Kuzmenko V. Philosophical methodological analysis of mathematical ontology paradigms

The object - are philosophical-methodological and naturally scientific installations, which determine fundamentals of mathematical problems and features of build-up of a mathematical building within the framework of researched paradigms of mathematical ontology. The purpose is the creation of the concept of mathematical ontology. Methods: the analysis and synthesis, system method, method of historically-cultural determinism, method of coincidence historical and logical, comparative and hermeneutic. Theoretical outcomes and their novelty. The factors which determined the methods of setting of mathematical problems and their solutions are generalized and classified; the reasons which have caused the change of expounding of the ontological status of mathematical essences in connection with mathematical speculations are uncovered. The practical value of the work consists in the research of the ontological status of mathematical essences in connection with mathematical speculations and reasons of its changes is the productive diagnostics defining possibility of the analysis and build-up new didactic of the mathematical knowledge concepts.