Logical reloading as overcoming of crisis in geometry

 Yuri A. Rylov

Institute for Problems in Mechanics, Russian Academy of Sciences
 101-1 ,Vernadskii Ave., Moscow, 119526, Russia
 email: rylov@ipmnet.ru
 Web site: http://rsfq1.physics.sunysb.edu/~rylov/yrylov.htm
or mirror Web site: http://gasdyn-ipm.ipmnet.ru/~rylov/yrylov.htm

Updated May 12, 2010

abstract

Properties of the logical reloading in the Euclidean geometry are considered. The logical reloading is a logical operation which replaces one system of basic concepts of a conception by another system of basic concepts of the same conception. The logical reloading does not change propositions of the conception. However, generalizations of the conception are different for different systems of basic concepts. It is conditioned by the fact, that some systems of basic concepts contain not only propositions of the conception, but also some attributes of this conception description. Properties of the logical reloading are demonstrated in the example of the proper Euclidean geometry, whose generalization leads to different results for different system of basic concepts.

There is text of the paper in English (pdf, ps) and in Russian (ps, pdf)