Axiomatic Systems from the Methodological Point Of View (I960)

Abstract

There are two disciplines which make the axiomatic systems the object of their research. One of them is the branch of mathematical logic named metamathematics, or metalogic, or more generally metascience. The other is the traditional methodology of sciences, which is treated in separate chapters in the textbooks of logic and deals with problems bordering upon the philosophical theory of knowledge. The achievements of metascience are so numerous, its notions so precise, and its proofs so exact, that they have dissuaded many from examining deductive systems from any point of view but that adopted by metascience; they have produced an impression as if metascience could be identified with the theory of deductive systems, and as if no other problems concerning those systems could be stated but those treated by metascience.