Essays on Gödel's reception of Leibniz, Husserl, and Brouwer
type: Item
instance of: scholarly article
title: Essays on Gödel's reception of Leibniz, Husserl, and Brouwer
zbMATH Open document ID: 1436.03014
DOI: 10.1007/978-3-319-10031-9
author: Mark van Atten
published in: Logic, Epistemology, and the Unity of Science
publication date: 2014-09-05T00:00:00Z
review text: The author presents in this volume a collection of essays on Kurt Gödel's work, authored or co-authored by him. His aim is to analyse historical and systematic aspects of Gödel's philosophical program, consisting of two stages: ``1. Use Husserl's transcendental phenomenology to reconstruct and develop Leibniz' monadology into an axiomatic metaphysics, 2. Apply the metaphysics thus obtained to develop a Platonistic foundation for classical mathematics'' (p. 2). The material is organized in four parts. After an ``Introduction'' (pp.\ 1--20) which discusses ``Gödel's commitment to phenomenology from about 1959 to the end of his life, the religious component in phenomenology, and the pragmatic value of Husserl's and Gödel's historical turns in philosophy'' (p.\ 1), Part I ``Gödel and Leibniz'' contains three essay. In ``A note on Leibniz's argument against infinite wholes'' (pp.\ 23--32), the author argues that Leibniz had ``all the means to device and accept'' (p.\ 24) B.\ Russell's refutation of Leibniz's argument against the existence of infinite wholes based on the part-whole axiom. The author shows furthermore that this refutation does not presuppose the consistency of Cantorian set theory and it does not concern the part-whole axiom as such. In ``Monads and sets: on Gödel, Leibniz, and the reflection principle'' (pp.\ 33--64), the author relates Leibniz's monadology to set theory as Gödel did, and discusses the role of Gödel's version of the reflection principle ``A \textit{structural} property, possibly involving \(V\), which applies only to elements of \(V\), determines a set; or, a subclass of \(V\) thus definable is a set'' (p.\ 41). In ``Gödel's Dialectica interpretation and Leibniz'' (pp.\ 65--74), the author reports on a shorthand note by Gödel on Leibniz that can be found among material related to the translation and revision of his \textit{Dialectica} paper of 1968. It shows that Leibniz's theory of truth served as a source of inspiration for Gödel. Part …
reviewed by: Volker Peckhaus
Mathematics Subject Classification ID: 03-06
Mathematics Subject Classification ID: 03-02
Mathematics Subject Classification ID: 03-03
Mathematics Subject Classification ID: 01A60
Mathematics Subject Classification ID: 00A30
Mathematics Subject Classification ID: 03A05
zbMATH DE Number: 6340802
zbMATH Keywords: foundations of mathematics
zbMATH Keywords: monadology
zbMATH Keywords: phenomenology
zbMATH Keywords: intuitionismus
zbMATH Keywords: constructivity
zbMATH Keywords: Dialectica interpretation
zbMATH Keywords: transcendental idealism
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-3-319-10031-9
OpenAlex ID: W4256122685
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description: scientific article; zbMATH DE number 6340802