Home – Home – Jornals – Philosophy of Sciences 2023 number 1

The article deals with the problem of describing reality in the language of mathematics and logic with regard to the intellectual intuition corresponding to a certain stage in the development of knowledge. The question is raised of how the basic requirements for mathematical theory and logic will change if we take some of the multiverse models of modern physics as a basis. Mathematics is considered in the context of various historical approaches; mutual criticism of intuitionism, logicism and formalism is analyzed. It is shown that some of the well-known requirements for a formal theory (such as consistency) may begin to play a different role if the multiverse hypothesis is accepted. Under the theories based on the idea of the plurality of worlds, disputes related to logical consequence, the law of Duns Scotus, the law of the excluded middle and other well-known facts of classical logic, due to intuitive unacceptability, become resolved. An approach based on paraconsistent logics is considered; such logics can be treated as the first to conform to the multiverse theories. The problem of the universality of the mathematical language and the accompanying intellectual intuition is proposed for discussion. Can mathematics describe any of the physically possible worlds and therefore become the basis for the “theory of everything” (not so much in the sense of the quantum gravity theory, but as describing all possible worlds) and in what epistemological consequences this can result? It is shown that in a unified theory that claims to describe multiverse models, the classical intuitive requirement of consistency becomes restrictive and serving the purpose of an approximate description of a particular world, rather than the whole of all possible worlds. This requires a change in the general methodology in describing the world by such a theory and a revision of current standards