In Defense of Logical Universalism: Taking Issue with Jean van Heijenoort [Book Review]

Logica Universalis 6 (3-4):553-586 (2012)

Philippe De Rouilhan
Centre National de la Recherche Scientifique
Van Heijenoort’s main contribution to history and philosophy of modern logic was his distinction between two basic views of logic, first, the absolutist, or universalist, view of the founding fathers, Frege, Peano, and Russell, which dominated the first, classical period of history of modern logic, and, second, the relativist, or model-theoretic, view, inherited from Boole, Schröder, and Löwenheim, which has dominated the second, contemporary period of that history. In my paper, I present the man Jean van Heijenoort (Sect. 1); then I describe his way of arguing for the second view (Sect. 2); and finally I come down in favor of the first view (Sect. 3). There, I specify the version of universalism for which I am prepared to argue (Sect. 3, introduction). Choosing ZFC to play the part of universal, logical (in a nowadays forgotten sense) system, I show, through an example, how the usual model theory can be naturally given its proper place, from the universalist point of view, in the logical framework of ZFC; I outline another, not rival but complementary, semantics for admissible extensions of ZFC in the very same logical framework; I propose a way to get universalism out of the predicaments in which universalists themselves believed it to be (Sect. 3.1). Thus, if universalists of the classical period did not, in fact, construct these semantics, it was not that their universalism forbade them, in principle, to do so. The historical defeat of universalism was not technical in character. Neither was it philosophical. Indeed, it was hardly more than the victory of technicism over the very possibility of a philosophical dispute (Sect. 3.2)
Keywords Jean van Heijenoort  philosophy of logic  history of logic  logical universalism  model theory
Categories (categorize this paper)
DOI 10.1007/s11787-012-0066-5
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 49,066
Through your library

References found in this work BETA

Outline of a Theory of Truth.Saul Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
Logic in the Twenties: The Nature of the Quantifier.Warren D. Goldfarb - 1979 - Journal of Symbolic Logic 44 (3):351-368.

View all 16 references / Add more references

Citations of this work BETA

Logical Contextuality in Frege.Brice Halimi - 2018 - Review of Symbolic Logic 11 (1):1-20.

Add more citations

Similar books and articles


Added to PP index

Total views
92 ( #97,958 of 2,311,196 )

Recent downloads (6 months)
9 ( #86,720 of 2,311,196 )

How can I increase my downloads?


My notes

Sign in to use this feature