 Two difficulties are immediately apparent regarding the realist aspiration to infer truth (approximate truth, existence of entities, etc.) from hypotheses or theories that are judged best on explanatory grounds. The first concerns the grounds themselves. In order to judge that one theory furnishes a better explanation of some phenomenon than another, one must employ some criterion or criteria on the basis of which the judgment is made. Many have been proposed: simplicity (whether of mathematical description or in terms of the number or nature of the entities involved); consistency and coherence (both internally, and externally with respect to other theories and background knowledge); scope and unity (pertaining to the domain of phenomena explained); and so on. One challenge here concerns whether virtues such as these can be defined precisely enough to permit relative rankings of explanatory goodness. Another challenge concerns the multiple meanings associated with some virtues (consider, for example, mathematical versus ontological simplicity). Another concerns the possibility that such virtues may not all favor any one theory in particular. Finally, there is the question of whether these virtues should be considered evidential or epistemic, as opposed to merely pragmatic. What reason is there to think, for instance, that simplicity is an indicator of truth? Thus, the ability to rank theories with respect to their likelihood of being true may be questioned.