Supervenience as a concept in philosophy was first introduced as a description of properties in a complex system that supervene on the lower-level (called "base" or subvenient) properties of the system's components. For example, the laws and properties of chemistry are consistent with, but supervenient on, the laws of physics.

More specifically, the properties of molecules supervene on atoms, the properties of biological cells supervene on molecules, plants and animal supervene on cells, etc. This view of supervenience was held by the "British emergentists," - C. Lloyd Morgan, Samuel Alexander, and C.D. Broad.

This is not to claim that the upper level emergents can be completely explained by and are reducible to the subvenient or "base" properties.

Reductionists are those who claim that causal laws of nature in the base level must causally determine the laws of the supervenient or emergent level. These thinkers usually have a highly simplistic, materialistic, and deterministic view of the most fundamental laws of nature, namely the laws of classical physics.

For example, Jaegwon Kim, the leading critic of supervenience as a non-reductive physicalism that explains mental causation, says:

The most fundamental tenet of physicalism concerns the ontology of the world. It claims that the content of the world is wholly exhausted by matter. Material things are all the things that there are; there is nothing inside the spacetime world that isn't material, and of course there is nothing outside it either. The spacetime world is the whole world, and material things, bits of matter and complex structures made up of bits of matter, are its only inhabitants.

(Physicalism, Or Something Near Enough. Princeton University Press (2005), p.150)

Donald Davidson gave the term supervenience a specific philosophical meaning within analytic philosophy in his 1970 essay "Mental Events."

In order to allow mental events to cause physical events, yet not be reducible to them, Davidson developed the following set of arguments.

1. "there cannot be two events alike in all physical respects, but differing in mental respects"
2. "at least some mental events interact causally with physical events"
3. "where there is causality, there must be a law: events related as cause and effect fall under strict deterministic laws."
4. "there are no strict deterministic laws on the basis of which mental events can be predicted and explained."

This last idea Davidson described as mental events being "anomalous." He viewed his work as extending that of Immanuel Kant on reconciling (eliminating the anomalous contradiction between) freedom and necessity. Davidson's rejection of strict deterministic laws for mental events is consistent with two-stage models of free will.

Supervenience is seen as the last hope for a nonreductive physicalism, which does not reduce the mental to the physical, the psychological to the neurophysiological. Davidson set two requirements:

1. a domain can be supervenient on another without being reducible to it (non reduction)
2. if a domain supervenes, it must be dependent on and be determined by the subvenient domain (dependence)

It is hard to see how the mind, if causally determined by the subvenient brain, is not therefore reducible to it. So we might assume that Davidson's point 2 implies a kind of "one-way causality," with mental causing physical, but not vice versa.

In his 1989 presidential address to the APA, Kim formulated the idea of "global supervenience" in terms of multiple possible worlds.

"Worlds that are indiscernible in all physical events are indiscernible in all mental events."

("The Myth of Nonreductive Physicalism," in Proceedings of the American Philosophical Association. Princeton University Press (1989), p.150)