Davidson argues for his identity theory by making the plausible assumption that all mental events causally interact with physical events. He also assumes that wherever there is causal interaction, there is a strict law of nature encompassing the interacting events. But if there were, then the mental would be reducible to the physical, which Davidson denies. It is extensional in the sense that if ' a caused b ' is true, then it remains true regardless of how we describe a and b - so 'The cause of b caused b ' is as good a statement of causation as ' a caused b '. It is not, however, a good causal explanation , and this is where laws come in.
Laws relate events only in so far as the events are described in a certain way.
So an event may instantiate a law under some descriptions but not under others. But they can't instantiate a psychophysical law, since there aren't any - so they must instantiate a physical law. But to instatiate a physical law, the mental events must have a physical description, and to have a physical description is to be a physical event. So all mental events are physical events. Davidson has developed these ideas as part of his theory of radical interpretation.