The Algebra of Construal: 5 Formalising Construal—Towards an Algebra

The previous episode demonstrated how multi-perspectival reasoning emerges from the interaction of construals. We now turn to formalisation. Construal is not merely a conceptual principle; it is a systematic operator with rules, types, and relational interactions. Formalising it as an algebra provides a framework to study, compare, and propagate meanings systematically.

Construal as an Algebraic Operator

At the most abstract level, a construal can be treated as an operator $C$ acting on a system $S$ through a perspective $P$, producing an instance $I$:

$$C:S\times P\to I$$

From this, several algebraic notions emerge:

1. Composition ($\circ$) – Sequential application of construals. If $C_1$ and $C_2$ are construals, their composition generates a new instance:

$$I=(C_2\circ C_1)(S,P)$$

The order matters if construals are non-commutative, producing different emergent instances.

2. Interaction ($\otimes$) – Parallel or relational application, where construals influence one another:

$$I=C_1\otimes C_2(S,P)$$

Here, the emergent instance reflects both the combinatory and interfering effects of the construals.

3. Transformation – A construal may alter the system itself, generating new potentialities for future actualisations:

$$S^{\mathrm{\prime }}=C(S,P)\text{where }{S}^{\mathrm{\prime }}\mathrm{\ne }S$$

Rules of the Algebra

While the algebra is not fully numerical, several operational rules can be postulated:

• Associativity: The sequential application of multiple construals is associative if the emergent outcome is independent of internal grouping.

• Non-commutativity: Order of construals often matters; perspective shapes the emergent instance.

• Identity: There exists a “neutral” construal $C_0$ that maps a system to itself without altering the instance.

• Inverse or Reflexivity: Some construals may be partially reversible, creating “undo” operations in relational propagation.

Illustrative Example: Emergent Social Meaning

Consider a social system where multiple agents apply distinct construals to a shared event:

• $C_A$ emphasises relational context.

• $C_B$ emphasises temporal dynamics.

• $C_C$ emphasises potential outcomes.

The emergent social meaning is not reducible to any single construal. Using the algebraic approach:

$$I_{emergent}=(C_A\otimes C_B)\circ C_C(S,P)$$

This formalism allows systematic exploration of how construals combine, interfere, and propagate, illuminating patterns that were previously implicit.

Implications

By formalising construal as an algebra:

• We provide a language to study relational generation of meaning.

• Interactions among construals become predictable in structure, even if outcomes remain emergent and context-dependent.

• We lay the groundwork for computational or mathematical models of relational epistemology, multi-agent reasoning, and the propagation of possibility.

Looking Ahead

The final episode of this series will examine applications and horizons: how the algebra of construal can inform cognitive science, social systems, linguistics, AI, and philosophy, demonstrating that relational ontology is not only descriptive but generative—a platform for new modes of reasoning and insight.

The Algebra of Construal: 4 Multi-Perspectival Epistemology

Episodes 2 and 3 established construal as a dynamic operator and examined how multiple construals interact to generate emergent meanings. In this instalment, we extend these insights into the domain of epistemology, exploring how relational ontology provides a framework for reasoning across simultaneous, non-commensurable perspectives.

The Problem of Perspective

Traditional epistemology assumes a single vantage point, or at least a commensurable set of observations, from which knowledge is derived. Relational ontology challenges this: every instance is perspectival, every construal shapes emergence, and perspectives may be mutually incompatible or partially overlapping.

The epistemic question becomes:

How can we reason coherently when phenomena are generated by interacting construals, each irreducible to the others?

Construal as Epistemic Operator

If construals are dynamic operators, epistemic reasoning can itself be framed as a meta-construal: a process that maps the network of construals across a system to a coherent understanding.

Formally:

$$\text{Epistemic Construal: (Construal Network) × Perspective → Knowledge Instance}$$

• Construal Network: the set of interacting construals within a system.

• Perspective: the meta-lens or reasoning frame applied to the network.

• Knowledge Instance: the emergent, relationally coherent insight generated by integrating multiple construals.

Principles of Multi-Perspectival Reasoning

Several principles emerge naturally from this framework:

1. Integration without Reduction: Distinct construals retain their integrity; knowledge does not require collapsing perspectives into a single, neutral view.

2. Propagation Awareness: Each construal influences others; reasoning must account for these relational effects to anticipate emergent insights.

3. Contextual Sensitivity: Knowledge is always situated; the epistemic frame must acknowledge the conditions under which construals were generated.

4. Dynamic Coherence: Reasoning is iterative; insights emerge progressively as construals interact and are reinterpreted.

Illustrative Example: Scientific Collaboration

Consider a multidisciplinary research team:

• One member approaches a phenomenon quantitatively.

• Another approaches it historically.

• A third takes an experiential perspective.

No single perspective can fully capture the system. Multi-perspectival epistemology does not seek a forced consensus but maps the interactions among construals, generating emergent knowledge that is richer than any single viewpoint. Conflicts, tensions, and overlaps are informative rather than problematic—they are signals of latent possibilities.

Implications

Multi-perspectival epistemology reframes knowledge as:

• Emergent: arising from the relational network of construals.

• Context-sensitive: inseparable from the perspectives that generate it.

• Non-linear: capable of producing insights inaccessible to linear or reductionist reasoning.

Looking Ahead

With the networked dynamics of construal and the principles of multi-perspectival reasoning established, the next step is to formalise these operations into an algebra of construal. This will allow us to systematically study how instances, construals, and their interactions propagate meaning, providing both conceptual clarity and a foundation for potential mathematical treatment.

The Algebra of Construal: 3 Interactions Between Construals

In the previous episode, we positioned construal as a dynamic operator, actively transforming systems and perspectives into emergent instances. But meaning rarely arises in isolation. Systems are complex, perspectives overlap, and construals interact, producing patterns that are irreducible to any single operator. This is the heart of relational generation: the interaction of construals as a source of novelty.

The Relational Multiplicity of Construals

Consider a system with multiple potential actualisations and multiple active perspectives. Each construal produces an instance, but these instances are not independent—they exist within a network of relational constraints and affordances.

Key principles emerge:

1. Compositional Interaction – Multiple construals can combine to form new instances that integrate aspects of each contributing perspective.

2. Interference and Divergence – Construals may conflict, highlighting alternative possibilities or generating tensions that reveal latent potentials.

3. Emergent Propagation – Construals can influence one another, producing chains of meaning that spread through systems.

In essence, meaning emerges not linearly, but relationally, in the space between construals.

Towards an Algebra of Construal

These interactions suggest a formal structure: if individual construals are operators, their combinations can be modelled using algebraic patterns:

• Composition: sequential application of construals, where the output of one becomes the input of the next.

• Commutation: situations where the order of construals affects—or does not affect—the emergent instance.

• Conflict resolution: rules for handling divergent construals within a system, preserving relational coherence.

This framework does not reduce meaning to a calculation; it maps the possibilities of interaction and the ways emergent phenomena propagate relationally.

Illustrative Example: Multi-Agent Social Systems

Imagine three agents observing the same event but applying different construals:

• Agent A prioritises temporal features.

• Agent B emphasises relational context.

• Agent C focuses on potential outcomes.

Individually, each construal produces an instance of the phenomenon. Together, the three construals generate an emergent “composite” understanding that is richer, more complex, and partially unpredictable. Tensions and alignments among construals illuminate possibilities that no single perspective could reveal.

Implications

The interaction of construals shows that meaning is:

• Relational: emerging in the space between operators, not within a single instance.

• Generative: capable of producing novelty beyond the original potentials.

• Dynamic: always evolving as construals propagate and influence one another.

Looking Ahead

With this foundation, the next episode will extend the discussion to multi-perspectival epistemology, showing how relational interactions of construals provide a formal scaffold for reasoning across simultaneous, non-commensurable views. We begin to see how relational ontology moves from description to systematic epistemic practice.

The Algebra of Construal: 2 Construal as Dynamic Operator

In the previous episode, we established construal as the foundational principle of relational ontology: phenomena are always mediated, and meaning emerges only through the interplay of potential, perspective, and actualisation. In this installment, we take the next step: construal is not merely a static relation—it is a dynamic operator, a generative process through which systems are actualised and meaning propagates.

From Static Product to Processual Operation

Traditional accounts often treat meaning as a fixed “output” of interaction or representation. Relational ontology, by contrast, positions construal as operative and transformative: it is the act through which potentials are realised in instances.

Formally, we can think of construal as:

$$\text{Construal: System × Perspective → Instance}$$

• System: the structured potential, the theoretical space of possibility.

• Perspective: the situational lens or cut, the context in which actualisation occurs.

• Instance: the emergent, perspectivally actualised phenomenon.

Here, construal functions as a mapping, not a mirror: it does not reflect a pre-existing world; it transforms potential into actualisation. The operator is dynamic because it acts differently depending on the system and the perspective, producing variation and novelty.

Types of Construal

Even at this stage, we can observe distinct modes of construal:

1. Selective Construal – prioritises certain features or potentials over others, shaping what emerges.

2. Compositional Construal – integrates multiple potentials into a coherent instance.

3. Transformative Construal – alters the system itself through the act of actualisation, creating new potentialities.

These types are not discrete “levels” but interacting modalities, capable of combining in complex patterns. Their interplay generates emergent phenomena that could not have been predicted from the system alone.

Implications for Meaning Propagation

When construal is treated as a dynamic operator, several consequences follow:

• Emergent novelty: Each instance is not predetermined; it arises relationally through the operator.

• Relational propagation: Construals can influence other construals, producing chains or networks of emergent meaning.

• Non-commensurable perspectives: Multiple construals can operate simultaneously, creating partially overlapping or even incompatible instances.

In other words, construal is not just a generator of meaning—it is a mechanism for the propagation of meaning across systems and perspectives, laying the groundwork for multi-perspectival epistemology.

Looking Ahead

Having positioned construal as a dynamic operator, the next instalment will explore interactions between multiple construals, the algebraic patterns they form, and the ways in which emergent meanings propagate across relational systems. This sets the stage for formalising an algebra of construal, where the operations themselves can be systematically studied and applied.

Construal, in motion, is the engine. Understanding its dynamics is the first step toward mapping the flow of possibility and meaning in relational terms.

The Algebra of Construal: 1 The Primacy of Construal

To understand relational ontology, one must begin with the inescapable fact: phenomena are always mediated. They are never “raw,” never free of perspective, never unconstrued. This is the principle of construal, and it is the generative heart of meaning itself.

Construal is not a lens through which reality is observed—it is the very act by which phenomena come into being as meaningful. Every instance, every emergent event, is an actualisation of potential through a perspectival cut. To ignore this is to mistake the output for the operator: to treat meaning as a static product rather than a dynamic process.

Construal as Foundational Principle

The early stages of relational ontology foreground construal precisely because it establishes a new relation between potentiality and actuality:

• Systems define structured potentials, the space of what might be.

• Instances are perspectival actualisations of those potentials.

• Construal is the active operation that bridges the two: it is the generator of first-order meaning.

This triad is irreducible. Systems without construal remain inert; instances without construal lack coherence; construal without potential or perspective is void. Meaning emerges only at the intersection of these three.

Implications for Thought

Recognising construal as primary reshapes our epistemic stance. Knowledge is no longer the passive reception of pre-existing entities. Instead, understanding is an engagement with emergent phenomena, always already mediated by perspective. To know is to participate in the act of actualisation.

Moreover, construal reveals the relational nature of reality itself: any phenomenon is only intelligible within the network of other phenomena and the perspectives through which they are construed. There is no neutral vantage; there is only situated emergence.

A Preview of the Series

This episode establishes construal as a dynamic operator. Subsequent episodes will:

1. Formalise construal as a transformative process.

2. Explore the interaction of multiple construals, and how they generate emergent meanings.

3. Extend these insights toward a multi-perspectival epistemology, where the relational ontology provides a formal scaffold for reasoning across non-commensurable perspectives.

4. Outline the beginnings of an algebra of construal, offering a pathway toward formalisation and application.

Construal is the engine. Meaning is its output. By following its operations, we begin to see not only how phenomena arise, but how knowledge, interpretation, and possibility themselves are generated. The algebra of construal will chart this engine in motion.

The Horizon Without End

At the edge of the world, Liora reached the horizon. It shimmered, shifting with each step she took. No matter how far she advanced, the horizon moved, not as a destination but as a relational effect of her own enactment.

She understood then that the journey was the horizon itself. Meaning did not lie in what lay beyond, nor in some fixed goal; it existed only in the interplay of motion and perception, in the enactment of distinctions along the ever-changing boundary between near and far.

Liora walked on, not to arrive, but to participate. Every step, every glance, was a cut into possibility, actualising a horizon that could never be possessed, only experienced. The landscape itself breathed with her passage, a luminous reminder that meaning occurs in relation, in movement, and in the unfolding of the possible.

The Forest of Divergence

Liora entered a forest where each tree seemed to grow according to its own peculiar rules. Branches spiralled and split differently depending on the angle from which she approached. Sometimes paths converged, sometimes they diverged, producing patterns of misalignment that were neither chaotic nor accidental.

The forest maintained an emergent coherence. Stability did not arise from agreement or symmetry, but from the persistence of admissible relations across scales. Liora’s steps altered the microstructure of the forest, yet the overall form persisted, resilient to individual divergences.

She walked slowly, noticing the contrasts, the branching differences, the subtle interplay of scale and perspective. Here, misalignment was not failure; it was constitutive. The forest existed as a living system of possible enactments, each revealing something about the patterns that could occur without appealing to outside purpose.

The Mirror That Was Not

By the lake, Liora paused. Its surface rippled as though alive, catching light and shadow in endless play. She leaned closer, expecting her reflection, but found none. The lake responded only to her movements, shifting forms with her gestures. No image stood still; no self was captured.

Here, the lake’s surface was meaning itself: an event enacted in relation to her presence, never stored, never possessed. Liora traced her fingers over the water, and the ripples traced back, revealing nothing about her and everything about the unfolding interaction.

She realised that understanding did not require a fixed image. Intelligibility occurred only in enactment — every gesture, every ripple, a distinction actualised in the interplay between being and environment.

The lake had no “aboutness,” and yet it spoke volumes, silently guiding Liora through the event of seeing without standing for anything.

The Path of Possibility

One morning, sunlight broke through the mist, illuminating a path that wound through the valley’s golden fields. Liora felt the horizon’s pull, yet as she stepped forward, she noticed that each choice shimmered differently: some stretches of the path accepted her presence, others seemed to fold away.

The valley itself was alive with the law of admissibility. Paths were not right or wrong; they were actualisable or not, depending on how she moved, the weight of her steps, and the angles of approach. Liora realised that opportunity was not offered, but emerged with her enactment. Each step illuminated the next, not as a promise but as a possibility.

By mid-morning, Liora walked without expectation. The valley responded to her presence, weaving and opening, constraining and freeing — a network of relations where nothing was fixed, yet everything was intelligible in the moment of passage.

After Representation: 7 What a Non-Representational Linguistics Would Require

If representation is to be genuinely displaced, it cannot be done piecemeal.

Adding interaction, embodiment, or social constraint to an otherwise representational framework alters how meaning is explained, but not what meaning is taken to be. A non-representational linguistics would therefore require not a new mechanism, but a change in ontological footing.

This final move is not a proposal for a new theory of language. It is an account of the conditions under which representation ceases to be explanatory at all.

Meaning as Event, Not Content

The first requirement is that meaning no longer be treated as a thing.

Meaning cannot be a content that exists prior to its expression, nor a unit that practices transmit or negotiate. It must be understood as something that occurs — an event constituted in the enactment of distinctions within a situation.

On this view, there is no meaning that is merely waiting to be realised. Meaning exists only as actualised.

This does not deny stability. It relocates it.

Stability Without Shared Representations

A non-representational account cannot appeal to shared mental contents or common meanings as the basis of coordination.

Stability must instead be explained as persistence across enactments: the recurrence of admissible distinctions, the durability of forms of action, the continued viability of certain cuts rather than others.

Agreement is no longer foundational. Coordination is.

Understanding is visible in what participants can do together, not in what they are presumed to share.

Systems as Possibility Spaces

Language, on this account, is not a repository of meanings but a structured space of possibility.

A linguistic system constrains what distinctions can be enacted, what relations can be established, and what continuations are admissible. It does not cause meanings, nor does it aim at outcomes.

Actualisation is therefore not a process driven by intention or mechanism. It is a perspectival selection among admissible cuts.

Teleology and causation have no explanatory role here.

Explanation Without Origins or Ends

Once meaning is treated as event rather than content, familiar explanatory questions lose their grip.

There is no need to ask what caused a meaning to occur, because meaning is not an effect. There is no need to ask what a meaning was for, because meaning is not a means.

Explanation remains immanent:

• Which distinctions were enacted?

• Under what constraints were they admissible?

• How did these enactments stabilise or transform the system?

These questions do not reach backward to origins or forward to goals.

Error, Misalignment, and Difference

Without representation, error cannot be misrepresentation.

Misalignment is not failure to reach a shared meaning, but divergence in enacted distinctions across perspectives or scales. Such divergence is not inherently pathological. It is often constitutive of system dynamics.

Correction, therefore, is not the restoration of accuracy, but the reconfiguration of admissibility.

What Changes — and What Does Not

A non-representational linguistics does not deny reference, communication, or social coordination. It denies that these are grounded in the transmission of content.

Reference becomes a secondary description of how distinctions function within activity. Communication becomes coordination across enacted cuts. Social meaning becomes the patterned persistence of admissible relations.

What changes is the level at which explanation is allowed to stop.

From Theories to Ontology

The repeated return of representation across linguistic and semiotic traditions is not a failure of theory-building. It is a sign that the ontological ground has remained fixed.

To move beyond representation requires shifting that ground.

This series has traced how representational explanation becomes installed, reinforced, softened, and extended. Its aim has not been to replace one theory with another, but to show that another kind of explanation is possible — one that does not require meaning to point beyond itself in order to be intelligible.

A non-representational linguistics would not begin by asking what meanings are. It would begin by asking what distinctions are possible, and what it takes for them to occur.

After Representation: 6 Linguistics After Representation

Many contemporary approaches announce a departure from representation.

Meaning is said to arise from use rather than reference, from interaction rather than encoding, from embodiment rather than mental content. Language is treated as action, coordination, or practice. At first glance, this appears to return to the orientations sketched at the beginning of this series.

Yet representation proves difficult to leave behind.

The Promise of Use and Interaction

Approaches that foreground use, interaction, and practice reject several core assumptions of representationalism.

Meaning is no longer treated as something transmitted from speaker to hearer. Communication is not the successful copying of inner content. Understanding is displayed in action rather than inferred from internal states.

These shifts matter. They reduce the explanatory burden placed on mental causation and weaken the appeal of teleology as an organising principle.

However, the promise of these approaches often outpaces their ontological commitments.

Practice as a Vehicle Rather Than a Site

In many post-representational accounts, practice is treated as the means by which meaning is expressed, negotiated, or conveyed.

Meaning is said to emerge through interaction, but it is still treated as something that emerges from it — something that can, in principle, be abstracted, stabilised, and theorised independently.

Practice thus becomes a vehicle rather than a site. It carries meaning without fully constituting it.

The representational frame survives in attenuated form.

The Persistence of Aboutness

Even when reference is officially downplayed, aboutness often remains tacit.

Utterances are analysed in terms of what they are about. Practices are said to convey information. Interactions are evaluated for accuracy or adequacy relative to a situation.

These moves reintroduce correctness as a central concern. Meaning is still measured against something beyond the act itself.

Representation returns, not as doctrine, but as habit.

Embodiment Without Ontology

Embodiment is frequently invoked as an antidote to mentalism.

Meaning is grounded in bodily activity, sensorimotor engagement, or environmental coupling. Cognition is distributed rather than internal.

Yet embodiment often functions as a supplement rather than a replacement. Bodily activity explains how representations are formed or constrained, not whether representation is basic.

The body becomes another mechanism for producing meaning-as-content.

Why the Slide Back Occurs

These approaches falter not because they are incoherent, but because they stop short of ontological revision.

Representation is criticised at the level of mechanism or method, but retained at the level of what meaning is taken to be. Meaning remains something that must be shared, matched, or recovered.

Without rethinking meaning itself, explanation defaults to familiar questions:

• How do participants arrive at the same meaning?

• What ensures understanding?

• How is miscommunication explained?

Teleology and causation quietly re-enter to answer these questions.

The Limits of Correction

Attempts to correct representational excesses often take the form of constraints: social norms, interactional rules, embodied affordances.

These constraints shape how meaning is expressed, but they do not displace the assumption that meaning pre-exists its enactment.

Correction presupposes a target. Constraint presupposes something constrained.

Representation remains intact.

What Would Actually Be Required

To move beyond representation, meaning must no longer be treated as a thing that practices carry.

It must be understood as something that occurs only in and as particular enactments. Stability must be reconceived as persistence across cuts, not agreement on content. Understanding must be visible in coordination, not inferred from shared representations.

Without this shift, linguistics after representation risks becoming linguistics around representation.

Toward an Ontological Break

The persistence of representational habits in post-representational approaches is itself diagnostic.

It shows how deeply the expectation of aboutness, correctness, and shared content has been installed. Leaving representation behind requires more than new terminology or expanded mechanisms. It requires a change in what explanation is allowed to appeal to.

The final move of this series therefore turns away from theories of language or meaning altogether, and toward the ontological conditions under which meaning can be said to occur.

After Representation: 5 Semiotics Generalised

If structuralism narrows the scope of representation, general semiotics expands it.

Where earlier accounts restricted signs to language or symbolic systems, semiotics generalised treats signification as a pervasive feature of reality. Gestures, images, practices, institutions, and even natural phenomena are redescribed as signs. Meaning is no longer a special property of language; it is the interpretability of anything whatsoever.

This expansion appears, at first, to complete the relational turn begun by structuralism. But in doing so, it reinstalls representational dependence at a deeper level.

When Everything Is a Sign

Generalisation removes the boundary between linguistic and non-linguistic meaning. Anything that can be taken as meaningful is taken as a sign.

This has an attractive consequence: meaning is no longer confined to inner states or symbolic codes. It is distributed across practices, artefacts, and environments.

Yet the price of this move is subtle. If everything is a sign, then meaning everywhere requires interpretation. And interpretation, in turn, presupposes something that is being interpreted.

Representation returns, now unbounded.

Interpretation as Explanatory Centre

In semiotics generalised, explanation shifts toward interpretation.

Meaning arises when something is taken as standing for something else by an interpreter. The sign–object relation is mediated by interpretive activity, often iterated indefinitely.

This framing resolves the problem of privacy introduced by mentalism: meaning is no longer locked inside minds. But it does so by universalising the representational schema.

Every meaningful phenomenon now owes an account of:

• what it stands for,

• how it is interpreted,

• why this interpretation rather than another is warranted.

Teleology and causation re-enter as questions about interpretive aims and processes.

Unlimited Semiosis and Explanatory Regress

One response to the instability of interpretation is to embrace it.

Meaning is said to arise through an open-ended chain of signs interpreting signs. There is no final referent, only further interpretation.

While this avoids naive reference, it does not escape representation. It multiplies it.

Explanation now risks regress. Each sign requires another sign to interpret it. Each interpretation calls for another account of how and why it occurred.

Causation proliferates; teleology diffuses rather than disappears.

The Return of Aboutness

Despite its relational rhetoric, semiotics generalised often restores aboutness as a default.

Signs are still about something, even if that something is another sign. Meaning remains a matter of standing-for, only now within a self-referential network.

The system becomes dynamic, but the ontology remains representational.

What changes is not what meaning is, but how far representation extends.

Why This Move Is Appealing

Generalisation promises inclusivity. It appears to avoid reductionism by allowing many forms of meaning to coexist.

It also appears to sidestep mentalism by locating meaning in practices of interpretation rather than inner content.

But these gains are achieved without abandoning the core assumption that meaning consists in representation.

The sign remains the explanatory unit. Interpretation remains the explanatory process. Standing-for remains the explanatory relation.

The Diagnostic Outcome

Semiotics generalised demonstrates how resilient representationalism is.

Even when mental content is displaced and reference is deferred, the demand that meaning be something interpretable sustains the representational frame.

Teleology and causation, once again, are not added by hand. They follow from the need to explain how interpretation occurs and what it aims to achieve.

Preparing the Next Turn

The next developments attempt to escape this spiral by foregrounding use, interaction, and embodiment. Meaning is relocated once more, this time into activity itself.

Yet without an explicit ontological break, these approaches repeatedly slide back into representation, treating practices as vehicles for meaning rather than as sites of actualisation.

To see why, we must look at what happens after representation is supposedly left behind.

After Representation: 4 Structuralism’s Partial Escape

Structuralism marks a genuine attempt to loosen the grip of representation.

In response to mentalism and the interiorisation of meaning, structural approaches redirect attention away from inner contents and toward systems of relation. Meaning is no longer sought in what a sign stands for, nor in what a speaker intends, but in the patterned differences that organise a system as a whole.

This move is not cosmetic. It alters what counts as an explanation. But it does not complete the ontological break it begins.

Difference Without Reference

At its strongest, structuralism suspends reference.

Signs do not derive meaning from a relation to objects, ideas, or mental contents. They derive meaning from their position within a system of contrasts. A sign is what it is because it is not other signs.

This reorientation does important work:

• Meaning is no longer anchored in mental representation.

• Explanation no longer requires tracing intentions or inner causes.

• Teleology loses much of its footing, since signs do not aim at outcomes.

Meaning becomes relational in a strong sense: internal to the system, not directed outward.

The System as Explanatory Ground

Structuralism elevates the system itself to explanatory primacy.

To explain a meaning is to show how it occupies a position within a structured whole. The focus shifts from events to relations, from acts to structure, from production to organisation.

This move allows explanation to remain largely immanent. One need not ask what caused a particular sign to mean what it does, only how it contrasts with others.

In this respect, structuralism offers a real escape from both teleology and psychological causation.

The Persistence of the Sign

Yet the escape is partial.

Even as reference is suspended, the sign itself remains intact as a basic unit. Meaning is still something signs have, even if that meaning is now differential rather than representational.

The system explains which meaning a sign has, but not what kind of thing meaning is.

As a result, structuralism often inherits representational expectations implicitly. Signs are still treated as bearers of content, even if that content is defined relationally.

Synchrony and Its Limits

Structural explanation privileges synchrony.

The system is treated as a static arrangement of relations at a given moment. Change, use, and activity are backgrounded in favour of structural coherence.

This bracketing is methodologically powerful, but ontologically costly. It risks treating structure as an object rather than as a space of possibility. Meaning appears fixed by the system, rather than enacted through it.

When diachrony and practice return, explanatory pressure re-emerges: how does the system change, and why?

Without ontological revision, causation begins to creep back in.

Why Representation Is Not Fully Displaced

Structuralism reduces the role of mental content, but it does not displace representation as an underlying orientation.

The sign still mediates meaning. The system still organises sign-values. Meaning is still something that can, in principle, be extracted, analysed, and compared.

What is missing is a reconception of meaning as actualised rather than assigned.

Without that shift, structuralism remains vulnerable to being reabsorbed into representational explanation, especially when questions of use, error, or change arise.

A Genuine Turning Point

This should not be read as a dismissal.

Structuralism demonstrates that much of what had been attributed to representation, intention, or mental causation can be accounted for relationally. It shows that coherence does not require aboutness.

But it also shows how difficult it is to complete the break. The explanatory habits installed by representation run deep.

Structuralism opens a door. It does not yet step fully through it.

The next development pushes in two directions at once: it generalises the sign to everything, extending relational explanation outward, while simultaneously intensifying representational dependence.

After Representation: 3 Mentalism and the Interiorisation of Meaning

If the sign as substitute introduces representation, mentalism secures it.

Once meaning is understood as something a sign stands for, a further question presses itself forward: where does that meaning reside when it is not being expressed? The answer increasingly given is that meaning exists as an internal entity — an idea, concept, or representation housed in the mind.

With this move, representation is no longer merely a relation between sign and world. It becomes a relation between inner content and outer expression. Meaning is interiorised.

Meaning as Inner Possession

In mentalist orientations, meaning is treated as something one has.

Words express pre-existing mental contents. Utterances externalise inner representations. Communication succeeds when one mind successfully transmits its contents to another.

This framing resolves a problem introduced by substitution: how meaning persists when signs are not in use. But it does so by relocating meaning into a hidden domain that must now bear explanatory weight.

Meaning is no longer enacted first and foremost in practice. It is stored, retrieved, and deployed.

The Doubling of Explanation

Interiorisation produces a distinctive explanatory structure: every meaningful act now requires two stories.

First, a psychological story:

• how a mental representation is formed,

• how it is activated,

• how it causes an utterance or action.

Second, a communicative story:

• what the utterance is meant to convey,

• how it represents a state of affairs,

• how it achieves uptake.

Causation enters decisively at the first level. Teleology becomes unavoidable at the second.

This is not an excess. It is the structural consequence of treating meaning as an inner object that must be expressed.

From Representation to Mechanism

Once meanings are internal representations, they must interact with other internal states. They must be processed, combined, and transformed.

Explanation therefore gravitates toward mechanism. Mental content becomes something that does work: triggering actions, guiding choices, producing behaviour.

The language of cause becomes indispensable. Thoughts lead to actions. Representations generate outputs. Meaning becomes a force.

At the same time, actions are now explained in terms of aims: intentions, goals, plans. Teleology is no longer a gloss added afterward; it is built into the architecture.

Privacy and the Problem of Access

Interiorisation also introduces a new difficulty. If meanings are inner entities, they are in principle private.

This raises familiar problems:

• How do different individuals share the same meaning?

• How can one ever know whether understanding has occurred?

• What anchors correctness if meanings are hidden?

The typical solution is further representation: shared conventions, abstract contents, or idealised meanings that transcend individual minds.

Thus the explanatory spiral tightens. Representation begets representation.

What Practice Can No Longer Do

At this stage, practice loses its explanatory sufficiency.

Use may reveal meaning, but it no longer constitutes it. Coordination may display understanding, but it no longer grounds it. The source of meaning lies elsewhere, behind the scenes.

As a result, explanation must always reach inward before it can reach outward.

The price of this move is permanence. Once meaning is interiorised, it cannot easily be returned to relation and practice without appearing incomplete.

Why This Orientation Persists

Mentalism endures because it solves problems created by substitution. It gives meaning a home. It stabilises content across contexts. It makes misrepresentation intelligible.

But it does so by transforming meaning into something that must be caused, processed, and aimed.

Causation and teleology are no longer symptoms at this stage. They are infrastructural.

The Path Ahead

Later developments attempt to soften or escape mentalism by appealing to structure, system, or interaction. But the interiorisation of meaning leaves a deep trace.

Even when representation is questioned, the expectation that meaning must reside somewhere — and must do causal work — often remains.

The next turn in the story is therefore ambivalent: a genuine attempt to displace mental content with relational structure, yet one that stops short of full ontological revision.

After Representation: 2 The Sign as Substitute

The shift to representation does not announce itself as a rupture. It enters quietly, under the guise of clarification.

Where earlier orientations treated meaning as enacted within patterned activity, representation introduces a new explanatory convenience: the idea that a sign can stand in for something else. Meaning is no longer only what is done; it is what is carried, conveyed, or substituted.

This move is neither arbitrary nor foolish. It answers real pressures. But it also installs a new kind of explanatory debt.

Substitution as an Explanatory Shortcut

To treat a sign as a substitute is to say that it can take the place of something absent. A word can stand for an object, an idea, a state of affairs. An utterance can represent a situation without reproducing it.

This is powerful. It allows meaning to travel across space and time. It allows coordination without co‑presence. It allows language to be abstracted from immediate activity.

But substitution also changes what must be explained.

Once a sign stands for something else, explanation can no longer remain immanent to use alone. It must now account for:

• how the sign comes to be linked to what it substitutes,

• how that link is maintained across contexts,

• how correct substitution is distinguished from incorrect substitution.

These questions do not arise when meaning is treated as participation in activity. They arise only once standing‑for is taken as basic.

The Installation of Directionality

Substitution quietly introduces direction.

A sign now points beyond itself. Meaning flows outward, from sign to referent. Understanding consists in recovering what the sign is about.

This directional structure reorients explanation:

• backward, toward the origin of the sign–referent link,

• outward, toward what the sign is meant to capture,

• forward, toward successful uptake by an interpreter.

None of this requires teleology or causation to be named explicitly. They are already implied by the structure of substitution itself.

From Use to Correctness

When meaning is enacted, appropriateness is primary. An action fits or does not fit a situation.

When meaning is representational, correctness takes centre stage. A sign must match what it stands for. Error becomes misrepresentation rather than miscoordination.

This distinction matters. Correctness demands standards that are independent of the particular act of use. Something must anchor the sign’s meaning beyond the interaction in which it appears.

With this, meaning acquires an external measure.

Why Substitution Invites Causation

If a sign represents something, then the relation between sign and referent must be established somehow.

Explanatory pressure therefore turns to questions of origin:

• How did this sign come to mean that?

• What caused this association to be formed?

Causation enters not as a metaphysical claim, but as an explanatory necessity. The sign–referent relation demands a story of production.

Similarly, explanation begins to ask what the sign is for: what outcome it is meant to secure, what understanding it aims to produce. Teleology follows just as quietly.

What Is Lost — and What Is Gained

The representational move does not simply replace one account with another. It reweights what counts as intelligible.

What is gained is abstraction, portability, and generality. Meaning can be detached from immediate practice and treated as an object of analysis.

What is lost is explanatory sufficiency at the level of relation and use. Meaning can no longer explain itself without appeal to something else.

The sign now depends on what it is not.

A Shift, Not a Fall

It is important not to moralise this transition. Representation is not a mistake to be undone. It is a structural reorientation with real affordances.

But it is also a point of no return. Once signs substitute, explanation must account for substitution. Directionality, correctness, causation, and teleology are no longer optional. They are the price of standing‑for.

The significance of this shift is not that it happens, but that it often goes unnoticed. Representation installs itself as common sense.

The next development intensifies this orientation further: meaning is no longer merely substituted in signs, but relocated inside minds, where representation becomes internal, private, and causal.

After Representation: 1 Before Representation: Form, Practice, and Relation

The purpose of this opening move is not to recover a pristine origin for meaning, nor to claim that representation was once absent and later introduced as a mistake. The point is more modest and more precise: to show that intelligible accounts of meaning and form existed in which standing-for was not yet doing explanatory work.

In these orientations, meaning is not treated as an object, content, or inner state that must be conveyed. It is treated as a mode of participation in patterned activity. Explanation therefore proceeds by describing forms of action, relations among practices, and the conditions under which distinctions are enacted.

Nothing here requires denial of reference. What is absent is the assumption that reference is ontologically basic.

Form as Patterned Activity

In pre-representational orientations, form is not a container for meaning but the shape of activity itself. A form is recognisable because it recurs as a pattern of doing, not because it encodes a content that can be extracted.

Grammatical forms, rhetorical figures, and poetic structures are understood as ways of acting in language. They constrain what can be done next, what responses are appropriate, and what distinctions are salient. Their intelligibility lies in their operation, not in their capacity to point elsewhere.

Explanation, accordingly, does not ask what a form represents. It asks what it makes possible, what it differentiates, and how it participates in a broader pattern.

Meaning as Use and Participation

Where meaning is approached through use or practice, it is not something possessed or transmitted. It is something enacted.

To mean is to take up a position within an ongoing activity: to respond appropriately, to recognise what counts, to orient oneself within a form of life. Meaning is therefore public without being representational, shared without being identical, and stable without being fixed.

Importantly, such accounts do not require a mental intermediary. There is no need to posit inner representations that language merely expresses. The intelligibility of meaning resides in the coordination of action itself.

Relation Without Aboutness

These orientations are relational, but not referential. Relations are established among actions, roles, and distinctions, not between a sign and an external object it stands for.

A word relates to other words through patterns of contrast and co-occurrence. An utterance relates to a situation through appropriateness and uptake. A form relates to a practice through the possibilities it opens and closes.

None of these relations requires aboutness. They are internal to the activity in which they function.

What Explanation Looks Like Here

Without representation, explanation does not reach outward. It remains immanent to the phenomenon.

To explain a meaning is to show:

• how a distinction is enacted,

• how a form constrains possible continuations,

• how a practice stabilises expectations,

• how participation coordinates action.

There is no pressure to ask what produced the meaning or what it was for. Those questions arise only once meaning is treated as something that must be caused or aimed.

Paths Not Yet Taken

Nothing in these orientations prevents the later emergence of representational accounts. But neither do they require it.

At this stage, meaning does not yet owe an account of its origin or its target. Coherence is achieved without appeal to causes or ends, and intelligibility does not depend on reference.

The significance of this point is not historical nostalgia. It is diagnostic. It shows that the explanatory grip of representation is contingent. Other ways of making sense were available, and were once sufficient.

The next step, then, is not a correction but a shift: the moment when meaning begins to be treated as a substitute for something else, and explanation is redirected accordingly.

After Representation: Preface

Where Representationalism Enters Linguistics and Semiotics: A Diagnostic Excavation

This series is not written as a corrective history. It does not aim to replace existing accounts, adjudicate intellectual winners, or recover an allegedly lost purity of thought. Its purpose is diagnostic.

The concern here is not who was right, but where certain explanatory habits entered, hardened, and began to feel inevitable. In particular, the series traces how representationalism comes to organise what counts as an explanation of meaning, often without being named or argued for.

Representationalism is treated neither as an error nor as a doctrine. It is approached as an orientation: a way of carving up phenomena such that meanings are taken to stand for something else, and explanation is therefore compelled to appeal to causes, origins, intentions, or ends. Once this orientation is in place, teleology and causation follow as symptoms, not as optional theoretical additions.

The historical movement traced here is therefore selective and structural rather than comprehensive. Moments are chosen not for their prominence, but for the specific commitments they install. Alternatives are noted not to valorise them, but to show that other paths were available — and that the dominance of representation was contingent, not necessary.

This is an excavation rather than a refutation. Its aim is to make visible the ground on which contemporary theories still stand, so that departures from representational explanation can be recognised as ontological shifts rather than local revisions.

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Series Aim

This series traces how representationalist assumptions come to organise linguistic and semiotic thought, not as an explicit doctrine, but as a background orientation that shapes what counts as explanation. The task is diagnostic rather than revisionist: to locate where and how representation becomes structural, and what alternative paths were available but largely foreclosed.

The argument proceeds historically, but not as intellectual history for its own sake. Each stop identifies a specific commitment—about signs, meaning, mind, or reference—that installs representational explanation and thereby invites teleology and causation.

Teleology as Symptom, Not Explanation

1. The Recurring Problem

Certain concepts have a habit of resurfacing even when they have been carefully excluded. Teleology and causation are among the most persistent. They reappear not because an argument has failed, but because a background assumption has remained untouched.

Whenever meaning, action, or systemic coherence is discussed, explanatory pressure seems to push inexorably toward questions of why this happened and what it was for. These questions feel natural, even unavoidable. Yet their apparent inevitability is itself a theoretical artefact.

The recurrence of teleology and causation is not evidence of their ontological necessity. It is evidence of a representationalist inheritance that continues to structure how explanation is expected to work.

2. Representation and Explanatory Debt

Representation carries obligations. If an event, form, or meaning is taken to stand for something beyond itself, then explanation must answer two further questions:

• What produced this representation?

• What purpose does it serve?

The first question installs causation; the second installs teleology. Neither is optional once representation is treated as basic. They are not independent explanatory tools, but structural consequences of assuming that phenomena point beyond themselves.

In this sense, teleology and causation are not neutral concepts. They arise only after a prior decision has been made about what kind of thing meaning is.

3. Directionality as a Hidden Commitment

Representational accounts quietly impose directionality in three distinct but related ways:

1. Temporal direction: earlier states are taken to generate later ones.

2. Intentional direction: actions are taken to aim at outcomes.

3. Semantic direction: meanings are taken to refer to something other than themselves.

Once these directions are assumed, explanation must move along them. One must trace causes backward, purposes forward, and references outward. Teleology and causation merely name the routes that explanation is now compelled to follow.

4. Why Teleology Is a Symptom, Not an Explanation

Teleology appears to explain coherence by appealing to ends or goals. But this explanation works only because representationalism has already done the real work. The goal explains the action only if the action is already understood as oriented toward representing or achieving that goal.

Seen this way, teleology is not explanatory at the ontological level. It is a symptom of a deeper commitment: the assumption that systems, actions, or meanings are fundamentally about something else.

Remove that assumption, and teleology loses its footing.

5. A Relational Alternative

A relational ontology of meaning does not begin with representation. It begins with structure.

• Systems are understood as structured spaces of possibility.

• Actualisation is not a process driven by causes, but a perspectival cut within that space.

• Meaning is not transmitted or aimed; it is construed.

• Stability is not goal maintenance, but the persistence of admissibility conditions.

Within such a framework, nothing needs to be for anything else, and nothing needs to produce an outcome in order for coherence to be intelligible.

Change does not require a cause; it requires a different cut.

Stability does not require a goal; it requires constraints that continue to hold.

6. Explanation Without Teleology or Causation

This is not an abandonment of explanation, but a re-grounding of it.

Instead of asking:

• What caused this?

• What was it for?

Explanation asks:

• What was admissible?

• What distinctions were enacted?

• What relations persisted across cuts?

These questions do not point beyond the phenomenon. They remain immanent to the structure within which the phenomenon appears.

7. The Source of Persistent Unease

The sense that something is missing when teleology and causation are absent is itself diagnostic. It signals an expectation that explanation must always move outward: toward origins, ends, or referents.

A relational ontology refuses that movement. Not by denial, but by showing that coherence, intelligibility, and persistence can be accounted for without it.

Teleology and causation, on this view, are not fundamental features of reality. They are strategies for coping with representation once representation has been assumed.

8. What This Makes Possible

Once teleology is recognised as a symptom rather than an explanation, several long-standing problems loosen their grip:

• Error no longer requires deviation from a correct representation.

• Misalignment no longer requires failure to reach a shared goal.

• Design no longer requires directing outcomes, only shaping possibility.

What remains is not a thinner ontology, but a more exact one: one that locates explanation in relation, admissibility, and perspectival cut, rather than in causes and ends.

Teleology fades not because it has been refuted, but because it is no longer needed.

Ontology and Theory of Meaning: Clarifying the Distinction

Meaning is often discussed as if it were a single phenomenon, yet two very different kinds of accounts can be offered: ontologies of meaning and theories of meaning. While they are related, they operate at distinct levels and serve different purposes.

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Ontology of Meaning

An ontology of meaning is concerned with what meaning is, in its most fundamental sense. It specifies the relational structure, potentiality, and conditions of existence for meaning itself. It addresses questions such as:

• What kinds of meaning events are possible?

• How do different instances of meaning relate to each other?

• How can meaning be actualised without reference to representation or convention?

Ontologies describe the space of possibility within which meaning occurs. They are meta-structural: they do not explain how meaning is encoded, interpreted, or communicated within specific systems, but rather outline the relational and structural conditions under which meaning can exist at all.

Illustrative Example: Cuts and Admissibility

In a relational ontology, a system defines the admissible cuts—the selections that can be actualised without violating the system’s structure. Consider a network of distinctions where each node represents a potential meaning. Some configurations are coherent and admissible, while others are impossible. The ontology defines this space of possibility, showing which cuts can exist and how they relate, but it does not dictate which cut will be realised in any instance.

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Theory of Meaning

A theory of meaning, by contrast, explains how meaning operates within a particular system or medium. Theories address questions such as:

• How are meanings represented and communicated?

• What mechanisms govern interpretation and understanding?

• How do signs, symbols, or grammatical structures produce coherent meanings?

Theories are applied and functional. They offer explanatory models for the processes, rules, and dynamics through which meaning manifests in specific contexts, whether in language, semiotics, or other symbolic systems.

Illustrative Example: Systemic Functional Linguistics

Within a language like English, a theory such as Hallidayan SFL explains how register, metafunctions, and clause structures realise meanings in context. It describes how actualisation of meaning occurs in linguistic practice, but it presumes the underlying space of possible meanings (the ontological ground) rather than defining it.

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Key Distinctions

Aspect	Ontology of Meaning	Theory of Meaning
Purpose	Describe the nature and structure of meaning itself	Explain how meaning functions within a system
Focus	Possibility, structure, relational potential	Representation, interpretation, operation
Level	Meta-structural, fundamental	Applied, functional
Scope	Universal; independent of specific systems	Contextual; system-specific
Examples	Relational ontology: systems, cuts, admissibility, actualisation	Hallidayan SFL: register, metafunctions, realisation, clause structures

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Why the Distinction Matters

Recognising this distinction clarifies the conceptual landscape of meaning. An ontology identifies what is possible, without dictating how it must be realised. A theory operates within that space, offering explanations for how meaning is produced, interpreted, and communicated.

This perspective allows multiple theories to coexist without conflict: they can be understood as modelling different slices of the ontological space, each concerned with particular modes of representation or interpretation. Ontology provides the ground of possibility, while theory provides the mechanics of operation within that ground.

Illustrative Example: Actualisation Across Perspectives

Suppose two observers interact with the same system of distinctions. Each may actualise different admissible cuts: one may emphasise certain relationships, while the other enacts a distinct configuration. The ontology allows for both, but a theory would describe how each observer’s cut manifests, is interpreted, or communicated within a given semiotic system.

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Conclusion

Separating ontology from theory illuminates the different levels at which meaning can be approached. Ontology addresses the conditions of possibility for meaning itself, while theory addresses the mechanisms of operation within specific systems. Illustrative examples from relational ontology—cuts, admissibility, and perspectival actualisation—demonstrate how ontology structures the space of potential meaning, while theories describe how meanings are realised and interpreted within that space. Understanding both levels enriches our grasp of meaning, offering a framework for thinking systematically about how meaning exists and how it functions.