Husserl's Two Notions of Completeness: Husserl and Hilbert on Completeness and Imaginary Elements in Mathematics
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Synthese 125 (3):417 - 438 (2000)
In this paper I discuss Husserl's solution of the problem of imaginary elements in mathematics as presented in the drafts for two lectures he gave in Göttingen in 1901 and other related texts of the same period, a problem that had occupied Husserl since the beginning of 1890, when he 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's terminology) for a formal axiomatic system. I present and discuss these notions here, establishing also parallels between Husserl's and Hilbert's notions of completeness.
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Jairo josé Silvdaa (2000). Husserl's Two Notions of Completeness. Synthese 125 (3).
Mirja Helena Hartimo (2007). Towards Completeness: Husserl on Theories of Manifolds 1890–1901. Synthese 156 (2):281 - 310.
Ulrich Majer (1997). Husserl and Hilbert on Completeness. Synthese 110 (1):37-56.
M. Hartimo (2012). Husserl's Pluralistic Phenomenology of Mathematics. Philosophia Mathematica 20 (1):86-110.
Guillermo E. Rosado Haddock (2006). Husserl's Philosophy of Mathematics: Its Origin and Relevance. [REVIEW] Husserl Studies 22 (3):193-222.
Stefania Centrone (2006). Husserl on the 'Totality of All Conceivable Arithmetical Operations'. History and Philosophy of Logic 27 (3):211-228.
Mirja Helena Hartimo (2008). From Geometry to Phenomenology. Synthese 162 (2):225 - 233.
Paul Ricœur (1967/2007). Husserl: An Analysis of His Phenomenology. Northwestern University Press.
R. O. Elveton (1970). The Phenomenology of Husserl. Chicago,Quadrangle Books.
Enrico Moriconi (2003). On the Meaning of Hilbert's Consistency Problem (Paris, 1900). Synthese 137 (1-2):129 - 139.
René Jagnow (2006). Edmund Husserl on the Applicability of Formal Geometry. In Emily Carson & Renate Huber (eds.), Intuition and the Axiomatic Method. Springer. 67--85.
Edmund Husserl (1994). Early Writings in the Philosophy of Logic and Mathematics. Kluwer Academic Publishers.
Roberto Poli (1993). Husserl's Conception of Formal Ontology. History and Philosophy of Logic 14 (1):1-14.
Claire Ortiz Hill (2002). Tackling Three of Frege's Problems: Edmund Husserl on Sets and Manifolds. [REVIEW] Axiomathes 13 (1):79-104.
Wojciech Buszkowski (1989). Presuppositional Completeness. Studia Logica 48 (1):23 - 34.
Added to index2011-05-29
Total downloads20 ( #98,384 of 1,679,366 )
Recent downloads (6 months)1 ( #183,761 of 1,679,366 )
How can I increase my downloads?