Set Theory and Logic

Reductio ad Absurdum: P ≠ NP is False

Authors: John Augustine McCain
Comments: 10 Pages. CC-BY-NC 4.0

We present a reductio ad absurdum argument demonstrating the epistemological absurdity of requiring exhaustive verification for building confidence in mathematical conjectures. Through the development of a counterexample-collapse engine for the Goldbach conjecture, we show that demanding exhaustive verification leads to unreasonable epistemic commitments: if exhaustive verification were truly required, then discovering a single potential counterexample should rationally collapse all confidence to near-zero indefinitely. Since this behavior is clearly unreasonable, we conclude that exhaustive verification requirements are epistemologically unjustified, and that probabilistic evidence accumulation represents superior reasoning about mathematical reality. This argument has profound implications for mathematical epistemology, computational verification, and the nature of reasonable belief formation.
Category: Set Theory and Logic