A quick note on “supervenience”

As a simple example of so-called “supervenience”, consider a container of gas at a given temperature. There are infinitely many possible molecular states for any given temperature, and statistically they are bound to differ. The one respect in which they will not differ is in their mean kinetic energy. It sounds strange to say that the property of the gas being at that temperature “supervenes” on the property of its molecules being in this or that state. I would call it downright misleading inasmuch as it suggests that phenomenological thermodynamics describes a different “realm” from that described by statistical mechanics.

In fact, phenomenological thermodynamics and statistical mechanics are just different theories, one of which reduces the other. The fact that they are actually inconsistent with one another is a stark reminder of the difference between them. Yet this remains a classic case of successful inter-theoretic reduction. Statistical mechanics is capable of mimicking phenomenological thermodynamics well enough to recreate Boyle’s Law and other laws of thermodynamics in statistical form. A part of statistical mechanics has the same taxonomy as phenomenological thermodynamics – a taxonomy represented by the tick marks on a thermometer. Rather than saying one property “supervenes” on another property – as if there were “levels of reality” – we should say that the taxonomic classes of two theories are identical. The smoothness of the inter-theoretic reduction between the theories entitles us to make such identity claims.

I use this example because it is not particularly mysterious. When we start talking about the “supervenience” of the mental on the physical, the (traditional, dualist) suggestion that there are two different “realms” is often overpowering.

3 thoughts on “A quick note on “supervenience”

  1. Supervenience is a technical notion. There is no reason for it to “sound strange,” be “downright misleading,” or have “overpowering” suggestions, if the definition is correctly understood.

    Let A and B be non-empty sets of properties. A supervenes on B if and only if, necessarily, for all x, if x has some property F in A, then for some property G in B such that x has G and for all y, if y is G, then y if F. That definition expresses the relationship of supervenience: two things cannot differ in their A-properties without also differing in their B-properties.

    From this definition, you can work out that supervenience is reflexive and transitive, but not always symmetric. You can also show this is a different relationship between properties than reduction, at least if reduction is taken to mean either entailment or identity. Supervenience refers to a specific relationship, logically distinct from entailment, identity, and reduction, between different sets of properties.

    In classical thermodynamics, the temperature of a gas supervenes upon its molecular momentum distribution. If two gases are at different temperatures, then they will have different molecular momentum distributions. In general, if two systems are in distinct macroscopic, thermodynamic states, then they must be in different microscopic, mechanical states. Macroscopic states supervene upon microscopic ones — no problem.

    In fact, classically, the temperature of a gas is directly proportional to the average molecular kinetic energy — it’s given directly by the second moment of the molecular momentum distribution. However, in quantum-mechanical systems, this will not be true in general.

  2. I’m OK with the sets-and-relations aspect of that, and thanks for clarifying it. But the way that conceptual apparatus is applied still “sounds strange” to me. We don’t need the concept of supervenience to understand how temperature is identical with mean molecular kinetic energy. We need the concept of inter-theoretic reduction, which I don’t understand as either entailment or identity. And the concept of supervenience doesn’t go very far to help us to understand how mental states are identical with physical states of the brain. Indeed it may suggest that they are type-type identical, which I think is just plain wrong.

    First, talk of “sets of properties” seems to presuppose that properties are a sort of entity which could be counted or regarded as identical. But imagine an object whose surface has a colour gradient applied to it. How many individual colours does it have? Which areas of its surface are so similar that they can be regarded as having “the same colour”? I don’t think we can treat properties as if they were entities in this way.

    Second, the concept of supervenience is typically applied to “the supervenience of the mental on the physical”. But it seems to me that many or most mental states – the ones that have “content” – do not have that content as a genuine (mental) property at all, let alone as a property that works like an entity in its own right. Like other forms of “meaning”, mental content is assigned through interpretation, and as such it depends on a larger context. To take a simple example, take the word ‘rot’, which means one thing in English but something else in German. Is “what it means” a property of that word? If it is a genuine property at all, it looks to me more like a property of the larger linguistic context in which the word is used than of the word considered in isolation. In which case, does it help to think of it as a property at all?

    Finally, although you deny that supervenience is reduction, it evidently involves higher and lower levels. It seems to me that some sort of reduction – or some sort of failure of reduction – is implicit in this sort of discussion. Whenever I come across the word ‘reduction’, I always ask: What is being reduced to what? If I take my bicycle apart, or imagine it as the mereological sum of its parts, then I am reducing a thing to smaller constituent things. On the other hand, in inter-theoretic reduction, one theory reduces another theory. I can make sense of that sort of reduction as well, and as I said above it isn’t simple entailment or identity. Nor is it the same as the reduction of a thing to smaller constituent things. I must confess I’m still pretty much in the dark when it comes to the reduction of one property or type of property to some other properties or types thereof.

    But I do appreciate your trying! Thanks!

  3. There is a set of interesting issues that have been raised here, so I think it is worth pressing the point a bit further. The main thing I wanted to argue was that there is a self-consistent and coherent notion of supervenience of properties: to wit, two things cannot differ in their A-properties without also differing in their B-properties. Whether that notion is illuminating or important in some particular application — philosophy of mind being only one — is a separate question. That is also a separate question from whether it is true that one set of properties supervenes upon another set of properties apart from whether it is in some sense illuminating.

    It is clear that we can talk about the identity of properties, quantify over them, count them, and so on: this is precisely what is formalized in second-order logics. For example, refractive index, viscosity, and density are distinct (i.e. non-identical) properties. There is a property that copper wire has in common with silver wire, namely electrical conductivity. It’s of course possible to imagine cases where the identity conditions of properties are unclear, but one can do this with physical objects, too. Properties, like individuals, are sometimes only vaguely defined — no problem.

    Reduction is a stronger relationship between sets of properties than supervience: a set of properties A reduces to set of properties B if and only if every for every property P in A, there is some subset B’ of B, such that the property P is identical to some “combination” of the elements of B’. For example, if we let A = {P1} and B = {P2, P3}, then A reduces to B if it turns out that P1 = P2-&-P3. The “reduction” of real number algebra to set theory is a non-trivial example. The real numbers and their properties and relations can be defined in terms of sets and membership.

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