**Download or read online books in PDF, EPUB and Mobi Format. Click Download or Read Online button to get book now. This site is like a library, Use search box in the widget to get ebook that you want.**

Author | Mark Balaguer | |

ISBN-10 | 0195143981 | |

Release | 2001 | |

Pages | 217 | |

Download Link | Click Here |

In this book, Balaguer demonstrates that there are no good arguments for or against mathematical platonism. He establishes that both platonism and anti-platonism are defensible views and introduces a form of platonism ("full-blooded platonism") that solves all problems traditionally associated with the view, proceeding to defend anti-platonism (in particular, mathematical fictionalism) against various attacks--most notably the Quine-Putnam indispensability attack. |

Author | Mark Balaguer | |

ISBN-10 | 0195352769 | |

Release | 1998-08-20 | |

Pages | 240 | |

Download Link | Click Here |

In this highly absorbing work, Balaguer demonstrates that no good arguments exist either for or against mathematical platonism-for example, the view that abstract mathematical objects do exist and that mathematical theories are descriptions of such objects. Balaguer does this by establishing that both platonism and anti-platonism are justifiable views. Introducing a form of platonism, called "full-blooded platonism," that solves all problems traditionally associated with the view, he proceeds to defend anti-platonism (in particular, mathematical fictionalism) against various attacks-most notably the Quine-Putnam indispensability attack. He concludes by arguing that it is not simply that we do not currently have any good arguments for or against platonism but that we could never have such an argument. This lucid and accessible book breaks new ground in its area of engagement and makes vital reading for both specialists and all those intrigued by the philosophy of mathematics, or metaphysics in general. |

Author | Mark Balaguer | |

ISBN-10 | 9780190284053 | |

Release | 1998-08-20 | |

Pages | 240 | |

Download Link | Click Here |

In this highly absorbing work, Balaguer demonstrates that no good arguments exist either for or against mathematical platonism-for example, the view that abstract mathematical objects do exist and that mathematical theories are descriptions of such objects. Balaguer does this by establishing that both platonism and anti-platonism are justifiable views. Introducing a form of platonism, called "full-blooded platonism," that solves all problems traditionally associated with the view, he proceeds to defend anti-platonism (in particular, mathematical fictionalism) against various attacks-most notably the Quine-Putnam indispensability attack. He concludes by arguing that it is not simply that we do not currently have any good arguments for or against platonism but that we could never have such an argument. This lucid and accessible book breaks new ground in its area of engagement and makes vital reading for both specialists and all those intrigued by the philosophy of mathematics, or metaphysics in general. |

Author | Reuben Hersh | |

ISBN-10 | 0195130871 | |

Release | 1997 | |

Pages | 343 | |

Download Link | Click Here |

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 | M. Panza | |

ISBN-10 | 9781137298133 | |

Release | 2013-01-21 | |

Pages | 306 | |

Download Link | Click Here |

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. |

Author | William Lane Craig | |

ISBN-10 | 9780191090554 | |

Release | 2016-10-20 | |

Pages | 280 | |

Download Link | Click Here |

God Over All: Divine Aseity and the Challenge of Platonism is a defense of God's aseity and unique status as the Creator of all things apart from Himself in the face of the challenge posed by mathematical Platonism. After providing the biblical, theological, and philosophical basis for the traditional doctrine of divine aseity, William Lane Craig explains the challenge presented to that doctrine by the Indispensability Argument for Platonism, which postulates the existence of uncreated abstract objects. Craig provides detailed examination of a wide range of responses to that argument, both realist and anti-realist, with a view toward assessing the most promising options for the theist. A synoptic work in analytic philosophy of religion, this groundbreaking volume engages discussions in philosophy of mathematics, philosophy of language, metaphysics, and metaontology. |

Author | Mark Balaguer | |

ISBN-10 | 9780262266154 | |

Release | 2012-01-13 | |

Pages | 216 | |

Download Link | Click Here |

In this largely antimetaphysical treatment of free will and determinism, Mark Balaguer argues that the philosophical problem of free will boils down to an open scientific question about the causal histories of certain kinds of neural events. In the course of his argument, Balaguer provides a naturalistic defense of the libertarian view of free will. The metaphysical component of the problem of free will, Balaguer argues, essentially boils down to the question of whether humans possess libertarian free will. Furthermore, he argues that, contrary to the traditional wisdom, the libertarian question reduces to a question about indeterminacy--in particular, to a straightforward empirical question about whether certain neural events in our heads are causally undetermined in a certain specific way; in other words, Balaguer argues that the right kind of indeterminacy would bring with it all of the other requirements for libertarian free will. Finally, he argues that because there is no good evidence as to whether or not the relevant neural events are undetermined in the way that's required, the question of whether human beings possess libertarian free will is a wide-open empirical question. |

Author | Michele Friend | |

ISBN-10 | 9781317493785 | |

Release | 2014-12-05 | |

Pages | 240 | |

Download Link | Click Here |

What is mathematics about? Does the subject-matter of mathematics exist independently of the mind or are they mental constructions? How do we know mathematics? Is mathematical knowledge logical knowledge? And how is mathematics applied to the material world? In this introduction to the philosophy of mathematics, Michele Friend examines these and other ontological and epistemological problems raised by the content and practice of mathematics. Aimed at a readership with limited proficiency in mathematics but with some experience of formal logic it seeks to strike a balance between conceptual accessibility and correct representation of the issues. Friend examines the standard theories of mathematics - Platonism, realism, logicism, formalism, constructivism and structuralism - as well as some less standard theories such as psychologism, fictionalism and Meinongian philosophy of mathematics. In each case Friend explains what characterises the position and where the divisions between them lie, including some of the arguments in favour and against each. This book also explores particular questions that occupy present-day philosophers and mathematicians such as the problem of infinity, mathematical intuition and the relationship, if any, between the philosophy of mathematics and the practice of mathematics. Taking in the canonical ideas of Aristotle, Kant, Frege and Whitehead and Russell as well as the challenging and innovative work of recent philosophers like Benacerraf, Hellman, Maddy and Shapiro, Friend provides a balanced and accessible introduction suitable for upper-level undergraduate courses and the non-specialist. |

Author | Mark Balaguer | |

ISBN-10 | 9780262525794 | |

Release | 2014-02-14 | |

Pages | 139 | |

Download Link | Click Here |

A philosopher considers whether the scientific and philosophical arguments against free will are reason enough to give up our belief in it. |

Author | Mary Leng | |

ISBN-10 | 9780199280797 | |

Release | 2010-04-22 | |

Pages | 278 | |

Download Link | Click Here |

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 | Ian Hacking | |

ISBN-10 | 9781107729827 | |

Release | 2014-01-30 | |

Pages | 212 | |

Download Link | Click Here |

This truly philosophical book takes us back to fundamentals - the sheer experience of proof, and the enigmatic relation of mathematics to nature. It asks unexpected questions, such as 'what makes mathematics mathematics?', 'where did proof come from and how did it evolve?', and 'how did the distinction between pure and applied mathematics come into being?' In a wide-ranging discussion that is both immersed in the past and unusually attuned to the competing philosophical ideas of contemporary mathematicians, it shows that proof and other forms of mathematical exploration continue to be living, evolving practices - responsive to new technologies, yet embedded in permanent (and astonishing) facts about human beings. It distinguishes several distinct types of application of mathematics, and shows how each leads to a different philosophical conundrum. Here is a remarkable body of new philosophical thinking about proofs, applications, and other mathematical activities. |

Author | Mark Balaguer | |

ISBN-10 | 9780262319782 | |

Release | 2014-01-10 | |

Pages | 40 | |

Download Link | Click Here |

Mark Balaguer argues that the question of libertarian free will reduces to a question about indeterminacy -- in particular, to a straightforward empirical question about whether certain neural events in our heads are causally undetermined in a certain specific way. In this BIT, refuting arguments both for and against determinism, Balaguer shows that the question of whether human beings possess libertarian free will is a wide-open empirical question. |

Author | James Robert Brown | |

ISBN-10 | 9781136580376 | |

Release | 2013-06-17 | |

Pages | 194 | |

Download Link | Click Here |

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. |

Author | Richard L. Tieszen | |

ISBN-10 | 9780199606207 | |

Release | 2011-05-05 | |

Pages | 245 | |

Download Link | Click Here |

Richard Tieszen analyzes, develops, and defends the writings of Kurt Gödel (1906-1978) on the philosophy and foundations of mathematics and logic. Gödel's relation to the work of Plato, Leibniz, Husserl, and Kant is examined, and a new type of platonic rationalism that requires rational intuition, called 'constituted platonism', is proposed. |

Author | Jeremy Gray | |

ISBN-10 | 1400829046 | |

Release | 2008-09-02 | |

Pages | 528 | |

Download Link | Click Here |

Plato's Ghost is the first book to examine the development of mathematics from 1880 to 1920 as a modernist transformation similar to those in art, literature, and music. Jeremy Gray traces the growth of mathematical modernism from its roots in problem solving and theory to its interactions with physics, philosophy, theology, psychology, and ideas about real and artificial languages. He shows how mathematics was popularized, and explains how mathematical modernism not only gave expression to the work of mathematicians and the professional image they sought to create for themselves, but how modernism also introduced deeper and ultimately unanswerable questions. Plato's Ghost evokes Yeats's lament that any claim to worldly perfection inevitably is proven wrong by the philosopher's ghost; Gray demonstrates how modernist mathematicians believed they had advanced further than anyone before them, only to make more profound mistakes. He tells for the first time the story of these ambitious and brilliant mathematicians, including Richard Dedekind, Henri Lebesgue, Henri Poincaré, and many others. He describes the lively debates surrounding novel objects, definitions, and proofs in mathematics arising from the use of naïve set theory and the revived axiomatic method--debates that spilled over into contemporary arguments in philosophy and the sciences and drove an upsurge of popular writing on mathematics. And he looks at mathematics after World War I, including the foundational crisis and mathematical Platonism. Plato's Ghost is essential reading for mathematicians and historians, and will appeal to anyone interested in the development of modern mathematics. |

Author | Harold G. Dales | |

ISBN-10 | 019851476X | |

Release | 1998 | |

Pages | 376 | |

Download Link | Click Here |

The nature of truth in mathematics is a problem which has exercised the minds of thinkers from at least the time of the ancient Greeks. This book is an overview of the most recent work undertaken in this subject, and is unique in being the result of interactions between researchers from both philosophy and mathematics. The articles are written by world leaders in their respective fields and are of interest to researchers in both disciplines. |

Author | Solomon Feferman | |

ISBN-10 | 9780195080308 | |

Release | 1998 | |

Pages | 340 | |

Download Link | Click Here |

Solomon Feferman is one of the leading figures in logic and the foundations of mathematics. This volume brings together a selection of his most important essays dealing with the light which results in modern logic cast on significant problems in the foundations of mathematics. It is essential reading for anyone interested in these subjects. Feferman presents key issues in the work of Cantor, Hilbert, Weyl, and Godel among others, and explains how they are dealtwith by proof theory and other parts of logic. A number of the papers appeared originally in obscure places and are not well-known, and others are published here for the first time. All of the material has been revised and annotated to bring it up to date. |