 Most theorems of standard logic break down when intermediate truth-values are involved. (An irregular minority, such as ‘If \(P\), then \(P\)’, survive.) Even the classical contradiction ‘Donald is bald and it is not the case that he is bald’ receives a truth-value of .5 when ‘Donald is bald’ has a truth-value of .5. Many-valued logicians note that the error they are imputing to classical logic is often so small that classical logic can still be fruitfully applied. But they insist that the sorites paradox illustrates how tiny errors accumulate into a big error.