3. Two Types of Fundamentality

Paul Humphreys, Emergence (OUP, 2016)

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.[1] 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.

[1] 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.


  1. A complete specification of the behaviour of the black and white pieces must include their behaviour in any situation – including at the target boundary. So the creation of the reds and blues (and their complete behaviour description) must be part of that. So it appears that the entire history does supervene on a full account of the “fundamental” laws.

  2. Paul Humphreys

    Thanks for the comment. That’s an important point and here’s a response. Suppose that we include at the outset a specification of what a white particle will do when interacting with a red particle (for example that in certain configurations it will be annihilated). This can be a dispositional property of white particles. The properties of white particles and black particles will not fully fix what red particles can do; for example those properties say nothing about what red particles can do in isolation, such as move backward. I agree that a complete specification of the behavior of black and white particles must include their behavior in any situation, but the behavior of red and blue particles is the behavior of a different type of particle. There is a way to get what you want, and that’s to dispositionally include all the properties of every color of particle at the initial stage. But the behavior of red and blue particles will not then supervene on just the manifest states of the black and white particles but on something else, the initial dispositions. I think that violates what the logical supervenience advocates are doing. It also introduces the origins of the universe problem along with it, although since transformational emergence also has that problem to deal with, it’s not a problem peculiar to the view I was arguing against. I do think your comment brings into the open the fact that there is a lot built into the laws that govern real physical entities that probably cannot be captured purely behaviorally.

  3. Eric Thomson

    Thanks a lot for posting this helpful summary of your book. I had a couple of questions.

    1. Parsing emergence into synchronic and diachronic forms seems useful, though I may be missing the surprise here. Won’t the reaction be: “Yes of course if you introduce new entities (blue particles) to the supervenience base then the behavior of the system no longer depends solely on the previous supervenience base (black and white particles)?” And when it comes to Chalmers, wouldn’t he just say he was referring to synchronic emergence? E.g., how is it that my brain, right now (or in this ten-second time window), is conscious? Ignore all questions of etiology, and just focus all of those pesky ‘Hard Problem’ questions on that.

    2. I’m concerned that these examples with the generation of new particles don’t really count as emergence in any traditional sense of the term (I think this gets at Alan’s concern).

    For instance, say there are some quantum vacuum fluctuations that makes gold particles spring into existence every ten seconds on average (with noise: make it Poisson). The white and black particle behavior depends on the gold particle behavior. Would the random introduction of the first gold particle in the system count as diachronic emergence? If so, I’m a little confused about what is really surprising or what it buys you to stretch the term ’emergence’ this far, when most traditional approaches would (on the surface anyway) absorb this without much concern. They would just say you just needed to expand your supervenience base to include the gold particle-generating mechanism, and the dynamics/interactions of the gold particles. Then there is nothing ’emergent’ or surprising there.

    Or maybe I’m begging the question by using the synchronic view of emergence, and your point is that the introduction of fundamentally new types of particles/dynamics into a system is itself a form of emergence, and this is a reasonable way to talk. Even if that introduction of new particles/entities is law-governed, it would be weird to insist that we not describe it as emergence. Am I getting close to your position?

  4. Paul Humphreys

    Thanks for your questions Eric. Addressing 1 first, let me try to clarify what the point is regarding synchronic accounts of the type I discussed in post 3. That position is presented in terms of global supervenience, which includes the entire temporal development of the world in its supervenience base. In so doing, the only way of addressing diachronic emergence is by segmenting the entire four dimensional supervenience base into temporal regions. But in so doing, we no longer have genuine global supervenience, because the supervenience base for the red particles, for example, does not involve the period up until just before the first change from a black to a red particle (and if all of the red particles eventually are annihilated to form green particles, it will also not involve the period after the last red particle is annihilated). The global supervenience advocates could just say `Well, we’re throwing everything in just to be on the safe side”, but in so doing, they are treating qualitatively different temporal periods with a single uniform base.
    Re Chalmers, yes, the argument was presented in purely synchronic form, but in his later paper `Strong and Weak Emergence’, there are three distinctive features. The first is that strong emergence is characterized in terms of deducibility. From some of his other papers, I think this is not syntactic deducibility, but whatever it is, it is not an ontological relation. The second is that in the later paper, consciousness is still the only example of strong emergence, which is clearly at odds with what transformational emergence is concluding. And the third is that he is still puting things in terms of supervenience and it all looks synchronic.

    Re question 2: This is an important worry and one that I didn’t have space to address in the blog. (It’s covered in the book). Part of the answer is given at the end of entry 4, which of course you didn’t have access to yesterday. It is very important that `emergence’ is not logically a mondadic predicate but a binary relation: B emerges from A. I’d need to have more details of your quantum fluctuation example, but one thing that does not count as emergent are spontaneous events, those that are not caused or otherwise brought about by something else. Let’s suppose the quantum vacuum is something, rather than nothing. Then under transformational emergence, the new entity has to be a result of transformations on the previous entity or entities. Otherwise, it’s probably just good old fashioned causation. It might be that what counts as a transformation has to be better clarified, but I think we have a pretty good grip on many cases via changes in essential properties. More generally, there is an extended discussion in the book of criteria for emergence, that tries to connect these diachronic accounts with recognizable philosophical traditions. But what’s interesting to me is how many other philosophical areas need rethinking once one goes diachronic, such as whether the laws of nature have changed over time, something that Peirce considered, for example.
    Anyway, hope this was helpful

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