Publication Details

Abstract

True or false are only synthetical sentences pronounced on the base of our subjective processes; we accept such sentences only if we are able to indicate the way of their verification. To accept objective validity of sentences, i. e. to avoid subjectivism and solipsism, we must accept realism, monism and determinism. Accepting certain sentences as axioms, we form an analytical system. Its sentences being logical tautologies do not pronounce anything about the real world, but they participate on its laws through the synthetical sentences chosen as axioms. Analytical system and its sentences are neither true nor false, such a system is an instrument only and therefore useful or unuseful, suitable or insuitable. We may decide about its usability by translating the deduced sentences into synthetical ones, i. e. through semantic. By codifying certain synthetical sentences as axioms, we create allways a conflict between theory and praxis; certain degree of that conflict compels us to choose new axioms. The analytical system of logic is of the same sort as other systems, it is an instrument to form new instruments. The proof of its usability is indirect. Modern natural sciences have proved, that the system of classical and formal logic is of no use and we are obliged to use dialectical logic. The analytical sentences of mathematics is a system of the same sort too, its axioms are in their origin synthetical sentences. We may unite the mathematical system with other systems, becuase its sentences refer to the widest class of objects. Its sentences are neither apriori nor necessary, but they are usually verified indirectly through sentences deduced mathematically in other systems. In applying mathematics on other systems we often modify the mathematical axioms and that enables us to deduce true sentences by means of formal mathematics, which contains logical discrepances and uses an insuitable logic. Application of mathematics increases the exactitude of other systems increasing in the same time the conflict between praxis and theory a such accelerating the evolution of sciences.