Platonism and Anti Platonism in Mathematics

Platonism and Anti Platonism in Mathematics

In this book, Balaguer demonstrates that there are no good arguments for or against mathematical platonism.

Author: Mark Balaguer

Publisher: Oxford University Press on Demand

ISBN: 0195143981

Category: Mathematics

Page: 217

View: 454

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)
Categories: Mathematics

What is Mathematics Really

What is Mathematics  Really

Tries to refine the philosophy of mathematics to reflect what mathematicians really do, and argues that mathematics must be understood in a social context.

Author: Reuben Hersh

Publisher: Oxford University Press, USA

ISBN: 0195130871

Category: Medical

Page: 343

View: 914

Tries to refine the philosophy of mathematics to reflect what mathematicians really do, and argues that mathematics must be understood in a social context.
Categories: Medical

Truth in Mathematics

Truth in Mathematics

This book contains an overview of the forefront of research into the nature of truth in mathematics, and is unique in being the result of interactions between researchers from both philosophy and mathematics.

Author: Harold G. Dales

Publisher: Oxford University Press

ISBN: 019851476X

Category: Mathematics

Page: 376

View: 597

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. The great advances in mathematics and philosophy in the twentieth centuryand in particular the proof of Godel's theorem and the development of the notion ofindependence in mathematicshave led to new viewpoints on this question in our era. This book is the result of the interaction of a number of outstanding mathematicians and philosophersincluding Yurii Manin, Vaughan Jones, and Per Martin-Lofand their discussions of this problem. It provides anoverview of the forefront of current thinking, and is a valuable introduction and reference for researchers in the area.
Categories: Mathematics

Platonism Naturalism and Mathematical Knowledge

Platonism  Naturalism  and Mathematical Knowledge

Baker, A. (2005) "Are There Genuine Mathematical Explanations of Physical
Phenomena?” Mind, 114, 223-238. Balaguer, M. (1998) Platonism and Anti-
Platonism in Mathematics. New York: Oxford University Press. Ballentine, L. (
1990) ...

Author: James Robert Brown

Publisher: Routledge

ISBN: 9781136580376

Category: Philosophy

Page: 194

View: 965

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.
Categories: Philosophy

An Aristotelian Realist Philosophy of Mathematics

An Aristotelian Realist Philosophy of Mathematics

As argued in Chapter 1, the Platonist-nominalist concept of 'abstract object' does
not fit the case of properties and ... in mathematics: anti-Platonist realism'),10 nor
in the recent wide-ranging Oxford Handbook of Philosophy of Mathematics and ...

Author: J. Franklin

Publisher: Springer

ISBN: 9781137400734

Category: Mathematics

Page: 308

View: 677

Mathematics is as much a science of the real world as biology is. It is the science of the world's quantitative aspects (such as ratio) and structural or patterned aspects (such as symmetry). The book develops a complete philosophy of mathematics that contrasts with the usual Platonist and nominalist options.
Categories: Mathematics

Constructibility and Mathematical Existence

Constructibility and Mathematical Existence

Concerned with the problem of existence in mathematics, this volume develops a mathematical system in which there are no existence assertions but only assertions of constructibility.

Author: Charles S. Chihara

Publisher: Oxford University Press

ISBN: 9780198239758

Category: Law

Page: 282

View: 133

This book is concerned with `the problem of existence in mathematics'. It develops a mathematical system in which there are no existence assertions but only assertions of the constructibility of certain sorts of things. It explores the philosophical implications of such an approach through an examination of the writings of Field, Burgess, Maddy, Kitcher, and others.
Categories: Law

Philosophy of Mathematics Oxford Bibliographies Online Research Guide

Philosophy of Mathematics  Oxford Bibliographies Online Research Guide

Platonism is among the most influential views in the philosophy of mathematics.
There are distinct versions of this view, but typically it tends to be committed to (1)
the existence of mathematical objects, (2) the independence of these objects
from our mental processes and ... Platonism and Anti-Platonism in Mathematics.

Author: Otavio Bueno

Publisher: Oxford University Press

ISBN: 9780199810512

Category:

Page: 26

View: 114

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.
Categories:

Why Is There Philosophy of Mathematics At All

Why Is There Philosophy of Mathematics At All

This truly philosophical book takes us back to fundamentals - the sheer experience of proof, and the enigmatic relation of mathematics to nature.

Author: Ian Hacking

Publisher: Cambridge University Press

ISBN: 9781107729827

Category: Science

Page: 212

View: 882

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.
Categories: Science

Philosophy of Mathematics

Philosophy of Mathematics

REALISM AND ANTI-REALISM IN MATHEMATICS Mark Balaguer The purpose
of this essay is (a) to survey and ... view that I have elsewhere called full-blooded
platonism, or for short, FBP) and that there is exactly one version of anti-realism ...

Author:

Publisher: Elsevier

ISBN: 0080930581

Category: Philosophy

Page: 733

View: 190

One of the most striking features of mathematics is the fact that we are much more certain about the mathematical knowledge we have than about what mathematical knowledge is knowledge of. Are numbers, sets, functions and groups physical entities of some kind? Are they objectively existing objects in some non-physical, mathematical realm? Are they ideas that are present only in the mind? Or do mathematical truths not involve referents of any kind? It is these kinds of questions that have encouraged philosophers and mathematicians alike to focus their attention on issues in the philosophy of mathematics. Over the centuries a number of reasonably well-defined positions about the nature of mathematics have been developed and it is these positions (both historical and current) that are surveyed in the current volume. Traditional theories (Platonism, Aristotelianism, Kantianism), as well as dominant modern theories (logicism, formalism, constructivism, fictionalism, etc.), are all analyzed and evaluated. Leading-edge research in related fields (set theory, computability theory, probability theory, paraconsistency) is also discussed. The result is a handbook that not only provides a comprehensive overview of recent developments but that also serves as an indispensable resource for anyone wanting to learn about current developments in the philosophy of mathematics. -Comprehensive coverage of all main theories in the philosophy of mathematics -Clearly written expositions of fundamental ideas and concepts -Definitive discussions by leading researchers in the field -Summaries of leading-edge research in related fields (set theory, computability theory, probability theory, paraconsistency) are also included
Categories: Philosophy

Physicalism in Mathematics

Physicalism in Mathematics

This collection of papers has its origin in a conference held at the Uni­ versity of Toronto in June of 1988. The theme of the conference was Physicalism in Mathematics: Recent Work in the Philosophy of Math­ ematics.

Author: A.D. Irvine

Publisher: Springer Science & Business Media

ISBN: 0792305132

Category: Science

Page: 366

View: 354

This collection of papers has its origin in a conference held at the Uni­ versity of Toronto in June of 1988. The theme of the conference was Physicalism in Mathematics: Recent Work in the Philosophy of Math­ ematics. At the conference, papers were read by Geoffrey Hellman (Minnesota), Yvon Gauthier (Montreal), Michael Hallett (McGill), Hartry Field (USC), Bob Hale (Lancaster & St Andrew's), Alasdair Urquhart (Toronto) and Penelope Maddy (Irvine). This volume supplements updated versions of six of those papers with contributions by Jim Brown (Toronto), John Bigelow (La Trobe), John Burgess (Princeton), Chandler Davis (Toronto), David Papineau (Cambridge), Michael Resnik (North Carolina at Chapel Hill), Peter Simons (Salzburg) and Crispin Wright (St Andrews & Michigan). Together they provide a vivid, expansive snapshot of the exciting work which is currently being carried out in philosophy of mathematics. Generous financial support for the original conference was provided by the Social Sciences & Humanities Research Council of Canada, the British Council, and the Department of Philosophy together with the Office of Internal Relations at the University of Toronto. Additional support for the production of this volume was gratefully received from the Social Sciences & Humanities Research Council of Canada.
Categories: Science

Issues in Theoretical Diversity

Issues in Theoretical Diversity

... and theoretical ideals.5 Finally, in Platonism and Anti-Platonism in
Mathematics, Mark Balaguer controversially argues ... there is no difference
between Platonism and fictionalism: both offer exactly the same vision of
mathematical practice.

Author: Kristie Lyn Miller

Publisher: Springer Science & Business Media

ISBN: 9781402052569

Category: Philosophy

Page: 258

View: 537

Our world is full of composite objects that persist through time: dogs, persons, chairs and rocks. But in virtue of what do a bunch of little objects get to compose some bigger object, and how does that bigger object persist through time? This book aims to answer these questions, but it does so by looking at accounts of composition and persistence through a new methodological lens. It thereby offers a completely novel view about persistence and composition.
Categories: Philosophy

Ludwig Wittgenstein The later Wittgenstein from Philosophical investigations to On certainty

Ludwig Wittgenstein  The later Wittgenstein   from Philosophical investigations to On certainty

Introduction Attempts to dispense with objects in the semantical analysis of
mathematical discourse have usually stumbled on the following problem: how to
account for the apparent objectivity of mathematics? Anti-platonist solutions to
this ...

Author: Stuart Shanker

Publisher: Psychology Press

ISBN: 0415149150

Category: Philosophy

Page: 336

View: 354

Wittgenstein scholarship has continued to grow at a pace few could have anticipated - a testament both to the fertility of his thought and to the thriving state of contemporary philosophy. In response to this ever-growing interest in the field, we are delighted to announce the publication of a second series of critical assessments on Wittgenstein, emphasising both the breadth and depth of contemporary Wittgenstein research.As well as papers on the nature and method of Wittgenstein's philosophy, this second collection also relates to a broader range of topics, including psychology, politics, art, music and culture.
Categories: Philosophy

The Bulletin of Symbolic Logic

The Bulletin of Symbolic Logic

Platonism and anti - platonism in mathematics . Oxford University Press , Oxford
and New York 1998 , x + 217 pp . There are two major challenges for the
philosophy of mathematics that present severe difficulties for any attempt to
defend ...

Author:

Publisher:

ISBN: UOM:39015072637120

Category: Electronic journals

Page:

View: 444

Categories: Electronic journals

Knowledge Cause and Abstract Objects

Knowledge  Cause  and Abstract Objects

If mathematical knowledge is as secure and ubiquitous as mathematical
platonists claim, then it is reasonable to ... AND PLATONISM Before turning to
platonist attempts to meet this obligation, I discuss another anti-platonist
argument.

Author: C. Cheyne

Publisher: Springer Science & Business Media

ISBN: 1402000510

Category: Law

Page: 236

View: 321

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.
Categories: Law

Doctor Who and Philosophy

Doctor Who and Philosophy

the past, so Field hasn't succeeded in translating a current scientific theory into
mathematics-free language. This doesn't ... In his book Platonism and Anti-
Platonism in Mathematics, he turns on the use of things called 'Hilbert Spaces',
which I ...

Author: Courtland Lewis

Publisher: Open Court

ISBN: 9780812697254

Category: Philosophy

Page: 288

View: 575

Not only is Doctor Who the longest-running science fiction TV show in history, but it has also been translated into numerous languages, broadcast around the world, and referred to as the “way of the future” by some British politicians. The Classic Doctor Who series built up a loyal American cult following, with regular conventions and other activities. The new series, relaunched in 2005, has emerged from culthood into mass awareness, with a steadily growing viewership and major sales of DVDs. The current series, featuring the Eleventh Doctor, Matt Smith, is breaking all earlier records, in both the UK and the US. Doctor Who is a continuing story about the adventures of a mysterious alien known as “the Doctor,” a traveller of both time and space whose spacecraft is the TARDIS (Time and Relative Dimensions in Space), which from the outside looks like a British police telephone box of the 1950s. The TARDIS is “bigger on the inside than on the outside”—actually the interior is immense. The Doctor looks human, but has two hearts, and a knowledge of all languages in the universe. Periodically, when the show changes the leading actor, the Doctor “regenerates.”
Categories: Philosophy

Realism and Anti Realism

Realism and Anti Realism

®Quantitative. Parsimony and Explanatory Power ̄. British Journal for the
Philosophy of Science 54, 245¥59. Balaguer, M. 1998. Platonism and Anti-
Platonism in Mathematics. Oxford: Oxford University Press. Barnes, B. & D. Edge
(eds) 1982.

Author: Stuart Brock

Publisher: Routledge

ISBN: 9781317494263

Category: Philosophy

Page: 224

View: 361

There are a bewildering variety of ways the terms "realism" and "anti-realism" have been used in philosophy and furthermore the different uses of these terms are only loosely connected with one another. Rather than give a piecemeal map of this very diverse landscape, the authors focus on what they see as the core concept: realism about a particular domain is the view that there are facts or entities distinctive of that domain, and their existence and nature is in some important sense objective and mind-independent. The authors carefully set out and explain the different realist and anti-realist positions and arguments that occur in five key domains: science, ethics, mathematics, modality and fictional objects. For each area the authors examine the various styles of argument in support of and against realism and anti-realism, show how these different positions and arguments arise in very different domains, evaluate their success within these fields, and draw general conclusions about these assorted strategies. Error theory, fictionalism, non-cognitivism, relativism and response-dependence are taken as the most important positions in opposition to the realist and these are explored in depth. Suitable for advanced level undergraduates, the book offers readers a clear introduction to a subject central to much contemporary work in metaphysics, epistemology and philosophy of language.
Categories: Philosophy

Philosophy of Mathematics

Philosophy of Mathematics

Philosophy of Mathematics is an excellent introductory text. This student friendly book discusses the great philosophers and the importance of mathematics to their thought.

Author: James Robert Brown

Publisher: Routledge

ISBN: 9781134806430

Category: Philosophy

Page: 232

View: 373

Philosophy of Mathematics is an excellent introductory text. This student friendly book discusses the great philosophers and the importance of mathematics to their thought. It includes the following topics: * the mathematical image * platonism * picture-proofs * applied mathematics * Hilbert and Godel * knots and nations * definitions * picture-proofs and Wittgenstein * computation, proof and conjecture. The book is ideal for courses on philosophy of mathematics and logic.
Categories: Philosophy

Husserl Or Frege

Husserl Or Frege

ON. ANTIPLATONISM. AND. ITS. DOGMAS. 1. Introduction ecent discussion in
the philosophy of mathematics, especially in the glo-American world, occurs
within the framework of some empiricist dogmas accepted as self-evident truths
by ...

Author: Claire Ortiz Hill

Publisher: Open Court Publishing

ISBN: 0812694171

Category: Philosophy

Page: 315

View: 558

Most areas of philosopher Edmund Husserl's thought have been explored, but his views on logic, mathematics, and semantics have been largely ignored. These essays offer an alternative to discussions of the philosophy of contemporary mathematics. The book covers areas of disagreement between Husserl and Gottlob Frege, the father of analytical philosophy, and explores new perspectives seen in their work.
Categories: Philosophy

Meaning and Method

Meaning and Method

I advocate a form of anti - platonist view about mathematics – one in which
modality plays a role , though a rather limited role ; and where the modality
involved is a modality of the least controversial kind . What my anti - platonism
involves is a ...

Author: George Boolos

Publisher: Cambridge University Press

ISBN: 0521360838

Category: Philosophy

Page: 380

View: 776

This volume is a report on the state of philosophy in a number of significant areas.
Categories: Philosophy

Derrida Badiou and the Formal Imperative

Derrida  Badiou and the Formal Imperative

... than in Wittgenstein's widely influential idea of correctness in the case of
mathematical or logical reasoning as a matter ... on the debate between
Platonism and anti-Platonism in recent analytic philosophy of mathematics might
seem to cast ...

Author: Christopher Norris

Publisher: A&C Black

ISBN: 9781441193971

Category: Philosophy

Page: 240

View: 148

In this path-breaking study Christopher Norris proposes a transformed understanding of the much-exaggerated differences between analytic and continental philosophy. While keeping the analytic tradition squarely in view his book focuses on the work of Jacques Derrida and Alain Badiou, two of the most original and significant figures in the recent history of ideas. Norris argues that these thinkers have decisively reconfigured the terrain of contemporary philosophy and, between them, pointed a way beyond some of those seemingly intractable issues that have polarised debate on both sides of the notional rift between the analytic and continental traditions. In particular his book sets out to show - against the received analytic wisdom - that continental philosophy has its own analytic resources and is capable of bringing some much-needed fresh insight to bear on problems in philosophy of language, logic and mathematics. Norris provides not only a unique comparative account of Derrida's and Badiou's work but also a remarkably wide-ranging assessment of their joint contribution to philosophy's current - if widely resisted - potential for self-transformation.
Categories: Philosophy