In this paper, under the assumption that ZFC axiom system is consistent, the following are proved: (a) there is no system whose object set consists of all systems; (b) any system is not an object of itself; (c) any system is constructed with basic elements (elements which are not systems). Based on these results, the following problems in epistemology are discussed: the feasibility of the definition of the theory so-called “science of science”; the existence of basic particles in the world; and the existence of absolute truths.