Logical reloading as overcoming of crisis in geometry

Details Logical reloading as overcoming of crisis in geometry Logical reloading as overcoming of crisis in geometry

2010-05-11

arxiv.org/abs/1005.2074v2

Mathematics

General Mathematics

15 pages, 0 figures, correction of misprints

Scientific paper

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.

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