In a 1989 paper in *Dialectica* titled "Structural Realism: The Best of Both Worlds?", John Worrall proposed that what survives across theory change in physics is not the entities science postulates but the structural relations encoded in its mathematics. The Fresnel equations survived the abandonment of the luminiferous ether; what was preserved was the structure, not the substance. Worrall's epistemic structural realism (we can know the structure but not the natures of the relata) became, over the next two decades, the most discussed form of scientific realism. James Ladyman pressed the position further. In "What is Structural Realism?" (1998) and then with Don Ross in *Every Thing Must Go* (2007), structural realism turned ontic: there are no relata with intrinsic natures awaiting our knowledge of them; reality is structures all the way down. Steven French's *The Structure of the World* (2014) gave the position its most systematic book-length defense. Michael Esfeld and Vincent Lam developed a moderate version on which objects are retained as nodes within the structure but stripped of independent intrinsic natures (Esfeld 2004; Esfeld and Lam 2008). Anjan Chakravartty's *A Metaphysics for Scientific Realism* (2007) defended a semirealist alternative: structures and detectable causal properties are real, with dispositional natures grounding the causal properties. The position now occupies a continuum: epistemic structural realism (Worrall) at one end; moderate ontic structural realism (Esfeld, Lam) in the middle; eliminativist ontic structural realism (Ladyman, Ross, French) at the other. The challenge to the present account is that the trio T, S, Φ (the three structural Conditions, borne by Time, Space, and Substance) may be a parochial selection from a much richer relational fabric the position describes, and the argument's necessity claim of [§2.8.5](<2.8.5 Necessity of Nature.md>) (Necessity of Nature), supported by the Modal Identity and Triconditional machinery of §[§2.6](<2.6 Triconditionality of Nature.md>)–2.7, may be the wrong claim about the wrong feature.

The challenge sits closer to the present account than to its standard rivals, and the reply is correspondingly cooperative. The present argument does not posit T, S, and Φ as objects with intrinsic natures; it identifies role-level conditions of genuine change-realizers. OSR's claim that the world is fundamentally relational is compatible with directed order, relational differentiation, and real bearing. Whether a given physical relational fabric also realizes temporal succession, spatial extension, and causal persistence is a further type-level question, not something settled merely by calling every relation Time, Space, or Substance. The disagreement concerns both the modal status of the roles and the step from roles to their realizers. OSR is typically silent on whether the relational structure it describes is necessary or contingent; the present argument fills in the modal claim. Three forms of the position sharpen what it can commit to and what each commitment costs.

*First.* The eliminativist form (Ladyman and Ross 2007; French 2014) eliminates objects entirely. There are no things; there are only patterns of relation. The challenge: any pattern of relations could constitute a world, and the trio T, S, Φ is a parochial choice from the space of relational fabrics. The reply runs through §[§2.6](<2.6 Triconditionality of Nature.md>)–2.7: any pattern of relations capable of supporting a configuration (any pattern offered as a realizer of change) must include the three roles at the appropriate resolution. Bare obtaining directly supports determinacy or difference, but does not by itself entail temporal extension or causal persistence. Those stronger types require the separate change-realizer arguments. French's careful development in *The Structure of the World* makes the point sharper, not weaker. The relations he identifies as fundamental (group-theoretic symmetries, gauge structures, permutation invariance) are relations among distinguishable items or positions (S). In familiar dynamical formulations, they are also articulated through an order of states or events (T) and through constraints or capacities that hold determinate physical difference in place (Φ). But a thoroughgoing atemporal-structure reading need not concede that the formal parameter in an equation is fundamental time. It owes a different account: how the atemporal structure grounds an emergent order in which real differences can occur, and how determinate capacities are available within that order. Merely redescribing the base as structure does not discharge those obligations; neither does the present argument certify that every timeless structural proposal meets them.

The division matters. T is the order of before and after; Φ is the determinate capacity or bearing condition that is exercised in that order. They are mutually required for real change but not the same role. The eliminativist version therefore does not by itself undermine the role-level claim. It reformulates ontology in relational terms and can resist intrinsic-nature-bearing objects. But it remains a live challenge at the type level: an eliminative structuralist may deny that relations require persistent causal bearers in the book's richer sense. The present account can reply that a relational fabric proposed as physical reality or as a realizer of change must meet the relevant type arguments; it does not treat eliminative OSR as defeated merely because relations are named. T, S, and Φ are roles; the configurations satisfying the roles need not be intrinsic-nature-bearing objects in the sense OSR rejects.

*Second.* The moderate form (Esfeld 2004; Esfeld and Lam 2008) retains objects as nodes within the structure but denies them independent intrinsic natures. The position is straightforwardly consistent with the present account: configurations are nodes within the structural fabric, and T, S, and Φ are the relational roles the fabric must include for any node to obtain. Esfeld's central claim (that nodes are exhausted by their relational profiles) itself requires the relational profiles to be temporally extended, relationally distinct, and persistent across the relations they enter into. The moderate OSR theorist and the present account converge: both deny that fundamental ontology requires intrinsic-nature-bearing objects; both affirm that fundamental ontology requires relational structure with the features the present account names. The disagreement, if there is one, is about whether the relational structure described by current physics (group symmetries, gauge invariance) exhausts what is fundamental, or whether the structural roles T, S, Φ are necessary at a level prior to physics. The present argument takes the second view and offers [§2.6](<2.6 Triconditionality of Nature.md>) for the Modal Identity result and the mutual-requirement / Triconditional machinery, and [§2.7](<2.7 Nothing to Consider.md>) for the collapse of the unstructured alternative: the three roles mutually require one another and cannot be reduced to a more primitive base.

Ladyman’s Principle of Naturalistic Closure gives the modal claim its sharpest methodological challenge: no metaphysical hypothesis should be accepted unless it serves to unify well-confirmed hypotheses from more than one specific science. The necessity of T, S, and Φ satisfies this constraint in an unusual but genuine way. The three structural roles are not a hypothesis derived from one science and then applied to others; they are the conditions on which any scientific inquiry operates. Temporal succession is presupposed by every state-evolution formalism in physics; it is equally presupposed by the experimental design structures in cognitive science, economics, and biology. Relational extension is constitutive of field theory, topology, and network science alike. Causal persistence is what conservation laws, developmental biology, and institutional economics each track, in different vocabularies, at different scales. The claim that T, S, Φ are necessary is not a physics claim that chemistry must accept on physics’s authority; it is a claim about conditions that each science independently instantiates whenever it describes anything at all. In Ladyman's own terms, this is a unification claim (identifying the structural joints across all sciences, not merely within one). And it is warranted not by rationalist intuition but by the demonstration in §[§2.6](<2.6 Triconditionality of Nature.md>)–2.7, specifically [§2.6.7](<2.6.7 Triconditional Cross-Entailment.md>) (Triconditional Cross-Entailment), where the physics-facing case is made that any nomological structure requires T, S, and Φ as co-instantiated, that the three roles mutually require one another and are jointly presupposed by any coherent structural description. The Principle of Naturalistic Closure rules out free-floating neoscholastic machinery; the present claim is not free-floating but confirmed at every juncture where a science describes structure, which is to say at every juncture where science operates.

*Third.* The semirealist form (Chakravartty 2007) retains both structure and detectable causal properties, treating dispositional natures as the ground of causal-property detectability. The position is the most ontologically committed of the OSR family and the most consistent with the present account. Chakravartty's detectable causal properties are configurations of T, S, and Φ at the level at which physics meets phenomena: dispositions are temporally extended (manifesting over time), relationally specified (manifesting in relation to other dispositions or stimulus conditions), and causally persistent (carrying their manifestation profile across the relations). The present account does not adjudicate between Chakravartty's dispositionalist commitments and the more austere ontologies of moderate OSR; what it requires is what all three positions concede when fully developed: the relational fabric instantiates the structural roles.

A kindred move worth marking. The structuralist tradition in philosophy of mathematics, Resnik (*Mathematics as a Science of Patterns*, 1997), Shapiro (*Philosophy of Mathematics: Structure and Ontology*, 1997), runs a parallel argument in the mathematical case: mathematical objects have only relational properties, and the structures themselves are what is real. The reply parallels the OSR reply: a mathematical structure contains distinguishable positions or relational differences, directly supporting the S-role. Stability across mathematical instances is not automatically physical persistence, and the temporal course of our inquiry is an act-side feature rather than a property of the abstract structure. Mathematical structuralism therefore supports the thin relational point while leaving T- and Φ-realization open. The argument's modal claim is consistent with both.

Two adjacent positions live elsewhere. The Tegmarkian "mathematical universe" hypothesis (Tegmark 2008, 2014) runs a parallel ontological-monism move with mathematics rather than relational structure as the fundament; it is engaged at [§4.3.7](<4.3.7 Mathematical Universe Hypothesis.md>). The information-theoretic ontology that treats reality as fundamentally informational is engaged at [§4.1.5](<4.1.5 Information-Theoretic Foundationalism.md>).

*What converges.* The present account converges with each of three forms of OSR (eliminativist, moderate, semirealist) at increasing levels of ontological commitment. Eliminativist OSR rejects intrinsic-nature-bearing objects, which the present account does not require. Moderate OSR retains nodes as structurally exhausted, which the present account already affirms. Semirealist OSR retains dispositional natures, which the present account is consistent with without requiring. The disagreement, where there is one, is about whether the trio T, S, Φ is necessary at a level prior to the relational fabric current physics describes, or merely one description among others of that fabric. The case for the prior-necessity reading is given at §[§2.6](<2.6 Triconditionality of Nature.md>)–2.7, with [§2.6.7](<2.6.7 Triconditional Cross-Entailment.md>) (Triconditional Cross-Entailment) providing the physics-facing demonstration that any nomological structure requires T, S, and Φ as co-instantiated, and OSR theorists who reject it owe a counter-argument, and what the literature has produced (group-theoretic symmetries, gauge invariance, permutation structure) does not yet supply one. What it supplies is rich confirmation that the relational fabric, however described, includes the structural roles.

Structural realism was proposed to reconcile the no-miracles argument for scientific realism with the pessimistic meta-induction from theory change. Two decades after Worrall, Ladyman and Ross gave the position its fullest ontic form. Two more decades later, French and Esfeld and Chakravartty have populated the space between epistemic and eliminativist with positions that disagree about objects but converge on structure. The present argument takes the convergence seriously. Whatever the relational fabric of fundamental physics turns out to be, T, S, and Φ are the conditions on its being a relational fabric at all.


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← [4.3.8 Non-Locality, Branching, and the Particle Concept](<4.3.8 Non-Locality, Branching, and the Particle Concept.md>) | [4.3.10 Bundle and Trope Theory](<4.3.10 Bundle and Trope Theory.md>) →
