3. SEMIOTIC METHODS. Sign and its three dimensions. Formalism. Essence of formalism - calculation. Application of calculation to non-mathematical subjects. Validation of formalism. Eidetic and operational sense. Models. ArtiScial language. Syntactic rules of sense. Construction of language. Atomic and molecular expressions. Notion of syntactic category. Functors and arguments. Examples of syntactic nonsense. Semantic functions and levels Two semantic functions of sign. Designation and signiScance. Semantic levels. Language and meta-language. Semantic meaning and veriSability. Rule of verifiability. Verification levels: technical possibility, physical possibility, logical possibility, transempirical possibility. Principle of intersubjectivity. Verifiability of general clauses.

4. AXIOMATIC METHOD. Structure of indirect cognition. Law and rule. Two basic forms of inference: deduction and reduction. Reliable and unreliable rules of inference. Concept of axiomatic system. Structure of axiomatic clause system. Requirements for axiomatic system. Constitutional system. Progressive and regressive deduction. Mathematical logic. Methodological significance. Implication and derivability. Definition and creation of concepts. Basic types of definition. Real and nominal definitions. Syntactic and semantic definitions. Analytical and synthetic deSnitions. Types of syntactic definitions: clear definitions, contextual definitions, recursive definitions, definitions by axiomatic system. Semantic deictic definitions. Real definitions. Application of axiomatic method. Axiomatization of logic of Hilbert-Ackermann clauses.