On rereading van Heijenoort's selected essays
type: Item
instance of: scholarly article
title: On rereading van Heijenoort's selected essays
zbMATH Open document ID: 1263.03003
author: Solomon Feferman
published in: Logica Universalis
publication date: 2013-03-15T00:00:00Z
review text: Irving H. Anellis, a student of Jean van Heijenoort (1912--1986), edited a special issue of the journal \textit{Logica Universalis} to commemorate the centennial of his teacher's birth. The article under review is a contribution to that collection; the other articles are listed as [Zbl 1268.03002; Zbl 1260.01016; Zbl 1260.01026; Zbl 1260.03001; Zbl 1270.03007; Zbl 1268.03006; Zbl 1268.03003; Zbl 1272.03001; Zbl 1272.03024; Zbl 1272.03005; Zbl 1267.03054; Zbl 1267.01028; Zbl 1405.03018; Zbl 1272.03048; Zbl 1272.03031]; note that [Zbl 1268.03006] was reviewed already as [\textit{J. van Heijenoort}, Mod. Log. 2, No. 3, 242--255 (1992; Zbl 0758.03004)]. Except for an introduction (Section 1, pp. 535 f.) and some concluding remarks (Section 5, pp. 548 f.), the article under review focuses on three topics. Section 2, ``Logic, mathematics and the emergence of model theory'' (pp. 537--540), provides a commentary on selected topics from \textit{J. van Heijenoort}'s influential 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, 324--330 (1967; Zbl 0154.00305)] along with its companion piece ``Absolutism and relativism in logic'' [in: Selected essays. Napoli: Bibliopolis. 75--83 (1985)]. Van Heijenoort distinguished between a universalist approach to logic, where individual variables and their quantifiers range over everything (e.g., in the works of Frege and Russell), and a more local approach, where formal languages are evaluated relative to specific domains of objects (e.g., in the work of Löwenheim); later he identified the two approaches with the traditional notions of a \textit{logica magna} and a \textit{logica utens} respectively. Besides taking issues with a number of minor points (e.g., that van Heijenoort failed to give proper due to the role Hilbert had played, or that he didn't mention set theory as the most natural candidate for a Leibnizian…
reviewed by: Bernd Buldt
Mathematics Subject Classification ID: 03-03
Mathematics Subject Classification ID: 03A05
Mathematics Subject Classification ID: 01A55
Mathematics Subject Classification ID: 01A60
Mathematics Subject Classification ID: 01A70
zbMATH DE Number: 6145488
zbMATH Keywords: Jean van Heijenoort
zbMATH Keywords: philosophy of logic
zbMATH Keywords: Gottlob Frege
zbMATH Keywords: history of logic
MaRDI profile type: Publication
full work available at URL: s11787-012-0058-5
OpenAlex ID: W2016518182
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DOI: 10.1007/S11787-012-0058-5
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description: scientific article; zbMATH DE number 6145488