We present an approach to the definition of an object-oriented modeling paradigm done in the scope of general system modeling. The paradigm includes a formally defined metamodel and its supporting philosophical and natural science foundations. The metamodel exhibits its internal consistency, supported by Russell's theory of types, and its consistency in interpretation of subjects of modeling, supported by Tarski's declarative semantics. We show a concrete example of the metamodel application, realized with the aid of concepts defined by RM-ODP (an ISO/ITU standard defining conceptual framework for modeling of distributed systems). This application was formalized in a computer-interpretable form, which allows for a computer-based verification of RM-ODP models. With the theoretical foundations of our metamodel, we deduce its defined structure and declarative semantics from the fundamentals of philosophy and natural science.