Frege's conception of logic
type: Item
instance of: scholarly article
zbMATH Open document ID: 1251.03005
author: Patricia A. Blanchette
publication date: 2012-07-02T00:00:00Z
Mathematics Subject Classification ID: 03-03
Mathematics Subject Classification ID: 00A30
Mathematics Subject Classification ID: 01A55
Mathematics Subject Classification ID: 01A60
Mathematics Subject Classification ID: 03A05
Mathematics Subject Classification ID: 51-03
zbMATH DE Number: 6051591
zbMATH Keywords: Frege's conception of logic
zbMATH Keywords: thoughts
zbMATH Keywords: conceptual content
zbMATH Keywords: axioms of geometry
MaRDI profile type: Publication
OpenAlex ID: W578399129
DOI: 10.1093/ACPROF:OSO/9780199891610.001.0001
title: Frege's conception of logic
review text: Part of the mind of great innovators often lives in a distant past, and their work contains not only revolutionary breakthroughs opening up unimagined vistas, but also, as if to counterbalance the daringness of their vision, archaic elements of concreteness. Copernicus retained the celestial spheres, for Pasch geometry was ``a branch of natural science'' and ``an empirical science'', and Frege, the inventor of the symbolic language of modern logic, believed that axioms cannot be chosen arbitrarily, as they have to be ``true'' (in an absolute way), turning logic in the mathematical context back to a time that perhaps -- if \textit{I. Tóth} [Fragmente und Spuren nichteuklidischer Geometrie bei Aristoteles. Beiträge zur Altertumskunde 280. Berlin: de Gruyter (2010; Zbl 1219.01005)] or \textit{V. Hösle} [I fondamenti dell'aritmetica e della geometria di Platone. Milano: Vita e Pensiero (1994)] are right -- even precedes Plato and Aristotle.NEWLINENEWLINEFrege's correspondence with Hilbert on the subject of Hilbert's axiomatic approach in \textit{Grundlagen der Geometrie}, carried between December 1899 and September 1900, which shows his thorough unwillingness to accept Hilbert's approach, an unwillingness that is espoused in public in [\textit{G. Frege}, Deutsche Math.-Ver. 12, 319--324, 368--375 (1903; JFM 34.0525.02)] as well, greatly diminished Frege's standing with mathematicians. Even before the onset of the ``Frege industry'' in philosophical circles (Frege being considered the father of analytic philosophy, still dominant in the English-speaking world), \textit{H. Freudenthal} would write in [Logic, methodology and philosophy of science, Proc. 1960 Int. Congr., 613--621 (1962; Zbl 0136.00205)]: ``Frege, rebuking Hilbert like a schoolboy, also joins the Bœtians. (I have never understood why he is so highly esteemed today)'' (p.\ 618).NEWLINENEWLINEThe aim of Blanchette's book is to explain, in as clear terms as possible, why Frege's understanding of logic, althoug…
reviewed by: Victor V. Pambuccian
description: scientific article; zbMATH DE number 6051591