One of the trends in the foundations of mathematics whose object
is to justify mathematics by reducing its initial concepts to
those of logic. The idea of reducing mathematics to logic was
expressed by G. Leibniz (end of the 17th century). The practical
realization of the thesis of logicism was undertaken at the end
of the 19th century and the beginning of the 20th century in
papers of G. Frege and B. Russell (see , ). The view of
mathematics as part of logic depends on the fact that in an
axiomatic system any mathematical theorem can be regarded as an
assertion about logical consequences. It just remains to define
all the constants that occur in such assertions in terms of
logical terms. At the end of the 19th century different forms of
numbers, including complex numbers, were defined in mathematics
in terms of the natural numbers and operations on them. An
attempt to reduce the natural numbers to logical concepts was
undertaken by Frege. In Frege's interpretation the natural
numbers were the cardinal number