Today’s entry addresses a type of argument that will be familiar to most of you, the argument that all higher level natural facts in our world logically supervene on the fundamental physical facts. Consider a very simple world, which we can call Checkers World. It behaves exactly like a game of checkers, except that there are laws of nature that apply to the fundamentalS particles rather than the functionally defined rules that govern games. Those fundamentalS particles come in two kinds, black and white, and in the early stages of this universe, the laws specify that the particles always move away diagonally from their initial position one spatial cell at a time. When a black particle is diagonally adjacent in the forward direction to a white particle, it moves to the cell immediately past the white particle on the diagonal and the white particle is annihilated. Similarly, mutatis mutandis, for white particles. These laws apply only to black and white particles which initially are the only entities in Checkers World.
Now consider the entire temporal sequence of system states in Checkers World. The first N states consist in various spatial rearrangements of the black and white particles, with occasional annihilations. Then at time-step N + 1, a new type of particle, a blue particle or a red particle, is created when a white or a black particle, respectively, reaches a square on the boundary of the world opposite to where it started. Blue and red particles are not composed of two or more fundamentalS particles; they too are fundamentalS. They behave differently from how the black and white particles behave. They can move forwards or backwards and, as in a standard checkers game, blue particles can annihilate both black and red particles and red particles can annihilate both white and blue particles.
How does this simple world relate to emergence? From an inferential perspective, it is not possible to predict, even from a full knowledge of the fundamental laws governing the black and the white particles and their positions up to N, what the states of the world will be after N. The laws covering the black and white particles determine that a black particle will transform into a red particle when it reaches the lower boundary, and that a white particle will transform into a blue particle when it reaches the upper boundary, but those laws are specific to the domain of the black and white particles. All of the original laws governing the black and white particles continue to operate when blue and red particles appear, but those laws do not specify how the red and blue particles behave. To gain that knowledge, experiment and observation are required after time point N. The blue and red particles do place constraints on the black and white particles that were not present before the emergence of the former, but the laws governing the red and blue particles operate alongside the laws governing the black and white particles and are consistent with them.
Now let us assume that in Checkers World, at some time N* + 1, all the particles are blue or red. At that point, neither red nor blue particles synchronically depend on the fundamentalD facts of the world, those facts that were present at the origins of Checkers World. They do not synchronically depend on the properties of any black or white particles, because there are none, and the laws that cover blue and red particles are not determined by the laws governing the black and white particles or by the particular black and white histories up to N*. More strongly, the properties of the Checkers World at N* + 1 and subsequent times do not globally supervene on the microphysical facts about white and black particles alone. The blue and red particles are new types of particles that are not composed of elementary particles. They behave differently from the black and white particles C they can move backwards, for example. The laws governing the behavior of the blue and red particles do supervene on the complete set of states of the system, including the states of the blue and red particles themselves, but they do not supervene on the states of the original black and white particles and their laws up to time N*, nor do they globally supervene on the history of the states of the original particles alone.
An appeal to global supervenience, in allowing the entire history of the world to be used as the supervenience base, erases the important distinction between coming to know the laws that govern emergent entities only through induction on their behavior after they have emerged, and knowing it by deduction prior to the appearance of those entities. Although I have put the point epistemically, it can also be made ontologically: the regularities that on a Humean view constitute the laws governing the emergent entities appear only subsequent to the regularities exhibited by the fundamentalD entities. Lumping the two together within a global supervenience formulation, or through an appeal to limit science, erases a crucial distinction upon which diachronic emergence rests.
Of course, it could be said that the “physics” of this toy world will simply expand to include red, blue, green, and brown particles, and so on. Fair enough, but then the ontology of this world no longer consists in original physicalism alone; it also includes new domains that develop over time, and the facts and laws about these new domains will not be fixed by the original facts. So, the claim that everything logically supervenes on the fundamentally physical depends on the assumption that the dynamics of the world do not produce new fundamentalS but nonfundamentalD entities at some point in the history of the world. But, in fact, we saw yesterday that such entities do exist in our world and so these conclusions about Checkers World can be applied to the world we inhabit.
Tomorrow’s final essay will draw some overall conclusions suggested by the first three entries.
 The original argument to which I am responding is in Chapter 2 of David Chalmers’ The Conscious Mind. Due to space limitations, I cannot give full justice to Chalmers’ ingenious argument here; for full details see section 6.3 of my Emergence book. The point of the counterargument given here is to highlight what is missing when we omit diachronic considerations.