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 formalized. Explanations of the basic notions of PMO and their interpretation in various philosophical traditions are given. In the second part of the paper ideas of PMO are used to interpret the main ideas of Plato's Parmenides. Original formal treatment of logics of the dialogue is given, the structure of Zeno's dialogue is reconstructed, levels of macro- and micro logics of the dialogue are sketched, and the author suggests the principles of their coordination on the way of constructing the full logical interpretation of the dialogue as a very important example of method of classic dialectics.