Platonism And Anti Platonism In Mathematics
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Platonism And Anti Platonism In Mathematics
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Author : Mark Balaguer
language : en
Publisher: Oxford University Press, USA
Release Date : 2001
Platonism And Anti Platonism In Mathematics written by Mark Balaguer and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
In this book, Balaguer demonstrates that there are no good arguments for or against mathematical platonism. He does this by establishing that both platonism and anti-platonism are defensible. (Philosophy)
Plato S Problem
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Author : M. Panza
language : en
Publisher: Springer
Release Date : 2013-01-21
Plato S Problem written by M. Panza and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-21 with Mathematics categories.
What is mathematics about? And how can we have access to the reality it is supposed to describe? The book tells the story of this problem, first raised by Plato, through the views of Aristotle, Proclus, Kant, Frege, Gödel, Benacerraf, up to the most recent debate on mathematical platonism.
Knowledge Cause And Abstract Objects
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Author : C. Cheyne
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Knowledge Cause And Abstract Objects written by C. Cheyne and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Philosophy categories.
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.
Autonomy Platonism And The Indispensability Argument
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Author : Russell Marcus
language : en
Publisher: Lexington Books
Release Date : 2015-06-11
Autonomy Platonism And The Indispensability Argument written by Russell Marcus and has been published by Lexington Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-11 with Philosophy categories.
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.
Mathematical Plato
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Author : Roger Sworder
language : en
Publisher:
Release Date : 2013
Mathematical Plato written by Roger Sworder and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Philosophy categories.
Plato is the first scientist whose work we still possess. He is our first writer to interpret the natural world mathematically, and also the first theorist of mathematics in the natural sciences. As no one else before or after, he set out why we should suppose a link between nature and mathematics, a link that has never been stronger than it is today. Mathematical Plato examines how Plato organized and justified the principles, terms, and methods of our mathematical, natural science. "Roger Sworder deserves our gratitude for drawing attention to the significance of mathematics in Plato's thought and writings. He lays the principal discussions out before us with clarity. He also presents Plato as a theorist of nature: of physics and not just metaphysics, to use Aristotle's distinction. Not all readers, we should admit, will be equally convinced of the usefulness of Plato's science for today, but they will all be led more deeply into Plato's vision of reality."--ANDREW DAVISON, Westcott House, Cambridge "Here is Plato for an anti-Platonic age. The author gives careful attention to some of the most important passages in the Platonic dialogues and offers new solutions to some of Plato's most famous mathematical puzzles. He then considers the implications of these penetrating studies for the philosophy of science, and the natural sciences especially. This is a book that revivifies the core themes of Platonism and restores science to worship. It shows Roger Sworder to be one of the foremost students of Plato writing today, and places him in the noble tradition of Thomas Taylor."--RODNEY BLACKHIRST, author of Primordial Alchemy and Modern Religion: Essays on Traditional Cosmology
What Is Mathematics Really
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Author : Reuben Hersh
language : en
Publisher: Oxford University Press
Release Date : 1997-08-21
What Is Mathematics Really written by Reuben Hersh and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-08-21 with Mathematics categories.
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.
Mathematics And Reality
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Author : Mary Leng
language : en
Publisher: OUP Oxford
Release Date : 2010-04-22
Mathematics And Reality written by Mary Leng and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-04-22 with Philosophy categories.
Mary Leng offers a defense of mathematical fictionalism, according to which we have no reason to believe that there are any mathematical objects. Perhaps the most pressing challenge to mathematical fictionalism is the indispensability argument for the truth of our mathematical theories (and therefore for the existence of the mathematical objects posited by those theories). According to this argument, if we have reason to believe anything, we have reason to believe that the claims of our best empirical theories are (at least approximately) true. But since claims whose truth would require the existence of mathematical objects are indispensable in formulating our best empirical theories, it follows that we have good reason to believe in the mathematical objects posited by those mathematical theories used in empirical science, and therefore to believe that the mathematical theories utilized in empirical science are true. Previous responses to the indispensability argument have focussed on arguing that mathematical assumptions can be dispensed with in formulating our empirical theories. Leng, by contrast, offers an account of the role of mathematics in empirical science according to which the successful use of mathematics in formulating our empirical theories need not rely on the truth of the mathematics utilized.
Platonism And The Objects Of Science
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Author : Scott Berman
language : en
Publisher: Bloomsbury Publishing
Release Date : 2020-02-20
Platonism And The Objects Of Science written by Scott Berman and has been published by Bloomsbury Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-20 with Philosophy categories.
What are the objects of science? Are they just the things in our scientific experiments that are located in space and time? Or does science also require that there be additional things that are not located in space and time? Using clear examples, these are just some of the questions that Scott Berman explores as he shows why alternative theories such as Nominalism, Contemporary Aristotelianism, Constructivism, and Classical Aristotelianism, fall short. He demonstrates why the objects of scientific knowledge need to be not located in space or time if they are to do the explanatory work scientists need them to do. The result is a contemporary version of Platonism that provides us with the best way to explain what the objects of scientific understanding are, and how those non-spatiotemporal things relate to the spatiotemporal things of scientific experiments, as well as everything around us, including even ourselves.
Philosophy Of Mathematics Oxford Bibliographies Online Research Guide
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Author : Otavio Bueno
language : en
Publisher: Oxford University Press
Release Date : 2010-06
Philosophy Of Mathematics Oxford Bibliographies Online Research Guide written by Otavio Bueno and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-06 with categories.
This ebook is a selective guide designed to help scholars and students of social work find reliable sources of information by directing them to the best available scholarly materials in whatever form or format they appear from books, chapters, and journal articles to online archives, electronic data sets, and blogs. Written by a leading international authority on the subject, the ebook provides bibliographic information supported by direct recommendations about which sources to consult and editorial commentary to make it clear how the cited sources are interrelated related. This ebook is a static version of an article from Oxford Bibliographies Online: Philosophy, a dynamic, continuously updated, online resource designed to provide authoritative guidance through scholarship and other materials relevant to the study Philosophy. Oxford Bibliographies Online covers most subject disciplines within the social science and humanities, for more information visit www.oxfordbibligraphies.com.
Platonism Naturalism And Mathematical Knowledge
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Author : James Robert Brown
language : en
Publisher: Routledge
Release Date : 2013-06-17
Platonism Naturalism And Mathematical Knowledge written by James Robert Brown and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-17 with Philosophy categories.
This study addresses a central theme in current philosophy: Platonism vs Naturalism and provides accounts of both approaches to mathematics, crucially discussing Quine, Maddy, Kitcher, Lakoff, Colyvan, and many others. Beginning with accounts of both approaches, Brown defends Platonism by arguing that only a Platonistic approach can account for concept acquisition in a number of special cases in the sciences. He also argues for a particular view of applied mathematics, a view that supports Platonism against Naturalist alternatives. Not only does this engaging book present the Platonist-Naturalist debate over mathematics in a comprehensive fashion, but it also sheds considerable light on non-mathematical aspects of a dispute that is central to contemporary philosophy.