NAND-Gate Abduction

Peirce made three discoveries and left them apart. He named abduction, the only inference that introduces a new idea. He found that NAND — what he called the ampheck — is logically complete, the single connective from which all others derive. In his existential graphs he reduced logic to a single primitive: the cut, a closed curve, one negation. He never joined these findings. Joining them changes what abduction does. When the observer's distinctions are made the input rather than the frame, the operation stops generating hypotheses and begins eliminating them. What cannot be eliminated without collapsing a real distinction is the remainder. When every candidate is eliminated, the output is silence — which is not failure but a specific kind of information. These are things Peirce had the equipment to say.