Incompleteness of axiomatic theories as truth of reality

The purpose of the study is to analyze consequences contained in the main thesis of the article, which consists in the following: even though for the purposes of the theory of knowledge, completeness is a desired quality of axiomatic theories, at the same time, it points at their epistemological “poverty”. And in particular, this study shows why this formal fact has crucial philosophical meaning and straightforwardly pertains both to the limits of ontology and the theory of subject. After the survey of historical development of formal deductive structures the author studies axiomatic structures themselves and analyses the limits of axiomatization of propositional logic and arithmetic. Incompleteness of the latter was established by Kurt Gedel. Possible connection between his famous incompleteness theorems and a theory of subject may be established since a man, by all means, can be construed as a “system powerful enough to speak about itself”. Methodology of this study borrows many ideas of contemporary French philosopher Alain Badiou, who thinks that mathematical results are not solely mathematical, but might point to the ontological structure of reality.