In applied problems mathematics is used as language or as a metalanguage on which metatheories are built, E.G., Mathematical theory of experiment. The structure of pure mathematics is grammar of the language. As opposed to pure mathematics, In applied problems we must keep in mind what underlies the sign system. Optimality criteria-Axioms of applied mathematics-Prove mutually incompatible, They form a mosaic and not mathematical structures which, According to bourbaki, Make mathematics a unified science. One of the peculiarities of applied mathematical (...) language is a variety of dialects: a problem can be presented in terms of various mathematical notions. Another peculiarity is polysemy: a problem can be presented in the framework of one dialect by a set of various models with equal right to exist. The pragmatic sense of distinction between applied and pure mathematics must lead to specific training in each case. (shrink)

The attention of scientists is now being drawn to a new branch of knowledge known as the “philosophy of science.” It is true, however, that philosophers of this country are not very happy about this word combination and often identify it with logical, positivism. Indeed, it would seem better to speak not of the philosophy, but of the logic of scientific development. Science has become an object of study, and there has emerged metascience, i.e., a science studying the logic of (...) scientific structures. This field of knowledge cannot so far boast of generally accepted results. But it has done something else: new acute questions have been formulated and discussed fruitfully and originally. With this paper we are making an attempt to enter the discussion. The philosophy of science has not certainly taught scientists to discover the truth but it has indubitably increased their criticism towards their own activities, and this is really a very important accomplishment. (shrink)