Natural philosophy necessarily combines the process of scientific observation
with an abstract (and usually symbolic) framework, which provides a logical
structure to the 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 the 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 research