Russell 20:27-32 (2000)
|Abstract||Russell held that the theory of natural numbers could be derived from three primitive concepts: number, successor and zero. This leaves out multiplication and addition. Russell introduces these concepts by recursive definition. It is argued that this does not render addition or multiplication any less primitive than the other three. To this it might be replied that any recursive definition can be transformed into a complete or explicit definition with the help of a little set theory. But that is a point about set theory, not number theory.|
|Keywords||Russell Peano axioms for arithmetic|
|Categories||categorize this paper)|
|Through your library||Configure|
Similar books and articles
Charles Sayward (2005). Why Axiomatize Arithmetic? Sorites 16:54-61.
J. Michael Dunn (1980). Quantum Mathematics. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1980:512 - 531.
Kenneth McAloon (1982). On the Complexity of Models of Arithmetic. Journal of Symbolic Logic 47 (2):403-415.
Henryk Kotlarski (1984). Some Remarks on Initial Segments in Models of Peano Arithmetic. Journal of Symbolic Logic 49 (3):955-960.
Shmuel Lifsches & Saharon Shelah (1997). Peano Arithmetic May Not Be Interpretable in the Monadic Theory of Linear Orders. Journal of Symbolic Logic 62 (3):848-872.
Fred G. Abramson & Leo A. Harrington (1978). Models Without Indiscernibles. Journal of Symbolic Logic 43 (3):572-600.
Richard Heck (1993). The Development of Arithmetic in Frege's Grundgesetze der Arithmetik. Journal of Symbolic Logic 58 (2):579-601.
C. Ward Henson, Matt Kaufmann & H. Jerome Keisler (1984). The Strength of Nonstandard Methods in Arithmetic. Journal of Symbolic Logic 49 (4):1039-1058.
Richard Kaye (1991). Model-Theoretic Properties Characterizing Peano Arithmetic. Journal of Symbolic Logic 56 (3):949-963.
J. Michael Dunn (1979). Relevant Robinson's Arithmetic. Studia Logica 38 (4):407 - 418.
Added to index2011-02-28
Total downloads8 ( #131,679 of 722,826 )
Recent downloads (6 months)1 ( #60,541 of 722,826 )
How can I increase my downloads?