Philosophy of Mathematics

A Contemporary Introduction to the World of Proofs and Pictures

Author: James Robert Brown

Publisher: Routledge

ISBN: 1135902399

Category: Mathematics

Page: 264

View: 4347

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.

An Introduction to the Philosophy of Mathematics

Author: Mark Colyvan

Publisher: Cambridge University Press

ISBN: 0521826020

Category: Mathematics

Page: 188

View: 1541

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 Economics

A Contemporary Introduction

Author: Julian Reiss

Publisher: Routledge

ISBN: 1136763325

Category: Philosophy

Page: 352

View: 5779

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.

Social Science

Beyond Constructivism and Realism

Author: Gerard Delanty

Publisher: U of Minnesota Press

ISBN: 9780816631278

Category: Social Science

Page: 159

View: 1550

It is argued that the conception of social science emerging today is one that involves a synthesis of radical constructivism and critical realism. The crucial challenge facing social science is a question of its public role: growing reflexivity in society has implications for the social production of knowledge and is bringing into question the separation of expert systems from other forms of knowledge.

How Mathematicians Think

Using Ambiguity, Contradiction, and Paradox to Create Mathematics

Author: William Byers

Publisher: Princeton University Press

ISBN: 9780691145990

Category: Mathematics

Page: 424

View: 1176

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.

Philosophies of Mathematics

Author: Alexander L. George,Daniel Velleman

Publisher: Wiley-Blackwell

ISBN: 9780631195443

Category: Science

Page: 244

View: 6466

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 Schopenhauer

Author: Dale Jacquette

Publisher: Routledge

ISBN: 1317494474

Category: Philosophy

Page: 320

View: 7247

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.

The New Critical Thinking

An Empirically Informed Introduction

Author: Jack Lyons,Barry Ward

Publisher: Routledge

ISBN: 1134881886

Category: Philosophy

Page: 362

View: 7471

Why is it so hard to learn critical thinking skills? Traditional textbooks focus almost exclusively on logic and fallacious reasoning, ignoring two crucial problems. As psychologists have demonstrated recently, many of our mistakes are not caused by formal reasoning gone awry, but by our bypassing it completely. We instead favor more comfortable, but often unreliable, intuitive methods. Second, the evaluation of premises is of fundamental importance, especially in this era of fake news and politicized science. This highly innovative text is psychologically informed, both in its diagnosis of inferential errors, and in teaching students how to watch out for and work around their natural intellectual blind spots. It also incorporates insights from epistemology and philosophy of science that are indispensable for learning how to evaluate premises. The result is a hands-on primer for real world critical thinking. The authors bring over four combined decades of classroom experience and a fresh approach to the traditional challenges of a critical thinking course: effectively explaining the nature of validity, assessing deductive arguments, reconstructing, identifying and diagramming arguments, and causal and probabilistic inference. Additionally, they discuss in detail, important, frequently neglected topics, including testimony, the nature and credibility of science, rhetoric, and dialectical argumentation. Key Features and Benefits: Uses contemporary psychological explanations of, and remedies for, pervasive errors in belief formation. There is no other critical thinking text that generally applies this psychological approach. Assesses premises, notably premises based on the testimony of others, and evaluation of news and other information sources. No other critical thinking textbook gives detailed treatment of this crucial topic. Typically, they only provide a few remarks about when to accept expert opinion / argument from authority. Carefully explains the concept of validity, paying particular attention in distinguishing logical possibility from other species of possibility, and demonstrates how we may mistakenly judge invalid arguments as valid because of belief bias. Instead of assessing an argument’s validity using formal/mathematical methods (i.e., truth tables for propositional logic and Venn diagrams for categorical logic), provides one technique that is generally applicable: explicitly showing that it is impossible to make the conclusion false and the premises true together. For instructors who like the more formal approach, the text also includes standard treatments using truth tables and Venn diagrams. Uses frequency trees and the frequency approach to probability more generally, a simple method for understanding and evaluating quite complex probabilistic information Uses arguments maps, which have been shown to significantly improve students’ reasoning and argument evaluation

On Philosophy, Politics, and Economics

Author: Gerald F. Gaus

Publisher: Cengage Learning

ISBN: 1111796963

Category: Philosophy

Page: 240

View: 6661

On Philosophy, Politics and Economics is an introductory text covering the basics of instrumental rationality, utility theory, game theory, axiomatic social choice theory and public choice theory. It is ideally suited to introductory courses on political economy and ppe programs, as well as advanced undergraduate social and political philosophy courses. The presentation is non-mathematical. On Philosophy, Politics, and Economics does not presuppose background in economics, and so is ideal for non-economists interested in formal analyses of social and political interaction.THE WADSWORTH PHILOSOPHICAL TOPICS SERIES presents readers with concise, timely, and insightful introductions to a variety of traditional and contemporary philosophical subjects. With this series, students of philosophy will be able to discover the richness of philosophical inquiry across a wide array of concepts, including hallmark philosophical themes and themes typically underrepresented in mainstream philosophy publishing. Written by a distinguished list of scholars who have garnered particular recognition for their excellence in teaching, this series presents the vast sweep of today's philosophical exploration in highly accessible and affordable volumes. These books will prove valuable to philosophy teachers and their students as well as to other readers who share a general interest in philosophy. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

An Introduction to Philosophical Logic

Author: Anthony C. Grayling

Publisher: Wiley-Blackwell

ISBN: 9780631199823

Category: Philosophy

Page: 352

View: 1079

An Introduction to Philosophical Logic has been a popular mainstay among students taking courses in philosophical logic and the philosophy of language since it was first published in 1982.

Philosophy of Language

A Contemporary Introduction

Author: William G. Lycan

Publisher: Routledge

ISBN: 1135907633

Category: Language Arts & Disciplines

Page: 240

View: 2216

Philosophy of Language: A Contemporary Introduction introduces the student to the main issues and theories in twentieth century philosophy of language, focusing specifically on linguistic phenomena. Topics are structured in four parts in the book. Part I, Reference and Referring Expressions, includes topics such as Russell's Theory of Desciptions, Donnellan's distinction, problems of anaphora, the description theory of proper names, Searle's cluster theory, and the causal-historical theory. Part II, Theories of Meaning, surveys the competing theories of linguistic meaning and compares their various advantages and liabilities. Part III, Pragmatics and Speech Acts, introduces the basic concepts of linguistic pragmatics, includes a detailed discussion of the problem of indirect force and surveys approaches to metaphor. Part IV, new to this edition, examines the four theories of metaphor. Features of Philosophy of Language include: new chapters on Frege and puzzles, inferentialism, illocutionary theories of meaning and relevance theory chapter overviews and summaries clear supportive examples study questions annotated further reading glossary.

The Laboratory of the Mind

Thought Experiments in the Natural Sciences

Author: James Robert Brown

Publisher: Routledge

ISBN: 1136943773

Category: Philosophy

Page: 240

View: 3580

Newton's bucket, Einstein's elevator, Schrödinger's cat – these are some of the best-known examples of thought experiments in the natural sciences. But what function do these experiments perform? Are they really experiments at all? Can they help us gain a greater understanding of the natural world? How is it possible that we can learn new things just by thinking? In this revised and updated new edition of his classic text The Laboratory of the Mind, James Robert Brown continues to defend apriorism in the physical world. This edition features two new chapters, one on “counter thought experiments” and another on the development of inertial motion. With plenty of illustrations and updated coverage of the debate between Platonic rationalism and classic empiricism, this is a lively and engaging contribution to the field of philosophy of science.

Social and Political Philosophy

A Contemporary Introduction

Author: John Christman

Publisher: Routledge

ISBN: 1317435982

Category: Philosophy

Page: 282

View: 1816

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.

Meditations on First Philosophy

with Selections from the Objections and Replies

Author: René Descartes

Publisher: OUP Oxford

ISBN: 0191604941

Category: Philosophy

Page: 336

View: 7565

'It is some years now since I realized how many false opinions I had accepted as true from childhood onwards...I saw that at some stage in my life the whole structure would have to be utterly demolished' In Descartes's Meditations, one of the key texts of Western philosophy, the thinker rejects all his former beliefs in the quest for new certainties. Discovering his own existence as a thinking entity in the very exercise of doubt, he goes on to prove the existence of God, who guarantees his clear and distinct ideas as a means of access to the truth. He develops new conceptions of body and mind, capable of serving as foundations for the new science of nature. Subsequent philosophy has grappled with Descartes's legacy, questioning many of its conclusions and even his basic approach, but his arguments set the agenda for many of the greatest philosophical thinkers, and their fascination endures. This new translation includes the Third and Fourth Objections and Replies in full, and a selection from the rest of these exchanges with Descartes's contemporaries that helped to expound his philosophy. ABOUT THE SERIES: For over 100 years Oxford World's Classics has made available the widest range of literature from around the globe. Each affordable volume reflects Oxford's commitment to scholarship, providing the most accurate text plus a wealth of other valuable features, including expert introductions by leading authorities, helpful notes to clarify the text, up-to-date bibliographies for further study, and much more.

Philosophy and Probability

Author: Timothy Childers

Publisher: Oxford University Press

ISBN: 0199661820

Category: Philosophy

Page: 194

View: 7256

Probability is increasingly important for our understanding of the world. What is probability? How do we model it, and how do we use it? Timothy Childers presents a lively introduction to the foundations of probability and to philosophical issues it raises. He keeps technicalities to a minimum, and assumes no prior knowledge of the subject. He explains the main interpretations of probability-frequentist, propensity, classical, Bayesian, and objective Bayesian-and uses stimulating examples to bring the subject to life. All students of philosophy will benefit from an understanding of probability, and this is the book to provide it.

The Crusade of Frederick Barbarossa

The History of the Expedition of the Emperor Frederick and Related Texts

Author: Frederick I (Holy Roman Emperor)

Publisher: Ashgate Publishing, Ltd.

ISBN: 1472413962

Category: History

Page: 225

View: 5869

This is the first English translation of the main contemporary accounts of the Crusade and death of the German Emperor Frederick I Barbarossa (ruled 1152-90). The principal text here, the 'History of the Expedition of the Emperor Frederick', was written soon after the events described, and is a crucial, and much under-used source for the Third Crusade. It narrates the preparations and recruitment for the Crusade, and the Crusade itself: the journey through the Balkans and the gruelling march through Asia Minor, beset by Turkish attack, until its arrival at Antioch on 21st July 1190, eleven days after the emperor had drowned while crossing a river in Cilician Armenia. The 'History' gives a vivid account of the sufferings of the German army as it traversed Asia Minor and appears to be, or to be based upon an eyewitness record, cast in the form of (often) a daily memoir. A number of subsidiary texts also translated illustrate and expand this main account, and place the crusade in context.

Taming the Infinite

Author: Ian Stewart

Publisher: Quercus

ISBN: 1623654734

Category: Mathematics

Page: 384

View: 4590

From ancient Babylon to the last great unsolved problems, Ian Stewart brings us his definitive history of mathematics. In his famous straightforward style, Professor Stewart explains each major development--from the first number systems to chaos theory--and considers how each affected society and changed everyday life forever. Maintaining a personal touch, he introduces all of the outstanding mathematicians of history, from the key Babylonians, Greeks and Egyptians, via Newton and Descartes, to Fermat, Babbage and Godel, and demystifies math's key concepts without recourse to complicated formulae. Written to provide a captivating historic narrative for the non-mathematician, Taming the Infinite is packed with fascinating nuggets and quirky asides, and contains 100 illustrations and diagrams to illuminate and aid understanding of a subject many dread, but which has made our world what it is today.