This article explains the relationship of supervenience as used in cognitive science and philosophy of mind.

The Short Story of Supervenience

The word ‘supervenience’ has enjoyed a long and tortuous history, and to this day it is easy to find pairs of authors, both of whom are writing about supervenience, but who are also writing about completely different things. A quick and easy way to understand supervenience is to take it as a relationship between two sets (usually sets of properties or propositions), where fixing one set — the supervenience base — fixes the other — the supervening set. A common example, taken from the early history of the word, suggests that moral properties supervene on physical properties. In other words, fixing all the physical properties in the world fixes all the moral properties. Alternatively, it is impossible that a world could be physically identical to the actual world while differing from it morally. If moral properties supervene on physical ones, then whatever moral evaluation applies to a given situation must apply to all physically identical situations. (Certain subtleties intrude according to whether we are concerned with a relationship of local supervenience — requiring equivalence of physical properties only in some local area — or global supervenience — requiring equivalence across the entire world — but these I’ll ignore for the moment.)

Within the context of cognitive science and philosophy of mind, supervenience usually refers to relationships between physical and mental properties of cognizers. For instance, one might consider whether consciousness supervenes on brain state. If it does, then by duplicating a given brain state one necessarily duplicates the consciousness. One might also consider whether consciousness supervenes on something at a higher level, such as functional state, where functional state in turn supervenes on brain state. If it does, then by duplicating the functional state (perhaps in a different medium), one necessarily duplicates the consciousness.

The Longer Story of Supervenience

Unfortunately, relationships of supervenience are not quite this clear-cut. Most of the subtleties come from the details of exactly how fixing one set fixes another — i.e., what sort of logical relationship obtains between them.

And making sense of the logical relationship depends on a few significant distinctions. The first important distinction derives from that between two varieties of meaning, traditionally called sense and reference but now often known as intension and extension. Temporarily over-simplifying, a word or phrase’s sense or intension is that which picks out its reference, or extension. For example, when I write of ‘the Professor who leads my group’, it is the phrase’s sense which allows us to pick out its referent, the actual physical person called Chris Winter. In other words, one evaluates intension to discover extension. Some words or phrases may have intension even while lacking extension. For instance, when I write of ‘the duckbilled platypus who leads my group’, this has a certain meaning (its intension), even though it lacks extension: there is no entity to which it refers, because my group is led not by a duckbilled platypus, but by a human being.

It gets more complicated. ‘Supervenience’ must be broken down into (at least) logical supervenience and metaphysical supervenience. The former is a relationship of a priori necessity, requiring that we take a concept’s intension as that which fixes reference for whatever world is actual. (A priori can be understood as describing things which are purely matters of definition, such as ‘all bachelors are male’; one doesn’t need to know anything about what is in the actual world to know that all bachelors are male.) That is, a concept’s extension is determined by its intension evaluated in the actual world. For instance, there is no possible world physically identical to the actual world in which those things we call ‘cats’ in the actual world are not also cats, with ‘cat’ understood in this-world language. Although there might be other possible worlds in which what we call ‘cats’ should in that world properly be called ‘splats’, this bears not at all on whether that-world splats are this-world cats. Likewise, if it had turned out that the actual world included soft, furry, aloof, cat-like animals with a metabolism based on ammonia rather than water, we might still have called them ‘cats’ (to the extent that our concept of cat does not preclude ammonia-based metabolism). This intension of ‘cat’ is independent of how the actual world turns out and just specifies how to pick out referents according to what we find in the actual world.

On this use of supervenience, facts about cat-hood thus supervene logically on physical facts. Typically (and incorrectly — see below), this is taken also to mean that anyone who knew the a priori intensions of the relevant concepts, those which determine reference in the actual world, could in principle derive all the supervening facts from those in the supervenience base without appealing to any other information.

By contrast, a posteriori necessity grounds ‘metaphysical supervenience’, which features principally in talk about consciousness: some theorists maintain that while physical facts do fix facts about consciousness, the particular way in which they do so is an a posteriori matter. (A posteriori can be understood as describing things which can only be known with the help of the real world, such as ‘some ducks are white’; one must have tested out some real ducks to know whether any are white.) Making sense of metaphysical supervenience depends on taking intensions as specifying how to pick out referents in counterfactual worlds, given actual world reference. (This is the so-called ‘rigid designator’, created by ‘rigidifying’ a concept so that whatever is picked out in the actual world gets picked out in all possible worlds.) It is according to the rigidified version of intension that Kripke (1980) and Putnam (1975a, b) correctly point out water is H2O in all possible worlds. On this intension, water is H2O in all worlds just because it is H2O in the actual world. Usually, metaphysical supervenience of consciousness facts on physical facts is understood to mean that the supervening facts are in principle derivable from the supervenience base provided account is taken of what the relevant concepts pick out in the actual world. The varieties of intension at work in the two sorts of supervenience relation of course need not coincide, and it is of crucial importance that candidate explanations of supervening facts in terms of the supervenience base acquire a very different status according to whether the supervenience relation is based on a priori necessity or a posteriori necessity. The differences between them relate closely to the different meanings sometimes accorded the word ’emergence’. (See the short introductory notes on emergence and levels of description.)

One Last Hitch

As if the subtleties separating different varieties of intension and of supervenience weren’t enough, there’s one last nuance which affects how we understand explanations given in terms of supervenience. This nuance has, as far as I am aware, received no attention in the literature apart from my own Mind Out of Matter.

Setting aside intensional differences, the definition of supervenience in terms of fixing one set of facts by fixing some other set requires only that supervening facts cannot differ, given a fixed supervenience base. It does not require that facts in the supervenience base imply the supervening facts, in the sense that the supervening facts should be derivable from the supervenience base. That implication (in the sense of there being a derivation) need not equal entailment (in the sense of impossibility) should be clear anyway, provided we are not restricted solely to the propositional calculus, but the case of incompleteness provides a helpful example: the set of facts ‘fixed’ by a suitably strong formal system properly contains the set of facts which can be logically derived within that system. (See the introductory notes on completeness.) The facts fixed form a proper superset of the logically derivable facts; alternatively, not all facts fixed by the formal system are theorems of that system. Some of these supervening facts — specifically, those not in the intersection of the supervening set and the derivable set — are, as Greg Chaitin puts it, true for no reason at all. A proposition naming supervening facts which are not derivable has greater information content than the formal system itself. Such a proposition carries additional information over and above what is contained in the formal system itself — yet it still supervenes on the facts which describe the formal system. For specificity, consider a proposition describing with n bits of precision the proportion of possible programs for a particular Turing Machine which halt. The basic facts about how the Turing Machine works fix the truth of such a proposition: no extra magic ingredient determines whether a Turing Machine halts, except the Turing Machine, and it is fully specified by its machine table. Yet the proposition cannot be derived for large n with just that information. (This proportion, which Chaitin calls Omega, is violently noncomputable and cannot be compressed; the only way to prove its value with greater precision than the number of bits in our chosen axioms is to assume what we want to prove.) Thus, establishing even logical supervenience does not automatically guarantee that all supervening facts may be logically derived from the supervenience base.

This article was originally published by on and was last reviewed or updated by Dr Greg Mulhauser on .

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