Robert Bruce Ware
Ex Nihilo: A Derivation of Logic, Mathematics, and Physics
At the turn of the twentieth century, the discovery of the logical antinomies led to a crisis
at the foundation of knowledge. That crisis was never resolved, but evaded instead by a variety
of strategies including axiomatized set theory, the theory of types, and, in a closely related
manner, the Copenhagen Interpretation of quantum mechanics. This paper shows how Cantor’s
antinomy may be reinterpreted to provide a natural foundation for set theory and logic. Cantor’s
set V of everything is conceived as a self-organizing process, which generates the categories of
class and member, symmetry, orthogonality, and a hierarchy of set theoretic types. This
development further derives the complex, real, and rational numbers, along with arithmetic,
trigonometry, analytic geometry, calculus, and the stereographic projection of the Riemann
Sphere upon. The Riemann Sphere provides a precise model for the collapse of the quantum
mechanical state vector. At the same time, this model provides an interpretation of the
uncertainty relations in quantum physics, and for the finite velocity of light and Lorentz
geometry in special relativity.