Examples of historical writing are analysed in detail, and it is demonstrated that, with respect to the statements which appear in historical accounts, their truth and value‐freedom are neither necessary nor sufficient for the relative acceptability of historical accounts. What is both necessary and sufficient is the acceptability of the selection of statements involved, and it is shown that history can be objective only if the acceptability of selection can be made on the basis of a rational criterion of relevance. ‘Relevance’ and ‘significance1 are distinguished. The conditions of rationality of a criterion of acceptability are examined with special reference to Popper's criterion of ‘falsifiability’, which is shown to fail to apply to historical writing. General conclusions are drawn about the implications of the argument for the possibility of the ‘unity of science’, and about the conditions which need to be met if history is to be objective.