In philosophy, supervenience is arguably defined as a dependency relation between 'higher-level' (e.g. mental) and 'lower-level' (e.g. physical) properties.
Informally, a group of properties X supervenes on (alternatively, is supervenient on) a group of properties Y exactly when the X-group properties are determined by the Y-group properties, where "determined by" is taken non-specifically.
Formally, X-group properties supervene on Y-group properties if and only if either of the following holds for all objects a and b:
(All of these formulations are logically equivalent, so if one of them holds, all of them do.)
An alternative claim, advanced especially by John Haugeland, is the claim of "weak supervenience" or, at its weakest, "global supervenience". To claim that mental properties globally supervene on physical properties is to claim, merely, that a change between two possible worlds with respect to their instantiated mental properties requires some change in the physical properties instantiated in at least one of those two worlds. Importantly, it does not claim that the mental properties of an individual person supervene only on that person's physical state.
The latter, weaker thesis, is particularly important in the light of direct reference theories, and semantic externalism with regard to the content both of words and (more relevant to our concerns here) of thoughts. Imagine two physically identical people, one of them looking at a dog and the other having a dog-image projected onto his retinae. It might be reasonable to say that the former is in the mental state of perceiving a dog, whereas the latter is not and merely (falsely) believes that he is.
There is also discussion amongst philosophers about mental supervenience and our experience of duration. If all mental properties supervene only upon some physical properties at durationless moments, then it may seem difficult to explain our experience of duration. The philosophical belief that mental and physical events exist at a series of durationless moments that lie between the physical past and the physical future is known as presentism, and is a form of belief in Galilean relativity.
These computer examples exemplify a more general principle: we will find supervenience wherever a message is conveyed by a representational medium. When we see a letter 'a' in a page of print, for example, the meaning "latin lowercase a" supervenes on the geometry of the boundary of the printed glyph, which in turn supervenes on the ink deposition on the paper.
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"Supervenience".
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