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Chapter 36

Emergence

Paul Humphreys

Modern interest in emergence is usually considered to begin with John Stuart Mill’s discussion of the difference between homopathic and heteropathic laws in his monu-mental work A System of Logic (Mill 1843).1 The publication of this work was followed by an extended period of interest in the topic involving the British Emergentist School, the French emergentists, and some American philosophers. Prominent members of the British group, with representative publications, were G. H. Lewes (1875), Samuel Alexander (1920), C. Lloyd Morgan (1923), and C. D. Broad (1925); of the French group, Henri Bergson (1907) and Claud Bernard; and of the American group William James, Arthur Lovejoy, Stephen Pepper (1926), and Roy Wood Sellars.2 After the 1930s, interest in emergence declined precipitously, and it was widely regarded as a failed research pro-gram, one that was even intellectually disreputable. In recent years, the status of claims about emergent phenomena has changed. The failure to carry through reductionist pro-grams in various areas of science, the appearance of plausible candidates for emergence within complex systems theory and condensed matter physics, what seems to be an ine-liminable holistic aspect to certain quantum systems that exist at or near the fundamen-tal level, and the invention of computational tools to investigate model- based claims of emergence have all led to a revival of interest in the topic.

The literature on emergence being vast, some restrictions on the scope of this chapter are necessary. Contemporary philosophical research on emergence tends to fall into two

AQ: Please note that this author name is Paul Humphreys in TOC and Contributor list. So we have deleted W. in this occurrence. Is it ok.

1 As usual, when assessing genesis claims, one can find earlier origins. William Uzgalis has noted (2009) that the English materialist Anthony Collins argued in the period 1706– 08 that there are real emergent properties in the world.

2 A standard, although partial, history of the British emergentist movement can be found in McLaughlin (1992), and a complementary treatment is Stephan (1992). A more diachronically oriented history is Blitz (1992). A comprehensive account of the French tradition in emergence, less discussed in the Anglophone world, can be found in Fagot- Largeault (2002) and of the influence of Claude Bernard on G. H. Lewes in Malaterre (2007). Works by later American philosophers are cited in the references for this chapter. Some relations between contemporary accounts of emergence and an ancient Indian tradition are presented in Ganeri (2011). Thanks to Olivier Sartenaer for some of these references.

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camps, between which there is a widening gap. The first is motivated by scientific inter-ests and is open to the possibility of emergence occurring within physics, chemistry, biology, or other sciences. The second is primarily driven by problems that arise within metaphysics and the philosophy of mind and, for better or for worse, generally lumps all of the nonintentional sciences under the generic category of the physical. In committing itself to this generous form of physicalism, the second camp turns its back on cases of emergence that occur within the natural sciences, focusing almost exclusively on mental phenomena. This is crippling to an understanding of emergence in general, and so this chapter will mostly be concerned with the first research program, although some atten-tion will need to be paid at various points to the second. The question of whether space and time are emergent features of the universe will not be covered.3

1 Methodological Considerations

Formulating a unified theory of emergence or providing a concise definition of the con-cept of emergence is not a feasible project at the current time. The term “emergent” is used in too wide a variety of ways to be able to impose a common framework on the area, and some of those different senses reflect essentially different concepts of emer-gence, some ontological, some epistemological, and some conceptual. There is another, methodological, reason to be skeptical of any claim to have a unified account of emer-gence. Compare the situations of causation and emergence. Although there are different theories of causation, and a now widely held view that there is more than one concept of causation, each of those theories can be tested against a core set of examples that are widely agreed to be cases of causation. There does not at present exist an analogous set of core examples of emergence upon which there is general agreement.

As an example of this disagreement, many philosophers deny that the world contains any examples of emergence (Lewis 1986, x), whereas others assert that it is rare and at most occurs in the mental realm (McLaughlin 1997). Yet other authors reject this parsi-mony and maintain that entangled quantum states or the effects of long- range correla-tions that result in such phenomena as ferromagnetism or rigidity constitute legitimate examples of ontological emergence (Batterman 2002; Humphreys 1997). Still others insist that some forms of emergence are common and come in degrees (Bedau 1997; Wimsatt 2007). This division appears to be based in part on the extent to which one subscribes to a guiding principle that we can call the rarity heuristic: any account of emergence that makes emergence a common phenomenon has failed to capture what is central to emer-gence. Those early twentieth- century writers who restricted emergence to phenomena that at the time seemed mysterious and little understood, such as life and consciousness, seemed to have been sympathetic to the rarity heuristic, although earlier philosophers, such as Mill, who considered chemical properties to be emergent, would have rejected it.

3 For this last topic see Butterfield and Isham (1999).



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Because of the lack of agreement on examples, it would be a useful project for phi-losophers of science to assemble candidate examples for emergence that can then be assessed for salient characteristics. To illustrate the variety of examples that have been suggested, some are chemical, as in the class of Belousov- Zhabotinsky reactions, one example of which occurs when citric acid is placed in a sulfuric acid solution in the presence of a cerium catalyst. Circular patterns dynamically emerge from the initially homogeneous color, and the colors subsequently oscillate from yellow to colorless and back to yellow. Such are considered to be examples of reactions far from equilibrium, nonlinear oscillators in which self- organizing behavior leads to emergent patterns. Other suggested examples are physical, involving spontaneous symmetry breaking or quantum entanglement. Some examples are biological, such as the existence of flocking behavior in certain species of birds that demonstrates the appearance of self- organizing higher level structure as a result of simple interactions between agents. Still others are computational, as when the probability that a random 3- SAT problem is satisfiable undergoes a phase transition as the ratio of clauses to variables crosses a critical thresh-old (Monasson, Zecchina, Kirkpatrick, Selman, and Troyansky 19994 for a longer list, see Humphreys forthcoming). One can see from this brief list of suggested examples the difficulty of identifying properties that are common to all cases of emergence or, conversely, understanding why all of these cases should count as emergent. Too often, especially in the sciences, an account of emergence is developed based on a small set of examples that are assumed to be emergent without any systematic arguments backing that assumption.

In the absence of canonical examples, one approach to understanding emergence is to draw upon broad theoretical principles and frequently used generic characteristics of emergence as a way to gain understanding of what emergence might be. Using a cluster definition approach, it is common to assert that an emergent entity must be novel, that there is some holistic aspect to the emergent entity, and that the emergent entity is in some sense autonomous from its origins. In addition, providing some account of the relation between the original entities and the emergent entity is desirable.

We can stay on reasonably firm taxonomical ground by distinguishing among onto-logical emergence, epistemological or inferential emergence, and conceptual emer-gence. All cases of ontological emergence are objective features of the world in the sense that the emergent phenomenon has its emergent features independently of any cogni-tive agent’s epistemic state.

4 The k- SAT problem is: for a randomly chosen Boolean expression in conjunctive normal form such that each clause in the conjunction contains exactly k literals, does there exist a truth value assignment under which it is satisfied? Determining whether such a Boolean sentence has a truth value assignment that makes it true (the satisfaction problem) has been shown to be an NP- complete problem for the 3- SAT case, and various forms of the k- SAT problem exhibit phase transitions. The 2- SAT problem, which has P class complexity, has a phase transition at M/ N equals one, where M is the number of clauses and N is the cardinality of the set of variables from which k are randomly drawn. Below that value, almost all formulas are satisfiable, whereas above it almost all are unsatisfiable. Phase transitions also occur for k = 3, 4, 5, 6.



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Schematically, A ontologically emerges from B when the totality of objects, proper-ties, and laws present in B are insufficient to determine A. In the case of epistemological emergence, limitations of our state of knowledge, representational apparatus, or inferen-tial and computational tools result in a failure of reduction or prediction. Schematically, A inferentially emerges from B when full knowledge of the domain to which B belongs is insufficient to allow a prediction of A at the time associated with B.5 Conceptual emer-gence occurs when a reconceptualization of the objects and properties of some domain is required in order for effective representation, prediction, and explanation to take place. Schematically, A conceptually emerges from B just in case the conceptual frame-works used in the domain to which B belongs are insufficient to effectively represent A.

These categories are not mutually exclusive. Epistemological emergence is often accompanied by conceptual emergence, and ontological emergence can give rise to epistemological emergence. Discussions of emergence would be less confusing if these modifiers of “ontological,” “epistemological,” and “conceptual” were regularly used, and I shall use them from now on in this chapter.

There is an alternative and often used terminology of strong and weak emergence but its use is not uniform. “Strong emergence” is sometimes used as a synonym for “ontolog-ical emergence” but usually with the additional requirement that downward causation is present: sometimes for any case of emergence in which ontologically distinct levels are present with sui generis laws (Clayton 2004), sometimes to cover cases for which truths about the emergent phenomenon are not metaphysically or conceptually necessitated by lower level truths (Chalmers 2006; McLaughlin 1997).6

Regarding weak emergence, a state description is often taken to be weakly emergent just in case it is not deducible— even in principle— from the fundamental law statements and the initial and boundary conditions for the system; in another widely discussed usage (Bedau 1997), it applies to states of a system that are derivable only by means of a step- by- step simulation. Finally, Chalmers (2006) denotes by “weak emergence” phenomena that are unexpected given the principles of a lower level domain. I shall here use the term “weak emergence” only in Bedau’s specific sense and “strong emergence” not at all.

2 Synchronic and Diachronic Emergence

Examples of emergence fall into two further types: synchronic emergence and dia-chronic emergence. Within the former category, the emergent entity and the things from

5 If A and B are atemporal, then the reference to time is vacuous. In other cases, such as global spatiotemporal supervenience, the time covers the entire temporal development of the universe.

6 In his article, Chalmers uses “nondeducibility” as an expository convenience, although what is meant is lack of necessitation.



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which it emerges are contemporaneous; within the latter category, the emergent entity develops over time from earlier entities. The earlier British and French traditions did discuss a form of diachronic emergence that was called “evolutionary emergence,” with an interest in how such things as life could emerge from inanimate matter over time, but most of this material was purely speculative. In the contemporary literature, some types of diachronic emergence (Bedau 1997) are compatible with synchronic ontological reduction, but, overall, the philosophical literature on emergence has a pronounced lean away from diachronic emergence, a bias that results from the contrast between emer-gence and synchronic reduction noted earlier. One can trace the line of descent from the mode of theoretical reduction favored by Ernest Nagel (Nagel 1961, ch. 11). Nagel required that, in the case of inhomogeneous reduction, the situation in which at least one theoretical term t was such that t appeared in T1, the theory to be reduced, but not in the reducing theory T2; reduction of T1 to T2 required the formulation of “bridge laws.”7 These provided necessary and sufficient conditions for the elimination of terms specific to T1, and the task was then to derive any prediction that could be derived from T1 using only the theoretical apparatus of T2 plus the bridge laws. Because at that time predic-tion and explanation were considered to have identical logical structure, this procedure also allowed reductive explanations of phenomena described in the vocabulary of T1. Keeping in mind that prediction can be synchronic as well as diachronic, the failure of reduction, in a somewhat crude manner, captures one aspect of the primary form of epistemological emergence, which is based on the essential unpredictability of the emergent phenomenon. If biology is Nagel- irreducible to physics and chemistry, then some biological phenomena cannot be predicted from the representational apparatus of those two sciences alone. The need to introduce specifically biological principles, or new biophysical and biochemical principles, in order to represent and predict certain biological phenomena is a reason to consider those biological phenomena as emergent from physics or chemistry. One can thus see that emergence had not disappeared in the 1960s; it had simply deflated from want of plausible examples and the optimistic outlook toward reduction.

Two other contemporary accounts of ontological emergence are diachronic. Fusion emergence, advocated by Humphreys (1997), rejects the position that there is a set of permanent basic objects, properties, or states in terms of which all others can be gener-ated and argues that emergent entities can occur when two or more prior entities go out of existence and fuse to become a single unified whole. Quantum entangled states are one example; the production of molecules by covalent bonding is another, assuming that at least one model of covalent bonding is veridical. O’Connor and Wong (2005) argue that nonstructural, higher level properties of composite objects are examples of dia-chronic emergent properties. The key idea concerning nonstructural properties is that the constituents of the system possess latent dispositions that result in a manifest and indecomposable property when the constituents causally interact and the complexity of

7 The term “bridge laws” is potentially misleading because whether these are necessarily true definitions or contingent associations has been the topic of significant disagreement.



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the system reaches a certain level. As with a number of other approaches to emergence, O’Connor and Wong’s primary examples are taken to fall within the realm of mental properties. Finally, a more theoretically oriented account of diachronic emergence is given in Rueger (2000) that appeals to changes in the topological features of attractors in dynamical systems theory.

3 Emergence and Reduction

Reduction and emergence are usually considered to be mutually exclusive, and, for some authors, the dichotomy is exhaustive. If we hold both positions, then emergence occurs if and only if reduction fails. Yet a failure of reduction cannot be sufficient for emergence. Fundamental entities are irreducible, but few— and on some conceptions of fundamentality, none— are emergent. Such cases tell us what is wrong with the sim-ple opposition between reduction and emergence. Fundamental entities, whether syn-chronically or diachronically fundamental, have nothing to which they can be reduced and, commensurately, nothing from which they can emerge. Although common par-lance simply notes A as emergent, the grammatical form is misleading. An emergent entity A emerges from some other entity B, and the logical form is relational: A emerges from B. When the context makes it clear what B is, it is appropriate to use the contracted version “A is emergent.”

There is an additional problem with treating the failure of reduction as sufficient for emergence; physics is not reducible to biology, and the semantic content of Lord Byron’s poems is not reducible to the ingredients for egg drop soup, but no emergence is involved because these pairs are not candidates for a reductive relation. So A must be a prima facie candidate for reduction to B in order for the failure of reduction to put emergence in the picture. “Prima facie” is an elusive idea; it is better to drop the view that a failure of reduction suffices for emergence.

Nor is the failure of reduction or of reductive explanation necessary for emergence. An increasing number of authors (Bedau 1997; Wimsatt 2007) have argued that certain types of emergence are compatible with reduction. Wimsatt formulates four conditions for aggregativity, suggests that emergence occurs when aggregativity fails, provides examples to illustrate that aggregativity is much rarer than is often supposed, and argues that reduction is possible even in the absence of aggregativity. Many authors, mostly in the scientific tradition of emergence, have provided accounts of emergence within which emergent phenomena are explainable (e.g., Batterman 2002; Rueger 2000), and, in light of this, the view that emergent phenomena are mysterious and inexplicable should be abandoned.

The simple opposition between reduction and emergence must be amended for another reason. Just as we have different types of emergence, so there are different types of reduction, theoretical, ontological, and conceptual, and we could have a failure of theoretical reduction in the presence of ontological reduction, thus allowing predictive



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or conceptual emergence in the presence of ontological reduction. This was the mes-sage, at least under one interpretation, of Philip Anderson’s widely cited article “More Is Different” (Anderson 1972). As with many scientists, Anderson was less than clear in his discussion about whether he was discussing laws or law statements, but, for him, onto-logical reduction was a given, whereas novel concepts were needed within condensed matter physics in order to allow effective prediction. Anderson himself did not use the term “emergence” in his article, but the common assumption is that this is what he meant and that ontological reduction and conceptual emergence are indeed compatible.

4 Emergence as Nomological Supervenience

Once the difficulties of achieving a complete Nagel reduction of one theory to another were realized, physicalists switched to less stringent types of relation between the two levels, such as logical or nomological supervenience, and realization. Focusing on the first, the idea is that the higher level properties, states, and objects are inevitably pres-ent whenever the appropriate lower level properties, states, and objects are present. That is, the “real” ontology lies at the lower level, usually the physical level, and once that is in place, the ontology of the higher levels— chemistry, biology, neuroscience, and so on— automatically and necessarily exists. Suitably configure the right kinds of fermions and bosons and you will, so it is claimed, necessarily get a red- tailed hawk. What kind of necessitation is involved? The most plausible option is conceptual necessitation; the object we call a hawk is ontologically nothing but the configured elementary particles, just reconceptualized as a hawk. There is no ontological emergence here, although if it is impossible to fully reduce the biological representation of hawks to chemical and physi-cal representations, there is scope for epistemological and conceptual emergence. More controversial is nonconceptual metaphysical necessitation— in every possible world where that configuration exists, so does the hawk— but this type of necessitation allows room for the hawk to exist as something different from the configured particles, thus opening the door to ontological emergence. In yet a third approach, if the necessitation is due to a fundamental law of nature that is not among the fundamental laws of the physical and chemical domains, and is thus what Broad called a “transordinal law,” the domain of fundamental physics is nomologically incomplete. We thus have the possibil-ity of the ontological emergence of certain parts of biology from physics and chemis-try. This is the essence of McLaughlin’s account of emergence (McLaughlin 1997).8 Thus, P is an emergent property of an individual a just in case P supervenes with nomolog-ical but not with logical necessity on properties that parts of a have in isolation or in other combinations, and at least one of the supervenience principles is a fundamental

8 McLaughlin’s position is a modification of an earlier position due to van Cleve (1990).



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law. McLaughlin suggests that increasing complexity in the base domain could result in such emergence but remained skeptical about whether any such cases exist outside the mental realm.

These necessitation- based approaches maintain an atemporal orientation, even when the positions are couched in the ontological rather than in the linguistic mode. For example, some versions of supervenience— and the more recent grounding— relations are presented as relations between properties rather than relations between concepts or predicates. Properties, whether construed extensionally, intensionally, or platonically, are atemporal, as are relations between them, and this reinforces the tendency toward an atemporal treatment. Even when property instances appear in nonreductive physical-ism, the approach is synchronic. The dominance of such approaches for a long period of time was a primary reason why diachronic accounts of emergence were neglected.

5 Unity and Emergence

If one could achieve a wholesale ontological reduction of the subject matters of all domains of correct science to that of one domain, usually taken to be that of fundamen-tal physics, that would be conclusive evidence for the ontological unity of our universe. Methodological, representational, and epistemological variety would remain, but, onto-logically, all would be physical. Conversely, it would seem that ontological emergence would be evidence for ontological disunity. Yet this overlooks the possibility of upward unification, an oversight that is probably due to a bias toward downward reduction. As Batterman (2002) has argued, the renormalization methods that are widely employed in condensed matter physics provide a considerable amount of theoretical unity via uni-versality classes, capturing in a precise way the higher level unification that is present in cases of multiple realizability. (For more on this approach, see Section 9 on universality). This kind of emergence, which is formulated in mathematical terms, would also provide evidence that otherwise widely successful methods, such as mereological decomposi-tion and experimental causal analysis, are not universally applicable. The scope of some other ontological and methodological positions, among them various “mechanistic” approaches, would also be called into question.

6 Emergence and Downward Causation

Ontological emergence is often dismissed on the grounds that it would result in the pres-ence of downward causation, and downward causation is inconsistent with the causal closure of physics. When properly articulated, this objection can be framed in terms of the exclusion argument. The argument has four premises: (1) every physical event E that



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is caused has a prior sufficient physical cause C;9 (2) if an event E has a prior sufficient cause C, then no event C* distinct from C that is not part of the causal chain or process from C to E is causally relevant to E; (3) the realm of the physical is causally closed and so all events in the causal chain or process from C to E are physical events; and (4) no emer-gent event C* is identical with any physical event. Therefore, (5) no emergent event C* is causally relevant to E. Therefore, emergent events are causally excluded from affecting physical events and hence are causally dispensable.

Much has been written about this argument, a clear version of which can be found in Kim (2006), and I shall not attempt to summarize that vast and heterogeneous literature. For the scope of the argument to be determined, however, we must specify the scope of the physical. Originally, “nonphysical” was taken to mean “mental,” but this fails to address the possibility of emergent events within the realm of the physical, broadly con-strued, and it is useful to consider this argument in terms either of “physical” as referring to the domain of physics proper or to the domain of fundamental physics. In the latter case, the argument, if sound, excludes any causally efficacious ontological emergence.

The term “downward causation” tacitly appeals to a hierarchy of levels— the causation is from objects, properties, laws, and other entities occurring or operating at a higher level to objects, properties, laws, and other entities occurring at a lower level. In the case of objects, a necessary condition for the ordering criterion for objects is usually based on a composition relation. Level j is higher than level i only if any object A at level j has objects occurring at level i as constituents. This allows objects at lower levels to be con-stituents of A. To find a sufficient condition is much harder. One cannot take the just described scenario as a sufficient condition on pain of expanding the number of lev-els far beyond what is usually considered reasonable. Even this simple ordering has its problems because molecules are not mereological composites of atoms, and only a par-tial ordering is possible once the subject matter of the social sciences is reached. Once a criterion for objects has been found, the appropriate level for a property or a law is the first level at which the property or law is instantiated. A more satisfactory solution is to avoid the appeal to levels altogether and, adopting a suggestion of Kim, use the neutral concept of domains instead.

There are two sources of concern about synchronic downward causation. The first worry involves whole- to- part causation. The objection appears to be that if a given sys-tem can causally affect its own components via holistic properties that have downward effects, then the cause will include the effect as one of its parts. Yet this concern needs to be better articulated. The situation is not in conflict with the widely held irreflexivity of the causal relation because the part does not, in turn, cause the whole; it is a constitu-ent of it. There is no analogous worry about downward causation when diachronic pro-cesses are involved.

The second source of worry about downward causation occurs when the causation is from some higher level entity but the effect does not involve a component of the system

9 The argument can be generalized to include probabilistic causes, but I shall not do that here.



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to which the cause is attached. Such a situation is problematical only if one is commit-ted to the causal closure of the domain to which the effect belongs. This commitment is common when the domain in question is that of the physical. What it is for the realm of the physical to be causally closed is often improperly formulated. A common formula-tion, as in premise (1) of the exclusion argument, is that every physical event has a suf-ficient prior physical event, but that is inadequate because it allows causal chains to go from the physical domain into the chemical domain and back into the physical domain, thus allowing downward causation without violating the formulation.10 The appropriate principle for events can be found in Lowe (2000): “Every physical event contains only other physical events in its transitive causal closure.”11

7 Emergence as Computational or Explanatory Incompressibility

Weak emergence is a concept designed to capture many of the examples of diachronic emergence found in complex systems. The characteristic feature of systems exhibiting weak emergence is that the only way to predict their behaviors is to simulate them by imitating their temporal development in a step- by- step fashion. In the original for-mulation (Bedau 1997), the emphasis was on derivation by simulation, but in more recent publications (e.g., Bedau 2008), Bedau has argued that this step- by- step process reflects a parallel causal complexity in the system. That is, successive interactions, either between components of the system or between the system and its environment, pre-clude predictive techniques that permit computational compressibility. The degree of computational effort needed to calculate the future positions of a body falling under gravity in a vacuum is largely independent of how far into the future we go, whereas, in the current state of knowledge, no such simple formula is available to calculate the future position of a bumper car subject to multiple collisions because a prediction of the car’s position requires calculations of each intermediate step in the trajectory of the car. A useful distinction here is between systems that can be represented by functions that have a closed- form solution and those that do not. In the former, the degree of compu-tational effort required to calculate any future state of the system is largely independent of how far into the future that state is. In chaotic systems, among others, the absence of a closed- form solution precludes such computational compression (Crutchfield, Farmer, Packard, and Shaw 1986, 49). With the switch in emphasis within computa-tional theory from abstract definitions of what is computable in principle to measures of degrees of computational complexity and what is feasibly computable, weak emer-gence is a contemporary version of the unpredictability approach to emergence that provides an explanation for why compressible predictions are unavailable. I note that

10 In the exclusion argument, this is blocked by premise (3).11 For an earlier statement of the point, see Humphreys (1997).



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weak emergence is a distinctively diachronic concept of emergence that is compatible with synchronic ontological reduction.

8 Unpredictability through Undecidability

The unpredictability approach to emergence originally relied on an unarticulated appeal to unpredictability in principle. In the 1920s, that idea was too vague to be of much use, but, with advances in computation theory, sharper accounts are now pos-sible. An approach to knowledge that dates back to Euclid of Alexandria attempts to capture the entire content of a domain, be it mathematical or natural, by an explicitly formulated set of fundamental principles. Usually, this takes the form of an axiomatic system formulated in a specific language. The content of the axioms is used in conjunc-tion with inference rules and definitions to extract all the implicit content of those fun-damental principles. This approach also makes sense when the fundamental principles are not representational items but laws of nature that apply to a domain D, the analog of the inference rules are causal or other agencies, and the development of the system under the action of those laws and agencies, together with the initial and boundary conditions of a given system that falls within D, generates all the evolving temporal states of that system. Famously, there is a gap between the representational version of this axiomatic approach and the ontological form when the representational apparatus is too weak to generate every natural state of every system lying within D. One can thus capture a substantial part of the unpredictability approach to emergence by noting that an emergent state is one belonging to a part of D that falls outside the representational resources brought to bear on D. As a result, knowledge of that state must be arrived at by further observations and experiments. This captures the idea, present in many of the early writings on emergence, that the only way to know an emergent state is to experience an instance of it. The domain D is often taken to be that of physics or some subdomain thereof. A sharp case of such representational inadequacy occurs when the theory T involved is undecidable in the standard logical sense that there is some sentence S formulatable within the language of T for which neither S nor ~S is deriv-able from T. Gu et al. (Gu, Weedbrook, Perales, and Nielsen 2009), following earlier work by Barahona (1982) showed that there are states of an Ising lattice representing a recognizably macroscopic physical property that are undecidable; hence, they can be known only through observation or, perhaps, by the introduction of a theory predic-tively stronger than T.12

12 The basic technique is to map temporal states of a one- dimensional Ising lattice onto a two- dimensional cellular automaton and to use Rice’s theorem to show undecidable states exist in the latter; see Humphreys (2015) for details.



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9 Emergence as Universality

It is a striking fact about the world that it allows for accurate description and manipula-tion of certain systems without the need to take into account the behavior of that sys-tem’s components. Such autonomy of a higher level from lower levels is often thought to be a characteristic feature of the higher level having emerged from the lower levels. In philosophy, this corresponds to the situation called multiple realizability and, in physics, to universality.13 The term “universality” is misleading because the independence from the substratum usually holds only for a restricted set of properties, but it has become standard. This autonomy is one reason why it has seemed natural to divide the world into levels, and it is frequently cited as an argument for the existence of new laws at a higher level (see Laughlin, Pines, Schmalian, Stojkovic, and Wolynes 2000).

Robert Batterman (2002) has argued that renormalization group methods provide a route for understanding why this kind of autonomy occurs in certain types of physical systems.14 The most important aspect of universality from the present point of view is that phenomena falling within a given universality class U can be represented by the same general principles, and these principles are satisfied by a wide variety of onto-logical types at the microlevel.15 This fact needs to be explained. As well as the ther-modynamical phenomena such as phase transitions that are discussed by Batterman, this independence from the details of the underlying dynamics is characteristic of many dynamical systems. The similarity is not surprising because both formalisms appeal to attractors, the first using fixed points in the space of Hamiltonians that fall within a basin of attraction; the second, as in the damped nonlinear oscillator example used by Rueger (2000), appeals to fixed points in phase space.16 However, Batterman’s approach is distinctive in that it relies on an appeal to specifically mathematical, rather than onto-logical, explanations of the universal phenomena and denies that the usual approach of using reductive explanations that start from fundamental laws is capable of explaining the universal behavior.

We can contrast Batterman’s approach to emergence with a different approach appeal-ing to physical principles. Order in complex systems is represented by structure that

13 The theme recurs in complex systems theory as well: “A common research theme in the study of complex systems is the pursuit of universal properties that transcend specific system details” (Willinger, Alderson, Doyle, and Li 2004, 130) The situations considered are different from those that allow us to predict the motion of a brass sphere in a vacuum without knowing the details of the interactions between the copper and zinc atoms that compose the brass. There, aggregating the masses of the constituents suffices. In other cases, such as not needing to know the exact quark configuration underlying donkey physiology in order to predict that the male offspring of a horse and a donkey will be infertile, it is possible that emergent phenomena are present but that the methods underlying universality in physics are unlikely to explain this, and conceptual emergence is clearly present.

14 See also Auyang (1999, 181– 183).15 Two systems are assigned to the same universality class if they exhibit the same behavior at their

critical points.16 There are other similarities, such as the appearance of qualitative changes at critical points.



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results from a loss of symmetry in the system, and a preliminary word of caution is nec-essary regarding the use of the term “symmetry.” “Symmetry” is often used in these con-texts to refer to a certain kind of homogeneity that is typically produced by a disordered spatial arrangement. Thus, the symmetry in many systems is just the presence of a ran-dom spatial arrangement of the values of a given property. In the ferromagnetic state, iron appears to have a great deal of symmetry since all of the spins are aligned, but this state has a lower degree of symmetry than the disordered state. What is called “spon-taneous symmetry breaking” is the appearance of order resulting solely from the local interactions between the elements of the system, although there may be some additional influence from a constant external field. A key aspect of spontaneous symmetry break-ing is that the aggregate order allows the energy in the system to be minimized.

Consider a ferromagnet the temperature of which can vary. The temperature is a con-trol parameter, a quantity that links the system with its environment, and the net mag-netization, which is the thermodynamical average of the spins, is an order parameter. More generally, an order parameter is a variable that determines when the onset of self- organization occurs and serves as a quantitative measure of the loss of symmetry.17 In a ferromagnet, the order parameter is the net magnetization M.18 M is a holistic property of the entire system; it emerges through the formation of local areas of uniform spin ori-entation called Weiss domains and then spreads throughout the system. There is no gen-eral method for finding order parameters, and identifying an order parameter is very system- specific.19 The critical temperature (and, more generally, a critical point) is a value of the control parameter at or near which a phase transition occurs and large- scale structure appears as the result of local interactions. At the critical point, scale invariance of the structures exists.

A phase is a region of the phase space within which the properties are analytic as functions of external variables; that is, they have convergent Taylor expansions. This means that, with small perturbations, the system stays within the phase, and all thermo-dynamical properties will be functions of the free energy and its derivatives. A point at which the free energy is nonanalytic is a phase transition. Looked at from the perspec-tive of perturbations, the nonanalyticity means that a small perturbation in the con-trol parameter can lead to a switch from one phase to another and corresponding large qualitative changes. Indeed, it is with this reference to nonanalyticity and the associated singularities that the phase transition from paramagentism to ferromagnetism is said to be explained.

There is a dispute about whether the singular infinite limits that play a central role in Batterman’s account are necessary for the existence of the critical points that are asso-ciated with emergence. Batterman (2011) argues that they are and that the limits are

17 More technically, an order parameter is a monotonic function of the first derivative of the free energy.

18 Other examples of order parameters are the director D of a nematic liquid crystal, the amplitude ρG of the density wave in a crystal, and the mean pair field in a superconductor ⟨ ⟩ψ, .r

19 See, e.g., Binney et al. (Binney, Dowrick, Fisher, and Newman 1992, 11).



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essential to providing understanding; the need for such limits is denied by Menon and Callender (2011) and by Butterfield (2011). Because this literature depends essentially on theoretical results, the application of those results to real finite systems requires care, and some parts of the physics literature are ambiguous about this issue. For a detailed, necessarily technical, discussion, I refer the reader to Landsman (2013).

10 Complexity, Nonlinearity, and Emergence

A great deal of traditional science has been based on analysis. The classic method of laboratory experimentation, for example, is based on the assumption that it is possible to isolate individual causal influences by controlling other variables and then to com-bine the results from different experiments. This decomposition and recomposition method is mirrored in many mathematical models using various versions of additivity principles. In recent years, much attention has been paid to the relations among nonlin-ear systems, complexity theory, and emergence, and it is often claimed that nonlinear systems form a subset of the set of complex systems and that complex systems give rise to emergent phenomena. This section is a brief guide to the origin of those claims.

Some of the early British emergentist literature argued that emergence occurred when the level of complexity of a system passed a certain point, and this tradition has sur-vived both within complexity theory and in the appeal to phase transitions as an exam-ple of emergence. One common definition is that a system is complex if it cannot be fully explained by understanding its component parts. Self- organization is often cited as a feature of complex systems, as is nonlinearity (Auyang 1999, 13; Cowan 1994, 1). Complexity theory, if it can fulfill its ambitions, would provide not just a degree of meth-odological unity, but also a kind of higher level ontological unity.

The property of linearity is best captured through its use in mathematical models. The term “linear system” can then be applied to systems that are correctly described by a linear model. Suppose that an input to the system at time t is given by x(t) and that the temporal development of the system is described by an operator O, so that the output of the system at time tʹ, where tʹ is later than t, is given by y t O x t( ) ( ) .′ = [ ] Then, if the system is presented with two distinct inputs x1(t) and x2(t), the system is linear just in case O ax t bx t ay t by t1 2 1 2( ) ( ) ( ) ( ),+[ ] = +′ ′ for any real numbers a and b. This superposition principle— that if f, g are solutions to an equation E, then so is af bg+ for arbitrary constants a,b— is the characteristic feature of linear systems, and it rep-resents a specific kind of additive compositionality. One important use of linearity is the ability to take a spatial problem, divide the region into subregions, solve the equa-tion for each subregion, and stitch the solutions together. Linear equations thus paral-lel the methods of analysis and decomposition. In contrast, as David Campbell (1987, 219) puts it: “one must consider a nonlinear problem in toto; one cannot— at least not



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obviously— break the problem into small subproblems and add the solutions.” So here we have a glimpse of the holistic feature that is characteristic of emergent phenomena. Linearity also captures the separability of influences on a system in this way: if all of the inputs Xi to the system are held constant except for Xj, then changes in the output of the system depend only upon changes in the value of Xj. Nonlinear systems, in con-trast, violate the superposition principle. For a simple, atemporal example, consider the stationary wave function given by sin( )θ . This describes a nonlinear system because in general, sin( ) sin( ) sin( ).a b bθ θ θ θ1 2 1 2+ ≠ +a As a result, the system cannot be mod-eled by decomposing the angle θ into smaller angles θ1 and θ2 , finding the solutions to sin(θ1) and sin(θ2 ) and adding the results. When using this definition of a linear system to represent a natural system, one must be careful to specify what the additive procedure “+” represents since it is the failure of the additivity property of linearity that lies behind the oft- quoted and misleading slogan about emergence “the whole is more than the sum of the parts.”

There are three characteristic differences between linear and nonlinear systems. The first is that they describe qualitatively different types of behavior. Linear systems are (usually) described by well- behaved functions, whereas nonlinear systems are described by irregular and sometimes chaotic functions. This difference can be seen in the transition from laminar to turbulent motion in fluids for which the former exhibits linear behavior whereas the latter is highly nonlinear. The second characteristic is that, in linear systems, a small change in parameters or a small external perturbation will lead to small changes in behavior. For nonlinear systems, such small changes can lead to very large qualitative changes in the behavior. This feature of linear systems is related to the characteristic of stability under external perturbations that is sometimes considered to be a feature of systems that do not exhibit emergent behaviors. The third characteristic is that linear systems exhibit dispersion, as in the decay of water waves moving away from a central source, whereas the stability of eddies in turbulent flow exhibits nondispersion.

These distinctions are not always sharp. It is often claimed that a linear system can be decomposed into uncoupled subsystems. Strogatz (1994, 8– 9), for example, claims that linearity characterizes systems that can be decomposed into parts, whereas nonlinear systems are those in which there are interactions, cooperative or inhibiting, between the parts. However, there are some nonlinear systems that are integrable and can thus be represented in a way that allows a decomposition into a collection of uncoupled sub-systems. Moreover, the equation of motion for a nonlinear pendulum can be given a closed- form solution for arbitrary initial conditions (Campbell 1987, 221).

11 Holism

The failure of decomposability can lead to holism, one of the most commonly cited characteristics of emergent phenomena. Suppose that we want to capture reduction in the ontological rather than the theoretical mode. A common theme in the emergence



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literature, stated with great clarity by C. D. Broad but recurring in subsequent litera-ture, is that emergence results from a failure of a certain type of generative principle. It is this:

Anti- holism: Consider the parts of a system S, each part being isolated from the oth-ers. Then when each part p of S combines with the other parts to form S as a whole, the properties of the part p within S follow from the properties of p in isolation or in simpler systems than S. Furthermore, any property of S must follow from properties of the parts of S.20

This principle attempts to capture the idea that there is nothing that S as a whole contributes to its properties. In contrast, if, for some property P to be present in S, it is necessary for all of the components of S to be in place and to stand in the rela-tions that make S what it is, then there is some ontological or epistemic aspect of S that requires S to be considered as a whole, and this runs counter to reductionist approaches. Much depends on what counts as “follows from.” Often, this is taken to be “is predictable from”; in other cases, it is taken to be “is determined by.” In Broad’s characterization, what you need for a mechanistic account is, first, the possibility of knowing the behavior of the whole system on the basis of knowledge of the pair-wise interactions of its parts; and, second, knowledge that those pairwise interactions between the parts remain invariant within other combinations. If these two items of knowledge give you knowledge of the features of the whole system, then it is not an emergent system. One way in which anti- holism can fail is when configurational forces appear in a system, and, as Butterfield (2012, 105) has pointed out, configura-tional forces are those that are not determined by the pairwise interactions between the elements of the system.21

12 Skepticism about Emergence

Perhaps because of unfavorable comparisons with the clarity of various reductive and generative approaches, emergence has been regarded with suspicion by many, either on grounds of obscurantism, lack of clear examples, or a commitment to analytic and constructive methods. It is frequently held that emergence, if it exists at all, is rare and to be found at most in the realm of conscious phenomena (Kim 1999; McLaughlin 1997). One early expression of this skepticism can be found in Hempel and Oppenheim (1948) where it is argued that any evidence in favor of a supposed example

20 For examples of this principle see Broad (1925, 59) and Stephan (1999, 51). Broad’s original formulation mentions “in other combinations,” rather than “simpler systems,” thereby allowing more, as well as less, complex systems than S, but that more general position eliminates some emergent features that result from threshold effects.

21 Much of McLaughlin’s account of British emergentism (McLaughlin 1992) is constructed around the idea of configurational forces.



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of emergence is the result of incomplete scientific knowledge and that the evidence will be undermined as science advances. Pairing Hempel’s deductive- nomological approach to scientific explanation with Ernest Nagel’s contemporaneous deductive approach to theory reduction, this skepticism was an expression of faith that, in time, all apparent examples of emergence would be reductively explained. At the time, there was what seemed to be inductive evidence in favor of that view, but, as confidence in our ability to fully reduce various domains of science to others has eroded and as numerous credible examples of emergence have been discovered, this skepticism has become less persuasive.

Anti- emergentism is a contingent position, and it is important to separate two aspects of the study of emergence. One project is to provide a systematic account of a particular type of emergence, be it inferential, ontological, or conceptual. Such an account will only be plausible if it is motivated by general principles and either has some connection with historical traditions in emergence or makes a persuasive a pri-ori case that the account is indeed one of emergence. The second project is to identify actual cases that satisfy the criteria given by the theoretical treatment of emergence. Assuming that a given account of emergence is consistent, it follows that there is at least one possible example of emergence of that type. So it would be an important discovery about our world if there were no actual instances of that possibility and perhaps one that required an explanation. Would it be because, as Wimsatt (2007) has suggested, our representational practices are biased toward models that possess nonemergent fea-tures; would it perhaps be the result of a very general principle that the novel element required for emergence cannot come from a basis that lacks that feature, a variant of the “never something from nothing” principle; or would it be because the laws and other conditions that are present in our universe preclude, or just happen not to have pro-duced, cases of emergence?

13 A Final Suggestion

Although I began this chapter by noting that there is no unified account of emergence, I conclude by suggesting a framework within which a number of emergentist positions can be accommodated. This is not a definition, but a schema, and no claim is made that all extant positions that address emergence are included— indeed, not all should be, because some are such that it is hard to tell why their subject matter counts as emergent. One can impose some order on the positions discussed by appealing to this, admittedly rough, principle:

Emergence as nonclosure: A is emergent from a domain B just in case A occurs as a result of B- operations on elements of B but falls outside the closure of B under closure conditions C. To give some sense of how this schema is applied, in a typ-ical application to ontological emergence, B is the domain of physics, the closure conditions on B are the laws of physics, and B- operations are physical interactions.



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On accounts of ontological emergence in which to be emergent is to be subject to laws that do not apply to the base domain, an emergent chemical phenomenon, for example, would then be one that results from physical interactions between physi-cal entities but is subject to a nonphysical, irreducibly chemical law. Similarly, for any account in which there are novel physico- chemical transordinal laws or in which the nomological supervenience of A upon B is licensed by a physico- chemical fundamental law.

In the case of inferential emergence, a statement A will be epistemologically emergent from the domain of statements B (usually taken to constitute a theory) just in case the statement A can be constructed within the representational apparatus of B using the syntactic or semantic operations licensed by B, but the inferential operations that con-stitute the closure conditions for B do not permit the derivation of A. This will cover not only cases in which homogeneous Nagel reduction fails but also cases in which adding definitions of terms in A that are not present in B result in a conservative extension of B, yet A still cannot be derived from B. The reader is encouraged to test his or her favorite account of emergence against the schema.

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Further Reading

Bedau, M., and Humphreys, P. (eds.). (2008). Emergence: Contemporary Readings in Philosophy and Science (Cambridge, MA: MIT Press). A collection of seminal contemporary articles on emergence.

Juarrero, A., and Rubino, C. A. (eds.). (2010). Emergence, Complexity, and Self- Organization: Precursors and Prototypes. (Litchfield Park, AZ: Emergent Publications). A collection of historical papers from many of the important early contributors to emergence.

An excellent survey article on emergence that has a stronger orientation toward metaphysical issues than does the present article is T. O’Connor and H. Y. Wong, “Emergent Properties,” in The Stanford Encyclopedia of Philosophy (Summer 2015 Edition), Edward N. Zalta (ed.), forthcoming, http:// plato.stanford.edu/ archives/ sum2015/ entries/ properties- emergent/ .



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