Criteria of demarcation to distinguish science from non-science are considered. The author argues that formal criteria, for example, proposed by logical empiricism, tried to fulfill simultaneously two tasks: (a) to find a logical standard of science, and (b) to discriminate science as it is customary conceived in scientific communities. However, both tasks conceive of science in two different meanings. The issue (a) is addressed to science as a system of sentences, propositions, etc. suitable for logical analysis, but the issue (b) treats science as a social phenomenon. Hence it is difficult to expect that one simple formula could effectively distinguish science from non-science and be applicable to both conceptions of what science is like. On the other hand, philosophical analysis of science is too atrractive to be abandoned as an enterprise. At the end of the paper, an account of rationality of science is outlined which is based on the concept of fair game. The proposal contrasts rational thinking and irrational ways of stating and solving problems.