Released on 2020-08-31Categories Mathematics

Wittgenstein’s Annotations to Hardy’s Course of Pure Mathematics

Wittgenstein’s Annotations to Hardy’s Course of Pure Mathematics

Author: Juliet Floyd

Publisher: Springer Nature

ISBN: 9783030484811

Category: Mathematics

Page: 322

View: 515

This monograph examines the private annotations that Ludwig Wittgenstein made to his copy of G.H. Hardy’s classic textbook, A Course of Pure Mathematics. Complete with actual images of the annotations, it gives readers a more complete picture of Wittgenstein’s remarks on irrational numbers, which have only been published in an excerpted form and, as a result, have often been unjustly criticized. The authors first establish the context behind the annotations and discuss the historical role of Hardy’s textbook. They then go on to outline Wittgenstein’s non-extensionalist point of view on real numbers, assessing his manuscripts and published remarks and discussing attitudes in play in the philosophy of mathematics since Dedekind. Next, coverage focuses on the annotations themselves. The discussion encompasses irrational numbers, the law of excluded middle in mathematics and the notion of an “improper picture," the continuum of real numbers, and Wittgenstein’s attitude toward functions and limits.
Released on 2020-12-30Categories Philosophy

Wittgenstein on Mathematics

Wittgenstein on Mathematics

Author: Severin Schroeder

Publisher: Routledge

ISBN: 9781000318296

Category: Philosophy

Page: 238

View: 312

This book offers a detailed account and discussion of Ludwig Wittgenstein’s philosophy of mathematics. In Part I, the stage is set with a brief presentation of Frege’s logicist attempt to provide arithmetic with a foundation and Wittgenstein’s criticisms of it, followed by sketches of Wittgenstein’s early views of mathematics, in the Tractatus and in the early 1930s. Then (in Part II), Wittgenstein’s mature philosophy of mathematics (1937-44) is carefully presented and examined. Schroeder explains that it is based on two key ideas: the calculus view and the grammar view. On the one hand, mathematics is seen as a human activity — calculation — rather than a theory. On the other hand, the results of mathematical calculations serve as grammatical norms. The following chapters (on mathematics as grammar; rule-following; conventionalism; the empirical basis of mathematics; the role of proof) explore the tension between those two key ideas and suggest a way in which it can be resolved. Finally, there are chapters analysing and defending Wittgenstein’s provocative views on Hilbert’s Formalism and the quest for consistency proofs and on Gödel’s incompleteness theorems.
Released on 2021-09-15Categories Philosophy

Wittgenstein's Tractatus Logico-Philosophicus

Wittgenstein's Tractatus Logico-Philosophicus

Author: Andreas Georgallides

Publisher: Cambridge Scholars Publishing

ISBN: 9781527574830

Category: Philosophy

Page: 205

View: 743

The collection explores Wittgenstein’s early work, with a particular focus on his Tractatus, which examines the relation between language and the world, and which makes the distinction between saying and showing. The book considers the topics of logic, ontology, metaphysics, and the epistemological and moral aspects of Tractatus.
Released on 2019-11-18Categories Philosophy

Philosophy of Logic and Mathematics

Philosophy of Logic and Mathematics

Author: Gabriele M. Mras

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 9783110657883

Category: Philosophy

Page: 559

View: 976

This volume presents different conceptions of logic and mathematics and discuss their philosophical foundations and consequences. This concerns first of all topics of Wittgenstein's ideas on logic and mathematics; questions about the structural complexity of propositions; the more recent debate about Neo-Logicism and Neo-Fregeanism; the comparison and translatability of different logics; the foundations of mathematics: intuitionism, mathematical realism, and formalism. The contributing authors are Matthias Baaz, Francesco Berto, Jean-Yves Beziau, Elena Dragalina-Chernya, Günther Eder, Susan Edwards-McKie, Oliver Feldmann, Juliet Floyd, Norbert Gratzl, Richard Heinrich, Janusz Kaczmarek, Wolfgang Kienzler, Timm Lampert, Itala Maria Loffredo D'Ottaviano, Paolo Mancosu, Matthieu Marion, Felix Mühlhölzer, Charles Parsons, Edi Pavlovic, Christoph Pfisterer, Michael Potter, Richard Raatzsch, Esther Ramharter, Stefan Riegelnik, Gabriel Sandu, Georg Schiemer, Gerhard Schurz, Dana Scott, Stewart Shapiro, Karl Sigmund, William W. Tait, Mark van Atten, Maria van der Schaar, Vladimir Vasyukov, Jan von Plato, Jan Woleński and Richard Zach.
Released on 2017-11-14Categories Mathematics

Wittgenstein, Mathematics and World

Wittgenstein, Mathematics and World

Author: Bob Clark

Publisher: Springer

ISBN: 9783319639918

Category: Mathematics

Page: 215

View: 977

This book uses Ludwig Wittgenstein’s philosophical methodology to solve a problem that has perplexed thinkers for thousands of years: 'how come (abstract) mathematics applies so wonderfully well to the (concrete, physical) world?' The book is distinctive in several ways. First, it gives the reader a route into understanding important features of Wittgenstein’s writings and lectures by using his methodology to tackle this long-standing and seemingly intractable philosophical problem. More than this, though, it offers an outline of important (sometimes little-known) aspects of the development of mathematical thought through the ages, and an engagement of Wittgenstein’s philosophy with this and with contemporary philosophy of mathematics on its own terms. A clear overview of all this in the context of Wittgenstein’s philosophy of mathematics is interesting in its own right; it is also just what is needed to solve the problem of mathematics and world.
Released on 2019-06-13Categories Philosophy

The Life and Philosophy of Elizabeth Anscombe

The Life and Philosophy of Elizabeth Anscombe

Author: John Haldane

Publisher: Andrews UK Limited

ISBN: 9781788360135

Category: Philosophy

Page: 357

View: 592

This volume in the St Andrews series contains a collection of essays from leading authors regarding the work of Elizabeth Anscombe, in particular issues in mind and metaphysics, and can be considered a partner work to 2016's The Moral Philosophy of Elizabeth Anscombe (also published by Imprint Academic Ltd.).
Released on 2018-09-10Categories Philosophy

Language, Form(s) of Life, and Logic

Language, Form(s) of Life, and Logic

Author: Christian Martin

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 9783110518283

Category: Philosophy

Page: 342

View: 472

This volume deals with the connection between thinking-and-speaking and our form(s) of life. All contributions engage with Wittgenstein’s approach to this topic. As a whole, the volume takes a stance against both biological and ethnological interpretations of the notion "form of life" and seeks to promote a broadly logico-linguistic understanding instead. The structure of this book is threefold. Part one focuses on lines of thinking that lead from Wittgenstein’s earlier thought to the concept of form of life in his later work. Contributions to part two examine the concrete philosophical function of this notion as well as the ways in which it differs from cognate concepts. Contributions to part three put Wittgenstein’s notion of form of life in perspective by relating it to phenomenology, ordinary language philosophy and problems in contemporary analytic philosophy.
Released on 2022-01-01Categories Social Science

Perceiving the Future through New Communication Technologies

Perceiving the Future through New Communication Technologies

Author: James Katz

Publisher: Springer Nature

ISBN: 9783030848835

Category: Social Science

Page: 239

View: 976

The volume offers multiple perspectives on the way in which people encounter and think about the future. Drawing on the perspectives of history, literature, philosophy and communication studies, an international ensemble of experts offer a kaleidoscope of topics to provoke and enlighten the reader. The authors seek to understand the daily lived experience of ordinary people as they encounter new technology as well as the way people reflect on the significance and meaning of those technologies. The approach of the volume stresses the quotidian quality of reality and ordinary understandings of reality as understood by people from all walks of life. Providing expert analysis and sophisticated understanding, the focus of attention gravitates toward how people make meaning out of change, particularly when the change occurs at the level of social technologies- the devices that modify and amplify our modes of communication with others. The volume is organised into three main sections: The phenomena of new communication technology in people's lives from a contemporary viewpoint; the meaning of robots and AI as they play an increasing role in people's experience and; broader issues concerning the operational, sociological and philosophical implications of people as they address a technology driven future.
Released on 2013-10-11Categories Religion

God and the Universe

God and the Universe

Author: Arthur Gibson

Publisher: Routledge

ISBN: 9781136365720

Category: Religion

Page: 404

View: 522

Ambitious, controversial and absorbing, God and the Universe tackles the highly-charged issue of God's relevance in the light of new scientific thinking on cosmology. Engaging with poststructuralism, ethics, mathematics, and philosophy through the ages, this persuasively argued book reinvigorates religious debate for the new millennium.