Olexiy Bilyk and Yaroslav Bilyk
  On Hilbert's Endeavour to Formalise
           Mathematics
     As by the end of 19th century narrowness of mathematical demonstration
became obvious, Hilbert endeavoured to revise it, however following
tradition, which was begun by Aristotle.
     In connection with problem of discrepancy of scientifical theories
Hilbert suggested program of formalisation of logical demonstration of
deductive theories, which presupposes not only obvious indication of all
initial concepts and initial axioms of every given theory, but also obvious
indication of all logical means, which are used in conclusions of this
theory.
     In 1899 Hilbert made severely axiomatic construction of Euclid's
geometry, which predestined subsequent development of research on
formalisation of scientific knowledge. However, this program wasn't carried
out. Besides, it was found that it is impracticable, because it was
demonstrated that full and simultaneously undiscrepant formalisation of
even such comparatively simple mathematical theories as arithmetic is
impracticable in the main, because they have some rest, which can't be
formalised.
     However, following circumstance attracts attention: mathematics was
endeavoured to formalise in accordance with rules of logic, which was
created by Aristotle on model of mathematical demonstration.

Olexiy Bilyk,
docent of department of philosophy of pedagogical institute of Berdyansk,
address: Olexiy Bilyk, Luxemburg st., 18, flat 40, Berdyansk, Ukraine,
332440
telephone 7-29-24, e-mail: skyth@comint.net
Yaroslav Bilyk,
docent of department of theory of culture of university of Kharkiv,
address: Yaroslav Bilyk, Korka st., 54, flat 142, Kharkiv, Ukraine, 310195.