David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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NTM International Journal of History and Ethics of Natural Sciences, Technology and Medicine 4 (1):129-143 (1996)
On the occasion of the 150th birthday of Georg Cantor (1845â1918), the founder of the theory of sets, the development of the logical foundations of this theory is described as a sequence of catastrophes and of trials to save it. Presently, most mathematicians agree that the set theory exactly defines the subject of mathematics, i.e., any subject is a mathematical one if it may be defined in the language (i.e., in the notions) of set theory. Hence the nature of formal definitions plays an important role within the logical foundations of mathematics. Its study is also helpful to answer the question of how it is possible that the set theory as a universal new ontology for the subject of mathematics (as people hoped around 1900) totally failed but nevertheless the language of set theory is successful in all the mathematical practice
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References found in this work BETA
K. Gödel (1931). Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I. Monatshefte für Mathematik 38 (1):173--198.
Paul Cohen (1963). The Independence of the Continuum Hypothesis. Proc. Nat. Acad. Sci. USA 50 (6):1143-1148.
R. L. Goodstein (1944). On the Restricted Ordinal Theorem. Journal of Symbolic Logic 9 (2):33-41.
I. Grattan-Guinness (1980). Georg Cantor's Influence on Bertrand Russell. History and Philosophy of Logic 1 (1-2):61-93.
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