Projective Explanation: How Theories Explain Empirical Data in Spite of Theory-Data Incommensurability

In scientific explanations, the explanans theory is sometimes incommensurable with the explanandum empirical data. How is this possible, especially when the explanation is deductive in nature? This paper attempts to solve the puzzle without relying on any particular theory of reference. For us, it is rather obvious that the geometric idea of projection plays a key role in Kepler's explanation of Tycho Brahe's empirical data. We discover that a similar mechanism operates in theoretic explanations in general. In short, all theoretic explanations are "projective" explanations. If so, there should be no logical reason why explanans theories cannot be incommensurable with explanandum data. For illustration, we analyse Einstein's explanation of the results of the Michelson-Morley experiment in some detail.