The Liar Paradox Without Self-Reference

The concept of paradox is discussed in the article. A distinction between a strict paradox and a non-strict paradox is made. The author formulates the non-strict finite liar paradox. This paradox is not self-referential, since no sentence in its formulation refers to itself. The result of the research can be considered as a critical argument in relation to the classical method of solving paradoxes which implies a ban on self-reference. A hierarchical approach to solving paradoxes going back to the studies of Bertrand Russell and Alfred Tarski suggested a complete blocking of self-reference in order to prevent the possibility of contradictions in thinking and in language. Russell and Tarski regarded self-reference as the reason for the formation of any paradoxes containing contradictions. Accordingly, using a hierarchical approach, it was possible to solve not only strict paradoxes such as the Russell paradox but also non-strict paradoxes such as the Epimenides (the classical liar) paradox because, as it was supposed, the prohibition on self reference would block even the likely appearance of contradictions. A non-strict liar without self-reference formulated in this article cannot be resolved with the help of Russell's and Tarski's hierarchical approach by imposing a ban on self-reference since no sentence in this paradox refers to itself.

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