Why Does Statistics Have Two Theories

The public image of statistics is changing, and recently the changes have been mostly for the better, as we've all seen. But occasional court cases, a few conspicuous failures, and even appeals to personal feelings suggest that careful thought may be in order. Actually, statistics itself has more than one theory, and these approaches can give contradictory answers, with the discipline largely indifferent. Saying "we are just exploring!" or appealing to mysticism can't really be appropriate, no matter the spin. In this paper for the COPSS 50th Anniversary Volume, I would like to examine three current approaches to central theory. As we will see, if continuity that is present in the model is also required for the methods, then the conflicts and contradictions resolve.