Historical development of modern logic
type: Item
instance of: scholarly article
title: Historical development of modern logic
zbMATH Open document ID: 1268.03006
author: Jean van Heijenoort
published in: Logica Universalis
publication date: 2013-03-15T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.rml/1204834850
review text: The article under review is a manuscript \textit{Jean van Heijenoort} never released; it was first published posthumously in [Mod. Log. 2, No. 3, 242--255 (1992; Zbl 0758.03004)] and was now included to a special, commemorative issue of the journal \textit{Logica Univeralis} (see [ibid. 6, No. 3--4, 249--267 (2012; Zbl 1268.03002)] for details). The article can quite naturally be broken down into three sections: (i) Frege (pp. 327--329); (ii) Löwenheim (pp. 329--331); and (iii) Herbrand (pp. 331--335; i.e., about half of the text). In accordance with distinctions the author had introduced earlier -- among others, in his better-known paper [``Logic as calculus and logic as language'', in: Boston Studies Philos. Sci. 3. Proc. Boston Colloq. Philos. Sci. 1964/66, 440--446 (1967; Zbl 0165.00809); Synthese 17, No. 3, 324--330 (1967; Zbl 0154.00305)] -- he portrays the development of logic in the hundred years from, roughly, 1870 to 1970 as the eventual synthesis of two different approaches to logic: Frege's syntactic approach universal in scope and Löwenheim's semantic approach limited to (fragments of) first-order logic. Both were amalgamated in the hands of Herbrand and in what the author sees as a direct consequence of the former's work: (semantic) tableaux and (analytic) trees. Reviewer's remarks: The reissue adds three new footnotes (3, 6, and 8 on pp. 328, 331, and 335, respectively) and features other minor updates (dates of death as well as footnotes 1 and 7 (on pp. 327 and 334)); it corrects a typo from the previous edition (see p. 331, footnote 6) and introduces two new ones: read ``definition'' instead of ``d'' on p. 327, line 8 from the top, and ``tables'' instead of ``tales'' on p. 334, line 7 from the top. If we take the manuscript's title at face value and expect a brief history of modern logic (and not, say, the (pre)history of the tree method), then its merits were already doubtful at the time it was composed in 1974 -- even if we grant that van Heijenoo…
reviewed by: Bernd Buldt
Mathematics Subject Classification ID: 03-03
Mathematics Subject Classification ID: 01A55
Mathematics Subject Classification ID: 01A60
Mathematics Subject Classification ID: 03A05
zbMATH DE Number: 6145481
zbMATH Keywords: history of logic
zbMATH Keywords: Jean van Heijenoort
zbMATH Keywords: Gottlob Frege
zbMATH Keywords: Leopold Löwenheim
zbMATH Keywords: Jaques Herbrand
MaRDI profile type: Publication
OpenAlex ID: W1991222302
cites work: Untersuchungen über das logische Schliessen. I
cites work: Q5590039
cites work: Q4236324
cites work: Q5573940
cites work: Q4357731
DOI: 10.1007/S11787-012-0064-7
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description: scientific article; zbMATH DE number 6145481