Critical analysis of the hierarchical approach to the solution of the paradox problem

The problem of logical paradoxes is considered in the article. In the first half of the 20th century, a hierarchical approach to solving paradoxes was formulated in the works of Bertrand Russell and Alfred Tarski. From the point of view of this approach the main reason for paradoxes is self-reference. Hence, the hierarchical approach completely prohibits self-reference in thinking and language. This is a solution to the paradox problem in the context of the approach. In the second half of the 20th century, the point of view of the hierarchical approach became generally accepted. Many encyclopedic philosophical writings consider the hierarchical approach as a clear and acceptable way of solving the paradox problem. However, in the research literature on logic, epistemology and the philosophy of mathematics in recent decades there appeared works criticising the hierarchical approach in various aspects. In particular, it was asserted that a) the hierarchical approach generates "revenge problems"; b) the hierarchical approach places undesirable limits for the development of mathematical theories and forces to abandon important results in the field of the philosophy of mathematics; c) the hierarchical approach is too radical for, first, some self-referential statements are paradoxical by accident and, second, some self-referential statements are obviously not paradoxical; d) the hierarchical approach does not cover all paradoxes for paradoxes can be formulated without self-reference; e) the hierarchical approach is absurd from a common sense point of view. Nevertheless, these critical studies were sporadic and unsystematic. Separately, they could not destroy the authority of the hierarchical approach to solving the paradox problem. The author of this article aims to accumulate various critical arguments to the hierarchical approach that were expressed in the research literature in order to demonstrate the importance of the whole variety of critical views, to show the vulnerability of the hierarchical approach in various aspects and to call into question the adequacy of this approach to solving the paradox problem.

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