NEWTON AND THE CONSTRAINT OF PHYSICAL REALIZABILITY A FOUNDATIONAL CLARIFICATION OF THE BOUNDARY BETWEEN MATHEMATICS AND PHYSICS

This paper isolates and formalizes a constraint implicit in Isaac Newton’s methodology: mathematical structures are admissible in physics only when they correspond to physically enforceable distinctions. By examining Newton’s refusal to assign physical reality to entities lacking operational enforcement—such as absolute space as a substance or speculative gravitational mechanisms—the paper clarifies the boundary between mathematical description and physical ontology. The analysis shows that Newton freely employed mathematics while systematically withholding ontological commitment where no interaction, constraint, or measurable effect could be enforced. The result is a physics-only criterion that separates formal possibility from physical realizability and preserves physics as an operational discipline rather than a catalog of consistent abstractions.