LetEO be the elementary ontology of Leniewski formalized as in Iwanu [1], and letLS be the monadic second-order calculus of predicates. In this paper we give an example of a recursive function , defined on the formulas of the language ofEO with values in the set of formulas of the language of LS, such that EO A iff LS (A) for each formulaA.

Logic today is a ramified discipline existing on many levels. It is actively pursued by philosophers, mathemeticians, and computer specialists. The reason is that it is widely employed to solve a number of problems both in the theory of knowledge and in mathematics and computer science. But the broad spectrum of application of contemporary logic does not change the fact that its basic content has the nature of philosophical methodology. In contemporary logic it is the forms of thought and the (...) methods of scientific cognition, the modes of organization of scientific knowledge, and the procedures for the introduction of various concepts, abstractions, and idealizations that are studied. This places logic in intimate contact with epistemology and methodology. The distinctiveness of the approach taken by formal logic to this particular subject consists simply of its studying all these procedures pertaining to concrete cognition through the use of special formal languages, of algebraic, topological, and other exact techniques. (shrink)

In an essential way I make use of Frege’s and Vasilev’s ideas. N. A. Vasilev distinguished two levels in a logic. The abstract logic depends on gnoeologic assumptions while the empirical part of logic depends on ontological ones. Vasilev did not change the external logic but he did change the internal one. His system can be viewed as a non-standard syllogistics based on classical propositional logic . Vasilev’s ideas become plain if we discern cleary acts of predication and acts of (...) assertion, the relation of mental contents with the way things are. The second sourse of the idea seems to Frege’s differentation of mental process and assertion, statement . As a symbol of assertion for Frege serves a vertical stroke |. A horizontal stroke following it is correlated with holding a proposition, it makes the sign determined everywhere. In the string of signs the one following the vertical stroke does not express a proposition, it describes a possible state of affairs. (shrink)