Graduate studies at Western
NTM International Journal of History and Ethics of Natural Sciences, Technology and Medicine 3 (1):65-86 (1995)
|Abstract||This paper gives a survey of David Hilbert's (1862â1943) changing attitudes towards logic. The logical theory of the GÃ¶ttingen mathematician is presented as intimately linked to his studies on the foundation of mathematics. Hilbert developed his logical theory in three stages: (1) in his early axiomatic programme until 1903 Hilbert proposed to use the traditional theory of logical inferences to prove the consistency of his set of axioms for arithmetic. (2) After the publication of the logical and set-theoretical paradoxes by Gottlob Frege and Bertrand Russell it was due to Hilbert and his closest collaborator Ernst Zermelo that mathematical logic became one of the topics taught in courses for GÃ¶ttingen mathematics students. The axiomatization of logic and set-theory became part of the axiomatic programme, and they tried to create their own consistent logical calculi as tools for proving consistency of axiomatic systems. (3) In his struggle with intuitionism, represented by L. E. J. Brouwer and his advocate Hermann Weyl, Hilbert, assisted by Paul Bemays, created the distinction between proper mathematics and meta-mathematics, the latter using only finite means. He considerably revised the logical calculus of thePrincipia Mathematica of Alfred North Whitehead and Bertrand Russell by introducing the Îµ-axiom which should serve for avoiding infinite operations in logic|
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
|Through your library||Configure|
Similar books and articles
Michael Stoeltzner, How Metaphysical is "Deepening the Foundations"? - Hahn and Frank on Hilbert's Axiomatic Method.
Colin Mclarty (1997). Poincaré: Mathematics & Logic & Intuition. Philosophia Mathematica 5 (2):97-115.
Panu Raatikainen (2001). Exploring Randomness. Notices of the AMS 48 (9):992-6.
Abraham Adolf Fraenkel & Yehoshua Bar-Hillel (eds.) (1966). Essays on the Foundations of Mathematics. Jerusalem, Magnes Press Hebrew University.
Volker Peckhaus (2003). The Pragmatism of Hilbert's Programme. Synthese 137 (1-2):141 - 156.
P. T. Johnstone (1987). Notes on Logic and Set Theory. Cambridge University Press.
Mary Tiles (1989/2004). The Philosophy of Set Theory: An Historical Introduction to Cantor's Paradise. Dover Publications.
Kai F. Wehmeier (1997). Aspekte der Frege–Hilbert-Korrespondenz. History and Philosophy of Logic 18 (4):201-209.
Paolo Mancosu (1999). Between Russell and Hilbert: Behmann on the Foundations of Mathematics. Bulletin of Symbolic Logic 5 (3):303-330.
Gregory H. Moore (1980). Beyond First-Order Logic: The Historical Interplay Between Mathematical Logic and Axiomatic Set Theory. History and Philosophy of Logic 1 (1-2):95-137.
Patricia A. Blanchette (2007). Frege on Consistency and Conceptual Analysis. Philosophia Mathematica 15 (3):321-346.
Added to index2010-09-01
Total downloads13 ( #95,683 of 739,168 )
Recent downloads (6 months)1 ( #61,778 of 739,168 )
How can I increase my downloads?