About Rationally Speaking

Rationally Speaking is a blog maintained by Prof. Massimo Pigliucci, a philosopher at the City University of New York. The blog reflects the Enlightenment figure Marquis de Condorcet's idea of what a public intellectual (yes, we know, that's such a bad word) ought to be: someone who devotes himself to "the tracking down of prejudices in the hiding places where priests, the schools, the government, and all long-established institutions had gathered and protected them." You're welcome. Please notice that the contents of this blog can be reprinted under the standard Creative Commons license.

Monday, October 22, 2012

Essays on emergence, part III

by Massimo Pigliucci

So far in this series we have examined Robert Batterman’s idea that the concept of emergence can be made more precise by the fact that emergent phenomena such as phase transitions can be described by models that include mathematical singularities, as well as Elena Castellani’s analysis of the relationship between effective field theories in physics and emergence. This time we are going to take a look at Paul Humphreys’ “Emergence, not supervenience,” published in Philosophy of Science back in 1997 (64:S337-S345).

The thrust of Humphreys’ paper is that the philosophical concept of supervenience, which is often brought up when there is talk of reductionism vs anti-reductionism, is not sufficient, and that emergence is a much better bet for the anti-reductionistically inclined.

The Stanford Encyclopedia of Philosophy defines supervenience thus: “A set of properties A supervenes upon another set B just in case no two things can differ with respect to A-properties without also differing with respect to their B-properties. In slogan form, ‘there cannot be an A-difference without a B-difference.’” A typical everyday example of supervenience is the relation between the amount of money in my pockets (A-property) and the specific make up of bills and coins I carry (B-property). While I am going to have the same amount of money (say, $20) regardless of the specific combination of coins and bills (say, no coins, 1 $10 bill and 2 $5 bills; or 4 25c coins, 9 $1 bills and 1 $10 bill), it is obvious that the total cannot possibly change unless I change the specific makeup of the coins+bills set (the opposite is not true, as we have just seen: we can change the composition of coins+bills without necessarily changing the total).

Again according to the SEP, “Supervenience is a central notion in analytic philosophy. It has been invoked in almost every corner of the field. For example, it has been claimed that aesthetic, moral, and mental properties supervene upon physical properties. It has also been claimed that modal truths supervene on non-modal ones, and that general truths supervene on particular truths. Further, supervenience has been used to distinguish various kinds of internalism and externalism, and to test claims of reducibility and conceptual analysis.”

Let’s say, for instance, that you think that mental properties supervene on the physical properties of the brain. What that means is that the same mental outcome (say, thought X, or feeling Y) could — in principle — be multiply instantiated, i.e., obtained by way of different brain states. This undermines a simplistic reductionism that would want to proclaim a one-to-one correspondence between physical and mental, but it still means that any change in the latter requires a change in the former, which is perfectly compatible with a physicalist interpretation of mental phenomena.

Humphreys claims that while accounts deploying supervenience often do so with an anti-reductionist aim, supervenience itself is no big foe of reductionism, for two reasons: (i) “If A supervenes upon B, then A is nothing but B’ talk”; and (ii) “if A supervenes upon B, then because A’s existence is necessitated by B’s existence, all that we need in terms of ontology is B.” I think that’s just about right, which explains why I’ve always felt that supervenience is an interesting philosophical concept, but has little to do with the debate about reductionism.

Well, what is supervenience good for, you might say? Humphreys gives the example of aesthetic judgment: “If aesthetic merit supervenes upon just spatial arrangements of color on a surface, and you attribute beauty to the Mona Lisa, you cannot withhold that [same] aesthetic judgement from a perfect forgery of the Leonardo painting.” Supervenience, then, becomes a way to assess consistency in the attribution of concepts, but has nothing interesting to say about ontological relationships, which is where the meat of the reductionism / anti-reductionism debate lies.

So for Humphreys one needs emergence, not just supervenience, to move away from reductionism. Fine, but we are still left with the need for a reasonable articulation of what emergent properties are. The author proposes a list of characteristics of emergence, though not all of them are necessary to identify a given phenomenon as emergent:

1) Novelty: “a previously uninstantiated property comes to have an instance.”
2) Qualitative difference: “emergent properties ... are qualitatively different from the properties from which they emerge.”
3) Absence at lower levels: “an emergent property is one that could not be possessed
at a lower level — it is logically or nomologically [1] impossible for this to occur.”
4) Law difference: “different laws apply to emergent features than to the features from which they emerge.”
5) Interactivity: “emergent properties ... result from an essential interaction between their constituent properties.”
6) Holism: “emergent properties are holistic in the sense of being properties of the entire system
rather than local properties of its constituents.”

Having thus set the stage, Humphreys goes on to consider some candidate examples of emergent properties. Interestingly, his first is none other than quantum entanglement, which provides the physical basis for higher level phenomena like superconductivity and superfluidity. According to Humphreys, quantum entanglement itself satisfies the 5th and 6th criteria (interactivity and holism), while when the phenomenon is considered as an explanation for, say, superconductivity, it minimally satisfies also criteria 1, 2 and 4 (novelty, qualitative difference and law difference).

The article then moves to a discussion of the general point that emergent properties can only manifest themselves in macroscopic systems, because they “enjoy properties that are qualitatively different from those of atoms and molecules, despite the fact that they are composed of the same basic constituents ... [properties] such as phase transitions, dissipative processes, and even biological growth, that do not occur in the atomic world.”

This is important because Humphreys then derives from his analysis a conclusion that is very much like the one Batterman arrived at in his paper, though beginning from a completely different starting point: “emergent properties cannot be possessed by individuals at the lower level because they occur only with [practically] infinite collections of constituents. Some of the most important cases of macroscopic phenomena are phase transitions, such as the transition from liquid to solid.” Hence the theoretical relevance of the mathematical singularities that describe phase transitions, which we have encountered in the first essay of this series.

The point is worth rewording more clearly: the reason mathematical singularities such as infinities pop up in description of emergent phenomena is because emergent phenomena occur when the number of components of a system is very large, effectively approaching infinity. Which in turns explains why only complex systems (of certain types) display emergent phenomena. Neat, no?

I know, I know, you are itching for less theory and more examples. Humphreys obliges, discussing the case of spontaneous ferromagnetism occurring below the Curie temperature. To wit:

“If one takes a ferromagnet whose Hamiltonian is spherically symmetric, then below the Curie temperature the system is magnetized in a particular direction, even though because of the spherically symmetric Hamiltonian, its energy is independent of that specific direction. This divergence between the symmetry exhibited by the overall system and the symmetry exhibited by the laws governing its evolution is an example of spontaneous symmetry breaking. We have here a case where there is a distinctively different law covering the N > infinity system than covers its individual constituents. This is exactly the kind of difference of laws across levels of analysis that we noted earlier as one criterion of a genuinely emergent phenomenon.”

To recap, supervenience — despite the crucial role it plays in many philosophical discussions — is not in fact a way to describe non reducible phenomena, for which task one really needs the more robust concept of emergence, with convincing examples to accompany it. This concept can be articulated in terms of Humphreys’ six criteria, and turns out to approximate Batterman’s approach based on the mathematics of phase transitions.


[1] For something to be nomologically impossible means that if instantiated it would violate a law of nature.


  1. Massimo: I found this (Part 3) to be especially helpful, particularly Humphreys' six-point list of criteria.

    I'm guessing that some folks will still be uncomfortable with the concept of emergence. Personally, I don't see what the problem is - provided that we have ample evidence for phenomena that meet these criteria.

    PS: My own introduction to this topic was Morrowitz's The Emergence of Everything: How the World Became Complex. I found it rewarding, but challenging, even though though it's geared towards a general audience.

    1. Question ... the one-star reviewers on Amazon all indicate they think Morowitz is bringing metaphysics in the back door some way or another? What's your take?

    2. Gadfly: It's been some years since I read Morowitz's book, but my recollection is that it's neither metaphysics-free nor metaphysics-heavy. Rather, it achieved just the right balance for my tastes between science and philosophy. Your mileage may differ, however.

  2. If I understand correctly, supervenience and emergence are entirely consistent with each other? Humphreys is not attacking the validity of supervenience, but rather, arguing for the insufficiency of supervenience to attack reductionism, and the sufficiency of emergence to do the same.

    I think it is possible that multiple conceptions of reductionism are flying around, because what I think of as reductionism is mere supervenience. Thus, if emergence and supervenience are consistent, then emergence and reductionism are consistent.

    1. Yes and no. Supervenience is indeed consistent with emergence, and emergence itself is consistent with a degree of reductionism. But it is not consistent with full fledged "turtles all the way down" type of reductionism.

  3. Supervenience actually sounds like it's useful for little more than Venn diagrams. And, Miller ... Massimo noted that supervenience wasn't "sufficient" for emergence, to follow up further.

  4. 4) Law difference: “different laws apply to emergent features than to the features from which they emerge.”

    Does this require that the laws are inherent to the structure of the universe? Or are you including laws that are not strictly accurate, but remain useful mathematical approximations? (E.g. Kepler's laws.)

    Suppose I created a deterministic particle simulation. If I could coax the particles into forming 'liquids' and 'solids' that held to certain rules that were different than the programming instructions the simulator applied to particles, would that count as emergence? Or would emergence require the simulator to have a separate set of instructions for dealing with 'liquids' and 'solids'?

  5. Fred,

    Good questions, which raise the whole different and interesting question of what is a "law" of nature, other than an empirical approximation / generalization. Remember that none of the authors I discuss argues for a non-naturalistic view of emergence, but it very much depends on what means by "inherent" in the structure of the universe.

    As for particles, individually they cannot undergo phase transitions. Indeed, a major point that emerges (so to speak) from this discussion is that emergent properties arise only in complex systems with very large numbers of particles.

    Finally, simulation: as I mentioned in another context, it depends on what one means by simulation. If the simulation is done by specifying a set of equations, then no, I wouldn't expect emergence, unless the equations were of a type that had the possibility of emergence built in (like those in solid state physics dealing with phase transitions). If simulation means somehow replicating a bunch of individual particles and letting them interact in the way they do in nature, then I suppose we would see emergent properties.

    1. That Menon and Callender paper concludes:

      Phase transitions are an important instance of putatively emergent behavior. Unlike many things claimed emergent by philosophers (e.g., tables and chairs), the alleged emergence of phase transitions stems from both philosophical and scientific arguments. Here we have focused on the case for emergence built from physics. We have found that when one clarifies concepts and digs into the details, with respect to standard textbook statistical mechanics, phase transitions are best thought of as conceptually novel, but not ontologically or explanatorily irreducible. And if one goes past textbook statistical mechanics, then an argument can be made that they're not even conceptually novel. In the case of renormalization group theory, consideration of infinite systems and their singular behavior provides a central theoretical tool, but this is compatible with an explanatory reduction. Phase transitions may be "emergent" in some sense of this protean term, but not in a sense that is incompatible with the reductionist project broadly construed.

      Aside from that, simple cellular automata, such as the Game of Life, are a classic example of complex phenomena emerging from simple rules. The number of interacting cells do not have to be particularly large. Entities such as "gliders" are supervenient on the computational substrate. But most people would agree although these were novel in the sense of surprising, and were largely discovered by trial-and-error experimentation, they are definitely inherent in the underlying structure of the computational universe of the game. Of course, to "see" this, you may have to carry out the equivalent amount of computation that the universe does, which comes back to being determined but unpredictable from inside the system.

    2. David,

      That may well be those authors' considered conclusion, but the authors I have cited reach a different conclusion by examining the same examples. So at the very least there is a debate going on, it's not a slam dunk.

      As for cellular automata, the example is pretty much irrelevant. Nobody is claiming that every complex system displays genuine emergent properties, so demonstrating that one particular example doesn't amounts to a very weak argument against emergence.

    3. "at the very least there is a debate going on...": it looks like a lot of activity at the moment.

      "cellular automata ... pretty much irrelevant": CA are the poster child of tractable emergent phenomena in the complexity literature, and apply to physical systems too eg

      The definition of "weak emergence" used in the complexity literature seems to be along the lines of

      "A macro-state P of S with micro-dynamic D is
      weakly emergent iff P can be derived from D and
      S’s external conditions but only by simulation."

      cited here.

      Statistics measuring this type of emergence for a given system have been proposed.

    4. Track its history to see how it became a table, a state of superfuidity, a black hole, or whatever. In practical work, you might isolate parts and decide what is replaceable and on what bases within a system, but I would avoid calling anything emergent.

    5. David,

      yes, but I'm much more interested in the possibility of strong emergence. The weak variety doesn't really seem to pose particularly interesting philosophical problems...

  6. Just for reader's convenience: you can download Humphrey's document from http://people.virginia.edu/~pwh2a/emergence%20not%20supervenience.doc

  7. A whole is just that, so any discussion of parts as individual or indivisible things is problematic from the outset. Humphrey merely relies on that lockout. The example from supervenience is simplisic in avoiding Humphrey's lockout. Better to say there are 'constiuents' (irreducibles) and they aggregate in various ways. Apes from 80% H and 20% He by logical development of H & He as fundamentals with potential understandable only in retrospect(or a lower level than H & He, if secure). There are no wholes, just irreducibles that aggregate in various ways.


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