Institute for Problems in Mechanics, Russian Academy of Sciences,
101-1, Vernadskii Ave., Moscow, 119526, Russia.
E-mail: rylov@ipmnet.ru
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.