Autonomy Platonism And The Indispensability Argument

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.

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.

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.

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.

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?

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.

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.