The interpretation and analysis of anomalies is itself theory-dependent, as illustrated in the case of the ox phos debate in biochemistry in the 1960s. Here, the perceived threat of six anomalies to an existing research lineage depended on perspective, or Kuhnian paradigm. The ambiguous status of anomalies sharpens the problem of Kuhnian incommensurability. But analysis of the details of the historical case—one way to pursue an empirical philosophy of science—also indicate a possible solution. The asymmetric organization of multiple anomalies strongly indicated that disagreement had shifted from an intraparadigm to an interparadigm level, where modes of effective argument and use of evidence differ. This diagnostic awareness of the type of disagreement can orient discourse and allow investigators to develop and present evidence appropriately. I briefly extend the results of this historical case analysis to Darwin’s synthesis and to gendered bias in craniology, to indicate the prospective generality of the analysis of anomaly asymmetry.