On rereading van Heijenoort's selected essays
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 \textit{lingua universalis}), the author's main criticism is that van Heijenoort's distinction according to the two \textit{logicae} fails to account for the distinction between general and subject-specific model theory and that only the latter can be said to resemble some sort of \textit{logica utens}. Section 3, ``Set-theoretic semantics and the semantics of natural languages'' (pp. 540--544), credits van Heijenoort ``Set-theoretic semantics'' [in: Logic colloquium 76, Proc. Conf., Oxford 1976, Stud. Logic Found. Math., Vol. 87, 183--190 (1977; Zbl 0418.03007)] with correctly identifying a number of issues that mass nouns raise for their formalized treatment but only to take him to task for being ignorant of the solutions that were being developed already at his time. Section 4, ``Van Heijenoort on Frege's \textit{Sinn}'' (pp. 544--548), deals with two related questions; first, if we presuppose Frege's famous distinction according to meaning and sense, how do we define what the sense of a sentence is, and, second, how do we formulate a theory of synonymity (i.e., identity of senses). While the author doesn't object to van Heijenoort's idea of identifying the sense of a sentence with its syntactical tree conceived as a typed combinatorial object, he wonders why van Heijenoort failed to connect the dots and added a theory of synonymity; for the latter, the author endorses the approach recently proposed by \textit{Y. N. Moschovakis} [``A logical calculus of meaning and synonymity'', Linguist. Philos. 29, No. 1, 27--89 (2006)]. Reviewer's remarks: In light of the fact that the author collaborated with van Heijenoort, it is a bit surprising to see that he doesn't mince his words but gives a candid assessment. He tries to blunt his own criticisms in Section 5, when he claims life issues as extenuating circumstances (pp. 548 f.). Be that as it may, I find the criticisms and perspectives well-taken; they provide welcome guidance for those who want to study the original essays.
scientific article; zbMATH DE number 6145488
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