Mathematics

Platonism and Anti-Platonism in Mathematics

Author: Mark Balaguer

Publisher: Oxford University Press on Demand

ISBN:

Category: Mathematics

Page: 217

View: 132

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.
Mathematics

What is Mathematics, Really?

Author: Reuben Hersh

Publisher: Oxford University Press, USA

ISBN:

Category: Mathematics

Page: 343

View: 748

Reflecting an insider's view of mathematical life, the author argues that mathematics must be historically evolved, and intelligible only in a social context.
Philosophy

Issues in Theoretical Diversity

Author: Kristie Lyn Miller

Publisher: Springer Science & Business Media

ISBN:

Category: Philosophy

Page: 258

View: 902

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.

Philosophy of Mathematics: Oxford Bibliographies Online Research Guide

Author: Otavio Bueno

Publisher: Oxford University Press

ISBN:

Category:

Page: 26

View: 844

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.
Mathematics

Truth in Mathematics

Author: Harold G. Dales

Publisher: Oxford University Press

ISBN:

Category: Mathematics

Page: 376

View: 729

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.
Philosophy

Philosophy of Mathematics

Author:

Publisher: Elsevier

ISBN:

Category: Philosophy

Page: 733

View: 707

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
Philosophy

Doctor Who and Philosophy

Author: Courtland Lewis

Publisher: Open Court

ISBN:

Category: Philosophy

Page: 288

View: 392

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.”
Philosophy

Realism and Anti-Realism

Author: Stuart Brock

Publisher: Routledge

ISBN:

Category: Philosophy

Page: 224

View: 958

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.
Philosophy

Derrida, Badiou and the Formal Imperative

Author: Christopher Norris

Publisher: A&C Black

ISBN:

Category: Philosophy

Page: 240

View: 218

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.
Mathematics

One Hundred Years of Russell ́s Paradox

Author: Godehard Link

Publisher: Walter de Gruyter

ISBN:

Category: Mathematics

Page: 671

View: 484

Die in diesem Band zusammengefassten Beiträge stellen die wesentlichen Forschungsergebnisse der internationalen Münchner Konferenz "100 Jahre Russell-Paradoxon" im Jahr 2001 dar, auf der an die Entdeckung des berühmten Russell Paradoxons vor 100 Jahren erinnert wurde. Die 31 Beiträge und der Einführungsessay des Herausgebers wurden alle - bis auf zwei Ausnahmen - ursprünglich für diesen Band verfasst.