From Dedekind to Gödel. Essays on the development of the foundations of mathematics
type: Item
instance of: scholarly article
title: From Dedekind to Gödel. Essays on the development of the foundations of mathematics
zbMATH Open document ID: 0841.03001
published in: Synthese Library
publication date: 1995-10-23T00:00:00Z
review text: [The articles of this volume will not be indexed individually.] The volume under review originated from a conference held at Boston University in April 1992 as a part of the 1991-92 program of the Boston Colloquium in the Philosophy of Science. One of the aims of the conference was to raise the consciousness of philosophers of the fact that still not much is known about the foundations of mathematics at the turn of the century, that though there are many books and papers on Frege and Russell, little attention was paid to many ideas in the foundational studies of various mathematicians like Weierstrass, Dedekind, Kronecker, Borel, Weyl, etc. The goal of the conference was to explore those important but relatively neglected episodes or lines in the development of the foundations of mathematics. Since the papers included in the book will not be reviewed individually, it is reasonable to present them shortly in this review. \textit{J. Webb}'s paper ``Tracking contradictions in geometry: The idea of a model from Kant to Hilbert'' discusses the problem of who actually discovered non-euclidean geometry, who actually believed in its consistency and why, and who can be said to have proved it to be free of contradiction. The author stresses the significance of the idea of a model in this domain. The paper ``Standard vs. nonstandard distinction'', by \textit{J. Hintikka}, is devoted to the discussion of a conceptual distinction, or a contrast, between the standard and the nonstandard interpretation of higher-order logic. A natural sequel to this paper is the paper ``Wittgenstein and Ramsey on infinity'' (not presented at the conference) by \textit{M. Marion}. It is shown in it that the standard/nonstandard distinction provides the proper context in which differences between Wittgenstein and Ramsey on identity are to be understood. \textit{H. M. Edwards} analyses in his paper Kronecker's views on the foundations of mathematics. \textit{D. Ch. McCart}'s paper ``The mysteries of …
reviewed by: Roman Murawski
Mathematics Subject Classification ID: 03A05
Mathematics Subject Classification ID: 00A30
Mathematics Subject Classification ID: 01A55
Mathematics Subject Classification ID: 01A60
Mathematics Subject Classification ID: 03-03
Mathematics Subject Classification ID: 00B20
Mathematics Subject Classification ID: 03-06
zbMATH DE Number: 808187
zbMATH Keywords: Foundations of mathematics
zbMATH Keywords: Essays
zbMATH Keywords: Dedekind
zbMATH Keywords: Gödel
zbMATH Keywords: free creation
zbMATH Keywords: Frege's letters
zbMATH Keywords: construction
zbMATH Keywords: transcendental idealism
zbMATH Keywords: Weierstrass
zbMATH Keywords: Kronecker
zbMATH Keywords: Borel
zbMATH Keywords: Weyl
zbMATH Keywords: foundations of mathematics
zbMATH Keywords: Kant
zbMATH Keywords: Hilbert
zbMATH Keywords: non-euclidean geometry
zbMATH Keywords: higher-order logic
zbMATH Keywords: Ramsey
zbMATH Keywords: continuity
zbMATH Keywords: continuum
zbMATH Keywords: Frege
zbMATH Keywords: Frege's principle
zbMATH Keywords: Frege's Axiom V
zbMATH Keywords: completeness
zbMATH Keywords: ideal elements
zbMATH Keywords: Archimedean complete ordered field
zbMATH Keywords: Hahn
zbMATH Keywords: magnitudes
zbMATH Keywords: correspondence of Russell and Couturat
zbMATH Keywords: paradox of the largest cardinal
zbMATH Keywords: Russell's Paradox
zbMATH Keywords: descriptive set theory
zbMATH Keywords: probability theory
zbMATH Keywords: existence
zbMATH Keywords: consistency
zbMATH Keywords: Skolem
zbMATH Keywords: metalogical relativism
zbMATH Keywords: Tarski
zbMATH Keywords: Wittgenstein
zbMATH Keywords: Gödel's incompleteness theorem
zbMATH Keywords: Husserl
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description: scientific article; zbMATH DE number 808187