Hostname: page-component-76fb5796d-x4r87 Total loading time: 0 Render date: 2024-04-26T17:00:10.826Z Has data issue: false hasContentIssue false
  • English
  • Français

INTERPRETATION, LOGIC AND PHILOSOPHY: JEAN NICOD’S GEOMETRY IN THE SENSIBLE WORLD

Part of: Philosophical aspects of logic and foundations General and miscellaneous specific topics History of mathematics and mathematicians

Published online by Cambridge University Press:  02 July 2021

SÉBASTIEN GANDON
SÉBASTIEN GANDON*
Affiliation:
LABORATOIRE PHILOSOPHIES ET RATIONALITÉS UNIVERSITÉ CLERMONT AUVERGNE F-63000 CLERMONT-FERRAND, FRANCE
*
E-mail: sebastien.GANDON@uca.fr
Get access Rights & Permissions [Opens in a new window]

Abstract

Jean Nicod (1893–1924) is a French philosopher and logician who worked with Russell during the First World War. His PhD, with a preface from Russell, was published under the title La géométrie dans le monde sensible in 1924, the year of his untimely death. The book did not have the impact he deserved. In this paper, I discuss the methodological aspect of Nicod’s approach. My aim is twofold. I would first like to show that Nicod’s definition of various notions of equivalence between theories anticipates, in many respects, the (syntactic and semantic) model-theoretic notion of interpretation of a theory into another. I would secondly like to present the philosophical agenda that led Nicod to elaborate his logical framework: the defense of rationalism against Bergson’s attacks.

Keywords

NicodRussellinterpretationmodel

MSC classification

Primary: 00A30: Philosophy of mathematics
Secondary: 01A60: 20th century 03A05: Philosophical and critical
Type
Research Article
Information
The Review of Symbolic Logic , Volume 16 , Issue 4 , December 2023 , pp. 1080 - 1109
Check for updates
Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

BIBLIOGRAPHY

Alquié, F. (1941). Bergson et la revue de métaphysique et de morale. Revue de Métaphysique et de Morale, 48, 315–328.Google Scholar
Awodey, S., & Reck, E. (2002). Completeness and categoricity, part 1: Nineteenth-century axiomatics to twentieth-century metalogic. History and Philosophy of Logic, 23, 1–30.Google Scholar
Bergson, H. (1910). Time and Free Will: An Essay on the Immediate Data of Consciousness. London: S. Sonnenschein & Co., 1889 for the first French edition.Google Scholar
Bergson, H. (1946). The Creative Mind. London: The Philosophical Library, 1934 for the first French edition.Google Scholar
Button, T., & Walsh, S. (2018). Philosophy and Model Theory. New York: Oxford University Press.Google Scholar
Chwistek, L. (2017). The Pluralities of Realities. Collected Essays. Warsaw: Jagiellonian University Press.Google Scholar
Corcoran, J. (1980). On definitional equivalence and related topics. History and Philosophy of Logic, 1, 231.Google Scholar
Ferreiros, J. (1999). Labyrinth of Thought. A History of Set Theory and Its Role in Modern Mathematics. New York: Birkhauser.Google Scholar
Grattan-Guinness, I. (2000). The Search for Mathematical Roots, 1870–1940: Logics, Set Theories and the Foundations of Mathematics from Cantor Through Russell to Gödel. New York: Princeton University Press.Google Scholar
Hintikka, J. (1988). On the development of the model-theoretic viewpoint in logical theory. Synthese, 77, 1–36.Google Scholar
Hodges, W. (1993). Model Theory. Cambridge University Press.Google Scholar
Lawlor, L. (2020). Bergson on the true intellect. In Lefebvre, A., and Schott, N. F., editors. Interpreting Bergson: Critical Essays. Cambridge University Press.Google Scholar
Linsky, B. (1999). Russell’s Metaphysical Logic. Stanford: CSLI Publications.Google Scholar
Nicod, J. (1917). Reduction of the number of primitive propositions of logic. Proceedings of the Cambridge Mathematical Society, 19, 32–41.Google Scholar
Nicod, J. (1922a). Les tendances philosophiques de Mr Bertrand Russell. Revue de Métaphysique et de Morale, 1, 77–84.Google Scholar
Nicod, J. (1922b). Mathematical logic and the foundations of mathematics. The Encyclopedia Britannica. London–New York, pp. 874–876.Google Scholar
Nicod, J. (1924). La géométrie dans le monde sensible. Paris: Presses Universitaires de France. Quoted from the English translation Geometry and Induction, Berkeley and Los Angeles: University of California Press, 1970.Google Scholar
Poincaré, H. (1902). La Science et l’Hypothèse. Paris: Alcan.Google Scholar
Quine, W. V. O. (1960). Word and Object. Boston: MIT Press.Google Scholar
Russell, B. (1903). The Principles of Mathematics. Cambridge: Cambridge University Press.Google Scholar
Russell, B. (1912). The philosophy of Bergson. The Monist, 22(3), 321–347.Google Scholar
Russell, B. (1914). Our Knowledge of External World as a Field for Scientific Method in Philosophy (1993 edition). London: Allen and Unwin.Google Scholar
Russell, B. (1956). Logical atonism. In Marsh, R. C., editor. Logic and Knowledge. London: Allen and Unwin, pp. 323–343.Google Scholar
Schiemer, G., & Reck, E. (2013). Logic in the 1930s: Type theory and model theory. Bulletin of Symbolic Logic, 19(4), 433–472.Google Scholar
Slater, J. G. (1992). The Collected Papers of Bertrand Russell, Vol. 6. New York: Routledge.Google Scholar
Szczerba, L. W. (1975). Interpretability of elementary theories. In Butts, R. E., and Hintikka, J., editors. Logic, Foundations of Mathematics, and Computability Theory. Amsterdam: Springer, pp. 129–145.Google Scholar
van Heijenoort, J. (1967). Logic as language and logic as calculus. Synthese, 17, 324–330.Google Scholar
Varzi, A. C. (2021). Points as higher-order constructs. Whitehead’s method of extensive abstraction. In Shapiro, S., and Hellman, G., editors. The History of Continua: Philosophical and Mathematical Perspectives. London: Oxford University Press, pp. 347–378.Google Scholar
Walsh, S. (2014). Logicism, interpretability, and knowledge of arithmetic. this Journal , 7(1), 84–119.Google Scholar
Whitehead, A. N. (1919). An Enquiry Concerning the Principles of Natural Knowledge. London: Cambridge University Press.Google Scholar
Wiener, N. (1915). Studies in synthetic logic. Proceedings of the Cambridge Philosophical Society, 18, 14–28.Google Scholar
Wishon, S. (2017). Russellian acquaintance and Frege’s puzzle. Mind, 126(502), 321–337.Google Scholar