Consistency and Some Other Requirements to a Formal Theory in the Context of Multiverse Models

The paper is devoted to the problem of describing reality in the language of mathematics and logic in connection with the intellectual intuition corresponding to a certain stage of knowledge development. The question is raised as to how the basic requirements to mathematical theory and logic will change if some of the multiverse models of modern physics are taken as the basis. Mathematics is considered in the context of various historical approaches, and mutual criticism of intuitionism, logicism, and formalism is analyzed. It is shown that some of the well-known requirements to a formal theory (such as consistency) may begin to play a different role if the multiverse hypothesis is accepted. In the framework of theories based on the idea of ​​multiple worlds, the logical consequence, the natural law of Duns Scotus, the law of excluded middle, and other well-known facts of classical logic which in some cases cause controversy due to their intuitive unacceptability are resolved. The paper discusses an approach based on paraconsistent logics – such logics can be considered the first ones to correspond to multiverse theories. The author raises the problem of universality of the mathematical language and the corresponding intellectual intuition – the issue of whether mathematics is able to describe any of the physically possible worlds and, consequently, to become the basis for a “theory of everything” (not so much in the sense of the theory of quantum gravity as in the sense of describing all possible worlds), and of what epistemological consequences that can lead to. It is shown that in a unified theory claiming to describe multiverse models, the classical intuitive requirement of consistency becomes restrictive and serves the purpose of approximate description of a particular world but not the totality of all possible ones. This calls for a shift in the general methodology of describing the world in the framework of such a theory, and for a revision of existing standards.