Russell's unknown logicism. A study in the history and philosophy of mathematics
type: Item
instance of: scholarly article
title: Russell's unknown logicism. A study in the history and philosophy of mathematics
zbMATH Open document ID: 1270.03004
DOI: 10.1057/9781137024657
author: Sébastien Gandon
published in: History of Analytic Philosophy
publication date: 2013-03-12T00:00:00Z
review text: The stated aim of this important study of neglected parts of the Russellian \textit{opus} is to show that ``the widespread view that logicism is a continuation of arithmetization ought to be rejected.'' (p.\ 7) This, in itself, could be read off a letter Whitehead wrote to Russell on 14 September 1909, in which he writes ``The modern arithmeticisation of mathematics is an entire mistake.'' However, the author goes into great length to show where Russell rejects that view and what takes the place of arithmetic in those instances. The two examples are Russell's rejection of ``the definition of geometrical space as a numerical manifold'' and of ``Dedekind's cut-construction of real numbers.'' (p.\ 7) The first three chapters are devoted to Russell's views on geometry, the next three deal with his views on quantity, and the last chapter tries to explain the tension between the universality of logic and the topic-specificity of his choices of formal set-ups in the cases of geometry and of the real numbers. In the chapters on geometry, after presenting a short history of projective geometry, a closer look at Chapter VI of [\textit{B. Russell}, The principles of mathematics. Vol I. Cambridge: University Press (1903; JFM 34.0062.14)] (to be referred to as PoM VI) and at [\textit{A. N. Whitehead}, The axioms of projective geometry. Cambridge: University Press (1906; JFM 37.0559.01)] (which ``is nothing else than an extension of Russell's PoM VI theory'') reveals that Russell, having rejected the ``Cartesian approach'' of treating projective geometry in its coordinatized variant, prefers \textit{M. Pieri}'s incidence-based approach from [Mem.\ Real.\ Accad.\ Sci.\ Torino (2) 48, 1--62 (1898; JFM 29.0407.01)] to \textit{M. Pasch}'s order-based approach from [Vorlesungen über neuere Geometrie. Leipzig: Teubner (1882; JFM 14.0498.01)]. The reason for this choice constitutes one of the main topics of the author's research. Russell appears to have considered projective geometry as…
reviewed by: Victor V. Pambuccian
Mathematics Subject Classification ID: 03-02
Mathematics Subject Classification ID: 03-03
Mathematics Subject Classification ID: 03A05
Mathematics Subject Classification ID: 51-03
Mathematics Subject Classification ID: 01A55
Mathematics Subject Classification ID: 00A30
zbMATH DE Number: 6143299
zbMATH Keywords: Russell
zbMATH Keywords: Pieri
zbMATH Keywords: projective geometry
zbMATH Keywords: Dedekind
zbMATH Keywords: logicism
zbMATH Keywords: real numbers
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1057/9781137024657
OpenAlex ID: W2506379004
description: scientific article; zbMATH DE number 6143299