PHILOSOPHY OF MATHEMATICS A CONTEMPORARY INTRODUCTION TO THE WORLD OF PROOFS AND PICTURES ROUTLEDGE CONTEMPORARY INTRODUCTIONS TO PHILOSOPHY

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Philosophy Of Mathematics

Author : James Robert Brown
ISBN : 9781135902384
Genre : Mathematics
File Size : 42.3 MB
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In his long-awaited new edition of Philosophy of Mathematics, James Robert Brown tackles important new as well as enduring questions in the mathematical sciences. Can pictures go beyond being merely suggestive and actually prove anything? Are mathematical results certain? Are experiments of any real value? This clear and engaging book takes a unique approach, encompassing non-standard topics such as the role of visual reasoning, the importance of notation, and the place of computers in mathematics, as well as traditional topics such as formalism, Platonism, and constructivism. The combination of topics and clarity of presentation make it suitable for beginners and experts alike. The revised and updated second edition of Philosophy of Mathematics contains more examples, suggestions for further reading, and expanded material on several topics including a novel approach to the continuum hypothesis.
Category: Mathematics

An Introduction To The Philosophy Of Mathematics

Author : Mark Colyvan
ISBN : 9780521826020
Genre : Mathematics
File Size : 62.65 MB
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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.
Category: Mathematics

How Mathematicians Think

Author : William Byers
ISBN : 0691145997
Genre : Mathematics
File Size : 22.43 MB
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To many outsiders, mathematicians appear to think like computers, grimly grinding away with a strict formal logic and moving methodically--even algorithmically--from one black-and-white deduction to another. Yet mathematicians often describe their most important breakthroughs as creative, intuitive responses to ambiguity, contradiction, and paradox. A unique examination of this less-familiar aspect of mathematics, How Mathematicians Think reveals that mathematics is a profoundly creative activity and not just a body of formalized rules and results. Nonlogical qualities, William Byers shows, play an essential role in mathematics. Ambiguities, contradictions, and paradoxes can arise when ideas developed in different contexts come into contact. Uncertainties and conflicts do not impede but rather spur the development of mathematics. Creativity often means bringing apparently incompatible perspectives together as complementary aspects of a new, more subtle theory. The secret of mathematics is not to be found only in its logical structure. The creative dimensions of mathematical work have great implications for our notions of mathematical and scientific truth, and How Mathematicians Think provides a novel approach to many fundamental questions. Is mathematics objectively true? Is it discovered or invented? And is there such a thing as a "final" scientific theory? Ultimately, How Mathematicians Think shows that the nature of mathematical thinking can teach us a great deal about the human condition itself.
Category: Mathematics

Platonism And Anti Platonism In Mathematics

Author : Mark Balaguer
ISBN : 0195143981
Genre : Mathematics
File Size : 72.23 MB
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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.
Category: Mathematics

Philosophy Of Mathematics Oxford Bibliographies Online Research Guide

Author : Oxford University Press
ISBN : 0199808937
Genre : Philosophy
File Size : 38.52 MB
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This ebook is a selective guide designed to help scholars and students of social work find reliable sources of information by directing them to the best available scholarly materials in whatever form or format they appear from books, chapters, and journal articles to online archives, electronic data sets, and blogs. Written by a leading international authority on the subject, the ebook provides bibliographic information supported by direct recommendations about which sources to consult and editorial commentary to make it clear how the cited sources are interrelated related. This ebook is a static version of an article from Oxford Bibliographies Online: Philosophy, a dynamic, continuously updated, online resource designed to provide authoritative guidance through scholarship and other materials relevant to the study Philosophy. Oxford Bibliographies Online covers most subject disciplines within the social science and humanities, for more information visit www.oxfordbibligraphies.com.
Category: Philosophy

An Historical Introduction To The Philosophy Of Mathematics A Reader

Author : Russell Marcus
ISBN : 9781472529480
Genre : Philosophy
File Size : 53.45 MB
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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.
Category: Philosophy

Continental Philosophy

Author : Andrew Cutrofello
ISBN : 0415242088
Genre : Philosophy
File Size : 68.82 MB
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Continental Philosophy: A Contemporary Introduction is ideal for students coming to the topic for the first time. It introduces the origins and development of the tradition, tracing it from Kant to the present day. Taking a clear thematic approach, Andrew Cutrofello introduces and assesses continental philosophy's relation to fundamental questions in philosophy, such as ethics, humanism, phenomenology, politics and metaphysics, centring the book around the following questions: What is knowledge? What is moral obligation? For what should we hope? What is 'man'? What is critique? Andrew Cutrofello's style is lively and engaging. He also introduces the major as well as the lesser-known thinkers of the continental tradition: from Kant, Mill and Nietzsche and Husserl to Heidegger, Merleau-Ponty, Sartre Levinas, Bataille and Kristeva.
Category: Philosophy

Philosophy Of Economics

Author : Julian Reiss
ISBN : 9781136763328
Genre : Philosophy
File Size : 69.49 MB
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Philosophy of Economics: A Contemporary Introduction is the first systematic textbook in the philosophy of economics. It introduces the epistemological, metaphysical and ethical problems that arise in economics, and presents detailed discussions of the solutions that have been offered. Throughout, philosophical issues are illustrated by and analysed in the context of concrete cases drawn from contemporary economics, the history of economic ideas, and actual economic events. This demonstrates the relevance of philosophy of economics both for the science of economics and for the economy. This text will provide an excellent introduction to the philosophy of economics for students and interested general readers alike.
Category: Philosophy

Social And Political Philosophy

Author : John Christman
ISBN : 9781317435983
Genre : Philosophy
File Size : 90.12 MB
Format : PDF, Kindle
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This accessible book is invaluable to anyone coming to social and political philosophy for the first time. It provides a broad survey of key social and political questions in modern society, as well as clear discussions of the philosophical issues central to those questions and to political thought more generally. Unique among books of this kind is a sustained treatment of specifically social philosophy, including topics such as epistemic injustice, pornography, marriage, sexuality, and the family. The relation between such social questions and specifically political topics is discussed. These topics include: political authority, economic justice, the limits of tolerance, considerations of community, race, gender, and culture in questions of justice, and radical critiques of current political theories.? Updates to the Second Edition emphasize the non-statist areas of the subject and include two brand new chapters on social philosophy and transnational justice. This Second Edition also includes revisions throughout and coverage of recent theoretical discussions and world events.
Category: Philosophy

Classical Modern Philosophy

Author : Jeffrey Tlumak
ISBN : 9781134475612
Genre : Philosophy
File Size : 89.53 MB
Format : PDF
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Classical Modern Philosophy introduces students to the key philosophers of the seventeenth and eighteenth centuries, and explores their most important works. Jeffrey Tlumak takes the reader on a chronological journey from Descartes to Kant, tracing the themes that run through the period and their interrelations. The main texts covered are: Descartes' Meditations on First Philosophy Spinoza's Ethics Locke's Essay Concerning Human Understanding Leibniz's Discourse on Metaphysics and Monadology Berkeley's A Treatise Concerning the Principles of Human Knowledge and Three Dialogues between Hylas and Philonous Hume's An Enquiry Concerning Human Understanding and Dialogues Concerning Natural Religion Kant's Critique of Pure Reason Classical Modern Philosophy is the ideal textbook to accompany a course in the history of modern philosophy, but each chapter can also be studied alone as an introduction to the featured philosopher or work. Jeffrey Tlumak outlines and assesses prominent interpretations of the texts, and surveys the legacy of each great thinker.
Category: Philosophy