Full Idea
If the mental supervenes on the physical, then whenever a physical cause brings about some effect, a mental cause comes along for the ride.
Gist of Idea
If mental supervenes on the physical, then every physical cause will be accompanied by a mental one
Source
Tim Crane (Elements of Mind [2001], 2.17)
Book Reference
Crane,Tim: 'Elements of Mind' [OUP 2001], p.61
A Reaction
This is why supervenience seems to imply epiphenomenalism. The very concept of supervenience is dubious.