Supervenience is a form of strong emergence characterized by independence in interdependence: a system A is causal independent from a system B, and yet physically embedded in it. To say that A supervenes on B means that B implements A: there can be no change in A without a change in B. In this sense, implementation is the opposite of supervenience. If a system A is embedded in and implemented by a system B, it is usually not possible to say who chances in system B affect system A. The system A can be unaffected, or it can stop to work at all. They are causal independent of each other. And yet there cannot be a difference in the system A without difference in the underlying system B, because the system A is embedded, realized and implemented by system B.
In a more formal way, supervenience is a kind of dependency relationship, typically held to obtain between sets of properties. A set of properties A is supervenient on a set of properties B, if and only if any two objects x and y which share all properties in B (are "B-indiscernible") must also share all properties in A.
Supervenience is related to trancendence, the state of being or existence above and beyond the limits of a system. It can be considered as a first step towards trancendence: if a system A which supervenes B is embedded and implemented in a system C, it has transcended B, because it exists above and beyond the limits of system B.
A common example is the mind (system A) which supervenes on the brain (system B): any change in one's mental state implies that there has been some kind of change in one's brain state. Another example is a virtual machine which runs on a host computer. A virtual machine is a software implementation of a machine (computer) that executes programs like a real machine. A program which is executed on the virtual machine is independent from the hardware of the host machine, and yet it is executed by it. The commom examples are:
- biological properties supervene on physical properties
- mental states supervene on neurophysiological states
- software supervenes on hardware
- a virtual machine supervenes on a a real computer