In philosophy, supervenience refers to a relation between sets of properties or sets of facts. X is said to supervene on Y if and only if some difference in Y is necessary for any difference in X to be possible. Examples of supervenience, in which case the truth values of some propositions cannot vary unless the truth values of some other propositions vary, include:
Whether there is a table in the living room supervenes on the positions of molecules in the living room. The truth value of (A) supervenes on the truth value of its negation, (¬A), and vice versa. Supervenience is of interest to philosophers because it differs from other nearby relations, for example entailment. Some philosophers believe it possible for some A to supervene on some B without being entailed by B. In such cases it may seem puzzling why A should supervene on B and equivalently why changes in A should require changes in B. Two important applications of supervenience involve cases like this. One of these is the supervenience of mental properties (like the sensation of pain) on physical properties (like the firing of 'pain neurons'). A second is the supervenience of normative facts (facts about how things ought to be) on natural facts (facts about how things are). The possibility of "supervenience without entailment" or "supervenience without reduction" is contested territory among philosophers.
History Supervenience, which means literally "coming or occurring as something novel, additional, or unexpected", from "super," meaning on, above, or additional, and "venire," meaning to come in Latin, shows occurrences in the Oxford English Dictionary dating back to 1844. Its systematic use in philosophy is considered to have begun in early 20th-century meta-ethics and emergentism. As G.E. Moore wrote in 1922, "if a given thing possesses any kind of intrinsic value in a certain degree, then... anything exactly like it, must, under all circumstances, possess it in exactly the same degree." This usage also carried over into the work of R. M. Hare. In the 1970s, Donald Davidson was the first to use the term to describe a broadly physicalist (and non-reductive) approach to the philosophy of mind, called anomalous monism. As he said in 1970, "supervenience might be taken to mean that there cannot be two events alike in all physical respects but differing in some mental respects, or that an object cannot alter in some mental respects without altering in some physical respects." In subsequent years Terence ("Terry") Horgan, David Lewis, and especially Jaegwon Kim formalized the concept and began applying it to many issues in the philosophy of mind. This raised numerous questions about how various formulations relate to one another, how adequate the formulation is to various philosophical tasks (in particular, the task of formulating physicalism), and whether it avoids or entails reductionism.
Definitions In the contemporary literature, there are two primary (and non-equivalent) formulations of supervenience (for both definitions let A and B be sets of properties). (1) A-properties supervene on B-properties if and only if all things that are B-indiscernible are A-indiscernible. Formally:
∀ x ∀ y ( ∀ X ∈ B ( X x ↔ X y ) → ∀ Y ∈ A ( Y x ↔ Y y ) ) {\displaystyle \forall x\forall y(\forall X_{\in B}(Xx\leftrightarrow Xy)\rightarrow \forall Y_{\in A}(Yx\leftrightarrow Yy))}
(2) A-properties supervene on B-properties if and only if anything that has an A-property has some B-property such that anything that has that B-property also has that A-property. Formally:
∀ x ∀ X ∈ A ( X x → ∃ Y ∈ B ( Y x ∧ ∀ y ( Y y → X y ) ) ) {\displaystyle \forall x\forall X_{\in A}(Xx\rightarrow \exists Y_{\in B}(Yx\land \forall y(Yy\rightarrow Xy)))}
For example, if one lets A be a set of mental properties, lets B be a set of physical properties, and chooses a domain of discourse consisting of persons, then (1) says that any two persons who are physically indiscernible are mentally indiscernible, and (2) says that any person who has a mental property has some physical property such that any person with that physical property has that mental property. Some points of clarification: first, the definitions above involve quantification over properties and hence higher-order logic. Second, in (1), expressions of the form ( ∀ X ( X x ↔ X y ) ) {\displaystyle (\forall X(Xx\leftrightarrow Xy))} capture the concept of sharing all properties, or being indiscernible with respect to a set of properties. Thus, (1) can be understood more intuitively as the claim that all objects that are indiscernible with respect to a base set of properties are indiscernible with respect to a supervenient set of properties, or, as it is also sometimes said, that B-twins are A-twins. Finally, supervenience claims typically involve some modal force, however, the way that modal force is specified depends on which more specific variety of supervenience one decides upon (see below). (1) and (2) are sometimes called "schemata" because they do not correspond to actual supervenience relations until the sets of properties A and B, the domain of entities to which those properties apply, and a modal force have been specified. For modal forms of supervenience, the modal strength of the relation is usually taken to be a parameter (that is, the possible worlds appealed to may be physically possible, logically possible, etc.). Also, note that in the early literature properties were not always central, and there remain some who prefer to frame the relation in terms of predicates, facts, or entities instead, for example.
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