In the first part of the paper the hypothesis of existence of so called Lingua Philosophica is propounded. Lingua Philosophica is an authentic philosophical language, which basic structures still fail to be expressed strictly. The author suggests a version of axiomatic system (so called Projective Modal Ontology, further PMO), which from his point of view could serve as the first adequate formal system, by means of which Lingua Philosophica can be

In the paper a new type of the formal theory, «L-inconsistent theory», is constructed and some properties of such theories are investigated. First a theory T* is defined as a set of limiting sequences of formulas from a theory T with a language L. A limiting sequence {An}∞n=1 of the formulas from T is said to be a theorem of the theory T* if there exists an m≥0 such that for any n≥m the formula An of the language L is a theorem of the theory