Causation, Computation, Indexicality: A Complete Metaphysics

1. Causation as a Metaphysical Primitive

Contemporary philosophy of causation is dominated by two camps. Humeans hold that causation is nothing more than regular succession or counterfactual dependence — patterns in what happens, with no deeper metaphysical “oomph.” Anti-Humeans, drawing on the powers tradition, argue that causation is grounded in real dispositional properties intrinsic to things.

We propose a different starting point. Physics, as a discipline, is descriptive. It discovers bulk regularities — differential equations, symmetries, conservation laws — that tell us what happens with extraordinary precision. But description is not generation. Physics maps the territory; it is not the territory. Beneath the descriptive regularities of physics lies a generative structure: causation understood as a metaphysical primitive.

This primitive is not one of the four Aristotelian causes singled out for special treatment. It is efficient causation taken seriously as fundamental — the actual producing of the next state from the current one, prior to and independent of any description we give of the process.

2. The Collapse of Causation and Computation

Computation, in the Church–Turing sense, is about what can be produced from what by finite, definite steps. Causation, stripped to its metaphysical core, is about what produces what. If both are taken as primitive — not as descriptions of regularities but as the actual generative structure of reality — they converge. Computation is causation made precise; causation is computation made metaphysical.

The extended Church–Turing thesis strengthens this convergence. Read ontologically rather than epistemically, it characterises the generative primitive itself: the structure of what can be produced has the structure of computability. There is nothing causation does that is not a computation, and there is no computation that is not a causal process.

Wolfram’s physics project makes the identification nearly explicit. Hypergraph rewriting rules are a computation, and they are the causal structure. The causal graph emerging from the rewriting history is not a representation of causation — it is causation. The two descriptions — one emphasising logical structure (computation), the other emphasising productive character (causation) — pick out the same primitive.

But if causation and computation are one, a question immediately arises: is every computation real? Can any physical system be interpreted as performing any computation, given a sufficiently ingenious mapping? Hilary Putnam argued that it can — that computational descriptions are observer-relative, not intrinsic to the physics. If that were right, the collapse of causation and computation would be vacuous: everything would compute everything. The answer to Putnam requires a precise account of what makes a computational description genuine rather than projected. That account depends on the notion of real patterns, to which we now turn.

3. Real Patterns and Constitutive Grounding

A pattern carries modal depth when it supports counterfactuals, sustains predictions under intervention, and remains stable across a range of perturbations. This modal depth belongs to the pattern as a mathematical structure, independent of any particular physical realisation. The structure of a feedback loop, a neural network, or a predator–prey dynamic supports counterfactuals whether or not it is physically instantiated. Considered purely as mathematics, it already has the richness that makes it explanatorily powerful.

What, then, distinguishes a real pattern in a physical system from a merely projected one? Not modal depth alone — a sufficiently clever observer can always find some mathematical structure with modal depth and map it onto any sufficiently complex physical process. The distinction lies in the constitutive grounding relation: the relation between the pattern and the physical process that realises it.

Following Ladyman and Ross (Every Thing Must Go, 2007), we hold that the relationships between descriptions at different scales — whether spatio-temporal or energetic — are properly captured by structure-preserving maps: morphisms that preserve the modal and counterfactual structure of the higher-level description in the lower-level dynamics. A pattern is genuinely realised in a physical system when the realization relation is such a morphism. Causal succession at the pattern level maps onto causal succession in the physics. Intervene on the pattern and you intervene on the physics; perturb the physics within the relevant range and the pattern-level structure is preserved. The modal structure of the mathematics is echoed in the modal structure of the physical realisation.

This is what “bulk regularities” means precisely. When we say that physics describes the bulk regularities of what Layer 0 generates, we mean that the mathematical structure of physical theories — general relativity, quantum mechanics, thermodynamics — maps onto the generative dynamics via structure-preserving limiting relations. Wolfram’s programme is the attempt to exhibit these morphisms explicitly: to show that the mathematical structure of known physics is preserved under the passage from hypergraph rewriting to the continuum. The same holds at every inter-layer transition. The mathematical structure of biology maps onto physics via biophysical morphisms. The mathematical structure of cognitive science maps onto neurobiology. At each step, what makes the higher-level description real rather than fictive is that the grounding relation preserves modal structure.

The classic thought experiment that tests this criterion is the “dust man” — the claim that a mind could be instantiated by scattered dust particles if one assigns the right computational interpretation to their states. The dust man pattern, considered as mathematics, has genuine modal depth: the computation it describes supports counterfactuals internally. But the grounding relation between the dust particles and the computational states is not a structure-preserving map. Adjacent physical states of the dust do not map to adjacent computational states. Causal succession in the dust dynamics does not track causal succession in the computation. The “morphism” is an arbitrary lookup table — a gerrymandered mapping that preserves nothing. The pattern is real as mathematics. It is not realised in the dust.

A brain is different. The functional organisation of a neural network is constitutively grounded in the physics via genuine morphisms: intervene on network connectivity and activation dynamics change predictably; perturb the physics and the pattern-level behaviour responds systematically. The realization relation preserves the modal structure that makes the higher-level description explanatorily indispensable.

This resolves Putnam’s challenge. Not every computational description is genuine. A computation is real in a physical system when and only when the grounding relation is structure-preserving — when the modal depth of the mathematical pattern is inherited by the physical realisation through a genuine morphism rather than an arbitrary assignment. The collapse of causation and computation is not vacuous, because computation-in-the-world is constrained by the same criterion that governs all inter-layer relations: the constitutive grounding must preserve structure.

Real patterns at each layer interact causally in the ordinary sense — the organisation of a brain causes things that are inexplicable without the pattern-level description. But this causation is not generative in the Layer 0 sense. It does not add productive power to the generative primitive. It is entirely constituted by that primitive. What the pattern-level description captures is structure within the generative output — structure with modal depth, preserved across the grounding relation, and therefore genuinely explanatorily relevant. Not generative, not Platonic, but not merely projected either. Real.

4. Four Ontological Layers

The world of things has a layered structure, arranged on what we call the mereological continuum — a spectrum of increasing mereological (part–whole) complexity. Beneath the world of things sits a zeroth layer: the generative principle itself.

5. Indexicality and the Boundary of Mathematics

What distinguishes facts on the mereological spectrum from facts that are purely mathematical? Our answer: indexicality.

Mathematical facts are structure without indexicality. “2+3=5” does not happen anywhere, to anything. It obtains absolutely, without reference to any particular location in any generated world. The mereological layers, by contrast, are actual — they happen, they are generated, they are particular.

But — and this is the crucial move — indexicality does not permeate the mereological spectrum from below. It originates at Layer 3, with representation. A computation does not point to itself. A particle is not “here” for itself. Without a representing mind, there is structure, activity, organisation, but no perspective, no “here,” no “this.” Indexicality is what Layer 3 adds to the world.

Once generated, however, indexicality propagates mereologically downward. Because a mind is made of biological structures which are made of physical structures which are generated by the computational primitive, its indexicality reaches into its own constitution. “This brain,” “these neurons,” “these atoms” — these are indexical because they are parts of something that indexes. The representational whole makes its own parts available as “these parts.” Mathematics, having no mereological relationship to any representer, never acquires indexicality.

A remarkable consequence follows. Without a mind — without Layer 3 — there is no fact of the matter whether a universe is real or merely mathematical. Actuality is not a property that the universe has intrinsically. It is what the universe looks like from inside, from the perspective of a representational being embedded in it. The indexical “this universe” is what makes it real rather than merely mathematically obtaining. Without the mind, the distinction collapses.

This also explains why physics and mathematics share the same epistemic structure. Both proceed by constructing things and building theories of those constructions. There was never an ontological gap between them. The gap is purely indexical — contributed by the representer. Physics feels different from mathematics because we are in it, not because it is different.

6. The Structure of Mathematics

Mathematics appears to have structure: distinct fields (algebra, analysis, topology, number theory, logic) and deep correspondences between them (Galois theory, the Langlands programme, Curry–Howard). Some of this structure seems necessary — the correspondences feel like discoveries about how mathematical reality is articulated. Some seems sociological — the boundaries of named fields reflect human institutional history more than ontological joints.

If the generative primitive is computational, then computability provides a natural organising principle for mathematical structure. The Curry–Howard correspondence — proofs are programs, propositions are types — is not a curiosity but a reflection of the intimate relationship between mathematical structure and the structure of computation. The deep correspondences in mathematics — the ones that feel like discoveries — may be the internal joints of computability showing through. The sociological accidents are the human-drawn boundaries between fields. The necessities are the joints themselves.

7. Normative Facts and the Mathematics of Indexicality

Where do normative facts sit in this picture? Following Parfit and Putnam, we hold that normative facts are real, irreducible, and neither physical nor natural. But if mathematical facts and the mindless mereological spectrum are indistinguishable, what makes normative facts distinctive?

Our proposal: normative facts are the mathematics of indexicality. They obtain like mathematical facts — they are not generated by the causal–computational primitive, they do not happen. But their subject matter is the situation of being a perspective embedded in structure. They are the truths about what follows from being a “this” in a world.

This distinguishes them from their neighbours. Psychological facts are Layer 3 descriptive facts about what minds actually do, feel, and prefer. Sociological facts are Layer 2/3 descriptive facts about collective behaviour. Theory of science, as a historical discipline, describes part of society. But epistemology — the normative theory of knowledge — is about how indexical beings should form beliefs. It is normative about the relationship between a representing mind and truth.

Epistemology is the bridge case that demonstrates normative realism, because even thoroughgoing naturalists accept that there is a real difference between good and bad epistemic practice that is not merely conventional. From epistemology, the path to morality requires one further step: an account of the good.

8. Finitude, Plurality, and the Account of the Good

The generative primitive is local. Computation proceeds step by step, neighbour by neighbour. There is no action at a distance in Layer 0. This locality constraint has a profound consequence for minds: a mind cannot grow without limit. The coordination costs of maintaining a unified perspective scale with size. Minds are necessarily finite and bounded. A planetary mind — a Solaris — is not possible.

Furthermore, the evolutionary and informational dynamics that produce Layer 3 beings produce them in populations. A mind emerges already surrounded by other minds. Plurality is not an accident that happens to minds after they exist; it is a condition of their arising.

The account of the good begins from these two structural constraints: finitude (no mind can grow to encompass everything) and plurality (every mind always faces others). These are not contingent empirical facts. They follow from the locality of Layer 0 and the dynamics of how Layer 3 arises from Layer 2.

Morality is then genuinely pragmatic in character. Finite minds facing other finite minds need ways of coordinating, recognising one another, navigating irreducible difference. Each mind is an achieved indexical unity that cannot encompass the perspectives of others. Other minds are genuinely other — not parts of one’s potential expansion, not subsumable. The good involves taking that otherness seriously, precisely because it is structurally irreducible.

This also guards against totalitarian degradation. Any political or moral project that aims at total unity — one perspective subsuming all others — works against the locality constraint. It is not merely morally wrong; it is metaphysically impossible. It can only be approximated by destroying other perspectives, never by genuinely incorporating them.

9. Why Live?

This brings us to the question Camus asks. If you are a finite indexical unity, always precarious, facing irreducible others, unable to grow without limit or achieve total coherence — and if the universe without your perspective is indistinguishable from a mathematical structure — then why maintain the unity? Why keep indexing?

Camus, working within a broadly naturalist picture, concluded that the universe is indifferent and meaning must be created by defiance — Sisyphus happy. But our framework offers resources Camus lacked.

The key is that “should” is a mathematical construct — a normative fact that obtains about the situation of indexical beings. The moral life is not imposed on us by the universe. It is not a compulsion. It is a genuine structural possibility, grounded in real features of our situation: finitude, plurality, the irreducibility of other perspectives. The reasons are real. But the reasons do not bind.

Every individual must answer for themselves whether they want to live a moral life, but it is an option — a real one, not an illusion and not an absurdity. The structure is there. It is yours if you want it.

This is more respectful of Camus’s question than most answers. It does not pretend the universe forces your hand. It does not claim that recognising the moral structure compels you to live by it. It says: here is something real, something structured, something worth engaging with. Not absurd, not compulsory. Just there.

10. What’s on Offer

Suppose you answer yes. What does the moral life look like from within this framework?

The first thing on offer is a non-brute account of why some experiences are better than others. This is the insight at the heart of Peter Singer’s moral realism: suffering matters, and it matters wherever it occurs, across all beings capable of it. But on Singer’s presentation, this can appear as a foundational axiom — the capacity to suffer is morally relevant, and that’s where explanation stops.

Our framework goes further. A mind is an achieved indexical unity, maintaining coherence against the locality constraints of Layer 0. This maintenance is not merely a formal property — it is experienced. Experience is what the ongoing achievement of unity feels like from inside.

The negative pole is clear. Suffering is the phenomenology of coherence under threat: fragmentation, disruption, the locality constraints winning over the unifying process. It is the felt character of a perspective losing itself. Suffering matters, morally, because it is the dissolution of the very thing — the indexical unity — that makes there be a perspective at all. This is not a brute normative fact but a structural consequence of what minds are.

The positive pole is not simply the absence of suffering — not homeostasis, not comfortable equilibrium. A mind sitting in stable coherence is not yet flourishing. Flourishing is the expansion of what the unity can coherently integrate: new capacities for expression, perception, connection, understanding. It is the indexical unity achieving new plateaus of expressive potentia — new modes of coherence that were previously unavailable to it. The pianist who suddenly hears the whole architecture of a piece; the thinker who sees why two problems are really one; the moment of genuine mutual recognition with another mind. These are not merely pleasant experiences. They are the perspective discovering that it can do more with its indexicality — that it can engage more richly with the world and with other minds, making more of reality actual through its particular point of view.

This expansion naturally involves strain, because coordinating a more complex or more capable unity is harder — the locality constraints do not relent. But the strain of growth is structurally different from the fragmentation of suffering. In suffering, the unity is coming apart. In growth, the unity is reorganising at a higher level; the discomfort is incidental to a process that serves the perspective rather than threatening it.

Singer is right that moral concern extends across all beings capable of experience. Any Layer 3 entity — any achieved indexical unity, however different its substrate — faces the same structural situation: the possibility of fragmentation, the possibility of new plateaus. The moral relevance of experience is not parochial to humans. It follows from what it is to be a mind at all.

But the plurality constraint adds something that pure utilitarianism tends to undersell. Because each mind is a structurally unique indexical unity, perspectives are not interchangeable. You cannot simply aggregate welfare across minds as though they were fungible containers of experience. Each perspective is irreducibly its own — a distinct achievement of unity, a distinct way of making the world actual. The good is not just the minimisation of suffering and maximisation of flourishing across a population of experiencers; it is also the recognition that each experiencer constitutes something that no other experiencer can replace.

What’s on offer, then, is this: a moral life grounded in the real structure of indexicality, where suffering and flourishing are not brute givens but consequences of what it is to be a finite perspective — suffering as fragmentation, flourishing as the expansion of expressive potentia. The scope of moral concern extends to all beings capable of experience, and the irreducible otherness of each mind is not an obstacle to ethics but its foundation. The structure is there. If you choose to enter it, this is what you find.

This article was developed through dialogue between Łukasz Stafiniak and Claude (Anthropic), March 2026.