Showing posts with label objectivity. Show all posts
Showing posts with label objectivity. Show all posts

21 September 2025

Toward a New Mythos of Meaning

In our time, we find ourselves at a crossroads—a moment when the old stories no longer suffice, yet new stories remain elusive. Science has transformed our understanding of the world, but often at the cost of sidelining the very meanings that make that world livable. Meanwhile, ancient myths seem distant, their forms and functions misunderstood or dismissed.

This series invites us to explore a different path: toward a new mythos of meaning.

Drawing on insights from relational ontology, systemic functional linguistics, and semiotics, we will trace how meaning itself can be understood not merely as communication or representation, but as the evolution of possibility. Meaning is not a layer added onto a given world—it is the semiotic architecture through which worlds become possible and real.

Over six posts, we will examine:

  • How meaning unfolds as the systemic differentiation of potential.

  • Why possibility is structured, patterned, and constrained—not infinite chaos.

  • How myth functions as a semiotic system that shapes what is thinkable, sayable, and enactable.

  • The limits imposed by the “myth of the given” and the challenge of moving beyond it.

  • What it means to consider meaning-making as sacred—a fundamental act of world-formation.

  • How to live within a mythos of meaning that embraces responsibility, emergence, and relationality.

This is not a return to ancient cosmologies, nor a simple critique of modernity. It is a reframing: a call to rethink meaning as an ontological force, a dynamic system, and a living process.

Through this series, we hope to open a space for conversation—among scholars, practitioners, and seekers—about how we might inhabit this mythos, and how it might guide new ways of knowing, being, and creating.

We invite you to join us on this journey toward a new understanding of meaning—one that honours both rigour and imagination, precision and poetry, system and story.


1 Meaning as the Evolution of Possibility

What if meaning is not a layer added to the world, but the very condition through which a world becomes possible?

This question—orients the direction of this series. It invites us to step outside familiar binaries: between fact and interpretation, matter and mind, biology and culture. It asks us to stop treating meaning as something that occurs after the world is given, and instead to see meaning as what allows any “given” to emerge at all.

We often imagine evolution as the transformation of things over time: forms changing, species adapting, systems complexifying. But from a relational perspective, the deeper movement is not the evolution of things—it is the evolution of possibility.

That is: what can happen, what can be enacted, what can be construed, is not fixed. It is always structured, but never closed. Meaning does not just respond to reality; it reconfigures the field of what is real, what is sayable, what is thinkable, what is livable. And this reconfiguration is not incidental—it is ontological.

Meaning, in this view, is the semiotic differentiation of potential. It does not represent the world—it patterns its emergence. This is why language matters. Not because it names what already exists, but because it enacts systemic pathways through which experience can be brought into being.

From this angle, evolution is not just about organisms or cultures. It is about the deepening articulation of affordances: new ways of cutting, relating, valuing, realising. And every such articulation is a construal—a meaning-event that shifts the terrain of the possible.

We are not just living in a universe of matter and energy. We are living in a universe of meaning-potentials. And these potentials are not static. They evolve—not as outcomes of external processes, but as internal reorganisations of the semiotic field.

This is not metaphor. It is a change in how we think about system, construal, and emergence.

It is also the beginning of a new mythos: not a return to ancient cosmologies, but a way of inhabiting meaning as the very substance of reality’s becoming.

In the next post, we will explore what it means to treat possibility itself as systemic—not infinite or formless, but structured, ordered, and shaped by the conditions of meaning.


2 Possibility as System, Not Substrate

If meaning is the evolution of possibility, then we must ask: what is possibility?

In many traditions—scientific, philosophical, even spiritual—possibility is treated as a kind of substrate: a blank openness, a space of infinite potential out of which things emerge. This gives rise to metaphors of chaos, void, formlessness. But these metaphors mislead. They treat possibility as undifferentiated, raw, awaiting form.

Relational ontology offers another view: possibility is not formless—it is structured. It is not a passive background, but an active system. And like all systems, it has its own organisation, its own internal topology, its own affordances and constraints.

This means that what is possible is not arbitrary. It is not infinite. It is systemically patterned—shaped by interdependencies, tendencies, modalities, and strata. Not everything is possible at every point. Possibility is always constrained by system—but never reducible to mechanism.

To speak of “system” here is not to invoke determinism. In SFL, as in relational thinking more broadly, a system is not a machine—it is a theory of the instance: a structured potential, a field of virtual relations, within which actualisation may occur in many different ways.

When we say that a clause is a choice within the system of mood, or that a social act is a move within a field of values, we are already working with systemic possibility. Every instantiation is a cut—a selection from a potential that is meaningfully structured. That structure is what we call system.

So too with the world itself.

We can no longer treat possibility as a metaphysical default. It is neither chaos nor chance. It is a relationally ordered field, in which constraints are not limits but conditions for meaningful emergence. Possibility is what becomes available when systems differentiate themselves.

This shifts the role of meaning. Meaning does not merely refer to what is real. It organises what can be real. It structures the field of possibility—not just semantically, but ontologically.

And this is where the mythic dimension returns.

For what we call myth may in fact be one of the oldest and most profound human attempts to model possibility not as abstract freedom, but as patterned system. Myth does not tell us what is true or false. It tells us what is available to be meant—and how different patterns of meaning bring different worlds into being.

In the next post, we will explore this more fully: not myth as story, but myth as semiotic architecture—a construal of possibility that shapes what reality is allowed to be.


3 Mythos as Construal of Possibility

What is myth, if not story? And what is story, if not the unfolding of meaning through time?

To think mythologically is not to believe in gods or spirits or origin tales. It is to engage with the world through a systemic construal of possibility—to inhabit a patterned way of meaning the real.

Myth, in this light, is not a belief system. It is a semiotic system: a way of cutting the world, making distinctions, assigning value, projecting causality, locating self and other across dimensions of time, space, and relation. It is not reducible to narrative form, but narrative is one of its natural modes of instantiation.

What makes myth mythic is not its content, but its function: it patterns possibility.

A mythos is not a set of statements about the world. It is a relational grammar for how the world is to be meant. It construes what kinds of entities can exist, what kinds of events can unfold, what counts as meaningful action, what scales of time and space are available for human participation.

In this sense, every worldview—scientific, religious, ideological, philosophical—is also a mythos: not because it is fictional or irrational, but because it offers a systemic organisation of meaning-potential. It tells us not just what is, but what could be, what should be, what must never be. It is a construal of the possible.

Modernity, in attempting to rid itself of myth, did not eliminate it. It simply disavowed the construal. It re-enacted mythic patterns—of progress, rupture, purification, mastery—while denying their semiotic nature. This is the legacy of the literalist cut: myth was recoded as falsehood, and thus stripped of its power as a construal system.

But myth was never about truth or falsehood. It was about structuring fields of emergence—creating orientations to time, space, value, and causality that made certain lived realities possible.

To reconceive myth as semiotic architecture is to recover its role as a meaning-system—one that does not merely explain the world, but shapes how the world becomes available to experience. Myth construes the boundaries of self, society, cosmos, and the sacred—not by asserting facts, but by patterning construal.

And in doing so, it conditions what it is possible to be.

This is why myth cannot be replaced by science. They do not operate at the same level. Myth is not a competitor to explanation—it is a prior construal of what counts as explainable, what counts as agentive, what counts as real. Every scientific paradigm rests on such patterned assumptions. So too does every politics, every religion, every theory of mind.

The question, then, is not whether to live within a mythos—but which ones we are already living within, and what they make possible or impossible.

In the next post, we will examine one of the most pervasive and restrictive mythic grammars of the modern world: the myth of the given—and the need to cut against it.


4 Cutting Against the Myth of the Given

There is a myth at the heart of modern thought. It does not wear the name of myth—indeed, it wears the name of truth. But it functions as all mythoi do: by shaping what is taken to be real, obvious, and beyond question.

This is the myth of the given.

The myth of the given insists that the world is already there: fully formed, pre-structured, knowable in principle and observable in fact. It teaches that reality is something we discover, not something we enact. Meaning, on this view, is a secondary layer—an interpretive veil cast over what is already objectively the case.

This myth is not just philosophical; it is deeply cultural. It underlies the logic of measurement, the authority of data, the fetish of objectivity. It feeds the fantasy that truth is what remains when all construal is stripped away.

But this fantasy is itself a construal—and a particularly powerful one. For by disavowing the role of meaning in the making of reality, it renders invisible the semiotic systems that structure the real. It pretends to speak from nowhere, while reinforcing a very particular somewhere: a world of bounded objects, discrete subjects, and linear causality.

To cut against this myth is not to abandon truth, but to reorient truth within the dynamics of construal.

Relational ontology makes this move explicit: what we take to be real is not passively received, but enacted through patterned meaning-relations. There is no unconstrued reality to fall back on—only different cuts, different systems of potential, different instantiations of experience.

This does not mean that anything goes. Quite the opposite. Once we recognise that all actuality arises from within systems of potential, we can begin to ask: What are the structures of possibility that condition this event? What are the systems through which this meaning becomes actual?

This is the move from description to systemic construal.

It is also a mythic move—not in the sense of fiction, but in the sense of founding logic. For every ontology rests on cuts: distinctions between what is and what is not, what counts and what does not. The myth of the given hides its cuts. A new mythos must bring them to light.

And here lies our task: not to reject myth, but to reconstrue it systemically—to build new architectures of possibility that do not pretend to speak from nowhere, but that speak from within meaning itself.

Such a project is neither nostalgic nor utopian. It is ontological. It invites us to inhabit meaning not as a veil over reality, but as the medium through which reality becomes—an open system, evolving, patterned, lived.

In the next post, we’ll ask: what kind of mythos might emerge if we took systemic construal itself as sacred? What if the deepest ritual were the act of making meaning?


5 When Meaning-Making Becomes Sacred

What happens when we take the act of meaning itself as sacred?

Not sacred in the sense of sanctified by religion, or protected by ritual taboos—but sacred in the deeper, systemic sense: as that which orients possibility, that which grounds worlds.

Traditional mythologies have often located the sacred in a realm beyond the human: the divine, the eternal, the transcendent. But a relational ontology has no “outside” in which to place the sacred. There is no ultimate reality beyond the cut—no cosmic substrate untouched by meaning.

Instead, the sacred must be understood within the system: not as a thing, but as a function—a way of organising meaning that reorganises possibility.

In this view, the sacred is not that which stands apart from meaning-making, but that which draws attention to it. It is the moment when meaning is no longer transparent, no longer taken for granted. The sacred is the flare of construal becoming visible.

This transforms ritual.

A ritual is not merely a repetition of inherited forms. It is an act of systemic re-alignment: a way of selectively actualising a field of potential, of marking a construal as consequential. When we light a candle, speak a name, cross a threshold—we are not simply expressing feeling. We are performing a cut. We are making meaning as if it mattered.

What if all meaning-making were like this?

What if every construal—linguistic, social, conceptual—were understood not just as functional, but as formative? What if to mean were to participate in the shaping of reality itself?

This would require a new grammar of sacredness. Not a grammar of purity, hierarchy, or transcendence—but a grammar of responsible construal: one that recognises the ethical force of each meaning-choice, not as moral pronouncement, but as ontological participation.

In this mythos, the sacred is not a fixed domain. It is a dynamic infolding of system and instance—a site where potential is opened, felt, cut, and reconfigured.

To treat meaning-making as sacred is to take seriously the insight that we do not live in a world, but in a construal of world. It is to honour the systems that make meaning possible—not as abstractions, but as lived architectures of becoming.

And perhaps this is what myth was always reaching for—not a supernatural order behind the real, but a heightened attention to the patterned nature of reality itself. Myth made meaning visible. It sacralised the cut.

In the final part of this series, we will ask: how might a new mythos for meaning itself take shape—not as a story we tell, but as a system we live?


6 Living a Mythos of Meaning

We have journeyed through the evolution of possibility, systemic construal, myth as semiotic architecture, the challenge of the myth of the given, and the sacredness of meaning-making. Now we arrive at the heart of the question: what does it mean to live a mythos of meaning itself?

To live a mythos is not to adopt a fixed story or ideology. It is to inhabit a relational architecture—a dynamic system of patterned potentials that shape what can be thought, felt, and enacted.

Such a mythos acknowledges that reality is not pre-given, but enacted through meaning. It recognises that every act of construal is a creative cut, an instance of systemic potential actualising itself in particular ways. Meaning is not a passive reflection; it is ontogenetic.

Living this mythos means embracing the responsibility and the possibility inherent in our ongoing acts of construal. It means becoming aware of the systemic patterns we participate in, and the affordances they open or foreclose. It is an invitation to co-create worlds with intention and insight.

This new mythos is not confined to language, nor to human cognition alone. It encompasses the interplay of systems at all scales: biological, social, cultural, symbolic. Meaning-making is the connective tissue of reality’s becoming.

In practice, living this mythos might look like:

  • Cultivating attentive awareness of how meanings are made and remade in everyday life.

  • Engaging with the systemic potentials of language, ritual, art, and science as ways of enacting new possibilities.

  • Recognising the interdependence of meaning and materiality, where symbolic action shapes embodied experience and vice versa.

  • Embracing the open-endedness of potential, resisting closure and dogma in favour of ongoing emergence.

  • Honouring the sacredness of construal as an ethical and ontological act.

In this way, the mythos of meaning is a living system—not a relic of the past, but a generative matrix for future worlds.

It is a call to rethink what it means to know, to believe, to imagine, and to be. To reimagine meaning not as a property of language alone, but as the evolving fabric of reality itself.

And in doing so, to open the way for a new kind of human engagement: one that is at once rigorous, poetic, and profoundly relational.


An Offering to the Conversation: Meaning Beyond the Mechanism

This series—Toward a New Mythos of Meaning—emerged from a simple but radical question: what if meaning is not a human overlay on an otherwise neutral world, but the very medium of its becoming?

In this, the series aligns itself with a wider and growing conversation: one that refuses the closure of mechanistic metaphysics, and that seeks to recover the possibility of reality as alive, patterned, emergent, and meaningful.

Among those voices, Rupert Sheldrake’s work stands out—not because of any shared theoretical framework, but because of a shared impulse: to ask what lies beyond the assumptions we’ve inherited, and to take seriously the idea that form, order, and novelty are not imposed from outside, but arise from within a field of evolving possibility.

Like Sheldrake’s critique of the “scientific creed,” this series challenges the notion that reality is best understood as passive, mechanical, and given. But rather than propose an alternative set of empirical hypotheses, it offers a semiotic reframing: a way of understanding meaning itself as systemic, ontological, and evolutionary.

We do not need to return to older cosmologies, nor invent a new metaphysics out of thin air. What we need is a renewed appreciation of meaning as a primary mode of being—not a by-product of brains, but the patterned articulation of potential at every level of system.

This is not a metaphor. It is not mysticism in disguise. It is an invitation to rethink what it means to know, to be, to evolve—and to do so with care, rigour, and humility.

To those, like Sheldrake, who have kept the doors open—sometimes at great personal cost—this series offers itself not as critique or correction, but as resonance: another wave in the field, another cut through the possible, another step in the evolution of meaning itself.

11 September 2025

Relational Cuts and Quantum Realities: Toward a Relational Ontology of Quantum Theory

1 Introduction: Bridging Gödel, Relational Ontology, and Quantum Foundations


Opening

The quest to understand reality at its most fundamental has long wrestled with profound limits to knowledge, completeness, and objectivity. Gödel’s Incompleteness Theorem famously revealed inherent limitations in formal systems, while quantum theory unsettled classical notions of determinacy and locality. Both domains challenge the metaphysical and epistemological assumptions that underlie much of modern science and philosophy.

This series begins an exploration of these challenges through the lens of relational ontology—a philosophical framework that reconceives being, meaning, and truth as perspectival, enacted, and fundamentally relational. Building on our earlier reframing of Gödel’s theorem, we now turn to quantum theory to examine how relational cuts illuminate quantum phenomena and open new pathways for foundational insight.


Revisiting Gödel Through Relational Ontology

Gödel’s Incompleteness Theorem is often interpreted as a technical limitation on formal axiomatic systems: any sufficiently rich, consistent system must be incomplete; there exist true statements unprovable within the system.

But this classical interpretation rests on assumptions that relational ontology questions:

  • The notion of a system as a fixed, closed totality.

  • The existence of truth as an external, system-independent fact.

  • The coherence of self-reference as an ontological given.

Relational ontology instead conceives systems as structured potentials—fields of possible construals actualised perspectivally through relational cuts. From this standpoint:

Incompleteness is not a failure but an ontological feature: every system necessarily entails its own outside as condition of meaningfulness.

This insight invites us to reconsider completeness, truth, and self-reference as perspectival phenomena—an orientation with profound resonance for quantum theory.


The Quantum Challenge: Contextuality, Measurement, and Entanglement

Quantum theory’s foundational puzzles—contextuality, the measurement problem, entanglement, and non-locality—echo Gödel’s themes of incompleteness and perspectival limitation.

  • Contextuality shows that measurement outcomes depend irreducibly on the measurement context.

  • Measurement problem raises questions about the nature of collapse and the quantum-classical boundary.

  • Entanglement exhibits non-separability that defies classical decomposition.

These features resist classical metaphysics of independent entities and absolute truth.


Toward a Relational Ontology of Quantum Theory

Relational ontology offers a promising framework:

  • Quantum states are structured potentials, actualised only through perspectival construal—the choice of measurement context or experimental arrangement.

  • The quantum-classical divide is not a hard boundary but a relational cut, a perspectival shift enacted through interaction.

  • Entanglement reflects the irreducible relationality of quantum phenomena, not metaphysical mystery.

  • Quantum logic and truth emerge internally within semiotic worlds instantiated by topoi, aligned with category theory.


Series Roadmap

In this series, we will systematically develop these ideas:

  1. Quantum Contextuality as Perspectival Construal

  2. The Quantum-Classical Boundary as a Relational Cut

  3. Entanglement and Non-Separability as Relational Phenomena

  4. Category Theory and Topos Approaches to Quantum Logic

  5. Quantum Measurement as Metasemiotic Transformation

  6. Reframing No-Go Theorems Through Relational Lenses

  7. Toward a Relational Quantum Metaphysics

Each post will balance philosophical rigour with systematic clarity, aiming to bring relational ontology and category theory into productive dialogue with quantum foundations.


Conclusion

By viewing quantum phenomena through relational cuts, we gain conceptual tools to transcend classical metaphysical impasses and reimagine quantum reality as a dynamic, perspectival network of meaning and being.

This is an invitation to rethink quantum theory—not merely as physics, but as a semiotic structure, a layered system of relational construals that echo and extend the insights revealed by Gödel’s theorem.


2 Quantum Contextuality as Perspectival Construal


Introduction

Quantum contextuality reveals a profound departure from classical assumptions about measurement and reality: the outcome of measuring a quantum property depends irreducibly on the experimental context in which the measurement is made. This phenomenon challenges notions of objective, observer-independent properties and forces a reconsideration of the meaning of quantum states.

Through the lens of relational ontology, contextuality is not a paradox to resolve, but a natural expression of perspectival construal—of relational cuts that actualise specific structured potentials within a field of possibilities.


The Classical Assumption vs Quantum Contextuality

Classically, it is assumed that physical properties exist independently of measurement—that systems possess definite values whether or not we observe them. This underpins a realist interpretation: properties have observer-independent truth values.

Quantum theory contradicts this via the Kochen-Specker theorem and related results, demonstrating that no assignment of context-independent definite values to quantum observables can be consistently made. The value of an observable is dependent on the full measurement context—a collection of compatible observables measured together.


Perspectival Construal: Cutting into Potential

Relational ontology reframes this situation as follows:

  • A quantum system is a structured potential, not a container of fixed properties.

  • Measurement contexts enact relational cuts that actualise certain potential properties while backgrounding others.

  • Each context corresponds to a particular perspectival construal, a semiotic act of foregrounding relations within the system’s potential.

  • Observable properties and outcomes are thus not absolute but meaningful only within specific perspectival frames.

This shift dissolves the puzzle of contextuality: properties are not hidden variables waiting to be uncovered, but relationally emergent phenomena dependent on the semiotic cut.


Implications for Objectivity and Realism

This perspectival view modifies classical objectivity:

  • Objectivity is not the existence of properties independent of observers or contexts.

  • Rather, objectivity is the intersubjective coherence among perspectival construals—the structured network of relational cuts.

  • The classical ideal of a “view from nowhere” is replaced by a web of partial, perspectival views, each legitimate within its context.

This is consonant with relational interpretations of quantum mechanics (Rovelli, et al.), but rooted in a more general metaphysics of relational cuts and category theory.


Connecting to Earlier Themes: Incompleteness and Structured Potential

Quantum contextuality echoes the ontological incompleteness we saw in Gödel’s theorem reframed: no system can fully internalise all its truth from within one perspective. Contextuality is a quantum manifestation of this ontological feature—the impossibility of totalising property assignment within a single, absolute frame.


Summary

Quantum contextuality, far from a paradox, exemplifies the core relational ontology insight:

Reality is constituted by structured potentials actualised perspectivally through relational cuts. Measurement outcomes emerge from specific semiotic acts of construal, not from observer-independent absolutes.


Coming Up Next

In Part 3, we will examine the quantum-classical boundary as a relational cut, exploring how measurement and collapse are perspectival shifts rather than physical discontinuities.


3 The Quantum-Classical Boundary as a Relational Cut


Introduction

The quantum-classical boundary—the enigmatic divide between quantum superpositions and classical definiteness—has long posed foundational puzzles. The measurement problem, decoherence, and wavefunction collapse highlight the difficulty of reconciling quantum indeterminacy with classical reality.

Relational ontology offers a fresh perspective: the boundary is not a physical divide but a relational cut, a perspectival act that actualises one construal from the potential manifold of quantum possibilities.


Classical and Quantum Worlds as Perspectival Construals

Rather than viewing classical and quantum realms as ontologically distinct layers, relational ontology treats them as different construals within a structured potential.

  • The quantum state encodes a field of potentialities—structured relations awaiting actualisation.

  • The classical world emerges as a partial perspectival actualisation, a cut that foregrounds definite properties.

  • This perspectival cut is not a physical process per se but a semiotic act that differentiates and actualises one set of relations from the potential whole.


Measurement as a Metasemiotic Transformation

Measurement is then reconceived as a metasemiotic transformation:

  • It is a natural transformation between functors—between different perspectival mappings of the system.

  • The “collapse” is not a mysterious physical event but a shift in construal, an enactment of a new relational cut.

  • Decoherence models how environmental entanglement stabilises this cut, making the perspectival actualisation robust.


Resolving the Measurement Problem?

By situating the quantum-classical divide within relational ontology, the measurement problem dissolves:

  • There is no universal wavefunction collapse “out there.”

  • There are only perspectival shifts enacted by relational cuts, each legitimate within its construal.

  • The apparent paradox arises from mistaking perspectival actualisation for absolute, observer-independent physical processes.


Parallels to Gödelian Incompleteness

Just as Gödel showed no system can fully internalise its own truth, no single construal can exhaustively capture quantum potentialities.

The quantum-classical boundary exemplifies this ontological incompleteness—a necessary feature of perspectival being.


Summary

The quantum-classical boundary is best understood as a relational cut, a perspectival construal that actualises classical reality from quantum potential.

Measurement is a metasemiotic shift—a transformation of perspective, not an ontological rupture.


Coming Up Next

In Part 4, we will explore entanglement and non-separability as foundational manifestations of relational ontology in quantum systems.


4 Entanglement and Non-Separability: Relationality at the Core


Introduction

Entanglement stands at the heart of quantum theory’s conceptual revolution. It defies classical intuitions of separability and locality, revealing that quantum systems can exhibit correlations that cannot be explained by independent states of their parts.

Through the lens of relational ontology, entanglement is not a puzzling exception but a natural consequence of relational cuts and structured potentialities that resist decomposition into isolated construals.


Classical Separability vs Quantum Holism

Classical physics assumes separability: the state of a composite system is fully determined by the states of its constituent parts, each existing independently.

Quantum entanglement violates this principle:

  • The joint state of an entangled system cannot be expressed as a product of individual states.

  • Measurement on one part instantaneously influences the state ascribed to the other, regardless of spatial separation.

This challenges classical notions of independent entities and signals a fundamental relationality.


Relational Cuts and Structured Potential

From a relational ontology perspective:

  • Quantum systems are structured potentials, fields of relational possibilities not yet actualised.

  • Entangled states represent relational potentials that cannot be factored into independent parts—they are intrinsically holistic.

  • Any attempt to cut the system into parts imposes a perspectival construal that foregrounds certain relations but inevitably background others.

Entanglement thus embodies the ontological incompleteness inherent in perspectival systems.


Implications for Locality and Realism

Entanglement challenges classical realism and locality but, within relational ontology, these notions are reframed:

  • Locality is not an absolute metaphysical fact but a perspectival feature of certain cuts.

  • Realism becomes the coherence of perspectival construals within the relational network, not a claim to observer-independent states.

Non-local correlations reflect the inherent relationality of quantum potentials actualised through relational cuts, not “spooky action at a distance.”


Connecting Back to Category Theory

Entanglement aligns with categorical notions:

  • The inability to decompose states corresponds to the failure of certain factorisations in categorical terms.

  • Entangled states can be modelled by morphisms that do not split as products, reflecting inseparability of morphisms.

  • Functorial perspectives and natural transformations encode how entangled systems relate to measurement contexts.


Summary

Entanglement exemplifies relational ontology’s core insight:

Quantum wholes are not mere aggregates but irreducible relational potentials, whose parts cannot be fully individuated independently of perspectival construal.


Coming Up Next

In Part 5, we will investigate category theory and topos approaches to quantum logic, linking the formal and ontological perspectives introduced so far.


5 Quantum Logic and Topos Theory: Internal Worlds of Meaning


Introduction

Quantum theory resists classical logic. Propositions about quantum systems do not obey the laws of Boolean logic: distributivity fails, negation behaves strangely, and truth values appear contextual. Rather than force quantum phenomena into a classical mould, some foundational approaches—especially those informed by category theory and topos theory—have proposed a different path: quantum logic as internal to the system itself.

In this post, we explore how topoi and internal logics articulate a vision of logic and truth that aligns powerfully with the commitments of relational ontology: truth is not global and fixed, but emergent, situated, and perspectival.


Classical vs Quantum Logic

Classical logic assumes:

Quantum logic, emerging from the structure of Hilbert spaces and the lattice of projection operators, violates these assumptions:

  • The distributive law fails.

  • The logic is non-Boolean, and often non-classical.

  • Propositions about systems are contextual—truth values depend on the full measurement setup.

These features reflect not epistemic limitations, but an ontological shift in the nature of meaning.


Topos Theory: Internal Logic and Semiotic Worlds

Topos theory generalises the category of sets, enabling categories that come equipped with:

  • A subobject classifier (a generalised notion of truth values)

  • Exponentials, limits, and a rich internal structure

  • An internal language, allowing logical reasoning within the topos

Each topos carries its own internal logic. That logic is not imposed externally but emerges from the internal structure—a perfect fit with relational ontology.

A topos is not just a container of objects; it is a semiotic world, a field of meaning whose logic is determined by its own relational structure.

In this framework, quantum systems can be modelled as topoi whose internal logic encodes contextual truth, perspectival construal, and the collapse of classical totalisation.


Quantum Topos Theory: The Isham–Döring Program

The Isham–Döring approach to quantum theory constructs a topos in which:

  • Propositions about quantum systems have truth values not in {true, false}, but in a Heyting algebra internal to the topos.

  • The topos reflects the contextual structure of measurement: each context corresponds to a commutative subalgebra of observables.

  • The internal logic encodes perspectival truth: what is “true” depends on the relational frame.

This models quantum reality not as incomplete or paradoxical, but as internally consistent within perspectival constraints—precisely the insight advanced by relational ontology.


Logic as a Feature of the Cut

Relational ontology treats truth as a function of construal: every relational cut defines a semiotic system with its own coherence. Topos theory gives this formal substance:

  • Different topoi correspond to different systems of construal, each with its own internal logic.

  • Geometric morphisms between topoi model transitions between perspectives, enabling metasemiotic comparison.

  • Logic itself becomes local and contextual, not universal.

This transforms logic from a metaphysical foundation to a relational feature of perspectival meaning.


Summary

Quantum logic resists classical totalisation not because quantum theory is broken, but because classical logic overreaches. Through topos theory:

Logic is recast as a property of semiotic worlds—emergent from relational structure, not externally imposed.

This marks a convergence of relational ontology and categorical foundations: both insist that meaning and truth are internal, not universal; perspectival, not absolute.


Coming Up Next

In Part 6, we will explore quantum measurement as metasemiotic transformation, reframing collapse and interpretation in terms of functorial shifts and construal dynamics.


6 Measurement as Metasemiotic Transformation


Introduction

Measurement has long been the most philosophically fraught element of quantum theory. What begins as a smooth, unitary evolution of the quantum state suddenly becomes discontinuous, definite, and classical upon observation. Interpretations abound—collapse, decoherence, branching worlds—but none have resolved the disjunction at the heart of the measurement problem.

Relational ontology offers a fresh framework. If measurement is not the intrusion of an external observer, but a shift in semiotic construal, then the so-called “collapse” is not a physical process but a metasemiotic transformation: a perspectival shift enacted through the reorganisation of meaning within a relational field.


Measurement as a Change of Construal

Under relational ontology:

  • A system is not a set of fixed states, but a structured potential—a manifold of relational possibilities.

  • Measurement does not extract a hidden value; it enacts a new construal—foregrounding certain relations, backgrounding others.

  • This shift is not epistemic (what we know), but ontological: the measurement reconfigures what is.

This directly reframes collapse:

Collapse is not a discontinuity in physical evolution, but a relational cut that reorganises the field of meaning.


Functors and Natural Transformations: The Metasemiotic Layer

Category theory models this shift precisely:

  • A functor represents a perspectival construal of a system.

  • A natural transformation between functors represents a higher-order mapping: a shift from one construal to another.

  • Measurement is such a shift—it recontextualises the system, moving from a construal of potential to a construal of actualised value.

This is not a brute physical event but a semiotic act—a metasemiotic movement that changes the system's semiotic structure.


Decoherence and Stability of the Cut

While decoherence is often invoked to “explain” classical outcomes without collapse, it still operates within the same metaphysical assumptions: quantum systems evolve, environments entangle, classicality emerges.

Relational ontology recasts this:

  • Decoherence marks the stabilisation of a relational cut—an actualisation robust enough to persist across interactions.

  • The system does not "become classical"; it enters a new construal regime.

  • Classicality is not an emergent layer but a semiotic product of constrained relational configurations.


No Collapse, No Observer: Only Relational Shift

In this framework, there is no need for:

  • A privileged observer to "collapse" the wavefunction.

  • A hidden mechanism that turns superpositions into definite outcomes.

  • A metaphysical bifurcation between quantum and classical.

Instead:

Measurement is a metasemiotic transformation: a shift in the relational field that constitutes the system’s reality.


Summary

Quantum measurement is not the resolution of uncertainty by an external gaze. It is a reorganisation of potential via perspectival construal—a change in meaning, not mechanics.

Through category theory, this transformation becomes legible: natural transformations model metasemiotic shifts, expressing how systems move from one relational frame to another.


Coming Up Next

In Part 7, we turn to quantum no-go theorems—Bell, Kochen-Specker, and others—and explore how their constraints reveal the limits of totalising construal and the necessity of perspectival incompleteness.


7 No-Go Theorems and the Limits of Totalising Construal


Introduction

Quantum theory’s no-go theorems—Bell, Kochen-Specker, Gleason, and others—are often treated as obstacles to realism. They reveal that no hidden variable theory can reproduce the predictions of quantum mechanics while preserving locality, determinacy, or non-contextuality.

But these theorems do more than block classical metaphysics: they illuminate the limits of totalising perspective. From a relational ontology viewpoint, they are not constraints on reality, but constraints on how meaning can be globally construed.


Reframing the No-Go Theorems

Let us briefly recall the content of three central theorems:

  • Bell’s Theorem: No local hidden variable theory can reproduce quantum correlations (as verified in entangled state experiments).

  • Kochen–Specker Theorem: It is impossible to assign non-contextual, definite values to all quantum observables in Hilbert spaces of dimension ≥ 3.

  • Gleason’s Theorem: Any assignment of probabilities to measurement outcomes must conform to the Born rule—leaving no room for hidden structures beneath quantum amplitudes.

These results rule out the possibility of a single, globally coherent construal of a quantum system that preserves classical expectations.


The Metaphysical Assumptions Challenged

Each of these theorems challenges specific metaphysical presumptions:

  • Bell undermines local separability—the idea that parts of the universe can be cleanly individuated.

  • Kochen–Specker rules out non-contextual realism—that properties exist independent of the measurement context.

  • Gleason excludes a hidden-layer epistemology—one that assumes that probabilities are ignorance about underlying definites.

In classical terms, these feel like losses. But for relational ontology, these are features, not bugs: they indicate where totalising construal fails, and relational structure asserts itself.


Relational Ontology: No-Go as Necessary Cut

From our perspective:

No-go theorems are not merely prohibitions; they formalise the impossibility of meaning without perspectival construal.

Each theorem identifies the impossibility of a global, unconstrued view of the system—precisely what relational ontology posits:

  • Systems cannot be fully specified independently of the cuts that make them meaningful.

  • There is no “view from nowhere” from which all relations are simultaneously resolved.

  • Quantum theory does not lack a foundation; it is the foundation of a perspectival world.

The no-go theorems thereby echo Gödel’s insight: any sufficiently expressive system will entail limits on self-reference and totalisation. But here, the system is the world, and the theorem is an ontological principle.


Category Theory and No-Go: Failure of Global Sections

In categorical language, many of these results can be seen as obstructions to global sections:

  • A global section is a consistent, context-independent assignment of values.

  • The Kochen–Specker theorem can be restated as the non-existence of global sections over the presheaf of quantum observables.

  • This frames the result in purely relational terms: no coherent global construal exists across all contexts.

This is not a breakdown; it is a mathematics of perspectival necessity.


Summary

No-go theorems are not pathologies to be resolved, but formal witnesses to the perspectival nature of reality. They make visible the cut—the impossibility of construing a totalised view without erasing the relational fabric that makes meaning possible.


Coming Up Next

In the final post, we will bring the series to a close by synthesising its insights. We will sketch the outlines of a relational metaphysics of quantum theory—one grounded in structured potential, perspectival construal, and categorical coherence.


8 Concluding Reflections: Toward a Relational Metaphysics of Quantum Theory


Revisiting the Journey

Over the course of this series, we have developed a sustained encounter between quantum theory, category theory, and relational ontology. We began with the observation that quantum foundations, like Gödel’s incompleteness, confront us with deep structural limits: on what can be known, what can be defined, and what can be made definite within a system.

Rather than read these limits as epistemic shortcomings or metaphysical gaps, we reframed them ontologically: they mark the necessity of relational cuts, perspectival construals that make meaning possible precisely because they are partial.

This shift—from metaphysical lack to ontological structure—has guided our reinterpretation of core quantum phenomena.


Key Insights Reframed

1. Quantum Contextuality

Measurement outcomes are not objective discoveries of pre-existing facts, but actualisations of structured potential within perspectival frames. Contextuality reflects not indeterminacy, but the irreducibility of the relational cut.

2. The Quantum-Classical Boundary

Rather than a metaphysical divide, the quantum–classical “boundary” is a semiotic shift—a construal move that stabilises one perspective. Collapse is not physical rupture, but a metasemiotic reorganisation of the relational field.

3. Entanglement and Non-Separability

Entangled systems manifest relational holism: the impossibility of decomposing meaning into independent parts. Their structure resists classical individuation because they are not “things” to be divided, but relations that cannot be severed without changing the very field in which they arise.

4. Topos Theory and Internal Logic

Quantum logic emerges not as a defect of quantum systems, but as the internal logic of semiotic worlds. A topos is a relational universe, with its own truth structure—coherent, local, and contextual. Logic itself is perspectival.

5. Measurement as Metasemiotic Transformation

Measurement is best understood as a natural transformation between construals: a transition not of physical states, but of meaning. It shifts the system into a new semiotic configuration, stabilising one construal within a broader potential.

6. No-Go Theorems as Ontological Markers

Bell, Kochen–Specker, and others articulate the limits of totalising perspective. They are not failures of realism, but formal expressions of perspectival necessity. There is no global section—not because the world is broken, but because the world is relationally structured.


Relational Metaphysics: What Emerges

What then is the metaphysical image of quantum theory that emerges from this integration?

  • Systems are not self-contained entities, but fields of potential meaning, structured by relations.

  • Truth is not external and universal, but internal to systems of construal—emergent from relational structure.

  • Observation is not a penetration into hidden being, but a perspectival act that constitutes what is.

  • Category theory and topos logic offer the formal language of this worldview: a rigorous mathematics of perspectival meaning.

This metaphysics does not seek to unify or totalise, but to articulate the conditions under which meaning becomes possible—how reality itself is cut into being through construal.


A Final Thought

The classical dream was to describe the universe from nowhere: to survey reality with absolute certainty, to complete the system. But the lesson of Gödel, and the lesson of quantum theory alike, is this:

There is no nowhere.
There is only here—a cut, a frame, a construal.
And in that frame, meaning lives.

Relational ontology does not lament this. It affirms it.
It sees not a broken world, but a relationally cut one—a world that becomes real in and through its perspectives.