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On Axiomatic and Genetic Construction of Mathematical Theories

  • S. S. Demidov
Part of the Synthese Library book series (SYLI, volume 145)

Abstract

There are two methods of constructing mathematical theories: genetic and axiomatic. The first of them implies the construction of a theory through successive generalizations, on the basis of simple concepts established earlier. For instance, one can construct in this way the theory of real numbers proceeding from the basic unit: by applying a certain natural process (that of counting) one obtains from it the series of positive integers 1, 2, 3, 4, 5,…; introduces the so called arithmetic operations for them; then, by making use of these operations, introduces the negative numbers and zero; then fractions as pairs of integers; and, finally, defines the real number as a section or fundamental sequence.

Keywords

Differential Calculus Axiomatic Theory XIXth Century Axiomatic Method Fundamental Sequence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© D. Reidel Publishing Company 1980

Authors and Affiliations

  • S. S. Demidov

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