Institute for Problems in Mechanics, Russian Academy of Sciences,
101-1, Vernadskii Ave., Moscow, 119526, Russia.
November 17, 2007
It is shown that slack mistakes, i.e. the mistakes which are not corrected in the course of long time (several decades or even centures), can appear in foundation of natural science. For instance, the statement on the Earth immobility in the Ptolemaic doctrine was a slack mistake. A slack mistake is shown to exist now in foundation of non-Euclidean geometry. Corollaries of this mistake are investigated. A long existence of the slack mistake in the science foundations does not stop its development, and it moves in blind alley. This generates special form of scientific theory called compensating conception. Appearance of compensating conception is accompanied by generation of special pragmatic style (P-style) of scientific investigations, which is suitable for working under condition of the slack mistake existence. This style is slightly suitable for working with the scientific theory which does not contain mistakes. Vice versa, the classical style of working is adapted to work with the theory which does not contain mistakes, but it is not suitable for working with the compensating conception, when there is a mistake in foundation of the theory. Discovery and correction of the slack mistake (or vice versa, appearance of a new mistake) changes the style of scientific investigations. The more effective under given conditions style replaces the less effective one. The style of scientific investigations is connected closely with education and training of scientific investigators. It is very conservative, and a change of styles is accompanied by conflicts in scientific community.