Introducing Philosophy of Mathematics

Author: Michele Friend

Publisher: Routledge

ISBN: 1317493796

Category: Philosophy

Page: 240

View: 2279

What is mathematics about? Does the subject-matter of mathematics exist independently of the mind or are they mental constructions? How do we know mathematics? Is mathematical knowledge logical knowledge? And how is mathematics applied to the material world? In this introduction to the philosophy of mathematics, Michele Friend examines these and other ontological and epistemological problems raised by the content and practice of mathematics. Aimed at a readership with limited proficiency in mathematics but with some experience of formal logic it seeks to strike a balance between conceptual accessibility and correct representation of the issues. Friend examines the standard theories of mathematics - Platonism, realism, logicism, formalism, constructivism and structuralism - as well as some less standard theories such as psychologism, fictionalism and Meinongian philosophy of mathematics. In each case Friend explains what characterises the position and where the divisions between them lie, including some of the arguments in favour and against each. This book also explores particular questions that occupy present-day philosophers and mathematicians such as the problem of infinity, mathematical intuition and the relationship, if any, between the philosophy of mathematics and the practice of mathematics. Taking in the canonical ideas of Aristotle, Kant, Frege and Whitehead and Russell as well as the challenging and innovative work of recent philosophers like Benacerraf, Hellman, Maddy and Shapiro, Friend provides a balanced and accessible introduction suitable for upper-level undergraduate courses and the non-specialist.

An Introduction to the Philosophy of Mathematics

Author: Mark Colyvan

Publisher: Cambridge University Press

ISBN: 0521826020

Category: Mathematics

Page: 188

View: 9398

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.

Philosophy of Mathematics

Selected Readings

Author: Paul Benacerraf,Hilary Putnam

Publisher: Cambridge University Press

ISBN: 1107268133

Category: Science

Page: N.A

View: 7663

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.

Towards a Philosophy of Real Mathematics

Author: David Corfield

Publisher: Cambridge University Press

ISBN: 9781139436397

Category: Philosophy

Page: N.A

View: 1232

In this ambitious study, David Corfield attacks the widely held view that it is the nature of mathematical knowledge which has shaped the way in which mathematics is treated philosophically and claims that contingent factors have brought us to the present thematically limited discipline. Illustrating his discussion with a wealth of examples, he sets out a variety of approaches to new thinking about the philosophy of mathematics, ranging from an exploration of whether computers producing mathematical proofs or conjectures are doing real mathematics, to the use of analogy, the prospects for a Bayesian confirmation theory, the notion of a mathematical research programme and the ways in which new concepts are justified. His inspiring book challenges both philosophers and mathematicians to develop the broadest and richest philosophical resources for work in their disciplines and points clearly to the ways in which this can be done.

Philosophy of Mathematics

An Introduction

Author: David Bostock

Publisher: John Wiley & Sons

ISBN: 1405189924

Category: Mathematics

Page: 332

View: 4233

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

An Historical Introduction to the Philosophy of Mathematics: A Reader

Author: Russell Marcus,Mark McEvoy

Publisher: Bloomsbury Publishing

ISBN: 1472529480

Category: Philosophy

Page: 896

View: 5200

A comprehensive collection of historical readings in the philosophy of mathematics and a selection of influential contemporary work, this much-needed introduction reveals the rich history of the subject. An Historical Introduction to the Philosophy of Mathematics: A Reader brings together an impressive collection of primary sources from ancient and modern philosophy. Arranged chronologically and featuring introductory overviews explaining technical terms, this accessible reader is easy-to-follow and unrivaled in its historical scope. With selections from key thinkers such as Plato, Aristotle, Descartes, Hume and Kant, it connects the major ideas of the ancients with contemporary thinkers. A selection of recent texts from philosophers including Quine, Putnam, Field and Maddy offering insights into the current state of the discipline clearly illustrates the development of the subject. Presenting historical background essential to understanding contemporary trends and a survey of recent work, An Historical Introduction to the Philosophy of Mathematics: A Reader is required reading for undergraduates and graduate students studying the philosophy of mathematics and an invaluable source book for working researchers.

Set Theory and its Philosophy

A Critical Introduction

Author: Michael Potter

Publisher: Clarendon Press

ISBN: 0191556432

Category: Philosophy

Page: 360

View: 3805

Michael Potter presents a comprehensive new philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. Potter offers a thorough account of cardinal and ordinal arithmetic, and the various axiom candidates. He discusses in detail the project of set-theoretic reduction, which aims to interpret the rest of mathematics in terms of set theory. The key question here is how to deal with the paradoxes that bedevil set theory. Potter offers a strikingly simple version of the most widely accepted response to the paradoxes, which classifies sets by means of a hierarchy of levels. What makes the book unique is that it interweaves a careful presentation of the technical material with a penetrating philosophical critique. Potter does not merely expound the theory dogmatically but at every stage discusses in detail the reasons that can be offered for believing it to be true. Set Theory and its Philosophy is a key text for philosophy, mathematical logic, and computer science.

Introducing Philosophy of Religion

Author: Chad Meister

Publisher: Routledge

ISBN: 1134141793

Category: Philosophy

Page: 256

View: 1045

Does God exist? What about evil and suffering? How does faith relate to science? Is there life after death? These questions fascinate everyone and lie at the heart of philosophy of religion. Chad Meister offers an up-to-date introduction to the field, focussing not only on traditional debates but also on contemporary concepts such as the intelligent creator. Key topics, such as divine reality and the self and religious experience, are discussed in relation to different faiths. Introducing Philosophy of Religion: • offers a lucid overview of contemporary philosophy of religion • introduces the key figures in the history of philosophy of religion • explores the impact of religious diversity and pluralism • examines the main arguments for and against the existence of God and the nature of the divine • looks at science and issues of faith and reason • explores how the different religions approach the concept of life after death. The wealth of textbook features, including tables of essential information, questions for reflection, summaries, glossary and recommendations for further reading make the book ideal for student use. Along with its accompanying Reader, this is the perfect introductory package for undergraduate philosophy of religion courses. Visit the book's companion website at www.routledge.com/textbooks/9780415403276. Features include: an interactive glossary a timeline powerpoint slides on all the chapters chapter outlines lists of objectives for study.

Platonism and Anti-Platonism in Mathematics

Author: Mark Balaguer

Publisher: Oxford University Press on Demand

ISBN: 9780195143980

Category: Mathematics

Page: 217

View: 1665

In this book, Balaguer demonstrates that there are no good arguments for or against mathematical platonism. He establishes that both platonism and anti-platonism are defensible views and introduces a form of platonism ("full-blooded platonism") that solves all problems traditionally associated with the view, proceeding to defend anti-platonism (in particular, mathematical fictionalism) against various attacks--most notably the Quine-Putnam indispensability attack.

The Philosophy of Schopenhauer

Author: Dale Jacquette

Publisher: Routledge

ISBN: 1317494474

Category: Philosophy

Page: 320

View: 7032

Dale Jacquette charts the development of Schopenhauer's ideas from the time of his early dissertation on The Fourfold Root of the Principle of Sufficient Reason through the two editions of his magnum opus The World as Will and Representation to his later collections of philosophical aphorisms and competition essays. Jacquette explores the central topics in Schopenhauer's philosophy including his metaphysics of the world as representation and Will, his so-called pessimistic philosophical appraisal of the human condition, his examination of the concept of death, his dualistic analysis of free will, and his simplified non-Kantian theory of morality. Jacquette shows how these many complex themes fit together in a unified portrait of Schopenhauer's philosophy. The synthesis of Plato, Kant and Buddhist and Hindu ideas is given particular attention as is his influence on Nietzsche, first a follower and then arch opponent of Schopenhauer's thought, and the early Wittgenstein. The book provides a comprehensive and in-depth historical and philosophical introduction to Schopenhauer's distinctive contribution to philosophy.

Plato's Problem

An Introduction to Mathematical Platonism

Author: M. Panza,A. Sereni

Publisher: Springer

ISBN: 1137298138

Category: Mathematics

Page: 306

View: 6876

What is mathematics about? And how can we have access to the reality it is supposed to describe? The book tells the story of this problem, first raised by Plato, through the views of Aristotle, Proclus, Kant, Frege, Gödel, Benacerraf, up to the most recent debate on mathematical platonism.

Philosophies of Mathematics

Author: Alexander L. George,Daniel Velleman

Publisher: Wiley-Blackwell

ISBN: 9780631195443

Category: Science

Page: 244

View: 8415

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.

The Philosophy of Mathematical Practice

Author: Paolo Mancosu

Publisher: Oxford University Press on Demand

ISBN: 0199296456

Category: Philosophy

Page: 447

View: 1523

This book gives a coherent and unified presentation of a new direction of work in philosophy of mathematics. This new approach in philosophy of mathematics requires extensive attention to mathematical practice and provides philosophical analyses of important novel characteristics of contemporary (twentieth century) mathematics and of many aspects of mathematical activity-such as visualization, explanation, understanding etc.-- which escape purely formal logicaltreatment.The book consists of a lengthy introduction by the editor and of eight chapters written by some of the very best scholars in this area. Each chapter consists of a short introduction to the general topic of the chapter and of a longer research article in the very same area. Theeight topics selected represent a broad spectrum of the contemporary philosophical reflection on different aspects of mathematical practice: Diagrammatic reasoning and representational systems; Visualization; Mathematical Explanation; Purity of Methods; Mathematical Concepts; Philosophical relevance of category theory; Philosophical aspects of computer science in mathematics; Philosophical impact of recent developments in mathematical physics.

Introducing Philosophy

God, Mind, World, and Logic

Author: Neil Tennant

Publisher: Routledge

ISBN: 1317560868

Category: Philosophy

Page: 456

View: 2813

Written for any readers interested in better harnessing philosophy’s real value, this book covers a broad range of fundamental philosophical problems and certain intellectual techniques for addressing those problems. In Introducing Philosophy: God, Mind, World, and Logic, Neil Tennant helps any student in pursuit of a ‘big picture’ to think independently, question received dogma, and analyse problems incisively. It also connects philosophy to other areas of study at the university, enabling all students to employ the concepts and techniques of this millennia-old discipline throughout their college careers – and beyond. KEY FEATURES AND BENEFITS: -- Investigates the philosophy of various subjects (psychology, language, biology, math), helping students contextualize philosophy and view it as an interdisciplinary pursuit; also helps students with majors outside of philosophy to see the relationship between philosophy and their own focused academic pursuits -- Author comes from a distinguished background in Logic and Philosophy of Language, which gives the book a level of rigor, balance, and analytic focus sometimes missing from primers to philosophy -- Introduces students to various important philosophical distinctions (e.g. fact vs. value, descriptive vs. prescriptive, norms vs. laws of nature, analytic vs. synthetic, inductive vs. deductive, a priori vs. a posteriori) providing skills that are important for undergraduates to develop in order to inform their study at higher levels. They are essential for further work in philosophy but they are also very beneficial for students pursuing most other disciplines -- Is much more methodologically comprehensive than competing introductions, giving the student the ability to address a wide range of philosophical problems – and not just the ones reviewed in the book -- Offers a companion website with links to apt primary sources, organized chapter-by-chapter, making unnecessary a separate Reader/Anthology of primary sources – thus providing students with all reading material necessary for the course -- Provides five to ten discussion questions for each chapter, helping instructors and students better interact with the ideas and concepts in the text

Sex and Death

An Introduction to Philosophy of Biology

Author: Kim Sterelny,Paul E. Griffiths

Publisher: University of Chicago Press

ISBN: 022617865X

Category: Science

Page: 456

View: 8130

Is the history of life a series of accidents or a drama scripted by selfish genes? Is there an "essential" human nature, determined at birth or in a distant evolutionary past? What should we conserve—species, ecosystems, or something else? Informed answers to questions like these, critical to our understanding of ourselves and the world around us, require both a knowledge of biology and a philosophical framework within which to make sense of its findings. In this accessible introduction to philosophy of biology, Kim Sterelny and Paul E. Griffiths present both the science and the philosophical context necessary for a critical understanding of the most exciting debates shaping biology today. The authors, both of whom have published extensively in this field, describe the range of competing views—including their own—on these fascinating topics. With its clear explanations of both biological and philosophical concepts, Sex and Death will appeal not only to undergraduates, but also to the many general readers eager to think critically about the science of life.

Introducing Philosophy of Science

A Graphic Guide

Author: Ziauddin Sardar

Publisher: Icon Books Ltd

ISBN: 1848319800

Category: Science

Page: 176

View: 9775

What do scientists actually do? Is science "value-free"? How has science evolved through history? Where is science leading us? "Introducing Philosophy of Science" is a clear and incisively illustrated map of the big questions underpinning science. It is essential reading for students, the general public, and even scientists themselves.

More Precisely

The Math You Need to Do Philosophy

Author: Eric Steinhart

Publisher: Broadview Press

ISBN: 9781770480094

Category: Philosophy

Page: 208

View: 2743

More Precisely provides a rigorous and engaging introduction to the mathematics necessary to do philosophy. It is impossible to fully understand much of the most important work in contemporary philosophy without a basic grasp of set theory, functions, probability, modality and infinity. Until now, this knowledge was difficult to acquire. Professors had to provide custom handouts to their classes, while students struggled through math texts searching for insight. More Precisely fills this key gap. Eric Steinhart provides lucid explanations of the basic mathematical concepts and sets out most commonly used notational conventions. Furthermore, he demonstrates how mathematics applies to many fundamental issues in branches of philosophy such as metaphysics, philosophy of language, epistemology, and ethics.

Mathematics

Author: Timothy Gowers

Publisher: Sterling Publishing Company, Inc.

ISBN: 9781402768972

Category: Mathematics

Page: 180

View: 5423

Mathematics is a subject we are all exposed to in our daily lives, but one that many of us fear. Timothy Gowers’s entertaining overview of the topic explains the differences between what we learn at school and advanced mathematics, and helps the math phobic emerge with a clearer understanding of such paradoxical-sounding concepts as “infinity,” “curved space,” and “imaginary numbers.” From basic ideas to philosophical queries to common sociological questions about the mathematical community, this book unravels the mysteries of space and numbers.