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Author: Justin Clarke-Doane
Publisher: Oxford University Press
ISBN: 0192556800
Category : Philosophy
Languages : en
Pages : 219
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Book Description
To what extent are the subjects of our thoughts and talk real? This is the question of realism. In this book, Justin Clarke-Doane explores arguments for and against moral realism and mathematical realism, how they interact, and what they can tell us about areas of philosophical interest more generally. He argues that, contrary to widespread belief, our mathematical beliefs have no better claim to being self-evident or provable than our moral beliefs. Nor do our mathematical beliefs have better claim to being empirically justified than our moral beliefs. It is also incorrect that reflection on the genealogy of our moral beliefs establishes a lack of parity between the cases. In general, if one is a moral antirealist on the basis of epistemological considerations, then one ought to be a mathematical antirealist as well. And, yet, Clarke-Doane shows that moral realism and mathematical realism do not stand or fall together -- and for a surprising reason. Moral questions, insofar as they are practical, are objective in a sense that mathematical questions are not, and the sense in which they are objective can only be explained by assuming practical anti-realism. One upshot of the discussion is that the concepts of realism and objectivity, which are widely identified, are actually in tension. Another is that the objective questions in the neighborhood of factual areas like logic, modality, grounding, and nature are practical questions too. Practical philosophy should, therefore, take center stage.
Author: Justin Clarke-Doane
Publisher: Oxford University Press
ISBN: 0192556800
Category : Philosophy
Languages : en
Pages : 219
Get Book Here
Book Description
To what extent are the subjects of our thoughts and talk real? This is the question of realism. In this book, Justin Clarke-Doane explores arguments for and against moral realism and mathematical realism, how they interact, and what they can tell us about areas of philosophical interest more generally. He argues that, contrary to widespread belief, our mathematical beliefs have no better claim to being self-evident or provable than our moral beliefs. Nor do our mathematical beliefs have better claim to being empirically justified than our moral beliefs. It is also incorrect that reflection on the genealogy of our moral beliefs establishes a lack of parity between the cases. In general, if one is a moral antirealist on the basis of epistemological considerations, then one ought to be a mathematical antirealist as well. And, yet, Clarke-Doane shows that moral realism and mathematical realism do not stand or fall together -- and for a surprising reason. Moral questions, insofar as they are practical, are objective in a sense that mathematical questions are not, and the sense in which they are objective can only be explained by assuming practical anti-realism. One upshot of the discussion is that the concepts of realism and objectivity, which are widely identified, are actually in tension. Another is that the objective questions in the neighborhood of factual areas like logic, modality, grounding, and nature are practical questions too. Practical philosophy should, therefore, take center stage.
Author: Nicholas Rescher
Publisher: Lexington Books
ISBN: 0739199781
Category : Philosophy
Languages : en
Pages : 256
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Book Description
The definitive mission of metaphilosophy is to facilitate an understanding of how philosophy works—the aim of the enterprise, the instrumental and procedural resources for its work, and the prospect of its success. Nicholas Rescher unites two facets of metaphilosophy to show that historical perspective and forward-thinking normative, or systematic, metaphilosophy cannot be independent of one another. The descriptive, or historical, metaphilosophy provides an account of what has been thought regarding the conduct of philosophical inquiry, and the prescriptive, or normative, metaphilosophy which deliberates about what is to be thought regarding the conduct of philosophizing. Rescher argues that metaphilosophy forms a part of philosophy itself. This is a unique feature of the discipline since the philosophy of biology is not a part of biology and the philosophy of mathematics is not a part of mathematics. Ultimately, the salient features of philosophizing in general—including the inherently controversial and discordant nature of philosophical doctrines—are also bound to afflict metaphilosophy. Thus, only by a careful analysis of the central issues can a plausible view of the enterprise be developed. Metaphilosophy: Philosophy in Philosophical Perspective challenges the static, compartmentalized view of metaphilosophy, providing insight for scholars and students of all areas of philosophy.
Author: Paul Horwich
Publisher: Oxford University Press (UK)
ISBN: 019966112X
Category : Philosophy
Languages : en
Pages : 243
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Book Description
Paul Horwich presents a bold new interpretation of Wittgenstein's later work. He argues that it is Wittgenstein's radically anti-theoretical metaphilosophy - and not his identification of the meaning of a word with its use - that underpins his discussions of specific issues concerning language, the mind, mathematics, knowledge, art, and religion.
Author: Mary Leng
Publisher: Oxford University Press
ISBN: 0199280797
Category : Language Arts & Disciplines
Languages : en
Pages : 289
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Book Description
Mary Leng defends a philosophical account of the nature of mathematics which views it as a kind of fiction (albeit an extremely useful fiction). On this view, the claims of our ordinary mathematical theories are more closely analogous to utterances made in the context of storytelling than to utterances whose aim is to assert literal truths.
Author: Stewart Shapiro
Publisher: OUP Oxford
ISBN: 0192893068
Category : Philosophy
Languages : en
Pages : 323
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Book Description
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.
Author: Jacqueline Feke
Publisher: Princeton University Press
ISBN: 069121039X
Category : Mathematics
Languages : en
Pages : 250
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Book Description
A stimulating intellectual history of Ptolemy's philosophy and his conception of a world in which mathematics reigns supreme The Greco-Roman mathematician Claudius Ptolemy is one of the most significant figures in the history of science. He is remembered today for his astronomy, but his philosophy is almost entirely lost to history. This groundbreaking book is the first to reconstruct Ptolemy’s general philosophical system—including his metaphysics, epistemology, and ethics—and to explore its relationship to astronomy, harmonics, element theory, astrology, cosmology, psychology, and theology. In this stimulating intellectual history, Jacqueline Feke uncovers references to a complex and sophisticated philosophical agenda scattered among Ptolemy’s technical studies in the physical and mathematical sciences. She shows how he developed a philosophy that was radical and even subversive, appropriating ideas and turning them against the very philosophers from whom he drew influence. Feke reveals how Ptolemy’s unique system is at once a critique of prevailing philosophical trends and a conception of the world in which mathematics reigns supreme. A compelling work of scholarship, Ptolemy’s Philosophy demonstrates how Ptolemy situated mathematics at the very foundation of all philosophy—theoretical and practical—and advanced the mathematical way of life as the true path to human perfection.
Author: Hartry H. Field
Publisher: Wiley-Blackwell
ISBN: 9780631180876
Category : Science
Languages : en
Pages : 290
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Book Description
Author: Eric Steinhart
Publisher: Broadview Press
ISBN: 155481345X
Category : Philosophy
Languages : en
Pages : 250
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Book Description
More Precisely is a rigorous and engaging introduction to the mathematics necessary to do philosophy. Eric Steinhart provides lucid explanations of many basic mathematical concepts and sets out the most commonly used notational conventions. He also demonstrates how mathematics applies to fundamental issues in various branches of philosophy, including metaphysics, philosophy of language, epistemology, and ethics. This second edition adds a substantial section on decision and game theory, as well as a chapter on information theory and the efficient coding of information.
Author: Reuben Hersh
Publisher: Oxford University Press
ISBN: 0198027362
Category : Mathematics
Languages : en
Pages : 368
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Book Description
Most philosophers of mathematics treat it as isolated, timeless, ahistorical, inhuman. Reuben Hersh argues the contrary, that mathematics must be understood as a human activity, a social phenomenon, part of human culture, historically evolved, and intelligible only in a social context. Hersh pulls the screen back to reveal mathematics as seen by professionals, debunking many mathematical myths, and demonstrating how the "humanist" idea of the nature of mathematics more closely resembles how mathematicians actually work. At the heart of his book is a fascinating historical account of the mainstream of philosophy--ranging from Pythagoras, Descartes, and Spinoza, to Bertrand Russell, David Hilbert, and Rudolph Carnap--followed by the mavericks who saw mathematics as a human artifact, including Aristotle, Locke, Hume, Mill, and Lakatos. What is Mathematics, Really? reflects an insider's view of mathematical life, and will be hotly debated by anyone with an interest in mathematics or the philosophy of science.
Author: Jared Warren
Publisher: Oxford University Press
ISBN: 0190086165
Category : Mathematics
Languages : en
Pages : 409
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Book Description
What is the source of logical and mathematical truth? This volume revitalizes conventionalism as an answer to this question. Conventionalism takes logical and mathematical truth to have their source in linguistic conventions. This was an extremely popular view in the early 20th century, but it was never worked out in detail and is now almost universally rejected in mainstream philosophical circles. In Shadows of Syntax, Jared Warren offers the first book-length treatment and defense of a combined conventionalist theory of logic and mathematics. He argues that our conventions, in the form of syntactic rules of language use, are perfectly suited to explain the truth, necessity, and a priority of logical and mathematical claims. In Part I, Warren explains exactly what conventionalism amounts to and what linguistic conventions are. Part II develops an unrestricted inferentialist theory of the meanings of logical constants that leads to logical conventionalism. This conventionalist theory is elaborated in discussions of logical pluralism, the epistemology of logic, and of the influential objections that led to the historical demise of conventionalism. Part III aims to extend conventionalism from logic to mathematics. Unlike logic, mathematics involves both ontological commitments and a rich notion of truth that cannot be generated by any algorithmic process. To address these issues Warren develops conventionalist-friendly but independently plausible theories of both metaontology and mathematical truth. Finally, Part IV steps back to address big picture worries and meta-worries about conventionalism. This book develops and defends a unified theory of logic and mathematics according to which logical and mathematical truths are reflections of our linguistic rules, mere shadows of syntax.
