At the heart of knowledge is logic, that is, certain laws of thinking that are used in the analysis of facts and the construction of hypotheses and theories.
The formal logic we use is imperfect. This is proved by the presence of so-called logical paradoxes (aporias). Aporias are not misunderstandings and ridiculous curiosities; they are indicators, if not of inferiority, then, in any case, of the limitations of our main tool of cognition - formal logic. Paradoxes of logic are logically correct conclusions that do not contradict the laws of formal logic and, at the same time, represent reasoning that leads to absurd conclusions or mutually exclusive results.
The paradox is two opposite, incompatible statements, for each of which there are seemingly convincing arguments. The sharpest form of paradox is antinomy, an argument that proves the equivalence of two statements, one of which is a negation of the other.
Logic is an abstract science. There are no experiments in it, not even facts in the usual sense of the word. In building its systems, logic ultimately proceeds from the analysis of real thinking. In creating a theory, a scientist starts from facts, from what can be observed in experience. The theory must tie the facts into a “smooth” system. A theory makes sense when it agrees with the facts about it. A theory that is at variance with facts has no value.
The discrepancy between logical theory and the practice of real thinking is often found in the form of a more or less acute logical paradox, and sometimes even in the form of a logical antinomy, which speaks of the internal contradiction of the theory. This explains the importance that is attached to paradoxes in logic, and the great attention that they use in it.
A well-known and well-studied class of contradictions arising in statements that contain a definition of something that implicitly refers to itself - the paradoxes of self-reference (self-reference).
The paradoxes of definitions are a vivid example of the ambiguity of the concepts of identity. Depending on how you ask it, there will be different answers. One can only discuss which definitions correspond to one or another idea of identity.