Taking knowledge as a starting point › Knowing Without Knowing That You Know

Chapter 5 applies related reasoning to the principle often called KK: if a person knows a proposition, that person knows that they know it. Williamson argues against even a suitably restricted guarantee of being in a position to achieve that further knowledge. Higher-order knowledge is an additional achievement. “Margins and Iterations,” section 5.1 develops the argument through inexact visual judgments about a tree's height.

An ordinary illustration helps distinguish the levels. You can recognize that a distant tree is taller than a chair without identifying its height to the nearest centimetre. Moving from a reliable broad judgment to an exact account of which judgments your eyesight supports requires more information. The illustration does not identify a specific KK failure by itself. It shows why the extra question about the limits of your knowledge deserves separate attention.

Margins for error belong to a family of ideas about reliability, safety, and the ease of making a mistake. They should not be converted into the requirement that a proposition remain true in every vaguely similar possible world, regardless of how the belief was formed. Circumstances, the basis of judgment, and the relevant possibilities matter. Nor does adding a safety condition automatically supply a complete analysis of knowledge; that would reverse the methodological direction Williamson is exploring.

The conclusion is compatible with much self-knowledge. It denies a universal guarantee. Someone may often know that they know a colleague's name while lacking the same assurance about a borderline perceptual judgment. This also differs from overconfidence, which involves taking oneself to know something one does not know. KK failure concerns knowledge that is present without the further knowledge. Treating the two phenomena as identical would obscure the argument.