The construction of the theory of dimensions and similarity, as well as any theory in general, is desirable to be carried out using the methods of the basic premises that are adequate to the essence of the theory. This construction makes it possible to clearly trace the boundaries and possibilities of the theory. This is especially necessary for the theory of dimensions and similarity, since you often have to meet with extreme opinions: on the one hand, about its omnipotence and, on the other, about its triviality. Both opinions cannot be considered correct.