The central challenge of the philosophy of history and historiography is to find a principled way to rank different interpretations of the past without assuming their truth in terms of correspondence. The narrativist insight of the narrative philosophy of historiography was to correctly question historical realism. It analyzed texts and showed that they cannot reflect the past as it is. However, the rejection of the truth-functional evaluation threatens to lead to an “anything goes” approach in terms of cognitive evaluation of historiography. In any case, no adequate theory of evaluation has so far been developed, although clearly not all historiographical interpretations are acceptable. Postnarrativist philosophy of historiography suggests that any history book includes a content-synthesizing unit, but that it is problematic to think that it is “narrative” that structures texts. It is better to think of historiography texts as presenting reasoning for views and theses about the past. Arguments for these theses should be considered not as being true but as more or less appropriate, fitting, or warranted. The historian aims to produce as highly rationally warranted and compelling a thesis of the past as possible; its rational appropriateness depends on three dimensions of cognitive evaluation: the epistemic, the rhetorical, and the discursive.