A Functional Basis for Concept Mastery

(Working Paper – Updated as of June 14, 2025 – Section 1 revised with expanded guidance on neuronal proxy structure.)

John Norman Independent Researcher jnormansp@gmail.com

Abstract

Philosophical accounts of concept mastery often wrestle with how to draw a meaningful line between deep understanding and mere competence – or worse, a kind of linguistic mimicry grounded in social deference (cf. Burge 1979). While externalist approaches have illuminated important dynamics of linguistic and communal coordination, they may leave underexamined the internal, functional state of the individual mind, a gap Rabin (2018) exposes by showing that mastery is not reducible to belief, inference, or intuition, though he stops short of specifying any functional process. The present paper offers a mechanistic framework that attempts to clarify what may be happening inside the individual cognitive system during this shift from deference to mastery. Grounded in cybernetic principles, the framework treats the brain as a unified control system – referred to here as the Brain at Large (BAL) – and distinguishes its global operations from a developmentally emergent internal feedback process, termed Looping, which builds upon the expressive pathways of a Proxy Transfer Device (PTD). Mastery, in this view, is not a matter of social status or external alignment, but a specific, internal functional achievement: the BAL’s ability to deploy well-integrated Neuronal Proxies (operational correlates of concepts) with autonomy, relying on Looping as a strategic tool rather than a crutch. In this way, the framework re-centers the phenomenon of understanding within the brain’s own organizational dynamics – offering a concrete alternative to purely social or abstract philosophical accounts.

Section 1: Introduction

The nature of genuine concept mastery remains one of the more persistent puzzles in philosophy of mind and language. How do we distinguish the understanding of an expert from the competence – or surface-level fluency – of someone who is merely following rules or deferring to others? Classic examples, like Burge’s well-known arthritis case (1979), illustrate how someone might use a concept without fully grasping it, and recent work, such as Rabin (2018), has rightly pushed the conversation toward a deeper inquiry: what is actually happening inside the mind of someone who understands something, as opposed to someone who’s merely performing?

This paper offers a preliminary account of a framework that attempts to address this internal dimension directly. Rather than leaning further into normative or socially distributed explanations – which have their place – it turns to physical and cybernetic principles (cf. Wiener 1948; Ashby 1956) to propose a mechanistic account of the individual mind. The central focus is on a core control system – the “Brain at Large” (BAL) – which guides goal-directed behavior, and on a developmentally emergent process called “Looping,” which enables internal examination of mental content. This looping process relies on a functional structure termed the “Proxy Transfer Device” (PTD), whose original role was likely communicative but which, through repeated use, becomes an engine of subjective experience.

The central claim, in brief, is this: what we call “mastery” corresponds to a functional transition. In the early stages of learning, the BAL must rely heavily on the effortful process of Looping to activate

and evaluate the relevant conceptual content. But over time, as internal structures become more refined, the BAL begins to operate directly and fluently on those structures – looping becomes optional, not obligatory.

This framework does not attempt to solve every question surrounding concept acquisition, language, or meaning. But it does aim to put a spotlight on something that many existing theories leave in the shadows: the functional architecture of understanding within the individual brain. By offering a model for how concepts might be physically instantiated, deployed, and eventually mastered, it invites further philosophical inquiry into the mechanisms behind representation, the shifting boundary between competence and insight, and the role of internal structure in cognitive development.

More broadly, clarifying this distinction between novice and expert – as it is played out in the internal operations of the brain – may give us a new foothold on questions of conscious experience, judgment, and the physical implementation of what we sometimes call “understanding.”

Section 2: The Foundational System: The Brain at Large and Neuronal Proxies

This framework begins not with language or even human cognition, but further back – at the level of general nervous system function as it evolved across species. The foundation is the brain as a physical control system, fundamentally cybernetic in nature (cf. Wiener 1948; Ashby 1956). For clarity and consistency, we refer to this whole-system control architecture as the Brain at Large (BAL): the integrated system that guides the organism’s actions, adapts through feedback, and maintains behavioral coherence in pursuit of biologically relevant goals.

The BAL works, in essence, to bring the organism from whatever state it’s currently in (its Initial State) toward some desirable outcome (a Goal State) – a stable internal condition like satiety or safety, or a favorable interaction with the environment. It accomplishes this by generating behavior that modifies either the external world or the organism’s internal milieu. But crucially, the BAL can only assess progress based on sensory input. It cannot internally “declare” that a goal has been met; it must observe some change in input that confirms this. In this sense, everything must pass through the channel of perception again, closing the cybernetic loop.

In order to act intelligently, then, the BAL constructs and refines what we can call an Internal Model. This model is not symbolic in the way philosophers often mean – not laden with intrinsic semantic content or mental representation in a traditional sense – but is instead a dynamic network of functional mappings. These internal structures allow the BAL to anticipate outcomes, coordinate movement, and interact with the world in ways that are predictively useful.

At the heart of this model are structures we refer to as Neuronal Proxies. A proxy, in this context, is any persistent neural configuration – whether distributed or localized – that reliably correlates with some aspect of the environment or the organism’s own internal state. A sharp shape in motion, a familiar vocal pattern, the fullness of the stomach – all of these can be tracked by stable proxy configurations. These are not mental pictures or conceptual tokens. They are functional correlates: neural formations that, by virtue of reliable interaction with sensory input and goal-driven behavior, become stand-ins for relevant entities or states.

That’s why they are called “proxies.” There is nothing complex or representational about them. Think instead of the traditional Micronesian stick charts – delicate lattices of wood and shell that mapped the sea by mirroring its features. No names, no coordinates, only a sort of one-to-one mapping. The structure was the knowledge. A curve of reed marked a current. A knot meant an island. The chart didn’t describe the ocean; it stood in for it. In just the same way, these neuronal proxies don’t “represent” things in the usual symbolic sense. They don’t explain the world. They hold its shape. And by adjusting their configuration, the Brain at Large can steer behavior – pushing the organism toward its next viable state, closer to what its biology demands. But once again it must be reiterated that the brain cannot change the states of these proxies directly, but only through interaction with the environment, because the states of the proxies are dictated by sensory input.

The identity of these proxies – their relationship to elements, relationships and qualities in the environment – can be deduced by observing behavioral patterns across species. Scientists observe, for example, squirrels with the ability to distinguish between perishable and nonperishable food as a basis for whether or not to store a food item (Hadj‑Chikh, Steele, & Smallwood, 1996), and ravens able to select and use appropriate tools in novel settings, in carefully designed experiments (Veit et al., 2025). Such observations reveal that internal structures corresponding to objects and qualities are formed through past experience – structures that exhibit a behaviorally verified, endurable fixed identity. In humans, there are further ways to identify these proxies, including certain “cloud chamber” effects, where associated bundles of qualities naturally seen as constituting a discrete element in the environment can split, recombine, or generalize. A classic example is the furriness transfer in Watson’s Little Albert experiment (Watson & Rayner, 1920). Some proxies reflect elemental features the brain uses to organize its internal model of the world – like a hard edge or a warm lap, as opposed to discrete objects an organism might interact with. Others are more layered, built up over time and shaped through reinforcement and repeated exposure. Their structure tends to be idiosyncratic and variable, and not necessarily ruled by the tidy categories of the words used in human language. In nonhuman animals, these proxies operate entirely without words. And even in humans, they retain their nonlinguistic form – they serve as a basis that informs language, which is superficial in relation to these underlying, nonlinguistic proxies. A detailed account of these architectures lies beyond the scope of the present paper, but readers interested in further exploration are referred to the author’s website (Norman, 2025).

These proxies are not static; they are learned and refined through experience. Their structure and strength are shaped by activity-dependent plasticity (Hebb 1949; Kandel 2001), and their usefulness depends entirely on their role in supporting successful interaction with the world. When

a proxy supports effective behavior – helping the BAL achieve its goals – it becomes part of the internal model.

Taken together, this web of proxies and their interrelations allows the BAL to operate intelligently. It can anticipate causal relationships, recognize affordances, and adaptively choose actions. Most animals, and most of what we do as humans, operates within this foundational architecture – without any need for language or reflective awareness. The BAL, in this view, is already doing the hard work of cognition, long before the arrival of anything that looks like conscious thought. Language and subjective introspection are important additions, of course, but they come later. First, there is the BAL, and the world it learns to navigate.

Section 3: Communication and Examination: The Proxy Transfer Device (PTD) and Looping

While the foundational BAL system is sufficient for remarkably complex and adaptive behavior – indeed, it accounts for much of what non-human animals accomplish – something quite distinctive occurred in human evolution: the emergence of a functional subsystem capable of transferring internal states between individuals. This capacity, which in many contexts overlaps with what we call language, is here approached from a slightly different angle. We define it by its function and refer to it as the Proxy Transfer Device (PTD).

The evolutionary advantage of such a system is intuitive. If one BAL can encode its internal state in a way that causes a similar state to be activated in another BAL, then coordination, teaching, and even cultural accumulation become possible. The PTD, as a mechanism, enables this kind of information transfer. In essence, it allows one internal model to reach across the gap between organisms and activate proxies in another, setting up shared reference points for behavior and knowledge.

To achieve this kind of transfer, the PTD has to operate through a transitive structure – one that can translate internal states into external signals, and then back again into internal states on the receiving end. This process has stages, forming a structured pathway between internal proxy configurations and the signals that carry them. On the expressive side, the process begins when the BAL selects a proxy configuration for outward transmission. Why? To achieve a goal. How? The same way it moves a hand or begins to walk – it simply initiates the action. After initiation, the signal passes through increasingly concrete stages as it moves toward externalization:

o1: From among its overall proxy configuration, the brain strategically selects a subset for interindividual transfer. (This is the specific content the BAL intends to externalize, that is, transfer to another brain.)

o2–o4: These are formatting stages. The system applies structure – first the highest level structure, then syntactic, then lexical, then phonological or gestural, starting at the level of higher order complexity and ending (in speech or writing), in a linear stream of discrete code units (cf. Levelt 1989).

o5: This is the final stage before contact with the world. Motor plans are set into motion – whether for speech, gesture, or writing – but the environment has not yet been affected.

(between the two series is the environment)

On the input side, the process begins with the arrival of a signal. This is followed by:

i1: The sensory organs detect the signal – sound waves, visual forms, physical marks on a surface.

i2–i4: The signal is decoded: it needs to be rendered into units corresponding to neuronal proxies. These require activation, then through reverberation they are ordered syntactically into configurations. In this way, strategically selected subset of neuronal proxy configurations in the transmitting brain is finally rendered in the receiver brain as a similar neuronal proxy configuration (i5), ideally matching what the sender had at o1, though with various idiosyncratic differences.

Together, these stages – o1 through o5, through the world, and then i1 through i5 – form the complete external series of the PTD. In communication between individuals, this series carries meaning from one BAL to another.

From infancy onward, producing PTD output (such as early vocalizations) often leads to receiving PTD input (hearing oneself). The correlation between expressive intent and resulting perception is unusually stable and, in computational terms, rich with signal. And given what we know about the BAL’s tendencies – its use of plasticity (Hebb 1949), its drive for efficient prediction (Friston 2010), its modeling of expected sensory consequences of action (Crapse & Sommer 2008) – it would be surprising if it didn’t exploit such a pattern.

And so, in the typical course of development, the BAL does just that. It learns to treat certain incipient expressive signals – especially those emerging in stages o2–o4 – as reliable activators of meaning. In time, it realizes it can short-circuit the external communicative loop altogether. By leveraging this learned association, the BAL begins to internally reactivate its own proxies using its own half-formed output. This self-triggering shortcut is what we refer to as Looping. It is important to emphasize that the only meaning in the Looping process lies in the reactivation of proxy configurations. The intermediary linguistic structures themselves – phonological fragments, syntactic templates, or serial encodings – matter only insofar as they serve as scaffolding within a broader functional process. These elements are transient formatting stages within the PTD, helping to trigger the reactivation of underlying proxy configurations. Proxy activation is not a side effect of Looping; it is its central functional purpose.

Looping is not a separate brain module or an evolutionarily hardwired mechanism. It’s a learned capacity – an emergent, functional adaptation that arises naturally from the architecture and operating principles already present. It’s a form of neuronal reuse (cf. Anderson 2010), an economical way of putting old pathways to new use. And once it comes online, it transforms the landscape of subjective experience.

Looping allows the BAL to examine its own proxy configurations without having to externalize anything. It supports reflection, imagination, hypothetical reasoning, recollection, the focused interpretation of sensory input, and more. These processes, diverse as they seem, are made possible by the BAL’s ability to internally reactivate proxies through partially formed expressive sequences.

There are two key features worth highlighting. First, Looping is serial – a bottlenecked process. One can only loop through one stream of expressive potential at a time. This explains, among other things, why we can’t vividly imagine a past event while consciously planning an unrelated future action. These acts may switch rapidly, but they don’t run in parallel.

Second, the loop-accessible domain is bounded. That is, only proxy configurations that can be formatted through the PTD are available for internal examination. If a proxy cannot be shaped into a potential expression – linguistic or otherwise – it cannot be looped.

In this light, conscious experience itself is not a passive reception but an active, internal reuse of expressive infrastructure. Looping, once in place, becomes the key that unlocks the domain of subjective thought.

Section 4: A Mechanistic Account of Concept Mastery

With the functional architecture in place – distinguishing the foundational operations of the Brain at Large (BAL) from the developmentally emergent capacity of Looping – we are now in a position to revisit the central philosophical question: what exactly constitutes concept mastery?

Within this framework, concepts are not abstract entities floating in a mental space, nor are they merely social-linguistic conventions to be deferred to. Instead, they are functionally realized as Neuronal Proxies, or more often, as complex configurations of proxies that become deeply embedded in the BAL’s internal model. The more richly connected, robust, and context-sensitive these configurations are, the more firmly the concept is rooted in the BAL’s operational repertoire.

Now consider the novice. In early encounters with a new concept, the relevant proxies are typically weak, unstable, or poorly integrated. The BAL lacks the internal scaffolding needed to apply the concept fluidly or intuitively. As a result, it must rely heavily on Looping – not just as a helpful tool, but as an essential mechanism. The novice BAL loops constantly: consulting remembered definitions, simulating examples, replaying linguistic formulations, and performing step-by-step evaluations in order to orient itself in conceptual space.

What we often interpret from the outside as effortful or “slow” thinking reflects this internal situation: the BAL is having to compensate for a lack of structural integration by running serial diagnostic checks through the Loop. In short, Looping is doing the heavy lifting.

But this is not where things stop. One of the BAL’s remarkable features – as emphasized earlier – is its capacity for long-term integration and plasticity. With repeated engagement, feedback, and environmental reinforcement, the proxy configurations involved in the concept begin to take shape. They stabilize, connect with other relevant structures, and eventually become accessible to the BAL without constant self-interrogation.

At this point, something important has changed. The BAL no longer needs to loop in order to access the concept. It can deploy the proxy configuration directly – fluently, adaptively, and in real time. The conceptual material is no longer something to be laboriously reconstructed. It is something the BAL has.

This, then, is what concept mastery amounts to in functional terms: the BAL’s acquired ability to act upon a well-integrated conceptual structure without needing to run it through the Loop every time. Mastery reflects not the disappearance of Looping, but its transformation – its repositioning from a constant guide to a specialized instrument.

Indeed, mastery does not mean the Loop goes silent. On the contrary, the masterful BAL still uses it, but in a very different way. When confronting ambiguous or genuinely novel situations, the BAL may bring Looping back online to help navigate uncertainty. Similarly, when reflecting on the concept itself – whether to understand it more deeply, troubleshoot a failure, or prepare to teach it to someone else – Looping again becomes relevant. The same applies in moments of explicit planning or high-level abstraction, where the BAL may need to deliberately walk through conceptual

structures that usually operate below the surface. In all of these cases, Looping is no longer the lifeline. It is the toolkit.

The BAL chooses to engage it when needed, but no longer depends on it for routine operation. In this light, the expertise we often observe – intuition, automaticity, ease – is simply the behavioral manifestation of a concept that has become native to the BAL’s internal landscape.

To borrow a familiar metaphor: where the novice must hold the map and follow the roads, the expert has become the terrain.

Section 5: Addressing Concept Mastery Debates (e.g., Deference)

With the mechanistic picture of concept mastery in place, we can now return to a longstanding philosophical tension – namely, the debate surrounding social deference. At issue is whether an individual can meaningfully be said to “have” or “use” a concept while relying primarily on the judgments or norms of others. This concern is perhaps most famously raised in Burge’s 1979 arthritis example, where a speaker mistakenly believes the term extends to the knee, yet still appears to be using the concept correctly by deferring to medical authority. While the example shows how linguistic meaning may be socially distributed, many have sensed – correctly, in our view – that such a model cannot capture the full story. There is, one feels, something missing about the individual’s grasp.

Rabin (2018), among others, has given voice to this intuition, arguing that mastery is not merely a matter of social positioning or deference to expert use, but involves something internal, something cognitive. The framework outlined here provides a way to specify what that internal something might be.

From a functional perspective, the deferential state corresponds to a specific operational mode of the BAL. In cases of partial or surface-level understanding, the relevant Neuronal Proxies are underdeveloped, fragmented, or weakly integrated. The BAL, lacking the necessary structure to operate directly on the concept, must lean heavily on the Looping process. It must consciously consult remembered definitions, mentally replay instructions, simulate others’ use, and rely on explicit reasoning in order to produce behavior that aligns – approximately – with community standards. In other words, social deference has a mechanistic correlate: it is what the BAL does when it cannot yet stand on its own.

Conversely, as described in the preceding section, genuine mastery reflects a different internal state altogether. Here, the BAL’s internal model has undergone the kind of structural refinement and integration that enables it to deploy the concept autonomously. The proxies are stable, richly connected, and deeply embedded in the system’s dynamics. As a result, the BAL no longer needs to lean on Looping for guidance in ordinary cases. Its responses arise directly from its own internal configuration. This is not imitation. It is ownership.

The transition from deference to mastery, then, is not merely a change in behavioral confidence or social intention. It is a shift in internal functional architecture. The BAL moves from dependence on explicit, self-directed rehearsal to fluency grounded in its own learned structure. The difference is not just philosophical – it is neural, procedural, and operational.

This distinction provides a useful bridge between philosophical intuitions and neurocognitive explanation. It supports the view that mastery is, in the end, a cognitive achievement – something that happens inside the individual. At the same time, it fully acknowledges the role of social input (via the PTD) in shaping that achievement. Language, instruction, correction, and comparison all

provide crucial input during the novice phase. But mastery itself – the ability to understand and apply a concept with fluency – emerges only when the BAL no longer needs to ask for help.

In that sense, this framework may help clarify why social deference feels insufficient as a definition of mastery. It points to what we’ve been missing all along: the internal state of the person doing the thinking.

Section 6: Conclusion and Perspective

This paper has proposed a functional framework, grounded in cybernetic principles, that offers a mechanistic account of concept mastery. By distinguishing between the foundational operations of the Brain at Large (BAL) and the developmentally emergent process of Looping – a self-reflective, expressive shortcut made possible by the Proxy Transfer Device (PTD) – we’ve aimed to illuminate the cognitive transition that takes place as a learner moves from novice to expert.

Within this account, mastery is not framed in terms of social status, deference, or externally imposed norms. Nor is it understood merely as a matter of linguistic coordination. Instead, it is located in the internal dynamics of the individual’s own cognitive system. The BAL, in its capacity to build and refine stable Neuronal Proxies, becomes increasingly able to deploy conceptual material directly. Looping, once essential to conceptual access, becomes optional – used selectively, and with purpose, as the BAL gains confidence in its own structure.

This shift is more than semantic. It offers a reorientation of our understanding of what it means to know something. Much of the existing literature – especially in philosophy of language and mind – has been shaped by a focus on conscious access, social interaction, and reportable knowledge. While these remain important, the present framework suggests that genuine mastery lives deeper down: not in the fleeting stream of introspective awareness, but in the quiet, durable configuration of the brain’s functional architecture.

This has implications not only for philosophical debates around meaning, reference, and deference, but also for broader questions concerning learning, expertise, and subjective experience. When we say that someone “understands” a concept, we are pointing to a shift in how their system operates. Their BAL no longer runs through the steps; it inhabits the structure. The feeling of knowing – intuition, fluency, flow – is simply what this internal fluency looks like from the inside.

At the same time, this framework does not minimize the role of Looping. On the contrary, Looping remains essential, particularly in moments that require explanation, planning, evaluation, or teaching. What changes is not its value, but its role. The masterful BAL no longer leans on it as a crutch; it picks it up as a tool, when needed, and then returns to its natural gait.

By placing the emphasis on the internal structure of the BAL and its non-looped operations, this framework offers a potential foundation for rethinking mastery – not as something vaguely mental or culturally inherited, but as something physically instantiated and dynamically refined. In doing so, it may help bridge philosophical accounts with neurofunctional ones, and provide a vocabulary for discussing learning and understanding in ways that are both precise and grounded.

Further research could explore how these mechanisms play out in specific cases – mathematical insight, moral reasoning, language acquisition – and how the architecture of the BAL interacts with different environmental and cultural learning contexts. Philosophical work, too, might benefit from this perspective, particularly in clarifying debates about grounding, representation, and the limits of conscious access (cf. Rabin 2020; forthcoming).

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