Essays on Gödel’s Reception of Leibniz, Husserl, and Brouwer

Nonfiction, Religion & Spirituality, Philosophy, Phenomenology, Science & Nature, Mathematics, Logic
Cover of the book Essays on Gödel’s Reception of Leibniz, Husserl, and Brouwer by Mark van Atten, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Mark van Atten ISBN: 9783319100319
Publisher: Springer International Publishing Publication: November 21, 2014
Imprint: Springer Language: English
Author: Mark van Atten
ISBN: 9783319100319
Publisher: Springer International Publishing
Publication: November 21, 2014
Imprint: Springer
Language: English

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 publishe

d 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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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 publishe

d 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.

More books from Springer International Publishing

Cover of the book Oxide Materials at the Two-Dimensional Limit by Mark van Atten
Cover of the book Software Engineering, Artificial Intelligence, Networking and Parallel/Distributed Computing by Mark van Atten
Cover of the book Finding One’s Way Through Wittgenstein’s Philosophical Investigations by Mark van Atten
Cover of the book Value Driven Healthcare and Geriatric Medicine by Mark van Atten
Cover of the book Communications and Networking by Mark van Atten
Cover of the book Design Thinking for Innovation by Mark van Atten
Cover of the book Functionalizing Graphene and Carbon Nanotubes by Mark van Atten
Cover of the book Data Analysis by Mark van Atten
Cover of the book Space and Subjectivity in Contemporary Brazilian Cinema by Mark van Atten
Cover of the book Physiological Aspects of Legged Terrestrial Locomotion by Mark van Atten
Cover of the book Stochastic Partial Differential Equations: An Introduction by Mark van Atten
Cover of the book Image Blending Techniques and their Application in Underwater Mosaicing by Mark van Atten
Cover of the book Service Research and Innovation by Mark van Atten
Cover of the book Cartilage Regeneration by Mark van Atten
Cover of the book Big Data – BigData 2018 by Mark van Atten
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy