philosophy mathematics 2024

Philosophy of Mathematics and Natural

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Princeton Philosophy of Mathematics and

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A digital copy of Philosophy of Mathematics and Natural Science by Hermann Weyl Download is immediately available upon purchase

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Philosophies of Mathematics

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This book provides an accessible critical introduction to the three main approaches that dominated work in the philosophy of mathematics during the twentieth century logicism intuitionism and formalism

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Philosophy of Mathematics

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Philosophies of Mathematics

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This book provides an accessible critical introduction to the three main approaches that dominated work in the philosophy of mathematics during the twentieth century logicism intuitionism and formalism

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Philosophy of Mathematics Selected Readings

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The twentieth century has witnessed an unprecedented crisis in the foundations of mathematics featuring a worldfamous paradox Russells Paradox a challenge to classical mathematics from a worldfamous mathematician the mathematical intuitionism of Brouwer a new foundational school Hilberts Formalism and the profound incompleteness results of Kurt Gödel In the same period the crossfertilization of mathematics and philosophy resulted in a new sort of mathematical philosophy associated most notably but in different ways with Bertrand Russell W V Quine and Gödel himself and which remains at the focus of AngloSaxon philosophical discussion The present collection brings together in a convenient form the seminal articles in the philosophy of mathematics by these and other major thinkers It is a substantially revised version of the edition first published in 1964 and includes a revised bibliography The volume will be welcomed as a major work of reference at this level in the field

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Philosophy of Mathematics Structure and

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Do numbers sets and so forth exist What do mathematical statements mean Are they literally true or false or do they lack truth values altogether Addressing questions that have attracted lively debate in recent years Stewart Shapiro contends that standard realist and antirealist accounts of mathematics are both problematic As Benacerraf first noted we are confronted with the following powerful dilemma The desired continuity between mathematical and say scientific language suggests realism but realism in this context suggests seemingly intractable epistemic problems As a way out of this dilemma Shapiro articulates a structuralist approach On this view the subject matter of arithmetic for example is not a fixed domain of numbers independent of each other but rather is the natural number structure the pattern common to any system of objects that has an initial object and successor relation satisfying the induction principle Using this framework realism in mathematics can be preserved without troublesome epistemic consequences Shapiro concludes by showing how a structuralist approach can be applied to wider philosophical questions such as the nature of an object and the Quinean nature of ontological commitment Clear compelling and tautly argued Shapiros work noteworthy both in its attempt to develop a fulllength structuralist approach to mathematics and to trace its emergence in the history of mathematics will be of deep interest to both philosophers and mathematicians

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Philosophy of Mathematics 5 Questions

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Philosophy of Mathematics 5 Questions is a collection of short interviews based on 5 questions presented to some of the most influential and prominent scholars in this field We hear their views aim scope use the future direction and how their work fits in these respects

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Philosophy of Mathematics in the

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In this illuminating collection Charles Parsons surveys the contributions of philosophers and mathematicians who shaped the philosophy of mathematics over the course of the past centuryParsons begins with a discussion of the Kantian legacy in the work of L E J Brouwer David Hilbert and Paul Bernays shedding light on how Bernays revised his philosophy after his collaboration with Hilbert He considers Hermann Weyls idea of a vicious circle in the foundations of mathematics a radical claim that elicited many challenges Turning to Kurt Gödel whose incompleteness theorem transformed debate on the foundations of mathematics and brought mathematical logic to maturity Parsons discusses his essay on Bertrand Russells mathematical logicGödels first mature philosophical statement and an avowal of his Platonistic viewPhilosophy of Mathematics in the Twentieth Century insightfully treats the contributions of figures the author knew personally W V Quine Hilary Putnam Hao Wang and William Tait Quines early work on ontology is explored as is his nominalistic view of predication and his use of the genetic method of explanation in the late work The Roots of Reference Parsons attempts to tease out Putnams views on existence and ontology especially in relation to logic and mathematics Wangs contributions to subjects ranging from the concept of set minds and machines to the interpretation of Gödel are examined as are Taits axiomatic conception of mathematics his minimalist realism and his thoughts on historical figures

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Philosophy of Mathematics 5 Questions

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Philosophy of Mathematics 5 Questions is a collection of short interviews based on 5 questions presented to some of the most influential and prominent scholars in this field We hear their views aim scope use the future direction and how their work fits in these respects

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Philosophy of Mathematics An Introduction

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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 nonpartisan discussion until the final chapter which gives the authors 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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Philosophy of Mathematics An Introduction

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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 nonpartisan discussion until the final chapter which gives the authors 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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Philosophy of Mathematics An Introduction

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Philosophy of Mathematics is an excellent introductory text This student friendly book discusses the great philosophers and the importance of mathematics to their thought It includes the following topics the mathematical image platonism pictureproofs applied mathematics Hilbert and Godel knots and nations definitions pictureproofs and Wittgenstein computation proof and conjectureThe book is ideal for courses on philosophy of mathematics and logic

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Philosophy of Mathematics and Mathematical

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The seventeenth century saw dramatic advances in mathematical theory and practice than any era before or since With the recovery of many of the classical Greek mathematical texts new techniques were introduced and within 100 years analytic geometry the geometry of indivisibles the arithmetic of infinites and the calculus had been developed Although many technical studies have been devoted to these innovations Paolo Mancosu provides the first comprehensive account of the relationship between mathematical advances of the seventeenth century and the philosophy of mathematics of the period Beginning with the Renaissance debates on the certainty of mathematics Mancosu leads the reader through the foundational issues raised by the emergence of these new mathematical techniques including the influence of the Aristotelian conception of science in Cavalieri and Guldin the foundational relevance of Descartes Geometrie the relationship between empiricist epistemology and infinitistic theorems in geometry and the debates concerning the foundations of the Leibnizian calculus In the process Mancosu draws a sophisticated picture of the subtle dependencies between technical development and philosophical reflection in seventeenth century mathematics

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The Philosophy of Mathematics Education

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First published in 1991 Routledge is an imprint of Taylor amp Francis an informa company

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Philosophy of Mathematics

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Slight shelf wear Marker mark fore edge Pages are clean Binding is tight

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Philosophy of Mathematics Selected Writings

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The philosophy of mathematics plays a vital role in the mature philosophy of Charles S Peirce Peirce received rigorous mathematical training from his father and his philosophy carries on in decidedly mathematical and symbolic veins For Peirce math was a philosophical tool and many of his most productive ideas rest firmly on the foundation of mathematical principles This volume collects Peirces most important writings on the subject many appearing in print for the first time Peirces determination to understand matter the cosmos and the grand design of the universe remain relevant for contemporary students of science technology and symbolic logic

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Philosophy of Mathematics in the

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In this illuminating collection Charles Parsons surveys the contributions of philosophers and mathematicians who shaped the philosophy of mathematics over the course of the past centuryParsons begins with a discussion of the Kantian legacy in the work of L E J Brouwer David Hilbert and Paul Bernays shedding light on how Bernays revised his philosophy after his collaboration with Hilbert He considers Hermann Weyls idea of a vicious circle in the foundations of mathematics a radical claim that elicited many challenges Turning to Kurt Gödel whose incompleteness theorem transformed debate on the foundations of mathematics and brought mathematical logic to maturity Parsons discusses his essay on Bertrand Russells mathematical logicGödels first mature philosophical statement and an avowal of his Platonistic viewPhilosophy of Mathematics in the Twentieth Century insightfully treats the contributions of figures the author knew personally W V Quine Hilary Putnam Hao Wang and William Tait Quines early work on ontology is explored as is his nominalistic view of predication and his use of the genetic method of explanation in the late work The Roots of Reference Parsons attempts to tease out Putnams views on existence and ontology especially in relation to logic and mathematics Wangs contributions to subjects ranging from the concept of set minds and machines to the interpretation of Gödel are examined as are Taits axiomatic conception of mathematics his minimalist realism and his thoughts on historical figures

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Philosophy of Mathematics An Introduction

Discover information, advice, and prices for Philosophy of Mathematics An Introduction sold for 99.16 $ , available in the Books & Magazines category; this product is sold by Abebooks.com and made by philosophy.

Philosophy of Mathematics is an excellent introductory text This student friendly book discusses the great philosophers and the importance of mathematics to their thought It includes the following topics the mathematical image platonism pictureproofs applied mathematics Hilbert and Godel knots and nations definitions pictureproofs and Wittgenstein computation proof and conjectureThe book is ideal for courses on philosophy of mathematics and logic

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Philosophy of Mathematics Education

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Although many agree that all teaching rests on a theory of knowledge there has been no indepth exploration of the implications of the philosophy of mathematics for education This is Paul Ernests aim Building on the work of Lakatos and Wittgenstein it challenges the prevalent notion that mathematical knowledge is certain absolute and neutral and offers instead an account of mathematics as a social construction This has profound educational implications for social issues including gender race and multiculturalism for pedagogy including investigations and problem solving and challenges hierarchical views of mathematics learning and ability Beyond this the book offers a wellgrounded model of five educational ideologies each with its own epistemology values aims and social group of adherents An analysis of the impact of these groups on the National Curriculum results in a powerful critique revealing the questionable assumptions values and interests upon which it rests The book finishes on an optimistic note arguing that pedagogy left unspecified by the National Curriculum is the way to achieve the radical aims of educating confident problem posers and solvers who are able to critically evaluate the social uses of mathematics

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philosophy mathematics


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