Private Language and Property Dualism

Physicalism says that all the facts, including all the
phenomenal facts, are metaphysically necessitated by the
physical facts. If physicalism is true at the actual world,
there is no metaphysically possible world, which is physically
identical to the actual world, but different in some
other respect. Note that "physicalism" is defined in terms of
metaphysical necessity, because everybody should endorse
law-like correlations between the mental and the physical,
and so can accept supervenience with nomological
necessity.