Humean Supervenience (henceforth HS) is a metaphysical doctrine postulated by David Lewis. According to Lewis, HS is the doctrine that “all the world has is a vast mosaic of particular facts. We have an arrangement of qualities; and nothing more. There is no difference without difference in the arrangement of qualities; and everything else supervenes on that” (Karakostas 1).
Thus, there is a distribution of local, intrinsic, qualitative properties that require more than spatiotemporal point. Spatiotemporal or occupational relations exist between the points to hold between point-objects and space-time, or both. These relations, however, do not supervene on the local, intrinsic, qualitative properties of the related object. Properties of all other things supervene on the distribution of the intrinsic properties at the space-time points. In other words, the world is fragmented into local matters of particular fact and every other thing supervenes upon them in concurrence with the spatiotemporal relations among them (Karakostas 2).
Supervenience acquires ‘dependence – determination’ relationship. Possessing upper-level or supervenient property requires that one must possess some lower-level or subvenient property. This is the dependence aspect. The determination aspect, on the other hand, is that the possession of subvenient property suffices for the possession of supervenient property. In other words, in order to possess a supervenient property, one must possess some subvenient property which suffices for the instantiation of the supervenient property. Therefore, supervenient properties only occur because of the subvenient or underlying properties which are sufficient to establish how the supervenient properties come about. Lewis, thus, postulates that a supervenience thesis is reductionist in a broader perspective.
According to HS, an analogous kind of entailment relation holds for the totality of all facts about the world. All global matters of fact supervene upon a spatiotemporal arrangement of local base facts (Karakostas 3). There are no necessities between and in the particular facts; all the particulars are in spatiotemporal existence, both nomologically and logically, independent of one another.
John Carroll’s Mirror Argument and why it is a putative counterexample to Humean Supervenience
The Mirror Argument asks us to consider two possible worlds, U1 and U2, with each world containing five x-particles, y-field, and a mirror with two settings. In U1, all the x particles have an up spin as they go through the y field. When the mirror’s setting is switched to the other position, the nearest x particle is deflected from the y field. Whichever way, all the particles have an up spin. Carroll supposes that this is a law of U1. In U2, the nearest x particle to the mirror doesn’t have an up spin while going into the y field. Therefore, there is no law of U2 that all the x particles must have an up spin when entering the y field. For the Humean, both worlds are unproblematic so far.
Imagine, however, that the setting of the mirror is changed in both the worlds such that the resulting worlds from U1 and U2 contain 4 x particles in the y fields with up spin, and 1 x particle deflected from the field. From “(SC*) if P is physically possible and Q is a law, then Q would (still) be a law if P were the case” (Roberts 431), it can then be derived that all x particles in the y fields have an up spin, would be a law in the world resulting from U1. From “(SC’) if P is physically possible and Q is not a law, then Q would still not be a law if P were the case” (Roberts 431), it can be derived that this would not be a law in the world resulting from U2. In nonnomic aspects, the resulting worlds are identical even though they differ nomically. This disapproves Humean supervenience, thus a putative counterexample.
For Carroll, HS is a thesis that a complete set of non-nomic features settles all the facts in a given possible world. In other words, no two possible worlds exist where there is an agreement on all non-nomic details when the laws of nature are different. For any possible world, the non-nomic features can be stated without making any reference to the concepts of laws, causation, counterfactuals, or other similar notions that share 'modal character' of laws (Roberts 426).
A response to the Mirror Argument on behalf of the Humean
For Humean supervenience thesis to be maintained, (SC*) or (SC’) must be denied. Carroll believes that the relationship between the laws and counterfactuals makes it possible for these principles to be derived, as captured by the principle “(SC) If P is physically possible and it is a law of nature that if P occurs Q will occur, then if P had occurred Q would have occurred” (Roberts 431).
According to the Humean explanation, a law is a summary of the events that unfold within a given world. Therefore, it doesn’t surprise if the modification of events of a world results in modification of the laws of the world. Based on John Carroll’s mirror argument, changing the mirror’s setting does not change the laws of the two worlds, though it’s physically possible. The resulting worlds go against the Humean supervenience in that they share all non-nomic aspects but have different laws. A non-legal world must therefore be permitted in normal counterfactual reasoning so that Humean supervenience is maintained.
The Mirror Argument crucially depends on two premises: In U1, it is physically possible that the total history is H; and in U2, it is physically possible that the total history is H (Roberts 433). If premise 1 were false, then U1* would not be physically possible. Same applies to premise 2. The argument also requires the notion of the physical possibility in the two premises to be interpreted in a certain manner; intuitive, weak, or strong interpretation. For the intuitive interpretation, P is physically possible in the world W if and only if P’s can be conceived as being the case in W with no offense to the physical intuitions. For the weak interpretation, the possibility is only if P is logically consistent with the laws of nature in W. For the strong interpretation, the possibility is only if there exists a possible world with exactly same laws of nature as W, where P is true. The Mirror Argument uses the strong interpretation while HS employs the weak interpretation.
I think Humean Supervenience is true. Even though the Mirror Argument tries to refute Humean Supervenience, by ruling out any theory of laws by which nomic is Humean supervenient, the argument itself is not sound and cannot be used to establish its own premise on pain of circularity. The argument is therefore unconvincing, or rather, incomplete.
Karakostas, V. Humean Supervenience in the Light of Contemporary Science. Metaphysica (2009) 10: 1-26. Web. December 20, 2012.
Roberts, J. Lewis, Carroll, and seeing through the looking glass. Australasian Journal of Philosophy, 76, 3(1998): 426 – 438. Web. December 20, 2012.