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Introducing Philosophy of Mathematics by Michele Friend Pdf
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.
Introduction to Mathematical Philosophy by Bertrand Russell Pdf
In the words of Bertrand Russell, "Because language is misleading, as well as because it is diffuse and inexact when applied to logic (for which it was never intended), logical symbolism is absolutely necessary to any exact or thorough treatment of mathematical philosophy." That assertion underlies this book, a seminal work in the field for more than 70 years. In it, Russell offers a nontechnical, undogmatic account of his philosophical criticism as it relates to arithmetic and logic. Rather than an exhaustive treatment, however, the influential philosopher and mathematician focuses on certain issues of mathematical logic that, to his mind, invalidated much traditional and contemporary philosophy. In dealing with such topics as number, order, relations, limits and continuity, propositional functions, descriptions, and classes, Russell writes in a clear, accessible manner, requiring neither a knowledge of mathematics nor an aptitude for mathematical symbolism. The result is a thought-provoking excursion into the fascinating realm where mathematics and philosophy meet — a philosophical classic that will be welcomed by any thinking person interested in this crucial area of modern thought.
Introducing Philosophy of Mathematics by Michele Friend Pdf
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.
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.
Philosophy of Mathematics by James Robert Brown Pdf
Philosophy of Mathematicsis clear and engaging, and student friendly The book discusses the great philosophers and the importance of mathematics to their thought. Among topics discussed in the book are the mathematical image, platonism, picture-proofs, applied mathematics, Hilbert and Godel, knots and notation definitions, picture-proofs and Wittgenstein, computation, proof and conjecture.
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
A sophisticated, original introduction to the philosophy of mathematics from one of its leading thinkers Mathematics is a model of precision and objectivity, but it appears distinct from the empirical sciences because it seems to deliver nonexperiential knowledge of a nonphysical reality of numbers, sets, and functions. How can these two aspects of mathematics be reconciled? This concise book provides a systematic, accessible introduction to the field that is trying to answer that question: the philosophy of mathematics. Øystein Linnebo, one of the world's leading scholars on the subject, introduces all of the classical approaches to the field as well as more specialized issues, including mathematical intuition, potential infinity, and the search for new mathematical axioms. Sophisticated but clear and approachable, this is an essential book for all students and teachers of philosophy and of mathematics.
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.
An Historical Introduction to the Philosophy of Mathematics: A Reader by Russell Marcus,Mark McEvoy Pdf
As the first comprehensive collection of historical readings in the philosophy of mathematics, this much-needed introduction reveals the rich history of the subject. Focusing on the philosophy of mathematics before the 20th-century, An Historical Introduction to the Philosophy of Mathematics: A Readerbrings together an impressive collection of primary sources from ancient, medieval 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 Plato, Aristotle, Descartes, Hume and Kant, it connects the major ideas of the ancients with modern thinkers. While a selection of recent texts offering insights the current state of the discipline, clearly illustrate the development of the subject. Presenting historical background essential to understanding contemporary trends, An Historical Introduction to the Philosophy of Mathematics: A Reader is required reading for undergraduates studying the philosophy of mathematics.
Philosophical Introduction to Set Theory by Stephen Pollard Pdf
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.
The Oxford Handbook of Philosophy of Mathematics and Logic by Stewart Shapiro Pdf
Mathematics and logic have been central topics of concern since the dawn of philosophy. Since logic is the study of correct reasoning, it is a fundamental branch of epistemology and a priority in any philosophical system. Philosophers have focused on mathematics as a case study for general philosophical issues and for its role in overall knowledge- gathering. Today, philosophy of mathematics and logic remain central disciplines in contemporary philosophy, as evidenced by the regular appearance of articles on these topics in the best mainstream philosophical journals; in fact, the last decade has seen an explosion of scholarly work in these areas. This volume covers these disciplines in a comprehensive and accessible manner, giving the reader an overview of the major problems, positions, and battle lines. The 26 contributed chapters are by established experts in the field, and their articles contain both exposition and criticism as well as substantial development of their own positions. The essays, which are substantially self-contained, serve both to introduce the reader to the subject and to engage in it at its frontiers. Certain major positions are represented by two chapters--one supportive and one critical. The Oxford Handbook of Philosophy of Math and Logic is a ground-breaking reference like no other in its field. It is a central resource to those wishing to learn about the philosophy of mathematics and the philosophy of logic, or some aspect thereof, and to those who actively engage in the discipline, from advanced undergraduates to professional philosophers, mathematicians, and historians.
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.
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
Mathematics: A Very Short Introduction by Timothy Gowers Pdf
The aim of this volume is to explain the differences between research-level mathematics and the maths taught at school. Most differences are philosophical and the first few chapters are about general aspects of mathematical thought.