Логика многомировых моделей и интеллектуальная интуиция
The article is concerned with the problem of reality describing in the language of mathematics and logic in connection with the intellectual intuition corresponding to a certain stage in knowledge development. The question of how the basic requirements for mathematical theory and logic will change if we take as a basis some of the many-worlds models of modern physics is raised. Mathematics is considered in the context of various historical approaches. The mutual criticism of intuitionism, logicism, and formalism is analyzed. Some of the well-known requirements for formal theory (such as consistency) are shown as playing a different role upon the acceptance of the many-worlds hypothesis. In contexts of theories based on the idea of a multitude of worlds, the logical consequence, the 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 intuitive unacceptability, are resolved. An approach based on paraconsistent logics is considered - such logics can be believed as the first corresponding to many-worlds theories.
The problem of the universality of the mathematical language and the accompanying intellectual intuition is requested for discussion. If mathematics is capable of describing any of the physically possible worlds, and, accordingly, becoming the basis for the "Theory of Everything" (not much in the sense of the theory of quantum gravity, but as describing all the possible worlds) and what epistemological consequences it can lead to.
In a unified theory that claims to describe many-worlds models, the classical intuitive requirement of consistency is shown to become restrictive and serving to the purpose of an approximate description of some particular world and not the totality of all possible ones. This requires a change of the language and general methodology within the framework of describing the world via such a theory and revision of existing standards.