This Special Issue aims to clarify “the theory of emergence,” across it’s many forms and definitions. This is no small task, for emergence--as a construct and a phenomenon--has long been examined and explained across all of the sciences: in physics (Prigogine et al., 1972; Haken, 1985; Nicolis, 1989), chemistry (Luisi, 2002; Sieroka et al., 2024), biology (Margulis, 1967; Csanyi and Kampis, 1985; Reid, 2007), evolutionary theory (Bergson, 1911; Morgan, 1923; Wicken, 1979; Weber et al., 1989), philosophy (Pepper, 1926; Klee, 1984; Humphreys, 1997; Sawyer, 2004; Gillett, 2016; Humphreys, 2016; Wilson, 2021), as well as psychology (Ashby, 1947; Weick, 1979), sociology (Durkheim 1898, Berger and Luckmann, 1967; Walker et al., 2006; French et al., 2022), organization science (Katz and Gartner, 1988; Anderson et al., 1999; Levinthal and Warglien, 1999; Chiles et al., 2004; Garud et al., 2006; Fulmer and Ostroff, 2015), and entrepreneurship (Fuller and Moran, 2001; Lichtenstein, 2002; McKelvey, 2004; Gartner and Brush, 2007; Roundy et al., 2018). Scholars in additional fields not listed also have much to contribute.

The challenge is that each of those disciplines examines emergence through it’s own nomological net (Kuhn, 1970), i.e., through models and parameters that are developed by that particular science. For example, thermodynamics models emergence in terms of energy flows, with the emergent outcome being a tangible “dissipative structure” within the closed system. A very different frame comes from the science of aerodynamics, which explains the emergence of the V-shape formation of geese flying. Specifically, that formation dramatically increases the aerodynamic capacity of the entire flock, allowing each bird to fly faster, thus enabling the flock to go much farther each day (Hainsworth, 1986; Cutts and Speakman, 1994). Both are exemplars of emergence, but the nomological differences make them seem to be totally different.

Separately, any given discipline may have more than one theory of emergence. For example, in physics, Dissipative Structures theory has long been explored through thermodynamics (Prigogine, 1955; Prigogine and Glansdorff, 1971; Nicolis, 1989). At the same time, the physics of light were explored by (Haken, 1985; Haken, 2008), who was able to extrapolate and pursue the “self-organization” of light, i.e., laser light. Although both scholars use the term “self-organization” their meanings are substantively different.

More theories of emergence can be found in other natural science disciplines, especially biology (Csanyi and Kampis, 1985; Reid, 2007). Likewise, exploring emergence in social systems has generated new theories of emergence in leadership (Uhl-Bien et al., 2007; Lichtenstein and Plowman, 2009; Lanaj and Hollenbeck, 2015), teams (Katz, 1993; Sawyer, 2001; Arrow and Burns, 2004; Kozlowski and Chao, 2012), innovations (Cheng and Van de Ven, 1996; Garud et al., 2006; Dougherty and Dunne, 2011; Garud et al., 2015; Inigo and Albareda, 2016), and new enterprises (Brush and Vanderwerf, 1992; Lichtenstein et al., 2006; Lichtenstein et al., 2007; Goldstein et al., 2010a; Nair et al., 2019); to name a few. The result is a plethora of emergence theories, leading to the presenting problem expressed in the Special Issues’ Call for Papers: “It will clarify the differences and commonalities of the many diverse and often conflicting conceptualizations of the theory of emergence…”

The present paper provides an alternative approach, reflecting a pluralistic view of emergence (Onnis, 2023), as initially suggested by Humphreys and Bedau (2008). Specifically, consider emergence as a science, rather than a (singular) theory. As a science, emergence can employ many different disciplines, each of which provides a unique context for understanding. Likewise there are often many theories within a science, as there are about emergence. Further, an active science is inherently self-correcting, as new findings and explanations resolve earlier conflicts. Over time, patterns and regularities of emergence have been found within disciplines. By framing this work as a science of emergence, we gain numerous “footholds” for exploring emergence in all of it’s forms.

The paper starts with definitions for emergence, highlighting the complementarity of emergence process and outcomes. Next I propose a series of Prototypes of emergence, as a structure for an emergence science. By focusing on one of these--Generative Emergence--I show the potential of patterns or “laws” within that Prototype. Finally I show how emergence can be applied to several social and human sciences.

The classic definition of emergence: a “whole that is greater than the sum of it's parts,” is perhaps more accurate than we give it credit. By “whole” the implication is that something new has been formed; “greater than the sum of it’s parts” suggests most of the Characteristics of emergence described below. Still, several emergence scholars have formalized definitions of emergence that more helpful.

For the social sciences, Fulmer and Ostroff (2015) define emergence as: “…a higher-level “whole” that is formed from the individual “parts” in the system. …A new pattern or form emerge[s] as a collective, higher-level phenomenon.” They use the classic language of a whole from it's parts, but describe the emergent whole as a “collective, higher-level phenomenon,” thus acknowledging the influence the emergent has in the system.

A broader definition is from De Wolf and Holvoet (2004), pg. 3): “A system exhibits emergence when there are coherent emergents at the macro-level that dynamically arise from the interactions between the parts at the micro-level. Such emergents are novel with regard to the individual parts of the system.” This definition identifies tangible emergents, which arise through an emerging process of interactions between the parts of the system; he combination of process and outcome is essential. Likewise they characterize emergents as being novel, which reflects numerous Characteristics such as semi-autonomous, unpredictable, and the potential to be agentic.

Consider Goldstein’s (1999) definition, which also incorporates process and outcomes: “[Emergence is] the arising of novel and coherent structures, patterns and properties during the process of self-organization in complex systems.” Goldstein identifies tangible examples of emergent outcomes, as “coherent structures, patterns and properties; ” equally his definition emphasizes both process and outcomes of emergence. Later Goldstein formulated this definition into a unique: emergence is “self-transcending construction.” Thus emergence is a process whereby new structures are ‘constructed’ by the entity’s parts, with outcomes that transcends the parts that make it (Goldstein, 2002; Goldstein, 2003). Overall, Goldstein’s definition is complete and descriptive, yet rather technical. All three definitions are acceptable, due to the vast range of “emergence” and “emergents.”

Another way to define emergence is to focus on it’s Characteristics, i.e., what it is defined by, including unpredictability, non-linearity, and coherence (see Table 1). As one would expect, emergence scholars have identified a small set of defining Characteristics for the phenomena of emergence. For example, De Wolf and Holvoet’s (2004) exhaustive literature review found the six most common characteristics of emergence; (Sawyer, 2004); identified seven structures of emergence, Goldstein (Goldstein, 1999; Goldstein, 2011), presented seven qualities of emergence, while Harper and Endres (2012) discerned six core features of an emergent social system. As shown in Table 1, these combined characteristics are quite correlated, with the most common terms being grouped onto the first column. Note the correlation of terms across scholars in Table 1.

The first six of these are commonly cited as being minimally necessary for emergence. Specifically: Macro properties are new global structures or qualities that are not found in the system’s micro-level components. Coherence reflects a high degree of order in the emergent system. Dynamical means the ordering may change over time without diminishing it’s function. Unpredictable in principle means irreducible to it’s components. Interaction complexity refers to the fact that emergence is often enacted through the interactions between system agents. Radical Novelty refers to a new level-of-analysis that emerges in the system.

In contrast to the first six Characteristics, the last two are not shared. Supervenience claims that the system’s macro-properties exhibit downward causation on it’s micro-level elements; a common example is how a group’s norms constrain the behaviors of it’s members. However some scientists dismiss supervenience, as it seems to suggest a “mysterious force” with the properties of downward causation, which is not permitted in natural science (Kim, 1984; Kim, 1992; Humphreys, 1997).

The last distinction is Goldstein’s term, Self-transcending construction (Goldstein, 2002). As mentioned above, construction references a tangible emergent with material outcomes in social systems. Goldstein explained Self-transcending, “Emergent order arises out of, yet transcends, lower level and antecedent conditions” (Goldstein, 2007, pg. 73). Further, the outcomes transcend the known capabilities of their components. Likewise, emergence assumes the co-creation of a new “level-of-analysis,” thus emphasizing the importance and influence of the new whole on it’s parts (Goldstein, 2001).

These qualities provide a sound basis for defining emergence, although as before it seems challenging to find a definitive definition. Perhaps the definition depends on how emergence is being expressed, i.e., on the type of emergence we are attending to. Following that logic, the proposed Science of Emergence is structured around Prototypes, i.e., core expressions of emergence, which operate across the natural and social world.

Consider the ontological phenomena of emergence, i.e., the specific ways that emergence gets expressed in the world. For example, on your way home from a family outing you suddenly get stuck in a traffic jam. But one of your kids suddenly sees a V-shaped flock of geese gliding across the sky. “Look!” says another, pointing to a rainbow overhead, emergent for a glorious moment. Each of these are emergents, but they operate in very different ways. Thus the idea of Prototypes for emergence (Goldstein, 2011). A prototype is a context for understanding a particular type of emergence; each one is developed through the combined studies of emergence scientists in that context. [See Table below]

As an example, the prototype of Biological emergence includes several ontological (tangible) examples, each of which is associated with a theory of emergence. One is symbiogenesis (Margulis, 1967; Margulis, 1971) whereby a group of macromolecules ingests neighboring macromolecules in the cell; these emerge as a mitochondria, which produces 2000% more energy for the cell compared to the original macro-molecules on their own. Another theory of emergence is called autopoiesis, meaning self-producing systems (Maturana and Varela, 1980; Csanyi and Kampis, 1985); it presents the minimum resources and conditions necessary for a self-producing system to emerge. Separately (Reid, 2007, pg. 323) identifies 12 theories of evolutionary emergence through intrinsic factors, as part of a grand theory of evolutionary self-organization developed by Jantsch (1980), Wicken (1980), Wicken (1986), and Laszlo (1987).

Other prototypes are better known, for example, Computational emergence, which includes all the models showing how order can unexpectedly emerge in computational systems. Among these are artificial life (Langton, 1986), complex adaptive systems (Holland, 1992; Holland, 1995; Holland, 2006), cellular automata (Neumann, 1966; Bedau, 1997; Watts and Strogats, 1998), genetic algorithms (Holland, 1992), NK landscapes (Kauffman and Levin, 1987; Bak and Chen, 1991; Axelrod and Bennett, 1993). Virtually all of these are affiliated with the Sante Fe Complexity Institute; to some these are the complexity science.

Organizing the science of emergence into Prototypes allows us to pursue each one in greater depth, thus gaining knowledge about the processes and outcomes of emergence across levels of analysis. Below are Prototypes of Emergence that I propose for a Science of Emergence. Additions, corrections and discussions are welcome. ¹

To begin, note the sheer range of emergents in the list, from molecular fusion, to the creation of a living cell, the evolution of biological creatures, the generation of organizations, the emergence of an economy (Foster and Metcalfe, 2012; Harper and Endres, 2012), as well as the self-organization of our global economic network (Li and Tesfatsion, 2012; Grodal et al., 2015; Mazzoni et al., 2021). The prototypes (See Table 2) provide a scaffolding for this wide range of emergence phenomena, a structure for organizing our knowledge about emergence. In a science of emergence, each prototype may contain several theories that explain emergence, from their viewpoint. As such there are likely to be many theories of emergence, each of which explains one aspect or facet of emergence. Instead of trying to reduce this to “a” theory, a science invites the full range of emergence to be identified and explored over time.

This suggests an important task for an emergence science is to identify and categorize any patterns within their prototype, such that each prototype is more deeply understood. Then, to use a metaphor, each of these become facets, which allow us to see a specific aspect of emergence. Further like a jewel, emergence can only be seen through (one of) it’s facets. Each facet provides a unique view into emergence; together they expand our insights and overall understanding (Onnis, 2023).

For some, a science is defined by it’s laws, as Physics was through Newton’s Laws of Motion. If so, what are the “Laws of Emergence?” This point is well taken, and it emphasizes the need for an Emergence Science, so researchers can pool knowledge about Emergence and find broad regularities. The diversity of emergence phenomena may preclude finding specific laws that cover all expressions of emergence, yet the query is valid, and worthy of an active science.

Within particular Prototypes we do have evidence of certain Laws. In Computational Emergence each model describes law-like outcomes from it’s unique algorithm. As an example consider the “Law of Interdependence” for NK Landscapes: As the interdependence (K) between elements of a system increases, the system’s performance landscape becomes more “rugged.” This lawful pattern has sparked an entire literature pursuing this and all of Kauffman’s original work (Kauffman and Levin, 1987; Kauffman, 1993; Levinthal, 1997; McKelvey et al., 2013).

Separately, the Dissipative Structures prototype was the basis for the Law of Maximum Entropy Production described by Swenson (1988), following work by Prigogine. “Given an open system far-from-equilibrium, the system will chose from the entire ensemble of possible pathways, that path that maximizes local entropy production. Empirically this [occurs]… when a dissipative structure emerges, such that order-creation is always the preferred path” (Swenson, 1988; Swenson, 1997; Reid, 2007). This idea has sparked a number of responses, including McKelvey’s (2004) “Oth Law of Thermodynamics,” explaining order creation through Swenson’s concept.

Equally, social applications of Dissipative Structures theory (Gemmill and Smith, 1985; Artigiani, 1987; Adams, 1988; Schieve and Allen, 2014) have revealed a specific sequence of dynamics that lead to an emergence event (Lichtenstein, 2014); these are the dynamics within Generative Emergence. Within that context here are four principles (not yet laws), which are well-documented and empirically confirmed empirically across several levels of analysis. These are proposed as Principles of Generative Emergence.

Principle 1

Generative Emergence is in disequilibrium.

Within this prototype, an emergence process will commence only when the system is in dis-equilibrium (Nicolis and Prigogine, 1989). In the social world, this state occurs when the system goes “outside the norm” -- in pursuit of an opportunity or to deal with an urgent crisis. In the science of thermodynamics, disequilibrium is a pre-requisite for self-organization (Prigogine, 1955; Nicolis, 1989). In Generative Emergence as well, disequilibrium creates the conditions within which emergence can occur (Goldstein, 1994; Kiel and Elliott, 1996; Meyer et al., 2005; Lichtenstein, 2014; Leong, 2021).

Being in disequilibrium changes the interdependencies between the agents in the system, across the scope of their daily interactions. Research has found that interdependencies between agents is likely to increase as the system is pushed farther away from equilibrium, in some cases becoming the catalyst for an emergence (Kauffman, 1993; Sorenson, 1997; Deacon, 2003). In practical terms this principle means that for emergence to occur, the system must leave it’s status quo and put resources into exploring new possibilities with unknown potential (McKelvey, 1999; McKelvey, 2004; Lichtenstein, 2009). Entrepreneurs are especially adept at taking action in disequilibrium situations, as has been well expressed by many including Smilor and Feeser (1991), Biggiero (2001), Fuller and Warren (2006), Dew et al. (2011), and Leong (2021).

Principle 2

Generative Emergence Increases Capacity.

One of the most important outcomes of emergence in thermodynamic systems is the dramatic increase in the capacity of the system, first shown by Prigogine et al. (1972). A re-analysis with more advanced tools showed that the emergence of dissipative structures increased the system’s capacity “by orders of magnitude” (Swenson, 1989). An exemplar in the biological world is a bees nest, which can host up to 60,000 bees for many generations. That emergent structure increases the capacity of it’s agents through higher productivity and longer lifespans, as well as to the beehive itself, which would perish without a central home. Furthermore they can pollinate a very large planted area, increasing the capacity of the entire ecosystem to grow and flourish.

A similar principle is at the heart of modern capitalism, as revealed by Smith (1776) and his pin factory. Whereas one individual can make only a few pins a day, by organizing workers and materials into a factory, a hundredfold times more pins can be made than if all of it’s employees were working separately, being 10,000% more effective.

In social emergence, many researchers have shown how new order can transform teams and organizations through the systemic increase in capacity (Schieve and Allen, 1982; Adams, 1988; Goldstein, 1988; Leifer, 1989; Corning and Kline, 1998; McKelvey, 2004). In sum, Generative Emergence increases the capacity of the system and it’s agents.

Principle 3

Successful Generative Emergence requires strong containers.

The study of dissipative structures requires a specific experimental set-up, which allows for a system that is materially closed but energetically open, i.e., a flow of heat travels from the bottom to the top of the container (Bénard, 1901; Prigogine, 1955). It turns out that the emergence of dissipative structures is dependent on the specific shape, size, and heat-absorbing characteristics of the container itself (Nicolis and Prigogine, 1989; Major, 2024).

More formally, the material and energetic containers that constrain a system’s behavior are highly correlated with the emergence of a new emergent (Swenson, 1991; Swenson, 1997; Goldstein, 2003). Likewise, Goldstein (2011) identified the constraints required for many forms of emergence including mathematical emergence, the emergence of attractors, the self-organization of laser light, the hexagonal shape of dissipative structures, and more. Note that according to Goldstein one of the problems with the term “self-organization” it’s lack of attention to the constraints that are necessary to emergence, thus implying a kind of “order for free” (Kauffman, 1993). As such, the importance of constraints for emergence is expressed through this Principle.

Principle 4

Emergence of emergents: Complementarity of process and outcome

Generative Emergence scholars hold two contrasting but complementary views as to what emergence entails. In one, emergence results in an outcome: emergence yields something tangible. For example, in Fulmer and Ostroff’s (2015) definition: “…A new pattern or form emerge[s], …a higher-level phenomenon.” Examples of this emergent form include a termite nest, the invention of a new tool, or the launch of a new enterprise. One benefit of this approach is the ability to measure specific outcomes of emergence in social systems (Crutchfield, 1994; Goldstein, 2000; Sawyer, 2004; Goldstein, 2018).

An equally valid view explores the process of Generative Emergence: How does new order come-into-being in a social system? This query has been pursued through careful empirical research by dozens of scholars including Goldstein (1988), Katz (1993), Holland (1995), Goldstein (2003), Sawyer (2004), and Kozlowski et al. (2013). Further, many complexity scholars exploring social emergence usually rely on process-based approaches, e.g., (Gartner, 1993; McKelvey, 1999; Van de Ven et al., 1999; Meyer et al., 2005; Garud et al., 2010; Kozlowski et al., 2013).

Together, the process view and the outcome view offer a more complete understanding of emergence. Essentially this principle highlights the complementarity of emergence process and emergent outcomes, arguing that both are necessary for a complete description, as earlier noted by Bateson (1980), Corning (1995), Corning (2002), Deacon (2003), Goldstein (2003), and Sulis (2004). An informative example is based on a small forest outside of a town. The forest is an emergent: It is a tangible place, locatable on a map, hopefully with trails for walking. At the same time the forest is emerging, as a thriving local ecosystem growing and renewing itself every day and throughout the yearly cycles. In the wonderful phrase of Gregory Bateson (1980), the forest is “forest-ing” itself. Forest-ing reveals the continuous unfolding of the forest in it’s every leaf and tree and all it’s creatures. Without this constant unfolding, there would be no physical forest to visit. Likewise without it’s formal boundaries and many acts of conservation, the ecosystem itself might not exist. This principle shows that any given emergent is not fixed, but continuously emerges.

In summary, these four Principles describe patterns and outcomes specific to the Generative Emergence prototype; each is backed by empirical and theoretical studies. Though, the emergence question remains: Are there correspondences and/or connection of these principles across prototypes? As an emergence scientist, I am most interested in this query; one of many in a science of emergence.