Abstract: The anti-luminosity argument is used to refute the KK principle that if one knows and one knows that one knows, or at least is in a position to know that one knows. Further iterations of knowledge are shown to involve similar cognitive gaps. The underlying phenomenon is diagnosed in terms of the need for a margin for error in knowledge. It is related to a family of ideas such as safety, reliability, robustness, stability, and close or easy possibility. The account is extended to knowledge of what others know.

Keywords: easy possibility, error, iteration, KK principle, Margin, reliability, robustness, safety, stability,