On the existence of other universes (1306.2266v2)

Abstract: Natural philosophy necessarily combines the process of scientific observation with an abstract (and usually symbolic) framework, which provides a logical structure to the practice and development of a scientific theory. The metaphysical underpinning of science includes statements about the process of science itself, and the nature of both the philosophical and material objects involved in a scientific investigation. By developing a formalism for an abstract mathematical description of inherently non-mathematical (physical) objects, an attempt is made to clarify the mechanisms and implications of the philosophical tool of Ansatz. Outcomes of this style of analysis include a possible explanation for the philosophical issue of the 'unreasonable effectiveness' of mathematics as raised by Wigner, and an investigation into formal definitions of the terms: 'principles', 'evidence', 'existence' and 'universes', that are consistent with the conventions used in physics. It is found that the formalism places restrictions on the mathematical properties of objects that represent the tools and terms mentioned above. This allows one to make testable predictions regarding physics itself (where the nature of the tools of investigation is now entirely abstract) just as scientific theories make predictions about the universe at hand. That is, the mathematical structure of objects defined within the new formalism has philosophical consequences (via logical arguments) that lead to profound insights into the nature of the universe, which may serve to guide the course of future investigations in science and philosophy, and precipitate inspiring new avenues of integrated research.