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Autonomy Platonism And The Indispensability Argument
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Book Synopsis Autonomy Platonism and the Indispensability Argument by : Russell Marcus
Download or read book Autonomy Platonism and the Indispensability Argument written by Russell Marcus and published by Lexington Books. This book was released on 2015-06-11 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical platonism is the view that mathematical statements are true of real mathematical objects like numbers, shapes, and sets. One central problem with platonism is that numbers, shapes, sets, and the like are not perceivable by our senses. In contemporary philosophy, the most common defense of platonism uses what is known as the indispensability argument. According to the indispensabilist, we can know about mathematics because mathematics is essential to science. Platonism is among the most persistent philosophical views. Our mathematical beliefs are among our most entrenched. They have survived the demise of millennia of failed scientific theories. Once established, mathematical theories are rarely rejected, and never for reasons of their inapplicability to empirical science. Autonomy Platonism and the Indispensability Argument is a defense of an alternative to indispensability platonism. The autonomy platonist believes that mathematics is independent of empirical science: there is purely mathematical evidence for purely mathematical theories which are even more compelling to believe than empirical science. Russell Marcus begins by contrasting autonomy platonism and indispensability platonism. He then argues against a variety of indispensability arguments in the first half of the book. In the latter half, he defends a new approach to a traditional platonistic view, one which includes appeals to a priori but fallible methods of belief acquisition, including mathematical intuition, and a natural adoption of ordinary mathematical methods. In the end, Marcus defends his intuition-based autonomy platonism against charges that the autonomy of mathematics is viciously circular. This book will be useful to researchers, graduate students, and advanced undergraduates with interests in the philosophy of mathematics or in the connection between science and mathematics.
Book Synopsis God and Abstract Objects by : William Lane Craig
Download or read book God and Abstract Objects written by William Lane Craig and published by Springer. This book was released on 2017-09-05 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an exploration and defense of the coherence of classical theism’s doctrine of divine aseity in the face of the challenge posed by Platonism with respect to abstract objects. A synoptic work in analytic philosophy of religion, the book engages discussions in philosophy of mathematics, philosophy of language, metaphysics, and metaontology. It addresses absolute creationism, non-Platonic realism, fictionalism, neutralism, and alternative logics and semantics, among other topics. The book offers a helpful taxonomy of the wide range of options available to the classical theist for dealing with the challenge of Platonism. It probes in detail the diverse views on the reality of abstract objects and their compatibility with classical theism. It contains a most thorough discussion, rooted in careful exegesis, of the biblical and patristic basis of the doctrine of divine aseity. Finally, it challenges the influential Quinean metaontological theses concerning the way in which we make ontological commitments.
Book Synopsis An Historical Introduction to the Philosophy of Mathematics: A Reader by : Russell Marcus
Download or read book An Historical Introduction to the Philosophy of Mathematics: A Reader written by Russell Marcus and published by Bloomsbury Publishing. This book was released on 2016-02-11 with total page 849 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Mathematics and Metaphilosophy by : Justin Clarke-Doane
Download or read book Mathematics and Metaphilosophy written by Justin Clarke-Doane and published by Cambridge University Press. This book was released on 2022-06-30 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Element discusses the problem of mathematical knowledge, and its broader philosophical ramifications. It argues that the challenge to explain the (defeasible) justification of our mathematical beliefs ('the justificatory challenge'), arises insofar as disagreement over axioms bottoms out in disagreement over intuitions. And it argues that the challenge to explain their reliability ('the reliability challenge'), arises to the extent that we could have easily had different beliefs. The Element shows that mathematical facts are not, in general, empirically accessible, contra Quine, and that they cannot be dispensed with, contra Field. However, it argues that they might be so plentiful that our knowledge of them is unmysterious. The Element concludes with a complementary 'pluralism' about modality, logic and normative theory, highlighting its surprising implications. Metaphysically, pluralism engenders a kind of perspectivalism and indeterminacy. Methodologically, it vindicates Carnap's pragmatism, transposed to the key of realism.
Book Synopsis Mathematics and Explanation by : Christopher Pincock
Download or read book Mathematics and Explanation written by Christopher Pincock and published by Cambridge University Press. This book was released on 2023-05-25 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Element answers four questions. Can any traditional theory of scientific explanation make sense of the place of mathematics in explanation? If traditional monist theories are inadequate, is there some way to develop a more flexible, but still monist, approach that will clarify how mathematics can help to explain? What sort of pluralism about explanation is best equipped to clarify how mathematics can help to explain in science and in mathematics itself? Finally, how can the mathematical elements of an explanation be integrated into the physical world? Some of the evidence for a novel scientific posit may be traced to the explanatory power that this posit would afford, were it to exist. Can a similar kind of explanatory evidence be provided for the existence of mathematical objects, and if not, why not?
Book Synopsis Indispensability Arguments for Mathematical Platonism by : Artemis Morou
Download or read book Indispensability Arguments for Mathematical Platonism written by Artemis Morou and published by . This book was released on 2000 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Philosophers in the Classroom by : Steven M. Cahn
Download or read book Philosophers in the Classroom written by Steven M. Cahn and published by Hackett Publishing. This book was released on 2018-09-15 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: In these essays, 24 of our most celebrated professors of philosophy address the problem of how to teach philosophy today: how to make philosophy interesting and relevant; how to bring classic texts to life; how to serve all students; and how to align philosophy with more "practical" pursuits. Selected and introduced by three leaders in the world of philosophical education, the insights contained in this inspiring collection illuminate the challenges and possibilities of teaching the academy’s oldest discipline.
Book Synopsis The Art of Teaching Philosophy by : Brynn F. Welch
Download or read book The Art of Teaching Philosophy written by Brynn F. Welch and published by Bloomsbury Publishing. This book was released on 2024-07-25 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: Teaching is a moral enterprise through which we reflect our most deeply held values. Thoughtful teaching begins before the syllabus is written and continues well beyond the end of the semester. In this book a team of over 30 renowned and innovative US philosophy teachers offer accessible reflections and practical suggestions for constructing a philosophy course. Our classroom can mimic dynamics that emerge in the broader society, or it can teach students new ways of engaging with one another. From syllabus design and classroom management to exercises and assessments, each chapter answers frequently asked questions: How do we balance lecture with discussion? What are our goals? When we're leading a discussion and a student (or several students) say false things, what should we do? What are the costs of correcting them? Here is an in-depth exploration of topics such as content selection, assessment design, mentorship, and making teaching count professionally. Each contribution balances reflective values with concrete advice emerging from tried-and-tested practices. Insightful discussions about theories of philosophy pedagogy feature throughout. Divided into The Philosophy Course, The Philosophy Classroom, Exercises and Assignments, and What Comes Next, chapters include insights from students on what they have learned from studying philosophy. For teachers of philosophy at any stage of their career this is a must-have resource.
Book Synopsis Mathematics in Early Childhood by : Oliver Thiel
Download or read book Mathematics in Early Childhood written by Oliver Thiel and published by Routledge. This book was released on 2020-11-05 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: Structured around Bishop’s six fundamental mathematical activities, this book brings together examples of mathematics education from a range of countries to help readers broaden their view on maths and its interrelationship to other aspects of life. Considering different educational traditions and diverse contexts, and illustrating theory through the use of real-life vignettes throughout, this book encourages readers to review, reflect on, and critique their own practice when conducting activities on explaining, counting, measuring, locating, designing, and playing. Aimed at early childhood educators and practitioners looking to improve the mathematics learning experience for all their students, this practical and accessible guide provides the knowledge and tools to help every child.
Book Synopsis Plato, Utilitarianism and Education (International Library of the Philosophy of Education Volume 3) by : Robin Barrow
Download or read book Plato, Utilitarianism and Education (International Library of the Philosophy of Education Volume 3) written by Robin Barrow and published by Routledge. This book was released on 2010-02-25 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: Three lines of argument are central to this book: that Plato's views as expounded in the Republic indicate that he was a utilitarian; that utilitarianism is the only acceptable ethical theory; that these conclusions have significant repercussions for education. Throughout the book the exposition of utilitarianism and the interpretation of the Republic are closely linked. The author assesses the nature of recent Platonic criticism and provides a critical summary of the Republic. He expounds and defends utilitarianismn and examines in greater depth the consequences for education of accepting a utilitarian position, showing how, for example, from this standpoint such key terms in educational debate as 'autonomy' and 'self-development' must be reassessed as educational objectives.
Book Synopsis The Philosophy of Mathematical Practice by : Paolo Mancosu
Download or read book The Philosophy of Mathematical Practice written by Paolo Mancosu and published by OUP Oxford. This book was released on 2008-06-19 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contemporary philosophy of mathematics offers us an embarrassment of riches. Among the major areas of work one could list developments of the classical foundational programs, analytic approaches to epistemology and ontology of mathematics, and developments at the intersection of history and philosophy of mathematics. But anyone familiar with contemporary philosophy of mathematics will be aware of the need for new approaches that pay closer attention to mathematical practice. This book is the first attempt to give a coherent and unified presentation of this new wave of work in philosophy of mathematics. The new approach is innovative at least in two ways. First, it holds that there are important novel characteristics of contemporary mathematics that are just as worthy of philosophical attention as the distinction between constructive and non-constructive mathematics at the time of the foundational debates. Secondly, it holds that many topics which escape purely formal logical treatment - such as visualization, explanation, and understanding - can nonetheless be subjected to philosophical analysis. The Philosophy of Mathematical Practice comprises an introduction by the editor and eight chapters written by some of the leading scholars in the field. Each chapter consists of short introduction to the general topic of the chapter followed by a longer research article in the area. The eight topics selected represent a broad spectrum of contemporary philosophical reflection on different aspects of mathematical practice: diagrammatic reasoning and representation systems; visualization; mathematical explanation; purity of methods; mathematical concepts; the philosophical relevance of category theory; philosophical aspects of computer science in mathematics; the philosophical impact of recent developments in mathematical physics.
Book Synopsis Knowledge, Cause, and Abstract Objects by : C. Cheyne
Download or read book Knowledge, Cause, and Abstract Objects written by C. Cheyne and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: According to platonists, entities such as numbers, sets, propositions and properties are abstract objects. But abstract objects lack causal powers and a location in space and time, so how could we ever come to know of the existence of such impotent and remote objects? In Knowledge, Cause, and Abstract Objects, Colin Cheyne presents the first systematic and detailed account of this epistemological objection to the platonist doctrine that abstract objects exist and can be known. Since mathematics has such a central role in the acquisition of scientific knowledge, he concentrates on mathematical platonism. He also concentrates on our knowledge of what exists, and argues for a causal constraint on such existential knowledge. Finally, he exposes the weaknesses of recent attempts by platonists to account for our supposed platonic knowledge. This book will be of particular interest to researchers and advanced students of epistemology and of the philosophy of mathematics and science. It will also be of interest to all philosophers with a general interest in metaphysics and ontology.
Download or read book Indispensability written by A. C. Paseau and published by Cambridge University Press. This book was released on 2023-06-08 with total page 111 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our best scientific theories explain a wide range of empirical phenomena, make accurate predictions, and are widely believed. Since many of these theories make ample use of mathematics, it is natural to see them as confirming its truth. Perhaps the use of mathematics in science even gives us reason to believe in the existence of abstract mathematical objects such as numbers and sets. These issues lie at the heart of the Indispensability Argument, to which this Element is devoted. The Element's first half traces the evolution of the Indispensability Argument from its origins in Quine and Putnam's works, taking in naturalism, confirmational holism, Field's program, and the use of idealisations in science along the way. Its second half examines the explanatory version of the Indispensability Argument, and focuses on several more recent versions of easy-road and hard-road fictionalism respectively.
Book Synopsis The Metaphysics of Autonomy by : M. Coeckelbergh
Download or read book The Metaphysics of Autonomy written by M. Coeckelbergh and published by Springer. This book was released on 2004-07-12 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: If we want to be autonomous, what do we want? The author shows that contemporary value-neutral and metaphysically economical conceptions of autonomy, such as that of Harry Frankfurt, face a serious problem. Drawing on Plato, Augustine, and Kant, this book provides a sketch of how 'ancient' and 'modern' can be reconciled to solve it. But at what expense? It turns out that the dominant modern ideal of autonomy cannot do without a costly metaphysics if it is to be coherent.
Book Synopsis Philosophy in an Age of Science by : Hilary Putnam
Download or read book Philosophy in an Age of Science written by Hilary Putnam and published by Harvard University Press. This book was released on 2012-04-17 with total page 672 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hilary Putnam's unceasing self-criticism has led to the frequent changes of mind he is famous for, but his thinking is also marked by considerable continuity. A simultaneous interest in science and ethicsÑunusual in the current climate of contentionÑhas long characterized his thought. In Philosophy in an Age of Science, Putnam collects his papers for publicationÑhis first volume in almost two decades. Mario De Caro and David Macarthur's introduction identifies central themes to help the reader negotiate between Putnam past and Putnam present: his critique of logical positivism; his enduring aspiration to be realist about rational normativity; his anti-essentialism about a range of central philosophical notions; his reconciliation of the scientific worldview and the humanistic tradition; and his movement from reductive scientific naturalism to liberal naturalism. Putnam returns here to some of his first enthusiasms in philosophy, such as logic, mathematics, and quantum mechanics. The reader is given a glimpse, too, of ideas currently in development on the subject of perception. Putnam's work, contributing to a broad range of philosophical inquiry, has been said to represent a Òhistory of recent philosophy in outline.Ó Here it also delineates a possible future.
Book Synopsis An Historical Introduction to the Philosophy of Mathematics: A Reader by : Russell Marcus
Download or read book An Historical Introduction to the Philosophy of Mathematics: A Reader written by Russell Marcus and published by Bloomsbury Publishing. This book was released on 2016-02-11 with total page 849 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis From Truth to Reality by : Heather Dyke
Download or read book From Truth to Reality written by Heather Dyke and published by Routledge. This book was released on 2009-06-02 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: Questions about truth and questions about reality are intimately connected. One can ask whether numbers exist by asking "Are there numbers?" But one can also ask what arguably amounts to the same question by asking "Is the sentence 'There are numbers' true?" Such semantic ascent implies that reality can be investigated by investigating our true sentences. This line of thought was dominant in twentieth century philosophy, but is now beginning to be called into question. In From Truth to Reality, Heather Dyke brings together some of the foremost metaphysicians to examine approaches to truth, reality, and the connections between the two. This collection features new and previously unpublished material by JC Beall, Mark Colyvan, Michael Devitt, John Heil, Frank Jackson, Fred Kroon, D. H. Mellor, Luca Moretti, Alan Musgrave, Robert Nola, J. J. C. Smart, Paul Snowdon, and Daniel Stoljar.
