An important part of the mind–brain problem arises because consciousness seems inherently resistant to scientific explanation. The solution to this dilemma is to recognize, first, that scientific explanation can only render comprehensible a selected aspect of what there is, and second, that there is a mode of explanation, the personalistic, different from, irreducible to, but as viable as, scientific explanation, in terms of which consciousness can be understood. The problem of explaining why experiential or mental aspects of brain processes or things should be correlated with certain physical processes or things is a non-problem because there is no kind of explanation possible in terms of which an explanation could be couched. A physical theory, amplified to include the experiential, might be predictive but would, necessarily, cease to be explanatory; and an amplified personalistic explanation could not succeed either. There is, in short, an explanation as to why there cannot be an explanation of correlations between physical and mental aspects of processes going on inside our heads. Despite this, there are important, as yet unsolved but solvable problems of knowledge and understanding concerning such correlations. The central serious task for research is to discover how the two explanatory accounts of what goes on inside our heads, physical and personal, are inter-related.