Cognitive Superiority
It is partly a term of the art (in the philosophy of sciences) and partly retains the commonsense usage. When one compares theories (in order to choose the best one among the rivals), one compares them with respect to the important properties that theories should have. What these properties are depends upon the philosophy of science one subscribes to. For instance, one might think that a theory should explain phenomena. If this demand is put, then one chooses a theory that does a better job at explaining the phenomenon. One might add additional conditions to this demand in order to clarify what it means to explain ‘better’. For instance, one might want to say that some theory X explains a phenomenon better than theory Y if X can explain some additional things as well, or explains things that theory Y cannot explain. One might further add that the theory X should be falsifiable or that it has more facts in its favor. Or, again, one could suggest that the theory X is better than Y because X solves more problems than Y. Or again, that X is more useful in prediction than Y. And so on. In other words, what constitutes ‘better’ (in the claim that theory X is better than theory Y) depends very much on the kind of philosophy of science that one accepts.
With respect to ‘The heathen…’, I suggest (and partially argue) the following. My theory is better than any other theory in the market place because it can fulfill the demands put across by the different philosophies of sciences. That is to say, the superiority of my theory is not dependent upon the choice of any particular conception of a scientific theory. I indicate this state of affairs by using the words ‘cognitively superior’. If you want to put in Webster’s definition of ‘cognitive’ it means the following: “Balu’s theory is superior to its competitors because it is better ‘based on empirical factual knowledge.'”
In short hand, you could also say that my theory provides knowledge about religion whereas my competitor theories do not. 🙂