Search Results: a-mathematical-prelude-to-the-philosophy-of-mathematics

A Mathematical Prelude to the Philosophy of Mathematics

Author: Stephen Pollard

Publisher: Springer

ISBN: 3319058169

Category: Science

Page: 202

View: 2015

This book is based on two premises: one cannot understand philosophy of mathematics without understanding mathematics and one cannot understand mathematics without doing mathematics. It draws readers into philosophy of mathematics by having them do mathematics. It offers 298 exercises, covering philosophically important material, presented in a philosophically informed way. The exercises give readers opportunities to recreate some mathematics that will illuminate important readings in philosophy of mathematics. Topics include primitive recursive arithmetic, Peano arithmetic, Gödel's theorems, interpretability, the hierarchy of sets, Frege arithmetic and intuitionist sentential logic. The book is intended for readers who understand basic properties of the natural and real numbers and have some background in formal logic.

Philosophical Introduction to Set Theory

Author: Stephen Pollard

Publisher: Courier Dover Publications

ISBN: 0486805824

Category: Mathematics

Page: 192

View: 2341

This unique approach maintains that set theory is the primary mechanism for ideological and theoretical unification in modern mathematics, and its technically informed discussion covers a variety of philosophical issues. 1990 edition.

Prelude to Mathematics

Author: W. W. Sawyer

Publisher: Courier Corporation

ISBN: 0486152774

Category: Mathematics

Page: 224

View: 4602

This lively, stimulating account of non-Euclidean geometry by a noted mathematician covers matrices, determinants, group theory, and many other related topics, with an emphasis on the subject's novel, striking aspects. 1955 edition.

The Life and Work of George Boole

A Prelude to the Digital Age

Author: Des MacHale

Publisher: N.A

ISBN: 9781782050049

Category: Biography & Autobiography

Page: 342

View: 7702

First edition published in 1985 as: George Boole: his life and work. Dublin: Boole Press, 1985.

Mathematics and Logic

Author: Mark Kac,Stanislaw M. Ulam

Publisher: Courier Corporation

ISBN: 0486670856

Category: Philosophy

Page: 170

View: 5728

Fascinating study of the origin and nature of mathematical thought, including relation of mathematics and science, 20th-century developments, impact of computers, and more.Includes 34 illustrations. 1968 edition."

Philosophical Dimensions in Mathematics Education

Author: Karen Francois,Jean Paul Van Bendegem

Publisher: Springer Science & Business Media

ISBN: 0387715754

Category: Education

Page: 242

View: 4245

This book brings together diverse recent developments exploring the philosophy of mathematics in education. The unique combination of ethnomathematics, philosophy, history, education, statistics and mathematics offers a variety of different perspectives from which existing boundaries in mathematics education can be extended. The ten chapters in this book offer a balance between philosophy of and philosophy in mathematics education. Attention is paid to the implementation of a philosophy of mathematics within the mathematics curriculum.

Introduction to Mathematical Philosophy

Author: Bertrand Russell

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: 208

View: 2533

The Philosophy of Set Theory

An Historical Introduction to Cantor's Paradise

Author: Mary Tiles

Publisher: Courier Corporation

ISBN: 0486138550

Category: Mathematics

Page: 256

View: 1860

DIVBeginning with perspectives on the finite universe and classes and Aristotelian logic, the author examines permutations, combinations, and infinite cardinalities; numbering the continuum; Cantor's transfinite paradise; axiomatic set theory, and more. /div

Mathematics and the Search for Knowledge

Author: Morris Kline

Publisher: Oxford University Press, USA

ISBN: 0198020619

Category: Mathematics

Page: 272

View: 8050

The Myth of Invariance

The Origin of the Gods, Mathematics, and Music from the Ṛg Veda to Plato

Author: Ernest G. McClain

Publisher: Red Wheel/Weiser

ISBN: 9780892540129

Category: Religion

Page: 216

View: 8626

Myth of Invariance explores the unifying symbolism of music and number so the reader can understand the secrets from Babylon, Egypt, Greece and the Bible - secrets hidden for centuries.

Wittgenstein and the Turning Point in the Philosophy of Mathematics

Author: S.G. Shanker

Publisher: Routledge

ISBN: 1317832035

Category: Philosophy

Page: 376

View: 4518

First published in 2005. Routledge is an imprint of Taylor & Francis, an informa company.

Emblems of the Mind

Author: Edward Rothstein

Publisher: Harper Perennial

ISBN: 9780380727476

Category: Mathematics

Page: 263

View: 1446

Unravels the mystery of the relationship between music and mathematics, discussing their differences and their surprising similarities--including their origins and historical links

Resonance

From Probability to Epistemology and Back

Author: Krzysztof Burdzy

Publisher: N.A

ISBN: 9781783269204

Category: Knowledge, Theory of

Page: 408

View: 1122

Resonance examines some building blocks of epistemology as a prelude to the careful analysis of the foundations of probability. The concept of resonance is introduced to shed light on the philosophical problems of induction, consciousness, intelligence and free will. The same concept is later applied to provide support for a new philosophical theory of probability. Although based on existing ideas and theories, the epistemological concept of resonance is investigated for the first time in this book. The best-known philosophical theories of probability, frequency and subjective, are shown to be unrealistic and dissociated from the two main branches of statistics: frequency statistics and Bayesian statistics. Written in an accessible style, this book can be enjoyed by philosophers, statisticians and mathematicians, and also by anyone looking to expand their understanding of the disciplines of epistemology and probability.

A Profile of Mathematical Logic

Author: Howard DeLong

Publisher: Courier Corporation

ISBN: 0486139158

Category: Mathematics

Page: 320

View: 8761

This introduction to mathematical logic explores philosophical issues and Gödel's Theorem. Its widespread influence extends to the author of Gödel, Escher, Bach, whose Pulitzer Prize–winning book was inspired by this work.

Theorems, Corollaries, Lemmas, and Methods of Proof

Author: Richard J. Rossi

Publisher: John Wiley & Sons

ISBN: 1118030575

Category: Mathematics

Page: 318

View: 3615

A hands-on introduction to the tools needed for rigorous and theoretical mathematical reasoning Successfully addressing the frustration many students experience as they make the transition from computational mathematics to advanced calculus and algebraic structures, Theorems, Corollaries, Lemmas, and Methods of Proof equips students with the tools needed to succeed while providing a firm foundation in the axiomatic structure of modern mathematics. This essential book: * Clearly explains the relationship between definitions, conjectures, theorems, corollaries, lemmas, and proofs * Reinforces the foundations of calculus and algebra * Explores how to use both a direct and indirect proof to prove a theorem * Presents the basic properties of real numbers * Discusses how to use mathematical induction to prove a theorem * Identifies the different types of theorems * Explains how to write a clear and understandable proof * Covers the basic structure of modern mathematics and the key components of modern mathematics A complete chapter is dedicated to the different methods of proof such as forward direct proofs, proof by contrapositive, proof by contradiction, mathematical induction, and existence proofs. In addition, the author has supplied many clear and detailed algorithms that outline these proofs. Theorems, Corollaries, Lemmas, and Methods of Proof uniquely introduces scratch work as an indispensable part of the proof process, encouraging students to use scratch work and creative thinking as the first steps in their attempt to prove a theorem. Once their scratch work successfully demonstrates the truth of the theorem, the proof can be written in a clear and concise fashion. The basic structure of modern mathematics is discussed, and each of the key components of modern mathematics is defined. Numerous exercises are included in each chapter, covering a wide range of topics with varied levels of difficulty. Intended as a main text for mathematics courses such as Methods of Proof, Transitions to Advanced Mathematics, and Foundations of Mathematics, the book may also be used as a supplementary textbook in junior- and senior-level courses on advanced calculus, real analysis, and modern algebra.

Introduction to the Foundations of Mathematics

Second Edition

Author: Raymond L. Wilder

Publisher: Courier Corporation

ISBN: 0486276201

Category: Mathematics

Page: 352

View: 1491

Classic undergraduate text acquaints students with fundamental concepts and methods of mathematics. Topics include axiomatic method, set theory, infinite sets, groups, intuitionism, formal systems, mathematical logic, and much more. 1965 second edition.

Mathematician's Delight

Author: W. W. Sawyer

Publisher: Courier Corporation

ISBN: 0486137007

Category: Mathematics

Page: 240

View: 8496

"Recommended with confidence" by The Times Literary Supplement, this lively survey was written by a renowned teacher. It starts with arithmetic and algebra, gradually proceeding to trigonometry and calculus. 1943 edition.

Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences

Author: Ivor Grattan-Guinness

Publisher: Routledge

ISBN: 1134957491

Category: Reference

Page: 1840

View: 9154

* Examines the history and philosophy of the mathematical sciences in a cultural context, tracing their evolution from ancient times up to the twentieth century * 176 articles contributed by authors of 18 nationalities * Chronological table of main events in the development of mathematics * Fully integrated index of people, events and topics * Annotated bibliographies of both classic and contemporary sources * Unique coverage of Ancient and non-Western traditions of mathematics

Thomas Kuhn's 'Linguistic Turn' and the Legacy of Logical Empiricism

Incommensurability, Rationality and the Search for Truth

Author: Dr Stefano Gattei

Publisher: Ashgate Publishing, Ltd.

ISBN: 1409485854

Category: Philosophy

Page: 292

View: 9783

Presenting a critical history of the philosophy of science in the twentieth century, focusing on the transition from logical positivism in its first half to the "new philosophy of science" in its second, Stefano Gattei examines the influence of several key figures, but the main focus of the book are Thomas Kuhn and Karl Popper. Kuhn as the central figure of the new philosophy of science, and Popper as a key philosopher of the time who stands outside both traditions. Gattei makes two important claims about the development of the philosophy of science in the twentieth century; that Kuhn is much closer to positivism than many have supposed, failing to solve the crisis of neopostivism, and that Popper, in responding to the deeper crisis of foundationalism that spans the whole of the Western philosophical tradition, ultimately shows what is untenable in Kuhn's view. Gattei has written a very detailed and fine grained, yet accessible discussion making exceptionally interesting use of archive materials.

The Cambridge Companion to Galileo

Author: Peter Machamer

Publisher: Cambridge University Press

ISBN: 1139825666

Category: Philosophy

Page: N.A

View: 1023

Not only a hero of the scientific revolution, but after his conflict with the church, a hero of science, Galileo is today rivalled in the popular imagination only by Newton and Einstein. But what did Galileo actually do, and what are the sources of the popular image we have of him? This 1998 collection of specially-commissioned essays is unparalleled in the depth of its coverage of all facets of Galileo's work. A particular feature of the volume is the treatment of Galileo's relationship with the church. It will be of interest to philosophers, historians of science, cultural historians and those in religious studies.

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