Among many different views about mind-body relations, Anomalous Monism proposed by D. Davidson has been discussed recently by many philosophers. Through the discussions, two problems, which are characterized by the tangled struggle between naturalism and anti-naturalism, appeared to be important to consider the causal connection between mental concepts and physical properties; one is the problem of externalism, the other the problem of the ontological reduction of the mental to the physical. Externalism is thought as a sort of the mixture of naturalism and anti-naturalism and I defend some of its naturalist proposals. However, at the same time we are led to the antinaturalistic conclusion that we can not realize mental events without their mental contents. Then, helped by the results of corresponding biological research, especially the theory of evolution, emergence, supervenience, realization, reduction and their relations are considered. What I want to show is that emergence and realizability are incompatible. If this conclusion is true, there is no way to maintain the physical status of mental property. That means mental properties are causally inertia. In order to save this situation, I propose two types of interpretations, one a narrow and the other a broad type interpretation. According to one of the broad type interpretations, which are naturalistic, we can think that mental properties are causally effective to physical properties, just as phenotypes of biological organisms are causally related to their genotypes through natural selection.