Mathematical Thought and its Objects


Book Description

Charles Parsons examines the notion of object, with the aim to navigate between nominalism, denying that distinctively mathematical objects exist, and forms of Platonism that postulate a transcendent realm of such objects. He introduces the central mathematical notion of structure and defends a version of the structuralist view of mathematical objects, according to which their existence is relative to a structure and they have no more of a 'nature' than that confers on them. Parsons also analyzes the concept of intuition and presents a conception of it distantly inspired by that of Kant, which describes a basic kind of access to abstract objects and an element of a first conception of the infinite.







Avenir Et Devenir Des Normes


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Einstein for the 21st Century


Book Description

More than fifty years after his death, Albert Einstein's vital engagement with the world continues to inspire others, spurring conversations, projects, and research, in the sciences as well as the humanities. Einstein for the 21st Century shows us why he remains a figure of fascination. In this wide-ranging collection, eminent artists, historians, scientists, and social scientists describe Einstein's influence on their work, and consider his relevance for the future. Scientists discuss how Einstein's vision continues to motivate them, whether in their quest for a fundamental description of nature or in their investigations in chaos theory; art scholars and artists explore his ties to modern aesthetics; a music historian probes Einstein's musical tastes and relates them to his outlook in science; historians explore the interconnections between Einstein's politics, physics, and philosophy; and other contributors examine his impact on the innovations of our time. Uniquely cross-disciplinary, Einstein for the 21st Century serves as a testament to his legacy and speaks to everyone with an interest in his work. The contributors are Leon Botstein, Lorraine Daston, E. L. Doctorow, Yehuda Elkana, Yaron Ezrahi, Michael L. Friedman, Jürg Fröhlich, Peter L. Galison, David Gross, Hanoch Gutfreund, Linda D. Henderson, Dudley Herschbach, Gerald Holton, Caroline Jones, Susan Neiman, Lisa Randall, Jürgen Renn, Matthew Ritchie, Silvan S. Schweber, and A. Douglas Stone.




Constituting Objectivity


Book Description

In recent years, many philosophers of modern physics came to the conclusion that the problem of how objectivity is constituted (rather than merely given) can no longer be avoided, and therefore that a transcendental approach in the spirit of Kant is now philosophically relevant. The usual excuse for skipping this task is that the historical form given by Kant to transcendental epistemology has been challenged by Relativity and Quantum Physics. However, the true challenge is not to force modern physics into a rigidly construed static version of Kant’s philosophy, but to provide Kant’s method with flexibility and generality. In this book, the top specialists of the field pin down the methodological core of transcendental epistemology that must be used in order to throw light on the foundations of modern physics. First, the basic tools Kant used for his transcendental reading of Newtonian Mechanics are examined, and then early transcendental approaches of Relativistic and Quantum Physics are revisited. Transcendental procedures are also applied to contemporary physics, and this renewed transcendental interpretation is finally compared with structural realism and constructive empiricism. The book will be of interest to scientists, historians and philosophers who are involved in the foundational problems of modern physics.




Epistemological Writings


Book Description

[1977] Hermann von Helmholtz in the History of Scientific Method In 1921, the centenary of Helmholtz' birth, Paul Hertz, a physicist, and Moritz Schlick, a philosopher, published a selection of his papers and lectures on the philosophical foundations of the sciences, under the title Schriften zur Erkenntnistheorie. Combining qualities of respect and criticism that Helmholtz would have demanded, Hertz and Schlick scrupulously annotated the texts. Their edition of Helmholtz was of historical influence, comparable to the influence among contemporary mathematicians and philosophers of Hermann Weyl's annotated edition in 1919 of Riemann's great dissertation of 1854 on the foundations of geometry. For several reasons, we are pleased to be able to bring this Schlick/ Hertz edition to the English-reading world: first, and primary, to honor the memory of Hermann von Helmholtz; second, as writings of historical value, to deepen the understanding of mathematics and the natural sciences, as well as of psychology and philosophy, in the 19th centur- for Helmholtz must be comprehended within at least that wide a range; third, with Schlick, to understand the developing empiricist philosophy of science in the early 20th century; and fourth, to bring the contributions of Schlick, Hertz, and Helmholtz to methodological debate in our own time, a half century later, long after the rise and consolidation of logical empiricism, the explosion of physics since Planck and Einstein, and the development of psychology since Freud and Pavlov.




Space, Time, and Mechanics


Book Description

In connection with the "Philosophy of Science" research program conducted by the Deutsche Forschungsgemeinschaft a colloquium was held in Munich from 18th to 20th May 1919. This covered basic structures of physical theories, the main emphasis being on the interrelation of space, time and mechanics. The present volume contains contributions and the results of the discussions. The papers are given here in the same order of presentation as at the meeting. The development of these "basic structures of physical theories" involved diverging trends arising from different starting points in philosophy and physics. In order to obtain a clear comparison between these schools of thought, it was appropriate to concentrate discussion on geometry and chronology as the common foundation of classical and quantum mechanics. As a rather simple and "Tell prepared field of study, geochronometry seemed suited to analysing these mutually exclusive positions. vii D. Mayr and G. Sussmann (eds.), Space, Time, and Mechanics, vii. Copyright © 1983 by D. Reidel Publishing Company. ACKNOWLEDGEMENT The editors gratefully appreciate the sponsorship of the Deutsche Forschungsgemeinschaft and the cooperation of the authors and publisher. It is also a pleasure to thank Frau M.-L. Grohmann and Frau I. Thies for their organisational and especially Frau B. Grund for typing and clerical work. D. MAYR G. SUSSMANN 1982 University of Munich viii INTRODUCTION The distinct positions present at the symposium may be roughly divided into three schools that differ in their philosophical interpretation of physics and their meta- .. . ~ .




Rudolf Carnap: Early Writings


Book Description

Rudolf Carnap (1891-1970) is generally acknowledged to have been one of the central figures of twentieth-century philosophy. He was the leading philosopher of the Vienna Circle, a group that was central to the international movement known as logical empiricism, which pursued the goal of making philosophy scientific and eliminating metaphysics that went beyond the limits of what humans can coherently comprehend. Carnap was not only well-versed in this area of thought but also contrary ideas; he interacted philosophically with Gottlob Frege, Bertrand Russell, Ludwig Wittgenstein, Edmund Husserl, and Martin Heidegger, and in his formative years he was influenced by the positivists Mach and Ostwald, neo-Kantians such as Cassirer and Natorp, and Husserl's phenomenology. Interest in logical empiricism waned in the decades following Carnap's death but was revived towards the end of the twentieth century; the wave of new scholarship that resulted identified Carnap as far more subtle and interesting than was previously understood. The complete fourteen-volume edition of Carnap's published writings builds upon these more recent interpretations of his philosophy. This first book contains Carnap's early publications up until 1928, none of which have previously been translated from their original German. The introduction and notes place the text in the relevant scientific and historical contexts, in addition to explaining obscure references or outdated notation and terminology. Carnap's neo-Kantian origins are more obvious in these works than in his later writings, and the overall figure which emerges from this volume is a very different Carnap to the caricature that many philosophers will know.




Conventionalism


Book Description

The daring idea that convention - human decision - lies at the root both of necessary truths and much of empirical science reverberates through twentieth-century philosophy, constituting a revolution comparable to Kant's Copernican revolution. This book provides a comprehensive study of Conventionalism. Drawing a distinction between two conventionalist theses, the under-determination of science by empirical fact, and the linguistic account of necessity, Yemima Ben-Menahem traces the evolution of both ideas to their origins in Poincaré's geometric conventionalism. She argues that the radical extrapolations of Poincaré's ideas by later thinkers, including Wittgenstein, Quine, and Carnap, eventually led to the decline of conventionalism. This book provides a fresh perspective on twentieth-century philosophy. Many of the major themes of contemporary philosophy emerge in this book as arising from engagement with the challenge of conventionalism.




Rudolf Carnap: Early Writings


Book Description

This volume is the first of a complete edition of the writings of Rudolf Carnap. Translated into English for the first time and supplemented with a detailed introduction, Carnap's early works are contextualised in extensive notes and critically discussed by an international team of scholars who specialize in different aspects of Carnap's thought.