 Williamson gives other examples of useful but imperfect heuristics. One concerns vagueness, and the so-called “tolerance principles”, such as “If \(n\) seconds after noon is noonish, \(n+1\) seconds after noon is noonish”. That is a useful rule of thumb, though not all of its instances can be true. For the epistemicist, one instance is false, but we don’t know which. On other views, all are at least very close to clearly true, but not all are clearly true. Another example is the problem the Liar Paradox presents for the principle that it is true that \(P\) if and only if \(P\). In both cases, the exceptions are rare and can normally be overlooked. He also mentions the heuristics involved in perceptual judgements, normally very reliable, which sometimes lead us astray. “Humans predictably resort to fast and frugal heuristics, reliable enough under normal conditions, but not perfectly reliable” he says, (p. 265). 