Reason's Nearest Kin

Philosophies of Arithmetic from Kant to Carnap

Author: Michael Potter

Publisher: Oxford University Press

ISBN: 019825041X

Category: Mathematics

Page: 305

View: 4250

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How do we account for the truth of arithmetic? And if it does not depend for its truth on the way the world is, what constrains the world to conform to arithmetic? Reason's Nearest Kin is a critical examination of the astonishing progress made towards answering these questions from the late nineteenth to the mid-twentieth century. In the space of fifty years Frege, Dedekind, Russell, Wittgenstein, Ramsey, Hilbert, and Carnap developed accounts of the content of arithmeticthat were brilliantly original both technically and philosophically. Michael Potter's innovative study presents them all as finding that content in various aspects of the complex linkage between experience, language, thought, and the world. Potter's reading places them all in Kant's shadow since it was hisattempt to ground arithmetic in the spatio-temporal structure of reality that they were reacting against; but it places us in Gödel's shadow since his incompleteness theorems supply us with a measure of the richness of the content they were trying to explain. This stimulating reassessment of some of the classic texts in the philosophy of mathematics reveals many unexpected connections and illuminating comparisons, and offers a wealth of ideas for future work in the subject.
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The Routledge Companion to Twentieth Century Philosophy

Author: Dermot Moran

Publisher: Routledge

ISBN: 1134424035

Category: Philosophy

Page: 1040

View: 3249

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The twentieth century was one of the most significant and exciting periods ever witnessed in philosophy, characterized by intellectual change and development on a massive scale. The Routledge Companion to Twentieth Century Philosophy is an outstanding authoritative survey and assessment of the century as a whole. Featuring twenty-two chapters written by leading international scholars, this collection is divided into five clear parts and presents a comprehensive picture of the period for the first time: major themes and movements logic, language, knowledge and metaphysics philosophy of mind, psychology and science phenomenology, hermeneutics, existentialism, and critical theory politics, ethics, aesthetics. Featuring annotated further reading and a comprehensive glossary, The Routledge Companion to Twentieth Century Philosophy is indispensable for anyone interested in philosophy over the last one hundred years, suitable for both expert and novice alike.
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Space, Number, and Geometry from Helmholtz to Cassirer

Author: Francesca Biagioli

Publisher: Springer

ISBN: 3319317792

Category: Philosophy

Page: 239

View: 2118

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This book offers a reconstruction of the debate on non-Euclidean geometry in neo-Kantianism between the second half of the nineteenth century and the first decades of the twentieth century. Kant famously characterized space and time as a priori forms of intuitions, which lie at the foundation of mathematical knowledge. The success of his philosophical account of space was due not least to the fact that Euclidean geometry was widely considered to be a model of certainty at his time. However, such later scientific developments as non-Euclidean geometries and Einstein’s general theory of relativity called into question the certainty of Euclidean geometry and posed the problem of reconsidering space as an open question for empirical research. The transformation of the concept of space from a source of knowledge to an object of research can be traced back to a tradition, which includes such mathematicians as Carl Friedrich Gauss, Bernhard Riemann, Richard Dedekind, Felix Klein, and Henri Poincaré, and which finds one of its clearest expressions in Hermann von Helmholtz’s epistemological works. Although Helmholtz formulated compelling objections to Kant, the author reconsiders different strategies for a philosophical account of the same transformation from a neo-Kantian perspective, and especially Hermann Cohen’s account of the aprioricity of mathematics in terms of applicability and Ernst Cassirer’s reformulation of the a priori of space in terms of a system of hypotheses. This book is ideal for students, scholars and researchers who wish to broaden their knowledge of non-Euclidean geometry or neo-Kantianism.
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Kant-Studien

Author: Hans Vaihinger,Max Scheler,Bruno Bauch,Max Frischeisen-Köhler,Arthur Liebert,Paul Menzer

Publisher: N.A

ISBN: N.A

Category: Philosophy

Page: N.A

View: 3937

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1904-26 (includes lists of members)
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Ludwig Wittgenstein: Early Works: Oxford Bibliographies Online Research Guide

Author: Denis McManus

Publisher: Oxford University Press

ISBN: 0199810753

Category:

Page: 26

View: 4074

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This ebook is a selective guide designed to help scholars and students of social work find reliable sources of information by directing them to the best available scholarly materials in whatever form or format they appear from books, chapters, and journal articles to online archives, electronic data sets, and blogs. Written by a leading international authority on the subject, the ebook provides bibliographic information supported by direct recommendations about which sources to consult and editorial commentary to make it clear how the cited sources are interrelated related. This ebook is a static version of an article from Oxford Bibliographies Online: Philosophy, a dynamic, continuously updated, online resource designed to provide authoritative guidance through scholarship and other materials relevant to the study Philosophy. Oxford Bibliographies Online covers most subject disciplines within the social science and humanities, for more information visit www.oxfordbibligraphies.com.
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Philosophy of mathematics

an introduction

Author: David Bostock

Publisher: Blackwell Pub

ISBN: 9781405189910

Category: Mathematics

Page: 332

View: 6391

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Philosophy of Mathematics: An Introduction provides a critical analysis of the major philosophical issues and viewpoints in the concepts and methods of mathematics - from antiquity to the modern era. Offers beginning readers a critical appraisal of philosophical viewpoints throughout history Gives a separate chapter to predicativism, which is often (but wrongly) treated as if it were a part of logicism Provides readers with a non-partisan discussion until the final chapter, which gives the author’s personal opinion on where the truth lies Designed to be accessible to both undergraduates and graduate students, and at the same time to be of interest to professionals
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