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.