The SEP article on supervenience claims "Just about everyone, even a Cartesian dualist, believes some version of this supervenience claim [that the mental nomologically supervenes on the physical]." and quotes Donald Davidson:
[M]ental characteristics are in some sense dependent, or supervenient, on physical characteristics. Such supervenience might be taken to mean that there cannot be two events alike in all physical respects but differing in some mental respect, or that an object cannot alter in some mental respect without altering in some physical respect
But some dualists, for example David Chalmers, claim that the existence of the mental cannot be predicted from the physical:
If all we knew about were the facts of physics, and even the facts about dynamics and information processing in complex systems, there would be no compelling reason to postulate the existence of conscious experience.
But if that is so, then we can think of a relation between physical and mental in which the mental does not nomologically supervene on the physical.
Suppose it makes sense to talk of the moment a human becomes conscious for the first time; we can suppose that moment is brought about by a particular physical condition which is (physically) sufficient for consciousness, but that once this condition is met, the first appearance of consciousness is a further spontaneous event, for example like in particle decay.
Out of my sleeve I can think of two further examples: first, you can think of the physical condition as a sort of adequate container that the universe then spontaneously fills with consciousness; or you can think of the interesting Norton's dome paradox in which an abstract ball perfectly balanced on the apex of a perfect dome, suddenly and indeterministically rolls down the dome - http://www.pitt.edu/~jdnorton/Goodies/Dome/
If so, then we can have an object that alters "in some mental respect without altering in some physical respect" in some appropriate sense of not altering the physical state (probably relative to other possible worlds, since in this world the physical is in flux).
We can further think of this happening every morning when we wake up from dreamless sleep; maybe what happens is that the brain enters a state required for consciousness, but consciousness appears at its leisure, one microsecond later, one minute later, once in an aeon maybe a year later, and only then that person proceeds to wake up.
Has anyone made a similar argument?
If so, how is it called?
Can you refer me to it?