Patricia Williams made a number of claims concerning the methods and practise of cladistic analysis and classification. Her argument rests upon the distinction of two kinds of hierarchy: a ‘divisional hierarchy’ depicting ‘evolutionary’ descent and the Linnean hierarchy describing taxonomic groups in a classification. Williams goes on to outline five problems with cladistics that lead her to the conclusion that systematists should “eliminate cladism as a school of biological taxonomy and to replace it either with something that is philosophically coherent or to replace it with ‘pure’ methodology, untainted by theory” (Williams 1992, 151). Williams makes a number of points which she feels collectively add up to insurmountable problems for cladistics. We examine Williams' views concerning the ‘two hierarchies’ and consider what cladists currently understand about the status of ancestors. We will demonstrate that Williams has seriously misunderstood many modern commentators on this subject and all of her “five persistent problems” are derivable from this misunderstanding.