Search Results for "truth-through-proof-a-formalist-foundation-for-mathematics"

Truth Through Proof

Truth Through Proof

A Formalist Foundation for Mathematics

  • Author: Alan Weir
  • Publisher: OUP Oxford
  • ISBN: 9780199541492
  • Category: Mathematics
  • Page: 296
  • View: 5056
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Truth Through Proof defends an anti-platonist philosophy of mathematics derived from game formalism. Alan Weir aims to develop a more satisfactory successor to game formalism utilising a widely accepted, broadly neo-Fregean framework, in which the proposition expressed by an utterance is a function of both sense and background circumstance.

An Introduction to the Philosophy of Mathematics

An Introduction to the Philosophy of Mathematics

  • Author: Mark Colyvan
  • Publisher: Cambridge University Press
  • ISBN: 1107377005
  • Category: Science
  • Page: N.A
  • View: 9579
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This introduction to the philosophy of mathematics focuses on contemporary debates in an important and central area of philosophy. The reader is taken on a fascinating and entertaining journey through some intriguing mathematical and philosophical territory, including such topics as the realism/anti-realism debate in mathematics, mathematical explanation, the limits of mathematics, the significance of mathematical notation, inconsistent mathematics and the applications of mathematics. Each chapter has a number of discussion questions and recommended further reading from both the contemporary literature and older sources. Very little mathematical background is assumed and all of the mathematics encountered is clearly introduced and explained using a wide variety of examples. The book is suitable for an undergraduate course in philosophy of mathematics and, more widely, for anyone interested in philosophy and mathematics.

Social Constructivism as a Philosophy of Mathematics

Social Constructivism as a Philosophy of Mathematics

  • Author: Paul Ernest
  • Publisher: SUNY Press
  • ISBN: 1438402112
  • Category: Philosophy
  • Page: 315
  • View: 9174
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Proposing social constructivism as a novel philosophy of mathematics, this book is inspired by current work in sociology of knowledge and social studies of science. It extends the ideas of social constructivism to the philosophy of mathematics, developing a whole set of new notions. The outcome is a powerful critique of traditional absolutist conceptions of mathematics, as well as of the field of philosophy of mathematics itself. Proposed are a reconceptualization of the philosophy of mathematics and a new set of adequacy criteria. The book offers novel analyses of the important but under-recognized contributions of Wittgenstein and Lakatos to the philosophy of mathematics. Building on their ideas, it develops a theory of mathematical knowledge and its relation to the social context. It offers an original theory of mathematical knowledge based on the concept of conversation, and develops the rhetoric of mathematics to account for proof in mathematics. Another novel feature is the account of the social construction of subjective knowledge, which relates the learning of mathematics to philosophy of mathematics via the development of the individual mathematician. It concludes by considering the values of mathematics and its social responsibility.

Principia Mathematica.

Principia Mathematica.

  • Author: Alfred North Whitehead,Bertrand Russell
  • Publisher: N.A
  • ISBN: N.A
  • Category: Logic, Symbolic and mathematical
  • Page: 167
  • View: 6609
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New Directions in the Philosophy of Mathematics

New Directions in the Philosophy of Mathematics

An Anthology

  • Author: Thomas Tymoczko
  • Publisher: Princeton University Press
  • ISBN: 9780691034980
  • Category: Mathematics
  • Page: 436
  • View: 4698
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The traditional debate among philosophers of mathematics is whether there is an external mathematical reality, something out there to be discovered, or whether mathematics is the product of the human mind. This provocative book, now available in a revised and expanded paperback edition, goes beyond foundationalist questions to offer what has been called a "postmodern" assessment of the philosophy of mathematics--one that addresses issues of theoretical importance in terms of mathematical experience. By bringing together essays of leading philosophers, mathematicians, logicians, and computer scientists, Thomas Tymoczko reveals an evolving effort to account for the nature of mathematics in relation to other human activities. These accounts include such topics as the history of mathematics as a field of study, predictions about how computers will influence the future organization of mathematics, and what processes a proof undergoes before it reaches publishable form. This expanded edition now contains essays by Penelope Maddy, Michael D. Resnik, and William P. Thurston that address the nature of mathematical proofs. The editor has provided a new afterword and a supplemental bibliography of recent work.

Outlines of a Formalist Philosophy of Mathematics

Outlines of a Formalist Philosophy of Mathematics

  • Author: N.A
  • Publisher: Elsevier
  • ISBN: 0444533680
  • Category: Electronic books
  • Page: N.A
  • View: 8478
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Mechanism, Mentalism and Metamathematics

Mechanism, Mentalism and Metamathematics

An Essay on Finitism

  • Author: J. Webb
  • Publisher: Springer Science & Business Media
  • ISBN: 940157653X
  • Category: Philosophy
  • Page: 285
  • View: 9380
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This book grew out of a graduate student paper [261] in which I set down some criticisms of J. R. Lucas' attempt to refute mechanism by means of G6del's theorem. I had made several such abortive attempts myself and had become familiar with their pitfalls, and especially with the double edged nature of incompleteness arguments. My original idea was to model the refutation of mechanism on the almost universally accepted G6delian refutation of Hilbert's formalism, but I kept getting stuck on questions of mathematical philosophy which I found myself having to beg. A thorough study of the foundational works of Hilbert and Bernays finally convinced me that I had all too naively and uncritically bought this refutation of formalism. I did indeed discover points of surprisingly close contact between formalism and mechanism, but also that it was possible to under mine certain strong arguments against these positions precisely by invok ing G6del's and related work. I also began to realize that the Church Turing thesis itself is the principal bastion protecting mechanism, and that G6del's work was perhaps the best thing that ever happened to both mechanism and formalism. I pushed these lines of argument in my dis sertation with the patient help of my readers, Raymond Nelson and Howard Stein. I would especially like to thank the latter for many valuable criticisms of my dissertation as well as some helpful suggestions for reor ganizing it in the direction of the present book.

The Mathematical Experience, Study Edition

The Mathematical Experience, Study Edition

  • Author: Philip Davis,Reuben Hersh,Elena Anne Marchisotto
  • Publisher: Springer Science & Business Media
  • ISBN: 0817682953
  • Category: Mathematics
  • Page: 500
  • View: 7071
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Winner of the 1983 National Book Award! "...a perfectly marvelous book about the Queen of Sciences, from which one will get a real feeling for what mathematicians do and who they are. The exposition is clear and full of wit and humor..." - The New Yorker (1983 National Book Award edition) Mathematics has been a human activity for thousands of years. Yet only a few people from the vast population of users are professional mathematicians, who create, teach, foster, and apply it in a variety of situations. The authors of this book believe that it should be possible for these professional mathematicians to explain to non-professionals what they do, what they say they are doing, and why the world should support them at it. They also believe that mathematics should be taught to non-mathematics majors in such a way as to instill an appreciation of the power and beauty of mathematics. Many people from around the world have told the authors that they have done precisely that with the first edition and they have encouraged publication of this revised edition complete with exercises for helping students to demonstrate their understanding. This edition of the book should find a new generation of general readers and students who would like to know what mathematics is all about. It will prove invaluable as a course text for a general mathematics appreciation course, one in which the student can combine an appreciation for the esthetics with some satisfying and revealing applications. The text is ideal for 1) a GE course for Liberal Arts students 2) a Capstone course for perspective teachers 3) a writing course for mathematics teachers. A wealth of customizable online course materials for the book can be obtained from Elena Anne Marchisotto ([email protected]) upon request.

Truth in Mathematics

Truth in Mathematics

  • Author: Harold G. Dales,Gianluigi Oliveri
  • Publisher: Oxford University Press
  • ISBN: 9780198514763
  • Category: Mathematics
  • Page: 376
  • View: 4556
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The nature of truth in mathematics is a problem which has exercised the minds of thinkers from at least the time of the ancient Greeks. This book is an overview of the most recent work undertaken in this subject, and is unique in being the result of interactions between researchers from both philosophy and mathematics. The articles are written by world leaders in their respective fields and are of interest to researchers in both disciplines.

Problem-Solving and Selected Topics in Euclidean Geometry

Problem-Solving and Selected Topics in Euclidean Geometry

In the Spirit of the Mathematical Olympiads

  • Author: Sotirios E. Louridas,Michael Th. Rassias
  • Publisher: Springer Science & Business Media
  • ISBN: 1461472733
  • Category: Mathematics
  • Page: 235
  • View: 9801
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"Problem-Solving and Selected Topics in Euclidean Geometry: in the Spirit of the Mathematical Olympiads" contains theorems which are of particular value for the solution of geometrical problems. Emphasis is given in the discussion of a variety of methods, which play a significant role for the solution of problems in Euclidean Geometry. Before the complete solution of every problem, a key idea is presented so that the reader will be able to provide the solution. Applications of the basic geometrical methods which include analysis, synthesis, construction and proof are given. Selected problems which have been given in mathematical olympiads or proposed in short lists in IMO's are discussed. In addition, a number of problems proposed by leading mathematicians in the subject are included here. The book also contains new problems with their solutions. The scope of the publication of the present book is to teach mathematical thinking through Geometry and to provide inspiration for both students and teachers to formulate "positive" conjectures and provide solutions.

The VNR Concise Encyclopedia of Mathematics

The VNR Concise Encyclopedia of Mathematics

  • Author: W. Gellert
  • Publisher: Springer Science & Business Media
  • ISBN: 1468482378
  • Category: Juvenile Nonfiction
  • Page: 760
  • View: 7835
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It is commonplace that in our time science and technology cannot be mastered without the tools of mathematics; but the same applies to an ever growing extent to many domains of everyday life, not least owing to the spread of cybernetic methods and arguments. As a consequence, there is a wide demand for a survey of the results of mathematics, for an unconventional approach that would also make it possible to fill gaps in one's knowledge. We do not think that a mere juxtaposition of theorems or a collection of formulae would be suitable for this purpose, because this would over emphasize the symbolic language of signs and letters rather than the mathematical idea, the only thing that really matters. Our task was to describe mathematical interrelations as briefly and precisely as possible. In view of the overwhelming amount of material it goes without saying that we did not just compile details from the numerous text-books for individual branches: what we were aiming at is to smooth out the access to the specialist literature for as many readers as possible. Since well over 700000 copies of the German edition of this book have been sold, we hope to have achieved our difficult goal. Colours are used extensively to help the reader. Important definitions and groups of formulae are on a yellow background, examples on blue, and theorems on red.

For the Learning of Mathematics

For the Learning of Mathematics

  • Author: N.A
  • Publisher: N.A
  • ISBN: N.A
  • Category: Mathematics
  • Page: N.A
  • View: 6200
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Foundations for New Economic Thinking

Foundations for New Economic Thinking

A Collection of Essays

  • Author: S. Dow
  • Publisher: Springer
  • ISBN: 1137000724
  • Category: Political Science
  • Page: 263
  • View: 8271
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New economic thinking is in demand in the light of the recent economic crisis. This book equips the reader with a better understanding of current ways of thinking as well as an awareness of other possibilities, providing the foundations for debate in theory and methodology alongside practical implications for policy.

Constantin Carathéodory

Constantin Carathéodory

Mathematics and Politics in Turbulent Times

  • Author: Maria Georgiadou
  • Publisher: Springer Science & Business Media
  • ISBN: 9783540203520
  • Category: Mathematics
  • Page: 651
  • View: 6283
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Constantin Carathéodory - Mathematics and Politics in Turbulent Times is the biography of a mathematician, born in Berlin in 1873, who became famous during his life time, but has hitherto been ignored by historians for half a century since his death in 1950, in Munich. In a thought-provoking approach, Maria Georgiadou devotes to Constantin Carathéodory all the attention such a personality deserves. With breathtaking detail and the appropriate scrutiny she elucidates his oeuvre, life and turbulent political and historical surroundings. A descendant of the the Greek élite of Constantinople, Carathéodory graduated from the military school of Brussels, became engineer at the Assiout dam in Egypt and finally dedicated a life of effort to mathematics and education. He studied and embarked on an international academic career, haunted by wars, catastrophes and personal tragedies. Over the last years of his life, he stayed in Munich despite World War II, an ambiguous decision upon which the author sheds unprecedented light. Carathéodory's most significant mathematical contributions were to the calculus of variations, the theory of point set measure and the theory of functions of a real variable, pde's, also to complex function theory. The interdisciplinary nature of the text allows easy access for both scholars and readers with a general interest in mathematics, politics and history. The thoroughness of the author’s research and evaluations is certain to leave everyone impressed and more knowledgeable.

Metamathematics, Machines and Gödel's Proof

Metamathematics, Machines and Gödel's Proof

  • Author: N. Shankar
  • Publisher: Cambridge University Press
  • ISBN: 9780521585330
  • Category: Computers
  • Page: 202
  • View: 4227
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Describes the use of computer programs to check several proofs in the foundations of mathematics.

Collected Works: Philosophy and foundations of mathematics, edited by A. Heyting

Collected Works: Philosophy and foundations of mathematics, edited by A. Heyting

  • Author: Luitzen Egbertus Jan Brouwer,Arend Heyting
  • Publisher: N.A
  • ISBN: N.A
  • Category: Mathematics
  • Page: 628
  • View: 9007
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Grundlagen der Analysis

Grundlagen der Analysis

  • Author: Moritz Pasch
  • Publisher: N.A
  • ISBN: 9783737223812
  • Category:
  • Page: 156
  • View: 9734
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Mathematics and the Roots of Postmodern Thought

Mathematics and the Roots of Postmodern Thought

  • Author: Vladimir Tasic
  • Publisher: Oxford University Press
  • ISBN: 9780195349955
  • Category: Mathematics
  • Page: 200
  • View: 396
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This is a charming and insightful contribution to an understanding of the "Science Wars" between postmodernist humanism and science, driving toward a resolution of the mutual misunderstanding that has driven the controversy. It traces the root of postmodern theory to a debate on the foundations of mathematics early in the 20th century, then compares developments in mathematics to what took place in the arts and humanities, discussing issues as diverse as literary theory, arts, and artificial intelligence. This is a straightforward, easily understood presentation of what can be difficult theoretical concepts It demonstrates that a pattern of misreading mathematics can be seen both on the part of science and on the part of postmodern thinking. This is a humorous, playful yet deeply serious look at the intellectual foundations of mathematics for those in the humanities and the perfect critical introduction to the bases of modernism and postmodernism for those in the sciences.

Formalism in Ai and Computer Science

Formalism in Ai and Computer Science

  • Author: Philip Leith
  • Publisher: Ellis Horwood Limited
  • ISBN: 9780133255492
  • Category: Computers
  • Page: 225
  • View: 8433
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Hans Reichenbach: Logical Empiricist

Hans Reichenbach: Logical Empiricist

  • Author: M.H. Salmon
  • Publisher: Springer Science & Business Media
  • ISBN: 9789027709585
  • Category: Science
  • Page: 793
  • View: 8312
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Logical empiricism - not to be confused with logical positivism (see pp. 40-44) - is a movement which has left an indelible mark on twentieth century philosophy; Hans Reichenbach (1891-1953) was one of its found ers and one of its most productive advocates. His sudden and untimely death in 1953 halted his work when he was at the height of his intellectual powers; nevertheless, he bequeathed to us a handsome philosophical inheritance. At the present time, twenty-five years later, we can survey our heritage and see to what extent we have been enriched. The present collection of essays constitutes an effort to do just that - to exhibit the scope and unity of Reichenbach's philosophy, and its relevance to current philosophical issues. There is no Nobel Prize in philosophy - the closest analogue is a volume in The Library of Living Philosophers, an honor which, like the Nobel Prize, cannot be awarded posthumously. Among 'scientific philosophers,' Rudolf Carnap, Albert Einstein, Karl Popper, and Bertrand Russell have been so honored. Had Reichenbach lived longer, he would have shared the honor with Carnap, for at the time of his death a volume on Logical Empiricism, treating the works of Carnap and Reichenbach, was in its early stages of preparation. In the volume which emerged, Carnap wrote, "In 1953, when Reichenbach's creative activity was suddenly ended by his premature death, our movement lost one of its most active leaders.