This paper is contentious, assertive and programmatic. It attempts to assay certain characteristics of a chronological history of science as practiced. It presents a model based on evolutionary theory that shows how to do that job better. After a brief excursion into the ontological assumptions of history writing, it goes on to sketch a different, systemic model. This systemic model is compatible with the traditional model, but will allow science better to be seen in its complex relation to other human and social aspects. As a leitmotif it is argued that intentionality and the mental or their teleological analogues, as an essential part of selectivity, are an ineliminable part of the history of science, however done.