Abstract
In this paper I discuss Husserl's solution of the problem of imaginary elements in mathematics as presented in the drafts for two lectures hegave in Göttingen in 1901 and other related texts of the same period,a problem that had occupied Husserl since the beginning of 1890, whenhe was planning a never published sequel to Philosophie der Arithmetik(1891). In order to solve the problem of imaginary entities Husserl introduced,independently of Hilbert, two notions of completeness (definiteness in Husserl'sterminology) for a formal axiomatic system. I present and discuss these notionshere, establishing also parallels between Husserl's and Hilbert's notions ofcompleteness.
Similar content being viewed by others
References
Bachelard, S.: 1968, A Study of Husserl's Formal and Transcendental Logic, Northwestern University Press, Evanston.
Cavaillès, J.: 1997, Sur la Logique et la Théorie de la Science, Vrin, Paris.
Frege, G. and E. Husserl: 1987, Frege-Husserl Correspondence, Editions T. E. R., Mauvezin.
Hill, C.: 1991, Word and Object in Husserl, Frege and Russell: the Roots of Twentieth-Century Philosophy, Ohio University Press, Athens.
Hill, C.: 1995, 'Husserl and Hilbert on Completeness', in J. Hintikka (ed.), From Dedekind to Gödel, Synthese Library v. 251, Kluwer, Dordrecht.
Hill, C. and G. Rosado Haddock: forthcoming, Meaning, Objectivity and Mathematics, Husserl and Mainstream Philosophy of Logic and Mathematics.
Husserl, E.: 1970, Philosophie der Arithmetik, mit ergänzenden Texten (1890–1901), Husserliana Volume XII, Martinus Nijhoff, The Hague.
Husserl, E.: 1970, Logical Investigations, Humanities Press, New York.
Husserl, E.: 1972, Ideas: General Introduction to Pure Phenomenology (English trans. of Ideen I), Collier-Macmillan, New York.
Husserl, E.: 1994, Early Writings in the Philosophy of Logic and Mathematics, trans. by Dallas Willard, Kluwer, Dordrecht.
Husserl, E.: 1995, Articles sur la Logique (1890–1913), PUF, Paris.
Majer, U.: 1997, 'Husserl and Hilbert on Completeness: A Neglected Chapter in Early Twenty Century Foundation of Mathematics', Synthese 110.
Poincaré, H.: 1968, La Science et l'Hypothèse, Flammarion, Paris (first published in 1902).
Scanlon, J.:1991, 'Tertium non Datur: Husserl's Conception of a Definite Multiplicity', in T. M. Seebohm, D. Follesdal and J. N. Mohanty (eds.), Phenomenology and the Formal Sciences, Kluwer, Dordrecht.
Sebestik, J.: 'Postface', in Cavaillès [1997], pp. 91–142.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Da Silva, J.j. Husserl's Two Notions Of Completeness. Synthese 125, 417–438 (2000). https://doi.org/10.1023/A:1005265017902
Issue Date:
DOI: https://doi.org/10.1023/A:1005265017902