Historical development of modern logic
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 Heijenoort was preoccupied with the tree method during that time (see p. 222 of [\textit{I. H. Anellis}, Van Heijenoort. Logic and its history in the work and writing of Jean van Heijenoort. Ames: Modern Logic Publ. (1994; Zbl 0822.01006)]). In light of its glaring omissions and blatant deficiencies the reasons for printing the manuscript a second time just escape me; I feel no one should be absolved from writing ``history'' like this (but compare \textit{I. H. Anellis}' introduction in [Log. Univers. 6, No. 3--4, 301--326 (2012; Zbl 1270.03007)]).
scientific article; zbMATH DE number 6145481
scientific article