Lectures On The Philosophy Of Mathematics

Author : Joel David Hamkins
Publisher : MIT Press
Page : 350 pages
File Size : 40,7 Mb
Release : 2021-03-09
Category : Mathematics
ISBN : 9780262542234

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Lectures on the Philosophy of Mathematics by Joel David Hamkins Pdf

An introduction to the philosophy of mathematics grounded in mathematics and motivated by mathematical inquiry and practice. In this book, Joel David Hamkins offers an introduction to the philosophy of mathematics that is grounded in mathematics and motivated by mathematical inquiry and practice. He treats philosophical issues as they arise organically in mathematics, discussing such topics as platonism, realism, logicism, structuralism, formalism, infinity, and intuitionism in mathematical contexts. He organizes the book by mathematical themes--numbers, rigor, geometry, proof, computability, incompleteness, and set theory--that give rise again and again to philosophical considerations.

Author : Joel David Hamkins
Publisher : MIT Press
Page : 350 pages
File Size : 43,6 Mb
Release : 2021-02-02
Category : Mathematics
ISBN : 9780262362658

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Lectures on the Philosophy of Mathematics by Joel David Hamkins Pdf

An introduction to the philosophy of mathematics grounded in mathematics and motivated by mathematical inquiry and practice. In this book, Joel David Hamkins offers an introduction to the philosophy of mathematics that is grounded in mathematics and motivated by mathematical inquiry and practice. He treats philosophical issues as they arise organically in mathematics, discussing such topics as platonism, realism, logicism, structuralism, formalism, infinity, and intuitionism in mathematical contexts. He organizes the book by mathematical themes--numbers, rigor, geometry, proof, computability, incompleteness, and set theory--that give rise again and again to philosophical considerations.

Author : Ludwig Wittgenstein
Publisher : Unknown
Page : 0 pages
File Size : 47,5 Mb
Release : 1989
Category : Mathematics
ISBN : OCLC:1391903096

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Wittgenstein's Lectures on the Foundations of Mathematics, Cambridge, 1939 by Ludwig Wittgenstein Pdf

Author : Andrea Iacona
Publisher : Springer Nature
Page : 228 pages
File Size : 55,5 Mb
Release : 2021-05-10
Category : Philosophy
ISBN : 9783030648114

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LOGIC: Lecture Notes for Philosophy, Mathematics, and Computer Science by Andrea Iacona Pdf

This textbook is a logic manual which includes an elementary course and an advanced course. It covers more than most introductory logic textbooks, while maintaining a comfortable pace that students can follow. The technical exposition is clear, precise and follows a paced increase in complexity, allowing the reader to get comfortable with previous definitions and procedures before facing more difficult material. The book also presents an interesting overall balance between formal and philosophical discussion, making it suitable for both philosophy and more formal/science oriented students. This textbook is of great use to undergraduate philosophy students, graduate philosophy students, logic teachers, undergraduates and graduates in mathematics, computer science or related fields in which logic is required.

Author : Mark Colyvan
Publisher : Cambridge University Press
Page : 199 pages
File Size : 51,7 Mb
Release : 2012-06-14
Category : Mathematics
ISBN : 9780521826020

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An Introduction to the Philosophy of Mathematics by Mark Colyvan Pdf

A fascinating journey through intriguing mathematical and philosophical territory - a lively introduction to this contemporary topic.

Author : Michael Kinyon,Glen van Brummelen
Publisher : Springer Science & Business Media
Page : 358 pages
File Size : 51,5 Mb
Release : 2006-06-18
Category : Mathematics
ISBN : 9780387282725

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Mathematics and the Historian's Craft by Michael Kinyon,Glen van Brummelen Pdf

The Kenneth May Lectures have never before been published in book form Important contributions to the history of mathematics by well-known historians of science Should appeal to a wide audience due to its subject area and accessibility

Author : Hermann Weyl
Publisher : Princeton University Press
Page : 338 pages
File Size : 47,8 Mb
Release : 2009-05-17
Category : Mathematics
ISBN : 0691141207

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Philosophy of Mathematics and Natural Science by Hermann Weyl Pdf

History of mathematics.

Author : Bruno de Finetti
Publisher : Springer Science & Business Media
Page : 239 pages
File Size : 44,5 Mb
Release : 2008-05-20
Category : Science
ISBN : 9781402082016

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Philosophical Lectures on Probability by Bruno de Finetti Pdf

Bruno de Finetti (1906–1985) is the founder of the subjective interpretation of probability, together with the British philosopher Frank Plumpton Ramsey. His related notion of “exchangeability” revolutionized the statistical methodology. This book (based on a course held in 1979) explains in a language accessible also to non-mathematicians the fundamental tenets and implications of subjectivism, according to which the probability of any well specified fact F refers to the degree of belief actually held by someone, on the ground of her whole knowledge, on the truth of the assertion that F obtains.

Author : Paul Benacerraf,Hilary Putnam
Publisher : Cambridge University Press
Page : 128 pages
File Size : 47,9 Mb
Release : 1984-01-27
Category : Science
ISBN : 9781107268135

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Philosophy of Mathematics by Paul Benacerraf,Hilary Putnam Pdf

The twentieth century has witnessed an unprecedented 'crisis in the foundations of mathematics', featuring a world-famous paradox (Russell's Paradox), a challenge to 'classical' mathematics from a world-famous mathematician (the 'mathematical intuitionism' of Brouwer), a new foundational school (Hilbert's Formalism), and the profound incompleteness results of Kurt Gödel. In the same period, the cross-fertilization 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 Anglo-Saxon 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.

Author : Joel David Hamkins
Publisher : MIT Press
Page : 132 pages
File Size : 48,5 Mb
Release : 2021-02-23
Category : Mathematics
ISBN : 9780262362566

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Proof and the Art of Mathematics by Joel David Hamkins Pdf

How to write mathematical proofs, shown in fully-worked out examples. This is a companion volume Joel Hamkins's Proof and the Art of Mathematics, providing fully worked-out solutions to all of the odd-numbered exercises as well as a few of the even-numbered exercises. In many cases, the solutions go beyond the exercise question itself to the natural extensions of the ideas, helping readers learn how to approach a mathematical investigation. As Hamkins asks, "Once you have solved a problem, why not push the ideas harder to see what further you can prove with them?" These solutions offer readers examples of how to write a mathematical proofs. The mathematical development of this text follows the main book, with the same chapter topics in the same order, and all theorem and exercise numbers in this text refer to the corresponding statements of the main text.

Author : Noam Greenberg,Joel David Hamkins,Denis Hirschfeldt,Russell Miller
Publisher : Cambridge University Press
Page : 205 pages
File Size : 40,9 Mb
Release : 2013-10-31
Category : Mathematics
ISBN : 9781107014510

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Effective Mathematics of the Uncountable by Noam Greenberg,Joel David Hamkins,Denis Hirschfeldt,Russell Miller Pdf

A comprehensive introduction to eight major approaches to computation on uncountable mathematical domains.

Author : Stewart Shapiro
Publisher : OUP Oxford
Page : 323 pages
File Size : 44,6 Mb
Release : 2000-07-13
Category : Philosophy
ISBN : 9780192893062

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Thinking about Mathematics by Stewart Shapiro Pdf

Thinking about Mathematics covers the range of philosophical issues and positions concerning mathematics. The text describes the questions about mathematics that motivated philosophers throughout history and covers historical figures such as Plato, Aristotle, Kant, and Mill. It also presents the major positions and arguments concerning mathematics throughout the twentieth century, bringing the reader up to the present positions and battle lines.

Author : William Demopoulos
Publisher : Harvard University Press
Page : 492 pages
File Size : 45,9 Mb
Release : 1995
Category : Mathematics
ISBN : 0674319427

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Frege's Philosophy of Mathematics by William Demopoulos Pdf

Widespread interest in Frege's general philosophical writings is, relatively speaking, a fairly recent phenomenon. But it is only very recently that his philosophy of mathematics has begun to attract the attention it now enjoys. This interest has been elicited by the discovery of the remarkable mathematical properties of Frege's contextual definition of number and of the unique character of his proposals for a theory of the real numbers. This collection of essays addresses three main developments in recent work on Frege's philosophy of mathematics: the emerging interest in the intellectual background to his logicism; the rediscovery of Frege's theorem; and the reevaluation of the mathematical content of The Basic Laws of Arithmetic. Each essay attempts a sympathetic, if not uncritical, reconstruction, evaluation, or extension of a facet of Frege's theory of arithmetic. Together they form an accessible and authoritative introduction to aspects of Frege's thought that have, until now, been largely missed by the philosophical community.

Author : James Byrnie Shaw
Publisher : Palala Press
Page : 218 pages
File Size : 49,9 Mb
Release : 2018-03-03
Category : Electronic
ISBN : 1379193753

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Lectures on the Philosophy of Mathematics by James Byrnie Shaw Pdf

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Author : Hao Wang
Publisher : Courier Corporation
Page : 292 pages
File Size : 51,6 Mb
Release : 2014-09-22
Category : Mathematics
ISBN : 9780486171043

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Popular Lectures on Mathematical Logic by Hao Wang Pdf

Noted logician discusses both theoretical underpinnings and practical applications, exploring set theory, model theory, recursion theory and constructivism, proof theory, logic's relation to computer science, and other subjects. 1981 edition, reissued by Dover in 1993 with a new Postscript by the author.