Abstract

This theorem is revolutionary. Throughout history, many major shifts—from Newton to Einstein, the Industrial Revolution, World War II, regime changes, and revolutions—can ultimately be traced back to failures in either propositions or definitions. And in our daily lives as well: Is it always correct for a parent to scold a child? Is it always incorrect for a child to scold a parent? The same structure applies to the relationships between bosses and subordinates, constitutions and laws, mathematics and axioms. Whenever we equate things without structural justification, refutation becomes harder than proof. Thus, I propose that “A = B” should always be treated as a provisional assumption, not a proof. The Proposition Refutation Theorem is not based on axioms, but is a theorem in its own right. Why not an axiom? Because in mathematics, an axiom must be unique. There must not be many.