  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.
