Van Atten Mark (67 results)

PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000.

Paperback. Condition: New. This book introduces the core ideas of L.E.J. Brouwer's approach to constructivity in mathematics, focusing on analysis, set theory, and topology, while considering his philosophical motivations. Brouwer's "intuitionism" offers a coherent alternative to classical (nonconstructive) mathematics.Starting with the rejection of the Principle of the Excluded Middle, the book reconstructs number systems and analysis using Cauchy sequences. It compares constructive and classical methods, highlights where classical theorems fail through "weak counterexamples", and examines Brouwer's classical and constructive versions of the Fixed-Point Theorem. Intuitionistic concepts like choice sequences and the Creating Subject lead to surprising results, such as the continuity of all total real functions and the existence of effective but non-recursive functions. Brief but fundamental comparisons are made with the later alternatives of Markov and Bishop.Intended as an introduction for undergraduates, this book is suitable for mathematics students interested in philosophy as well as philosophers with some mathematical background.…

Paperback. Condition: New. This book introduces the core ideas of L.E.J. Brouwer's approach to constructivity in mathematics, focusing on analysis, set theory, and topology, while considering his philosophical motivations. Brouwer's "intuitionism" offers a coherent alternative to classical (nonconstructive) mathematics.Starting with the rejection of the Principle of the Excluded Middle, the book reconstructs number systems and analysis using Cauchy sequences. It compares constructive and classical methods, highlights where classical theorems fail through "weak counterexamples", and examines Brouwer's classical and constructive versions of the Fixed-Point Theorem. Intuitionistic concepts like choice sequences and the Creating Subject lead to surprising results, such as the continuity of all total real functions and the existence of effective but non-recursive functions. Brief but fundamental comparisons are made with the later alternatives of Markov and Bishop.Intended as an introduction for undergraduates, this book is suitable for mathematics students interested in philosophy as well as philosophers with some mathematical background.…

Paperback. Condition: Brand New. 181 pages. 6.10x0.39x9.25 inches. In Stock.

Hardcover. Condition: As New.

Paperback. Condition: Brand New. 181 pages. 6.10x0.39x9.25 inches. In Stock.

Condition: New.

Condition: New.

Softcover. Condition: Very good. Great condition. Bottom corner of front cover is lightly creased. Inside is clean and unmarked.

Paperback. Condition: New. This book introduces the core ideas of L.E.J. Brouwer's approach to constructivity in mathematics, focusing on analysis, set theory, and topology, while considering his philosophical motivations. Brouwer's "intuitionism" offers a coherent alternative to classical (nonconstructive) mathematics.Starting with the rejection of the Principle of the Excluded Middle, the book reconstructs number systems and analysis using Cauchy sequences. It compares constructive and classical methods, highlights where classical theorems fail through "weak counterexamples", and examines Brouwer's classical and constructive versions of the Fixed-Point Theorem. Intuitionistic concepts like choice sequences and the Creating Subject lead to surprising results, such as the continuity of all total real functions and the existence of effective but non-recursive functions. Brief but fundamental comparisons are made with the later alternatives of Markov and Bishop.Intended as an introduction for undergraduates, this book is suitable for mathematics students interested in philosophy as well as philosophers with some mathematical background.…

Condition: New.

Paperback. Condition: New. This book introduces the core ideas of L.E.J. Brouwer's approach to constructivity in mathematics, focusing on analysis, set theory, and topology, while considering his philosophical motivations. Brouwer's "intuitionism" offers a coherent alternative to classical (nonconstructive) mathematics.Starting with the rejection of the Principle of the Excluded Middle, the book reconstructs number systems and analysis using Cauchy sequences. It compares constructive and classical methods, highlights where classical theorems fail through "weak counterexamples", and examines Brouwer's classical and constructive versions of the Fixed-Point Theorem. Intuitionistic concepts like choice sequences and the Creating Subject lead to surprising results, such as the continuity of all total real functions and the existence of effective but non-recursive functions. Brief but fundamental comparisons are made with the later alternatives of Markov and Bishop.Intended as an introduction for undergraduates, this book is suitable for mathematics students interested in philosophy as well as philosophers with some mathematical background.…

Condition: New. In English.

Buch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - With logicism and formalism, intuitionism is one of the main foundations for mathematics proposed in the twentieth century; and since the seventies, notably its views on logic have become important also outside foundational studies, with the development of theoretical computer science.The aim of the book is threefold: to review and complete the historical account of intuitionism; to present recent philosophical work on intuitionism; and to give examples of new technical advances and applications of intuitionism. This volume brings together 21 contributions by today's leading authors on these topics, and surveys the philosophical, logical and mathematical implications of the approach initiated in 1907 in L.E.J. Brouwer's dissertation.…

Condition: New. Intuitionism is one of the main foundations for mathematics proposed in the twentieth century and its views on logic have also notably become important with the development of theoretical computer science. This book presents philosophical work on intuitionism and gives examples of technical advances and applications. Editor(s): Van Atten, Mark; Boldini, Pascal; Bourdeau, Michel; Heinzmann, Gerhard. Series: Publications des Archives Henri Poincare / Publications of the Henri Poincare Archives / Science Autour de / Around 1900. Num Pages: 422 pages, biography. BIC Classification: HPCF; HPK. Category: (UP) Postgraduate, Research & Scholarly; (UU) Undergraduate. Dimension: 239 x 165 x 29. Weight in Grams: 794. . 2008. Hardback. . . . .…

Condition: New. In English.

Condition: New. pp. 440.

Condition: New. Intuitionism is one of the main foundations for mathematics proposed in the twentieth century and its views on logic have also notably become important with the development of theoretical computer science. This book presents philosophical work on intuitionism and gives examples of technical advances and applications. Editor(s): Van Atten, Mark; Boldini, Pascal; Bourdeau, Michel; Heinzmann, Gerhard. Series: Publications des Archives Henri Poincare / Publications of the Henri Poincare Archives / Science Autour de / Around 1900. Num Pages: 422 pages, biography. BIC Classification: HPCF; HPK. Category: (UP) Postgraduate, Research & Scholarly; (UU) Undergraduate. Dimension: 239 x 165 x 29. Weight in Grams: 794. . 2008. Hardback. . . . . Books ship from the US and Ireland.…

Condition: Sehr gut. Zustand: Sehr gut | Seiten: 422 | Sprache: Englisch | Produktart: Bücher | Keine Beschreibung verfügbar.

Condition: New. In English.

Taschenbuch. Condition: Neu. Essays on Go¿del's Reception of Leibniz, Husserl, and Brouwer | Mark van Atten | Taschenbuch | Logic, Epistemology, and the Unity of Science | xiv | Englisch | 2016 | Springer | EAN 9783319376578 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu. …

Condition: New. In English.

Buch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - This volume tackles Gödel's two-stage project of first using Husserl's transcendental phenomenology to reconstruct and develop Leibniz' monadology, and then founding classical mathematics on the metaphysics thus obtained. The author analyses the historical and systematic aspects of that project, and then evaluates it, with an emphasis on the second stage.The book is organised around Gödel's use of Leibniz, Husserl and Brouwer. Far from considering past philosophers irrelevant to actual systematic concerns, Gödel embraced the use of historical authors to frame his own philosophical perspective. The philosophies of Leibniz and Husserl define his project, while Brouwer's intuitionism is its principal foil: the close affinities between phenomenology and intuitionism set the bar for Gödel's attempt to go far beyond intuitionism.The four central essays are `Monads and sets', `On the philosophical development of Kurt Gödel', `Gödel and intuitionism', and `Construction and constitution in mathematics'. The first analyses and criticises Gödel's attempt to justify, by an argument from analogy with the monadology, the reflection principle in set theory. It also provides further support for Gödel's idea that the monadology needs to be reconstructed phenomenologically, by showing that the unsupplemented monadology is not able to found mathematics directly. The second studies Gödel's reading of Husserl, its relation to Leibniz' monadology, and its influence on his published writings. The third discusses how on various occasions Brouwer's intuitionism actually inspired Gödel's work, in particular the Dialectica Interpretation. The fourth addresses the question whether classical mathematics admits of the phenomenological foundation that Gödel envisaged, and concludes that it does not.The remaining essays provide further context. The essays collected here were written and published over the last decade. Notes have been added to record further thoughts, changes of mind, connections between the essays, and updates of references.…

Taschenbuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - This volume tackles Gödel's two-stage project of first using Husserl's transcendental phenomenology to reconstruct and develop Leibniz' monadology, and then founding classical mathematics on the metaphysics thus obtained. The author analyses the historical and systematic aspects of that project, and then evaluates it, with an emphasis on the second stage.The book is organised around Gödel's use of Leibniz, Husserl and Brouwer. Far from considering past philosophers irrelevant to actual systematic concerns, Gödel embraced the use of historical authors to frame his own philosophical perspective. The philosophies of Leibniz and Husserl define his project, while Brouwer's intuitionism is its principal foil: the close affinities between phenomenology and intuitionism set the bar for Gödel's attempt to go far beyond intuitionism.The four central essays are `Monads and sets', `On the philosophical development of Kurt Gödel', `Gödel and intuitionism', and `Construction and constitution in mathematics'. The first analyses and criticises Gödel's attempt to justify, by an argument from analogy with the monadology, the reflection principle in set theory. It also provides further support for Gödel's idea that the monadology needs to be reconstructed phenomenologically, by showing that the unsupplemented monadology is not able to found mathematics directly. The second studies Gödel's reading of Husserl, its relation to Leibniz' monadology, and its influence on his published writings. The third discusses how on various occasions Brouwer's intuitionism actually inspired Gödel's work, in particular the Dialectica Interpretation. The fourth addresses the question whether classical mathematics admits of the phenomenological foundation that Gödel envisaged, and concludes that it does not.The remaining essays provide further context. The essays collected here were written and published over the last decade. Notes have been added to record further thoughts, changes of mind, connections between the essays, and updates of references.…

Taschenbuch. Condition: Neu. Brouwer meets Husserl | On the Phenomenology of Choice Sequences | Mark van Atten | Taschenbuch | Synthese Library | xiii | Englisch | 2010 | Springer | EAN 9789048172818 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu. …

Buch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - Can the straight line be analysed mathematically such that it does not fall apart into a set of discrete points, as is usually done but through which its fundamental continuity is lost And are there objects of pure mathematics that can change through time Mathematician and philosopher L.E.J. Brouwer argued that the two questions are closely related and that the answer to both is 'yes''. To this end he introduced a new kind of object into mathematics, the choice sequence. But other mathematicians and philosophers have been voicing objections to choice sequences from the start.This book aims to provide a sound philosophical basis for Brouwer's choice sequences by subjecting them to a phenomenological critique in the style of the later Husserl.…

Taschenbuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - Can the straight line be analysed mathematically such that it does not fall apart into a set of discrete points, as is usually done but through which its fundamental continuity is lost And are there objects of pure mathematics that can change through time Mathematician and philosopher L.E.J. Brouwer argued that the two questions are closely related and that the answer to both is 'yes''. To this end he introduced a new kind of object into mathematics, the choice sequence. But other mathematicians and philosophers have been voicing objections to choice sequences from the start.This book aims to provide a sound philosophical basis for Brouwer's choice sequences by subjecting them to a phenomenological critique in the style of the later Husserl.…

Condition: New.

Condition: New. pp. 222.

Condition: New. pp. 224.