Emergence and I

“Emergence” is probably the most overused (and misused) term in the context of complex systems. With probability very near to one, it will pop up in any sufficiently long discussion about quantum mechanics, brains, computers, networks, artificial intelligence, and the like. There is talk of emergent phenomena, emergent properties, weak emergence, strong emergence, etc., most of it either needlessly confusing or hopelessly confused. I’ll confess: I don’t like this term. Instead, I prefer to talk of system properties, i.e., descriptions that make sense (or are operationally coherent, in the sense described by Hasok Chang in Realism for Realistic People) for a given system (or asssemblage, if you will) when we take into account the structure of the system and the context in which it is situated, but lose their operational coherence when we try to isolate only certain aspects of the system—for example, by focusing on specific components while ignoring various relations between them and/or their environment. In what follows, I will lay out my thoughts and motivations on this; in particular, I will argue that we already have a powerful language for talking about such system properties based on the concept of Fundierung (or foundation) originating in Edmund Husserl’s Logical Investigations. I will be mainly following the interpretation proposed by Gian-Carlo Rota in his article “Fundierung as a logical concept”1.

It will be useful to start with a few examples before formulating generalities. A nice discussion of emergence can be found in Sunny Auyang’s Foundations of Complex-System Theories in Economics, Evolutionary Biology, and Statistical Physics. In that book, she makes a useful distinction between resultant and emergent properties (or, using her terminology, resultant and emergent characters). According to Auyang, for a system consisting of a large (potentially infinite) number of components, “resultant characters are more closely tied to the material content of the constituents; they include aggregative quantities such as mass, energy, force, momentum, and quantities defined exclusively in terms of them. Emergent characters mostly belong to the structural aspect of systems and stem mainly from the organization of their constituents.” On this reading, temperature defined as the average kinetic energy of molecules in a given medium in thermal equilibrium with its environment is a resultant character, while something like superconductivity is an emergent character. The definition of temperature as an average rests on an assumption of quasi-independence, where we only take into account the interaction between individual molecules and their environment, but not between different molecules. This set of background facts makes the operation of computing averages meaningful and intelligible. By contrast, superconductivity is a property that depends on context (e.g., temperature), structure (e.g., type of material), and interaction (e.g., the mechanism underlying the formation of Cooper pairs).

Phase transitions are another standard example of emergent phenomena. These include phenomena like freezing or the transition from ferromagnetism to paramagnetism in magnetic materials like iron. Mathematical models of such critical phenomena introduce various constructs that are operationally coherent only when we treat systems as wholes2—these include idealizations like the thermodynamic limit and the concept of an infinite-volume Gibbs measure. Again, context, structure, and interaction play key roles. For example, the low-temperature phase transition in the Ising model in two or more dimensions can be described mathematically, in the Dobrushin-Lanford-Ruelle framework, as the existence of two distinct infinite-volume Gibbs measures consistent with the same local (i.e., finite-volume) specifications. These are defined as the conditional probability distributions of the configuration of Ising spins within an arbitrary finite region given the boundary conditions and encode the structure (spins on a regular lattice), the type of interaction between the spins (nearest-neighbor, with energetic preference for neighboring spins to be aligned), as well as the context (external magnetic field and temperature). Here, the temperature plays the role of a control parameter since the Gibbsian non-uniqueness only manifests itself when the temperature is below a certain critical value. The DLR framework is operationally coherent only at the system level, since its constructs make no sense at the level of finite collections of spins, no matter how large. Macroscopically, the system possesses two distinct characters (a stable all-spins-up or a stable all-spins-down configuration). Anticipating our later discussion of the Husserlian concept of Fundierung, we can view this non-uniqueness in functional terms—e.g., as a simple model of memory that can store a single bit with high reliability. Thus, external context, the system’s dealing with the world, instantiates a particular macroscopic character (0 or 1, up or down).

We can go beyond physics. In control engineering, system properties that arise in the presence of feedback are a good candidate for emergent characters. For example, if we connect a linear time-invariant system in a negative feedback loop with a controller that has an adjustable gain parameter, we can observe a rich set of phenomena that characterize the system as a whole. As we start increasing the control gain past the value of 0 (when control is absent), we can alter the global stability properties of the overall system in complicated ways. These are encoded in the coefficients of the so-called characteristic polynomial of the system. (The system is stable if its poles, i.e., the roots of the characteristic polynomial, have negative real parts.) These coefficients depend functionally on the controller gain, and we can observe transitions from stability to instability, changes in the number of distinct roots, their location in the complex plane, etc. Control engineers visualize this using root locus diagrams.3 An experienced engineer can glean all sorts of quantitative and qualitative insights about a given system by looking at the root locus, and can assess the relative merits of different feedback designs in terms of the root locus. (Mathematicians can also find inherent beauty there in connection with Galois groups and related structures.) The selection of closed-loop poles as a function of the control gain is another example of macroscopic (system-level) characters playing functional roles—when the feedback system is embedded in its environment, its closed-loop poles affect its ability to respond meaningfully to control inputs over short and long timescales and to reject disturbances. Moreover, the idea of closed-loop stability is operationally coherent only when we go beyond individual constituents (the plant, the controller, the sensors, etc.) and take context, structure, and interaction into account. It cannot be located in any of the system components; it is neither a property of the plant nor of the controller alone, but is co-extensive with the structural arrangement of the plant and the controller in a negative feedback loop.

A theme that emerges4 is that certain descriptions of system properties must be framed in a language that is appropriate only at the system level. We already saw examples of this in physical and engineering contexts (phase transitions, global properties of control systems, etc.). Such a language will necessarily contain constructs and concepts that run orthogonal to the decomposition of the system into individual constituents, echoing the key distinction between levels and layers in a complex system architecture. This is, again, a matter of operational coherence and intelligibility, and it is even more prominent in the social sciences. The Wittgensteinian turn in sociology was founded precisely on the realization that social phenomena cannot be abstracted away from their context. For example, when Max Weber describes workers in a factory getting paid and spending money in terms of them receiving pieces of metal and exchanging them with other people for various objects, the mismatch between this analytic language and the synthetic language of economic relations is rather glaring. In her book on complex-system theories, Sunny Auyang subjects the relation between macroeconomics and microeconomics to a similar critique, arguing that macroeconomic concepts cannot be coherently framed only in terms of supposedly “more fundamental” microfoundations. Context, structure, and interactions inevitably intervene.

Unsurprisingly, the majority of the discussions of emergence in the context of consciousness and minds are a tangled mess. As it happens, Auyang also has a book devoted to this subject, titled Mind in Everyday Life and Cognitive Science. In that book, she proposes “a model of an open mind emerging from the self-organization of intricate infrastructural processes … . The model is analyzed into three parts: a mind open to the world, which is what we are familiar with in our everyday life; mind’s infrastructure, which consists of the unconscious processes studied by cognitive science; and emergence, the relation between the open mind and its infrastructure.” She is very careful to emphasize that the everyday language of mental concepts and subjective experience is appropriate precisely because it is operationally coherent in our dealings with the world. Her approach rests on four main themes:

1. Monism: mind is not a nonphysical entity but a kind of emergent dynamical property in certain complex physical entities, notably human beings.

2. Infrastructure: the locus of current cognitive science is not mind as we experience it in our everyday life but its infrastructure consisting of its underlying processes.

3. Emergence: conscious mental processes emerge from the self-organization of many unconscious infrastructural processes.

4. Openness: the basic characteristic of mind is its openness to the world; the subject is aware of himself only as he engages in the intelligible natural and social world.

While the underlying infrastructure is indispensable, the categories and concepts used by neuroscientists, cognitive scientists, and artificial intelligence researchers to describe and analyze this infrastructure do not lend themselves to an intelligible, operationally coherent description of the mind in its everyday aspects. There is, however, a specific type of relation between the mind and these infrastructural goings-on. As it happens (even though Auyang does not frame it this way), this relation is an example of the phenomenological concept of Fundierung, particularly its interpretation as a logical concept due to Gian-Carlo Rota.

According to Rota, Fundierung is a relation involving two terms, which he calls function and facticity. The function is the relevant system aspect and the facticity is the supporting material substrate for the function. In all of our examples above (phase transitions, control systems, the mind), the function is the emergent character and the facticity is the infrastructure supporting it. Paradoxically, even though the function matters more than the facticity, it exists less in the sense that, unlike the facticity which has autonomous standing, the function depends on the facticity yet is not reducible to it, it has no autonomous standing. To illustrate the relevant ideas, Rota gives several examples, including some from the work of Wittgenstein and Gilbert Ryle. The example from Wittgenstein has to do with reading and its relation to text. In this setting, the Fundierung relation involves the content of the text as function and the printed text itself as facticity. Ryle’s example is on the role (or function) of the queen of hearts in a game like bridge or poker, as founded on the material facticity of the card as a physical object and embedded in the context of the game with its rules, relations, and social aspects.

As Rota puts it very nicely,

this relationship between facticity and function is not reducible to any other kind of “relationship.” It requires careful phenomenological description to bring out its universal occurrence. Facticity plays a “supporting role” to function. Only the function is relevant. The text is the facticity that lets the content function as relevant. …

Fundierung is a primitive relation, one that can in no way be reduced to simpler (let alone to any “material”) relations. It is the primitive logical notion that has to be admitted and understood before any experimental work on perception is undertaken. Confusing function with facticity in a Fundierung relation is a case of reduction. Reduction is the most common and devastating error of reasoning in our time. Facticity is the essential support, but it cannot upstage the function it founds.

Function alone is relevant. Nevertheless, function lacks autonomous standing: take away the facticity, and the function disappears with it. This tenuous umbilical cord linking relevant function to irrelevant facticity is a source of anxiety. It is hard to admit that what matters, namely functions, lacks autonomy; every effort will be made to reduce functions to facticities which can be observed and measured. Psychologists and brain scientists will see to it (or so we delude ourselves) that functions are comfortingly reduced to “something concrete,” something that will relieve us of the burden of admitting the lack of “existence” of “what matters.”

This is a useful and powerful concept which is, in my view, superior to the ideas underlying emergence in all of its myriad variants. Phase transitions and other critical phenomena are functions that are founded on the facticity of large physical systems consisting of multiple interacting components, with all of the contextual, structural, and interactional aspects (or, in Manuel DeLanda’s terminology, material and expressive components) working in concert to implement (or to found) the function. Moreover, the Fundierung view lends itself nicely to thinking about system architecture following the ideas of John Doyle and his collaborators. In a Fundierung relation, facticity is the constraint that deconstrains the function in its dealings with the world. It allows the function to be realized (often in multiple ways, speaking to the concept of universality in physics or multiple realizability in cybernetics, control, and cognitive science) while remaining largely obscured and unobtrusive. At the end of his article, Rota lays out a few open questions pertaining to Fundierung. The first two of his questions can be immediately interpreted through the architectural lens:

1. Fundiering-relations may be layered. … The facticity in one Fundierung relation may be the function of a “lower” Fundierung relation. How can this be?

2. Whenever the relevant function functions as it is meant to function, the “underlying” facticities are not thematized, they are unobtrusive. In playing a bridge game, the material composition of the cards is irrelevant, if the cards are properly made. Facticity is thematized in a breakdown. How does such a change of view happen?

The theme of emergence has been periodically re-emerging in the context of AI. In that setting, we can find some talk of “emergent abilities” of large language models, for example those that are not present in smaller models but arise in larger ones, or, more ominously, those that were deemed a priori unpredictable and are, therefore, potentially dangerous. The question of whether we can legitimately view the newest large language models as minds looms large on the minds of their designers—not that long ago, Chris Olah, one of the founders of Anthropic, was not only standing on the stage next to Pope Leo XIV during the official presentation of Magnifica Humanitas, the “encyclical letter on safeguarding the human persion in the time of artificial intelligence,” but was even given an opportunity to present his competing vision of AI systems diverging from the Pope’s firm disavowal of machine minds. The Vatican’s vision of human nature is, of course, firmly grounded in the profoundly religious idea of the soul, so the Pope’s stance on machine minds could not have been anything different. However, even if we reject the dualist frame and view the mind naturalistically as a dynamic function founded upon the facticity of neurophysiological infrastructures, the fact that our subjective mental experience is right there while its infrastructural facticities remain unobtrusive and hidden from view is still a source of vexing scientific and philosophical problems.

Seizing on this problematique of consciousness, some AI researchers then execute the following maneuver: Since we have such limited understanding of how our own minds arise out of all those myriad infrastructures, on what grounds can we deny the possibility that Claude or ChatGPT has (or is) a mind? In my view, this objection loses its force once we acknowledge that the computational infrastructural facticities on which the functions of AI systems are founded are readily thematizable (to use Rota’s term) compared to the neurobiological facticities that are founding the functions of mind in humans. Because it is so easy to probe these infrastructures in LLMs and to intervene in them, it is also easy to succumb to the fallacy of misplaced concretness (a.k.a. the reification fallacy) and to project these findings back onto humans. This is not a new observation at all; it is, in fact, the main thesis of Jean-Pierre Dupuy’s book On The Origins of Cognitive Science: The Mechanization of the Mind. Once again, we are confronted with the fact that complex phenomena must be discussed using an appropriate language in order to retain their intelligibility and operational coherence. The language of mechanistic interpretability may be ok for chatbots, but it is not the right one for talking about human minds and their social milieu.