_Solving the Problem of Material Implication_

The paradox of material implication has been a mystery to philosophers and logicians since antiquity. This article brings the final solution to the problem. In the course of the conducted research, the true nature of the implication was identified, which turned out to be the competition, occurring in two varieties – strong and weak, which is the logical equivalent of the difference of sets in set theory. Therefore, postulates were put forward regarding changes in nomenclature, adding logical connectives and taking over the role of the existing implication by the biconditional. A proposal for a system of axioms of logic and changes to the formula of the rule of identity and the names of some other logic rules were given. Finally, the issue of agreeing the names of logical functions and the names of the corresponding Boolean functions in computer science and logic gates in electronics was discussed