Historic-philosophical
perception of mathematics
Petrova V.V.
Peopels Friendship University of Russia
The
students of the nonmathematical specialties who have studied a university
course of mathematics, should, in our opinion, not only seize knowledge and
skills of application of mathematical models and methods, but also to come to
understanding of its role and a place in system of sciences.
The
French theologian and the philosopher of the period of the High Middle Ages,
Pierre Abelyar (1079-1142) wrote about mathematics that «it is a science which
occupation is disgusting» [1]. It is possible to assume that other medieval
scientists allocated for mathematics this dark role. The member correspondent
of AN of USSR A.N.Bogolyubov explained it to that at the time of Abelyar the
mathematics was used for astrological calculations [1].
Eventually
dominating views changed. During an era of early Education, in the middle of
the 17th century the English theologian and philosopher Thomas Gobbs in the
book «Six lessons for professors of mathematics» (1656) assimilated social
sciences of geometry, opposing them to natural sciences. He wrote [2]: «Of
arts, some are demonstrable, others indemonstrable; and demonstrable are those
the construction of the subject whereof is in the power of the artist himself,
who, in his demonstration, does no more but deduce the consequences of his own
operation. The
reason whereof is
this, that the science of every subject is derived from a precognition of the
causes, generation, and construction of the same; and consequently where the
causes are known, there is place for demonstration, but not where the causes
are to seek for. Geometry therefore is demonstrable, for the lines and
ourselves; and civil philosophy is demonstrable, because we make the commonwealth
ourselves. But because of natural bodies we know not the construction. But seek
if from the effects, there lies no demonstration of what the causes be we seek
for, but only of what they may be».
Thus,
according to Gobbs, exact, demonstrative statements of rather geometrical
objects are possible so far as ourselves design them. While we enter such
concepts as a point and a straight line on the plane, we define length and an
angular measure, we thereby define that the sum of corners of a triangle is
equal to 180 degrees, and length of the party of this triangle less the sum of
two other parties. Thereby, ãåîìåòð is engaged only in
extraction of that truth which he created implicitly.
As the
American philosopher Y. Shapiro notes, Gobbs's reasonings lie in the tideway of
logic of «the privilege of the founder» (workmanship idea): there is a
theological argument that God âñåâåäóù as he created the
world. The creator thoroughly knows the creation as he knows, what principles
put in its basis. Geometr is the same creator for the world of points and
straight lines therefore it is capable to do exact, demonstrative statements
about them. Contrary to it, the person can't do demonstrative statements about
the natural nature as not he created it. Respectively, natural sciences aren't
demonstrative, the person can only try to find the basic principles.
Similar
classification of branches of knowledge: the mathematics and social sciences on
the one hand, natural sciences with another looks quite unusual from positions
of today's time. Let's note that a starting point for this classification was
the theology – possibly, most deeply developed science of that time.
Today
mathematics group with physics more often. To it point, for example, names of
scientific degrees in Russia: doctor or candidate of physical and mathematical
sciences. The sheaf of mathematics and physics became possible thanks to
enormous successes of mathematical methods and models when studying the
physical phenomena and processes.
Thus,
it is possible to tell that the mathematics place in system of sciences isn't
constant size, it depends on cultural conditions, from current situation in the
mathematics and other sciences.
Literatures
1. A.N.Bogolyubov. How magician Herbert got to
M.A.Bulgakov's novel?//Nature. – Ì.: 1988, ¹8, p.122-126
2. T.Hobbes. Six Lessons to the Professors of
Mathematics. 1656
3. http://oyc.yale.edu/transcript/802/plsc-118