Thinkers

Author: James Robert Brown
Publisher: A&C Black
ISBN: 1441142002
Category: Science
Page: 320
View: 1866
A guide to the key figures in the Philosophy of Science from Plato and Aristotle through to Popper, Puttnam and Cartwright.

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: 4517
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: 3263
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.

Foundations of Logic, 1903-05

Author: Bertrand Russell,Alasdair Urquhart,Albert C. Lewis
Publisher: Psychology Press
ISBN: 9780415094061
Category: Philosophy
Page: 743
View: 3110
This volume covers the period from the beginning of Russell's work on Volume Two of the Principles of Mathematics to the critical discovery of the theory of descriptions in 1905. Foundations of Logic gives a vivid picture of Russell wrestling with the logical paradoxes, often unsuccessfully, as he tries out one foundational scheme after another. This volume provides the key to both Bertrand Russell's philosophy of logic and philosophy of mathematics. It includes unpublished work on the theory of denoting which predates Russell's famous article of 1905 and unpublished manuscripts on the so-called "zig-zag" theory with which Russell attempted to provide a type-free foundation for mathematics. The volume also gathers together for the first time a number of reviews and survey articles, along with two talks on modality and truth. It will be an essential addition to any Bertrand Russell collection.-- Publisher description.

The Blackwell Guide to the Philosophy of Science

Author: Peter Machamer,Michael Silberstein
Publisher: John Wiley & Sons
ISBN: 0470756527
Category: Science
Page: 360
View: 2581
This volume presentsa definitive introduction to the core areas of philosophy of science.