An Introduction to the Philosophy of Mathematics

Author: Mark Colyvan

Publisher: Cambridge University Press

ISBN: 0521826020

Category: Mathematics

Page: 188

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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.

An Introduction to the Philosophy of Art

Author: Richard Eldridge

Publisher: Cambridge University Press

ISBN: 1107041694

Category: Art

Page: 326

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A clear and compact survey of philosophical theories of the nature and value of art, in a new, expanded edition.

An Introduction to Decision Theory

Author: Martin Peterson

Publisher: Cambridge University Press

ISBN: 1107151597

Category: Business & Economics

Page: 348

View: 8813

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Now revised and updated, this introduction to decision theory is both accessible and comprehensive, covering topics including decision making under ignorance and risk, the foundations of utility theory, the debate over subjective and objective probability, Bayesianism, causal decision theory, game theory, and social choice theory. No mathematical skills are assumed, with all concepts and results explained in non-technical and intuitive as well as more formal ways. There are now over 140 exercises with solutions, along with a glossary of key terms and concepts. This second edition includes a new chapter on risk aversion as well as updated discussions of numerous central ideas, including Newcomb's problem, prisoner's dilemmas, and Arrow's impossibility theorem. The book will appeal particularly to philosophy students but also to readers in a range of disciplines, from computer science and psychology to economics and political science.

An Introduction to the Philosophy of Language

Author: Michael Morris

Publisher: Cambridge University Press

ISBN: 1139459805

Category: Philosophy

Page: N.A

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In this textbook, Michael Morris offers a critical introduction to the central issues of the philosophy of language. Each chapter focusses on one or two texts which have had a seminal influence on work in the subject, and uses these as a way of approaching both the central topics and the various traditions of dealing with them. Texts include classic writings by Frege, Russell, Kripke, Quine, Davidson, Austin, Grice and Wittgenstein. Theoretical jargon is kept to a minimum and is fully explained whenever it is introduced. The range of topics covered includes sense and reference, definite descriptions, proper names, natural-kind terms, de re and de dicto necessity, propositional attitudes, truth-theoretical approaches to meaning, radical interpretation, indeterminacy of translation, speech acts, intentional theories of meaning, and scepticism about meaning. The book will be invaluable to students and to all readers who are interested in the nature of linguistic meaning.

An Introduction to the Philosophy of Science

Author: Kent W. Staley

Publisher: Cambridge University Press

ISBN: 0521112494

Category: Science

Page: 300

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This book explores central philosophical concepts, issues, and debates in the philosophy of science, both historical and contemporary.

An Introduction to the Philosophy of Religion

Author: Michael J. Murray,Michael C. Rea

Publisher: Cambridge University Press

ISBN: 9781139469654

Category: Philosophy

Page: N.A

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An Introduction to the Philosophy of Religion provides a broad overview of the topics which are at the forefront of discussion in contemporary philosophy of religion. Prominent views and arguments from both historical and contemporary authors are discussed and analyzed. The book treats all of the central topics in the field, including the coherence of the divine attributes, theistic and atheistic arguments, faith and reason, religion and ethics, miracles, human freedom and divine providence, science and religion, and immortality. In addition it addresses topics of significant importance that similar books often ignore, including the argument for atheism from hiddenness, the coherence of the doctrines of the Trinity and the Incarnation, and the relationship between religion and politics. It will be a valuable accompaniment to undergraduate and introductory graduate-level courses.

An Introduction to Gödel's Theorems

Author: Peter Smith

Publisher: Cambridge University Press

ISBN: 1107328489

Category: Mathematics

Page: N.A

View: 452

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In 1931, the young Kurt Gödel published his First Incompleteness Theorem, which tells us that, for any sufficiently rich theory of arithmetic, there are some arithmetical truths the theory cannot prove. This remarkable result is among the most intriguing (and most misunderstood) in logic. Gödel also outlined an equally significant Second Incompleteness Theorem. How are these Theorems established, and why do they matter? Peter Smith answers these questions by presenting an unusual variety of proofs for the First Theorem, showing how to prove the Second Theorem, and exploring a family of related results (including some not easily available elsewhere). The formal explanations are interwoven with discussions of the wider significance of the two Theorems. This book - extensively rewritten for its second edition - will be accessible to philosophy students with a limited formal background. It is equally suitable for mathematics students taking a first course in mathematical logic.

An Introduction to Non-Classical Logic

From If to Is

Author: Graham Priest

Publisher: Cambridge University Press

ISBN: 9781139469678

Category: Science

Page: N.A

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This revised and considerably expanded 2nd edition brings together a wide range of topics, including modal, tense, conditional, intuitionist, many-valued, paraconsistent, relevant, and fuzzy logics. Part 1, on propositional logic, is the old Introduction, but contains much new material. Part 2 is entirely new, and covers quantification and identity for all the logics in Part 1. The material is unified by the underlying theme of world semantics. All of the topics are explained clearly using devices such as tableau proofs, and their relation to current philosophical issues and debates are discussed. Students with a basic understanding of classical logic will find this book an invaluable introduction to an area that has become of central importance in both logic and philosophy. It will also interest people working in mathematics and computer science who wish to know about the area.

An Introduction to the Theory of Knowledge

Author: Noah Lemos

Publisher: Cambridge University Press

ISBN: 1139461850

Category: Philosophy

Page: N.A

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Epistemology or the theory of knowledge is one of the cornerstones of analytic philosophy, and this book provides a clear and accessible introduction to the subject. It discusses some of the main theories of justification, including foundationalism, coherentism, reliabilism, and virtue epistemology. Other topics include the Gettier problem, internalism and externalism, skepticism, the problem of epistemic circularity, the problem of the criterion, a priori knowledge, and naturalized epistemology. Intended primarily for students taking a first class in epistemology, this lucid and well-written text would also provide an excellent introduction for anyone interested in knowing more about this important area of philosophy.

An Introduction to the Philosophy of Science

Author: Rudolf Carnap

Publisher: Courier Corporation

ISBN: 0486140865

Category: Science

Page: 336

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Stimulating, thought-provoking text by one of the 20th century's most creative philosophers makes accessible such topics as probability, measurement and quantitative language, causality and determinism, theoretical laws and concepts, more.

An Introduction to Ethics

Author: John Deigh

Publisher: Cambridge University Press

ISBN: 052177246X

Category: Philosophy

Page: 241

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This book examines the central questions of ethics through a study of the great ethical works of Western philosophy.

Genetics and Philosophy

An Introduction

Author: Paul Griffiths,Karola Stotz

Publisher: Cambridge University Press

ISBN: 1107354765

Category: Science

Page: N.A

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In the past century, nearly all of the biological sciences have been directly affected by discoveries and developments in genetics, a fast-evolving subject with important theoretical dimensions. In this rich and accessible book, Paul Griffiths and Karola Stotz show how the concept of the gene has evolved and diversified across the many fields that make up modern biology. By examining the molecular biology of the 'environment', they situate genetics in the developmental biology of whole organisms, and reveal how the molecular biosciences have undermined the nature/nurture distinction. Their discussion gives full weight to the revolutionary impacts of molecular biology, while rejecting 'genocentrism' and 'reductionism', and brings the topic right up to date with the philosophical implications of the most recent developments in genetics. Their book will be invaluable for those studying the philosophy of biology, genetics and other life sciences.

Philosophy of Mathematics

A Contemporary Introduction to the World of Proofs and Pictures

Author: James Robert Brown

Publisher: Routledge

ISBN: 1135902380

Category: Mathematics

Page: 264

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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.

Philosophy of Mathematics

Selected Readings

Author: Paul Benacerraf,Hilary Putnam

Publisher: Cambridge University Press

ISBN: 1107268133

Category: Science

Page: N.A

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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.

An Introduction to Formal Logic

Author: Peter Smith

Publisher: Cambridge University Press

ISBN: 9780521008044

Category: Mathematics

Page: 357

View: 5195

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Formal logic provides us with a powerful set of techniques for criticizing some arguments and showing others to be valid. These techniques are relevant to all of us with an interest in being skilful and accurate reasoners. In this highly accessible book, Peter Smith presents a guide to the fundamental aims and basic elements of formal logic. He introduces the reader to the languages of propositional and predicate logic, and then develops formal systems for evaluating arguments translated into these languages, concentrating on the easily comprehensible 'tree' method. His discussion is richly illustrated with worked examples and exercises. A distinctive feature is that, alongside the formal work, there is illuminating philosophical commentary. This book will make an ideal text for a first logic course, and will provide a firm basis for further work in formal and philosophical logic.

Sex and Death

An Introduction to Philosophy of Biology

Author: Kim Sterelny,Paul Griffiths,Paul E. Griffiths

Publisher: University of Chicago Press

ISBN: 9780226773049

Category: Science

Page: 440

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In this 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 debates shaping biology at the end of the 20th century.

An Introduction to the Philosophy of Psychology

Author: Fred Adams,Daniel Weiskopf,Kenneth Aizawa

Publisher: Cambridge University Press

ISBN: 0521519292

Category: Philosophy

Page: 328

View: 1350

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"Our topic here is psychology, the self-styled science of the mind. Psychology's aim is to explain mental phenomena by describing the underlying processes, systems, and mechanisms that give rise to them. These hidden causal levers underlie all of our mental feats, including our richest conscious perceptions, our most subtle chains of reasoning, and our widest-ranging plans and actions. While the phenomena of mind are intimately related to events occurring in the brain, these psychological explanations are, we will argue, distinct and autonomous from explanations in terms of neural processes and mechanisms. According to the view we present here, psychology and neuroscience are different enterprises. We certainly wouldn't claim that our ever-increasing understanding of how the brain works has nothing to say to psychology: on the contrary, they are complimentary, since neuroscience can provide invaluable input to psychological theorizing (and vice versa, a point that we think is not stressed often enough). But our task will be to give a thorough account of the scope, methods, content, and prospects for a distinctive science of our mental lives"--

Principia Mathematica to *56

Author: Alfred North Whitehead,Bertrand Russell

Publisher: Cambridge University Press

ISBN: 9780521626064

Category: Mathematics

Page: 410

View: 6737

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The great three-volume Principia Mathematica (CUP 1927) is deservedly the most famous work ever written on the foundations of mathematics. Its aim is to deduce all the fundamental propositions of logic and mathematics from a small number of logical premises and primitive ideas, establishing that mathematics is a development of logic. This abridged text of Volume I contains the material that is most relevant to an introductory study of logic and the philosophy of mathematics (more advanced students will of course wish to refer to the complete edition). It contains the whole of the preliminary sections (which present the authors' justification of the philosophical standpoint adopted at the outset of their work); the whole of Part I (in which the logical properties of propositions, propositional functions, classes and relations are established); section A of Part II (dealing with unit classes and couples); and Appendices A and C (which give further developments of the argument on the theory of deduction and truth functions).