A Semantic, Empirical and Metaphysical Audit

1. Introduction

Scientific theories make indispensable use of temporal and spatiotemporal vocabulary. Clocks register proper-time intervals; dynamical laws are written with temporal parameters; relativistic geometry encodes causal and inertial structure. It is natural to infer from this indispensability that time or spacetime must be a fundamental feature of the world. The central question of this paper is whether that inference is justified. The guiding thought is simple: indispensability for representation does not, by itself, settle questions of ontology. Many representational tools in physics – coordinate systems, gauge potentials, phase-space parameters – are indispensable for formulating theories but do not correspond to fundamental entities. Temporal and spatiotemporal vocabulary may be similar. The challenge is to determine whether time or spacetime performs irreducible empirical or explanatory work beyond the roles already discharged by physical change and relational structure.

To address this challenge, the paper develops a three-part conceptual audit:

• Semantic audit: identifies how polysemy, metaphor, indexicality, and reification in temporal language enable unlicensed transitions from representational claims to ontological ones.
• Empirical audit: examines what experiments actually measure – change-events, correlations, geometric relations – and how these underdetermine temporal ontology.
• Metaphysical audit: clarifies when explanatory roles attributed to time or spacetime can be discharged by change and lawful dependence relations.
  

On the basis of this audit, the paper introduces the Ontological Necessity Criterion (ONC): A representational posit is ontologically necessary only if removing it leaves empirical or explanatory content unaccounted for. ONC is deliberately modest. It does not claim that temporal or spatiotemporal entities are never ontologically necessary. It claims only that such necessity must be demonstrated rather than assumed. The resulting Conditional Redundancy Thesis holds that if change and relational structure discharge the empirical and explanatory roles attributed to time or spacetime, then temporal and spatiotemporal ontology is redundant. The argument is situated within contemporary debates about spacetime functionalism, effective geometry, dynamical approaches, timelessness, and scientific representation.

Functionalist and relationalist views already separate roles from ontology; the present paper aims to sharpen this separation by isolating the additional premise required to move from temporal representation to temporal ontology. The increment is twofold: a semantic mechanism – polysemy-driven ontological transfer – and a methodological criterion – ONC – that together clarify when temporal and spatiotemporal vocabulary commits us to ontology and when it does not. The structure of the paper is as follows. Section 2 situates the argument within historical and contemporary debates and articulates its position relative to spacetime functionalism, effective geometry, dynamical approaches, timelessness, and work on scientific representation. Section 3 introduces ONC and states its distinction from spacetime functionalism. Section 4 develops the semantic, empirical, and metaphysical audits, including examples from general relativity and causal set theory. Section 5 considers metric-field realism, sophisticated substantivalism, ontic structural realism, temporal realism, and explanatory necessity. Section 6 concludes by summarising the Conditional Redundancy Thesis and its implications for the metaphysics of time and spacetime.

2. Background and Motivation

Philosophical debates about the ontology of time and spacetime have long been shaped by two broad traditions. One treats temporal and spatiotemporal structure as fundamental features of the world; the other treats them as derivative, emergent, or representational. The present paper does not attempt to adjudicate between these traditions directly. Instead, it examines a conceptual mechanism that operates across them: the way temporal vocabulary is used, and the metaphysical assumptions that can be smuggled in through that usage

2.1 Historical Context

Classical substantivalism treated time as an independent container within which events occur. Relational approaches, from Leibniz to Mach, argued that temporal structure arises from relations among physical events. The development of relativity complicated this landscape. Minkowski spacetime suggested a unified geometric structure, while later work in quantum gravity raised the possibility that spacetime itself may be emergent.

Across these debates, temporal vocabulary has been used in multiple senses: as a coordinate, as a measure of change, as an experiential phenomenon, and as a metaphysical entity. These senses are rarely distinguished explicitly. As a result, arguments for the fundamentality of time often rely on transitions between them without acknowledging the additional metaphysical premises required.

2.2 Contemporary Motivations

Current discussions in philosophy of physics often focus on whether spacetime is fundamental, emergent, or representational. Structural realists emphasise the metric as a physical field; relationalists emphasise dynamical relations; functionalists emphasise the roles played by temporal and spatiotemporal structures. Meanwhile, debates about the “flow” or “passage” of time continue to draw on experiential and phenomenological considerations. The present paper is motivated by a methodological question that cuts across these debates: What empirical or explanatory work would justify positing a fundamental temporal or spatiotemporal entity? This question is not answered by pointing to the indispensability of temporal representation.

Many indispensable representational tools – coordinate systems, gauge potentials, phase-space parameters – do not correspond to fundamental entities. The challenge is to determine whether temporal or spatiotemporal entities perform irreducible empirical or explanatory work beyond that supplied by physical change and relational structure.

2.3 Why a Conceptual Audit Is Needed

Three observations motivate the conceptual audit developed in this paper:

– Temporal vocabulary is polysemous. Without explicit disambiguation, arguments risk transferring conclusions licensed in one sense of time to claims expressed in another.

– Empirical evidence underdetermines temporal ontology. Experiments detect physical processes and relations, not a temporal entity in addition to these.

– Representational indispensability does not entail ontological fundamentality.

Temporal coordinates and proper-time intervals are indispensable for expressing dynamical relations, but indispensability alone does not justify ontological commitment.

2.4 Position in the Contemporary Literature

The paper complements rather than replaces existing accounts. Spacetime functionalism asks how spacetime’s empirical roles might be realised; Knox analyses effective geometry at relevant scales; Brown explains inertial structure through dynamics; Baron, Miller, and Tallant examine temporal concepts in agency and deliberation; and representation theorists caution against reading a model’s structure directly as an inventory of reality (Lam & Wuthrich, 2018; Knox, 2013; Brown, 2005; Baron et al., 2022; van Fraassen, 1980; Suarez, 2010; Frigg & Nguyen, 2020). These works give distinct reasons to separate role, representation, and ontology. The question developed here is what additional reason would support the ontological posit after relevant roles have been identified.

Increment

The contribution is limited: the paper identifies polysemy-driven ontological transfer and formulates ONC as a diagnostic for the remaining ontological question. It does not refute the approaches above or establish that no temporal or spatiotemporal ontology can be necessary.

Background and Motivation

Philosophical debates about the ontology of time and spacetime have long been shaped by two broad traditions. One treats temporal and spatiotemporal structure as fundamental features of the world; the other treats them as derivative, emergent, or representational. The present paper does not attempt to adjudicate between these traditions directly. Instead, it examines a conceptual mechanism that operates across them: the way temporal vocabulary is used, and the metaphysical assumptions that can be smuggled in through that usage.

2.1 Historical Context

Classical substantivalism treated time as an independent container within which events occur. Relational approaches, from Leibniz to Mach, argued that temporal structure arises from relations among physical events. The development of relativity complicated this landscape. Minkowski spacetime suggested a unified geometric structure, while later work in quantum gravity raised the possibility that spacetime itself may be emergent.

Across these debates, temporal vocabulary has been used in multiple senses: as a coordinate, as a measure of change, as an experiential phenomenon, and as a metaphysical entity. These senses are rarely distinguished explicitly. As a result, arguments for the fundamentality of time often rely on transitions between them without acknowledging the additional metaphysical premises required.

2.2 Contemporary Motivations

Current discussions in philosophy of physics often focus on whether spacetime is fundamental, emergent, or representational. Structural realists emphasise the metric as a physical field; relationalists emphasise dynamical relations; functionalists emphasise the roles played by temporal and spatiotemporal structures. Meanwhile, debates about the “flow” or “passage” of time continue to draw on experiential and phenomenological considerations. The present paper is motivated by a methodological question that cuts across these debates: What empirical or explanatory work would justify positing a fundamental temporal or spatiotemporal entity? This question is not answered by pointing to the indispensability of temporal representation.

Many indispensable representational tools – coordinate systems, gauge potentials, phase-space parameters – do not correspond to fundamental entities. The challenge is to determine whether temporal or spatiotemporal entities perform irreducible empirical or explanatory work beyond that supplied by physical change and relational structure.

2.3 Why a Conceptual Audit Is Needed

Three observations motivate the conceptual audit developed in this paper:

– Temporal vocabulary is polysemous. Without explicit disambiguation, arguments risk transferring conclusions licensed in one sense of time to claims expressed in another.

– Empirical evidence underdetermines temporal ontology. Experiments detect physical processes and relations, not a temporal entity in addition to these.

– Representational indispensability does not entail ontological fundamentality.

Temporal coordinates and proper-time intervals are indispensable for expressing dynamical relations, but indispensability alone does not justify ontological commitment.

2.4 Position in the Contemporary Literature

The paper complements rather than replaces existing accounts. Spacetime functionalism asks how spacetime’s empirical roles might be realised; Knox analyses effective geometry at relevant scales; Brown explains inertial structure through dynamics; Baron, Miller, and Tallant examine temporal concepts in agency and deliberation; and representation theorists caution against reading a model’s structure directly as an inventory of reality (Lam & Wuthrich, 2018; Knox, 2013; Brown, 2005; Baron et al., 2022; van Fraassen, 1980; Suarez, 2010; Frigg & Nguyen, 2020). These works give distinct reasons to separate role, representation, and ontology. The question developed here is what additional reason would support the ontological posit after relevant roles have been identified.

Increment

The contribution is limited: the paper identifies polysemy-driven ontological transfer and formulates ONC as a diagnostic for the remaining ontological question. It does not refute the approaches above or establish that no temporal or spatiotemporal ontology can be necessary.

3. Methodological Framework

The conceptual audit developed in this paper has three components: a semantic audit, an empirical audit, and a metaphysical audit. Together, these components support the Ontological Necessity Criterion (ONC), which evaluates when representational indispensability justifies ontological commitment. This section introduces ONC and clarifies how it differs from existing approaches, particularly spacetime functionalism.

3.1 Representational Indispensability and Ontological Commitment

Temporal and spatiotemporal vocabulary is indispensable for expressing dynamical relations. Proper-time intervals, coordinate assignments, and geometric structures are required to represent physical processes. But indispensability for representation does not, by itself, justify ontological commitment. Many indispensable representational tools – gauge potentials, coordinate systems, phase-space parameters – do not correspond to fundamental entities. The methodological question is therefore: What empirical or explanatory work would require positing a temporal or spatiotemporal entity as an additional ontological constituent?

This question motivates ONC.

3.2 The Ontological Necessity Criterion (ONC)

The Ontological Necessity Criterion states: A representational posit is ontologically necessary only if removing it leaves empirical or explanatory content unaccounted for. The criterion is deliberately modest. It does not claim that temporal or spatiotemporal entities never perform irreducible work. It claims only that such work must be demonstrated rather than assumed. ONC is designed to identify the additional premise required to move from temporal representation to temporal ontology. This premise is often left implicit in arguments for the fundamentality of time or spacetime.

Two clarifications are needed if the criterion is not to be misread. First, “change and relational structure” is not restricted to relations among material clocks or material events. It includes whatever physical states, relations, and dynamics the theory actually employs. If a metric-field realist is right that gravitational degrees of freedom, vacuum curvature, or radiative structure belong to that inventory, those structures count as part of the relational and dynamical content against which ONC is applied. Second, ONC then asks a narrower question: after those states, relations, and dynamics have been specified, does anything further—a temporal substance, a container, a flowing entity, or spacetime understood as an additional constituent over and above that structure—still make an irreducible empirical or explanatory contribution? Convenience of temporal vocabulary is not such a contribution. A residual difference in prediction or explanation would be.

3.3 ONC and the Conceptual Audit

The conceptual audit supports ONC in three ways:

– Semantic audit: identifies how polysemy, metaphor, indexicality, and reification enable unlicensed transitions from representational claims to ontological ones.

– Empirical audit: shows that empirical evidence typically constrains physical processes and relations, not temporal entities.

– Metaphysical audit: clarifies when explanatory roles attributed to time or spacetime can be discharged by change and relational structure.

Together, these audits provide the evidential and conceptual basis for ONC.

3.4 ONC and Spacetime Functionalism (Lam & Wuthrich 2018)

Spacetime functionalism begins by asking which roles associated with spacetime are required for the empirical phenomena described by physics and whether those roles can be realized by structures that are not themselves spatiotemporal. ONC takes the next step in the argument rather than competing with that reconstruction. The distinction can be stated as follows: Functionalism asks: what roles must be played, and what can play them? ONC asks: once those roles have been recovered, does the role-filler itself make an irreducible empirical or explanatory contribution?

Consider clock readings and inertial structure. A functionalist analysis can seek a structure that reproduces the relevant clock behaviour and inertial effects without treating spacetime as fundamental. If the recovery succeeds, a straightforward inference to fundamental spacetime is blocked. ONC then asks a different question: is there some residual phenomenon, prediction, or explanation that remains unaccounted for unless the role-filler is itself added to the ontology? Here “residual” has a specific methodological meaning. It is not whatever is described more conveniently using temporal or geometric vocabulary. It is an empirical or explanatory difference that survives after the relevant physical states, relations, and dynamics have been specified. If no such residue can be identified, representational indispensability does not by itself establish ontological necessity. If such a residue can be identified, ONC leaves room for the corresponding ontological posit. ONC therefore sharpens rather than displaces spacetime functionalism. Functional recovery addresses how the relevant roles can be realised; ONC makes explicit the further burden of showing why the realiser must itself be an additional constituent of reality.

4. The Conceptual Audit

The conceptual audit has three components: a semantic audit, an empirical audit, and a metaphysical audit. Together, these components support the Ontological Necessity Criterion (ONC) by identifying where additional metaphysical assumptions enter arguments for the fundamentality of time or spacetime.

4.1 Overview

Arguments for the fundamentality of time often rely on transitions between different senses of temporal vocabulary. These transitions are rarely made explicit. The semantic audit identifies the linguistic mechanisms that enable such transitions; the empirical audit shows that empirical evidence typically underdetermines temporal ontology; the metaphysical audit clarifies when explanatory roles attributed to time can be discharged by change and relational structure.

4.2 Semantic Audit: Polysemy-Driven Ontological Transfer

Temporal vocabulary is polysemous. Words such as “time”, “flow”, “rate”, “before”, “after”, “beginning”, and “end” have multiple senses across scientific, operational, experiential, and metaphysical contexts. Without explicit disambiguation, arguments risk transferring conclusions licensed in one sense to claims expressed in another. This section identifies four linguistic mechanisms that facilitate such transfer.

4.2.1 Reification

Reification occurs when a representational construct is treated as a physical entity. Example:

– Operational claim: “Clocks measure proper time.”

– Reified inference: “Proper time is a physical substance that flows.”

The operational claim concerns a relation between worldlines and the metric. The reified inference introduces a metaphysical entity (“time itself”) not present in the operational description.

4.2.2 Metaphor

Metaphor introduces imagery that can be mistaken for literal ontology. Example:

– “Time flows.”

– “Time speeds up.”

– “Time slows down.”

These metaphors describe experiential or representational features, not physical processes. The semantic audit identifies when metaphorical vocabulary is mistakenly taken to describe physical ontology.

4.2.3 Indexicality

Temporal vocabulary often contains implicit indexicals (“now”, “present”, “before”, “after”). Example:

– “The present moment moves.”

Indexical expressions refer to context-dependent features of representation, not to physical entities. Treating indexical structure as ontological structure is a form of polysemy-driven transfer.

4.2.4 Ambiguity

Temporal terms often have multiple legitimate scientific meanings. Example:

– “Time dilation” can mean: (i) differential proper-time accumulation along worldlines, or (ii) a physical slowing of “time itself”.

The first is a geometric relation; the second is a metaphysical interpretation. Ambiguity enables transitions between them.

4.2.5 Worked Examples

Example 1: Time Dilation (Ambiguity + Reification) Operational meaning: differential proper-time accumulation. Unlicensed inference: “Time itself slows down.” Mechanisms: ambiguity (two senses of “time”), reification (treating geometric relation as substance).

Example 2: The Flow of Time (Metaphor + Indexicality) Experiential meaning: phenomenological passage. Unlicensed inference: “Flow is a physical process.” Mechanisms: metaphor (flow), indexicality (“now”).

Example 3: Time Began at the Big Bang (Ambiguity) Cosmological meaning: metric structure becomes undefined at singularity. Unlicensed inference: “A temporal substance came into existence.” Mechanism: ambiguity (metric vs metaphysical entity).

These examples illustrate how semantic mechanisms enable ontological transfer. ONC is designed to block such transfer unless irreducible empirical or explanatory work is demonstrated.

4.3 Empirical Audit: What the Data Show

Empirical evidence typically constrains physical processes and relations, not temporal entities. Experiments detect change-events, correlations, and geometric relations among worldlines. They do not detect a temporal substance in addition to these.

4.3.1 Proper Time and Differential Aging

Proper time is operationally robust and invariant. Differential aging experiments – Hafele- Keating, GPS synchronisation, Pound-Rebka – measure differences in accumulated proper time along distinct worldlines.

What the data constrain:

– the metric relation along worldlines

– the invariance of proper-time intervals

– the correlation between clock readings and geometric structure

What the experiments do not, by themselves, discriminate:

– whether any measured difference should be interpreted as a change in a temporal substance

– whether temporal language denotes a physical flow in addition to the measured processes

– whether a fundamental temporal dimension is required beyond the physical and geometric relations captured by the theory

4.3.2 Why the Data Underdetermine Ontology

Consider GPS synchronisation. The system relies on relativistic corrections to proper-time accumulation. The empirical result is: Clock readings match metric predictions along worldlines. This result is compatible with multiple ontological interpretations:

1. Metric-field realism: the metric is a physical field.

2. Dynamical relationalism: geometric structure arises from matter fields.

3. Emergent geometry: spacetime is effective, not fundamental.

4. Causal-set ontology: geometry emerges from discrete order structure.

The empirical phenomenon – differential proper time – does not discriminate among these interpretations. ONC therefore requires additional empirical or explanatory work before positing a temporal entity.

4.4 GR Audit: Manifold, Metric, Geometry

General relativity distinguishes:

– the manifold (topological structure)

– the metric field (geometric structure)

– the physical interpretation of geometry (inertial and causal structure)

 The present argument does not treat these as synonymous. The metric is indispensable for representing inertial and causal relations, but indispensability alone does not justify ontological commitment. ONC asks whether the metric performs irreducible empirical or explanatory work beyond representing change and relational structure.

4.5 Quantum Gravity Audit: Causal Set Theory

Causal set theory (CST) provides a concrete existence case for the underdetermination claim, not a proof of the Conditional Redundancy Thesis. At the fundamental level it replaces the continuum description with a locally finite partially ordered set. The order is intended to recover causal precedence, while the number of elements in a region supplies a discrete analogue of spacetime volume. In a suitable continuum approximation, these structures are intended to support the recovery of manifold-like causal and metric geometry (Surya, 2019).

4.5.1 Basic Idea

A causal set consists of elementary events related by a partial order. The order relation is transitive and acyclic, and local finiteness says that only finitely many elements lie between any two related elements. The proposal therefore begins with discrete order and counting structure rather than a continuous metric manifold. The order aims to recover causal structure; counting aims to recover volume; together, in an appropriate manifold-like regime, they are expected to support continuum geometric quantities.

4.5.2 What CST Shows and What It Does Not

CST shows that a serious quantum-gravity programme can formulate fundamental structure without taking a continuous metric spacetime as basic. It therefore illustrates how some roles associated with continuum spacetime may be approached through a different structure. It does not establish that the relevant continuum limit exists for the physical world, that all the required dynamics and geometric observables have been recovered, or that temporal ontology is redundant. The recovery of manifold-like behaviour and the construction of empirically adequate dynamics remain substantive research problems (Surya, 2019). For ONC, the question within CST is specific: once causal order, local finiteness, dynamics, and any successful continuum recovery are specified, does an additional temporal entity explain or predict anything that this structure leaves unaccounted for? CST makes that question intelligible; it does not settle it.

4.5.3 Underdetermination Illustrated

A measurement of differential proper-time accumulation constrains physical processes and geometric relations, but does not by itself decide whether the metric is fundamental, effective, or recoverable from a discrete structure. These options are not thereby shown to be empirically equivalent. The narrower point is that a successful measurement alone does not select among their metaphysical interpretations.

4.6 Metaphysical Audit: Change and Dependence

Change requires physically distinct states connected by lawful dependence relations. Distinctness is grounded in physical properties; connection is grounded in lawful structure. Temporal representation provides one way of expressing such dependence; it is not constitutive of the dependence itself.

Lawful dependence is not the same as temporal ordering. A dependence relation holds when the physical state of one system, or of one region of a theory’s configuration, constrains or determines another according to the theory’s laws. That relation may be represented by a time parameter, by proper-time accumulation along a worldline, or by an order relation in a discrete structure. The representation supplies a convenient index or sequence; it does not create the constraint. Temporal ordering is therefore one possible encoding of dependence, not a further constituent required for dependence to obtain. Once the relevant states and laws are specified, treating the encoding itself as an additional entity mistakes a mode of representation for part of the ontology.

This distinction prevents representational features from being mistaken for ontological ones.

4.7 ONC Applied

The audits leave a precise burden for the ontological inference. An advocate of fundamental time or spacetime must identify what remains empirically or explanatorily unaccounted for after the relevant physical states, relations, and dynamics have been specified. Convenience, invariance, and representational indispensability do not by themselves identify such a residue.

4.7.1 The Additional Premise

The additional premise required for the ontological inference is that the empirical and explanatory roles attributed to time or spacetime cannot be discharged by change and relational structure alone. The paper does not claim that this premise is false in every theory. It claims that the premise requires independent support.

4.7.2 Falsifiability

The Conditional Redundancy Thesis would be challenged by a physical theory in which a temporal or spatiotemporal degree of freedom made an irreducible contribution to empirical prediction or explanation, such that the relevant phenomena could not be recovered from physical states, relations, and dynamics without it. Such a result would supply the kind of residual contribution ONC treats as relevant to ontological commitment.

5. Objections and Replies

The Conditional Redundancy Thesis is modest: it claims that temporal and spatiotemporal ontology is unnecessary if change and relational structure discharge the empirical and explanatory roles attributed to time or spacetime. This section considers metric-field realism, sophisticated substantivalism, ontic structural realism, temporal realism, and explanatory necessity. The replies apply ONC without assuming that these realist positions fail.

5.1 Objection from Metric-Field Realism

A metric-field realist can argue that the metric is not merely a convenient representation of relations among material events. In general relativity, gravitational dynamics include degrees of freedom not fixed by the local distribution of matter. Vacuum solutions need not be geometrically trivial: non-zero Weyl curvature and propagating gravitational waves provide a serious candidate for physical content carried by the gravitational field itself (Wald, 1984). A realist may therefore contend that the metric contributes real dynamical structure even where no material clock or matter source is present. If that structure is irreducible, the paper’s appeal to change and relations among material events has not recovered the relevant role.

This is a substantive challenge, and the empirical audit does not answer it merely by observing that clocks register differential proper time. Nor does the fact that geometry can be represented relationally show that gravitational degrees of freedom are reducible to matter relations. The candidate residue is the independent dynamical content of the gravitational field, including vacuum and radiative degrees of freedom. A realist who establishes that such content is indispensable to prediction or explanation has met the kind of challenge ONC is designed to recognize.

The remaining issue is what the success establishes ontologically. It may support realism about the metric or gravitational field; it does not automatically show that a further temporal substance, or spacetime understood as an entity over and above the metric-field structure, must also be posited. To support that stronger conclusion, the realist would need to identify an additional contribution made by that further posit. Conversely, a recovery account that derives the relevant gravitational degrees of freedom and their dynamics from a more basic structure would strengthen the redundancy claim, but CST or relational language alone does not yet provide such a completed recovery. ONC therefore leaves metric-field realism open and makes the unresolved recovery question explicit.

5.2 Objection from Sophisticated Substantivalism

The hole argument targets a form of substantivalism that assigns primitive identities to manifold points independently of the physical fields, making diffeomorphically related models appear to represent distinct possibilities (Earman & Norton, 1987). Sophisticated substantivalists reject that haecceitistic commitment. They treat such models as physically equivalent, or they individuate spacetime points through the metric and other fields rather than through primitive identities of bare manifold points (Hoefer, 1996; Pooley, 2013). Spacetime is then a structured entity, not a featureless container.

This response avoids the standard hole-argument worry, but it leaves the present question open. ONC is compatible with sophisticated substantivalism if the structured spacetime so conceived contributes irreducible empirical or explanatory work. The proponent must specify that contribution beyond the metric relations and dynamics already represented. If the only work identified is the work already done by those fields and their lawful dependencies, the posit may remain representationally indispensable without being shown to be an additional ontological constituent in the sense ONC requires.

5.3 Objection from Ontic Structural Realism

Ontic structural realists argue that relational structure is ontologically basic and that objects are derivative or non-fundamental (Ladyman, 1998). They may therefore claim that temporal or spatiotemporal structure is fundamental because it belongs to the relational structure represented by our best physics.

OSR is compatible with ONC, but it sharpens the question of what counts as a residue. ONC does not deny that relational structure may be fundamental, and it does not infer that relations are merely representational because they are not objects. Rather, it asks whether the temporal or spatiotemporal structure posited by a particular OSR account is itself part of the irreducible structure, or whether the relevant ordering and geometric roles can be recovered from a more basic non-temporal structure. That is a substantive metaphysical and physical question, not a consequence of the label “structural realism.”

If OSR treats temporal relations as fundamental, its proponent must explain why that structure cannot be recovered from a more basic organisation. In CST, for example, causal order and cardinality are proposed as basic while continuum temporal and metric notions are recovered only in appropriate regimes; whether that recovery succeeds in the physically relevant cases remains open (Surya, 2019). OSR therefore faces the same evidential constraint as substantivalism: identify irreducible work or treat temporal vocabulary as representational.

5.4 Objection from Temporal Realism

A temporal realist may accept the semantic distinction between representation and ontology while maintaining that temporal structure represented in physics corresponds to a real physical structure. The realist might appeal to temporal ordering, temporal asymmetry, or the directionality of physical processes as evidence that time is not merely representational.

ONC does not reject this position at the outset. The relevant question is whether the realist can identify a residual empirical or explanatory contribution made by temporal structure as such. The existence of temporal asymmetries, for example, is not by itself enough: statistical structure, boundary conditions, coarse-graining, and system-environment relations can enter the physical explanation of asymmetry without requiring an additional temporal entity.

The same applies to temporal ordering. If ordering relations are indispensable to the physical explanation, the realist must still show why those relations require an additional temporal constituent rather than being features of the underlying physical structure and its lawful dependencies. Conversely, if a theory shows that a temporal degree of freedom has an irreducible explanatory role, ONC permits the realist inference. The criterion therefore does not settle temporal realism in advance; it identifies what would be needed to support it.

5.5 Objection from Explanatory Necessity

One might argue that even if temporal or spatiotemporal entities do not perform irreducible empirical work, they perform irreducible explanatory work. For example, temporal structure may be said to explain persistence, causation, or dynamical evolution.

ONC distinguishes empirical indispensability from explanatory indispensability.

Explanatory indispensability can justify ontology only if the explanation cannot be reformulated in terms of change and relational structure. Many explanations that appear to require temporal entities – persistence, causation, evolution – can be reformulated in terms of dependence relations among physical states. If an explanation genuinely requires a temporal entity, ONC permits the posit. If not, ONC treats the entity as explanatorily redundant.

5.6 Summary

These objections locate the relevant burden rather than settle it. Vacuum gravitational degrees of freedom are a serious candidate for irreducible metric content; sophisticated substantivalism and OSR offer developed accounts of structured ontology; temporal and explanatory realists may identify further residues. ONC permits these conclusions where the claimed contribution survives an adequate specification of physical states, relations, and dynamics. The audits establish no general elimination result.

6. Conclusion

Temporal and spatiotemporal vocabulary is indispensable in scientific representation, but representational indispensability does not by itself determine ontology. The semantic audit shows how polysemy, metaphor, indexicality, and reification can facilitate transitions from representational claims to ontological ones without making the intervening premise explicit. The empirical audit shows that experimental results constrain physical changes, correlations, and geometric relations, while leaving open the metaphysical interpretation of those results. The metaphysical audit then asks whether the roles attributed to time or spacetime can be discharged by change and lawful dependence relations.

The Ontological Necessity Criterion isolates the methodological question that remains: once the relevant empirical and explanatory roles have been accounted for, is there any residual work that requires a temporal or spatiotemporal posit as an additional constituent of reality? If there is, ONC permits the posit. If there is not, representational indispensability does not establish ontological necessity. The Conditional Redundancy Thesis is therefore conditional rather than eliminative in advance: temporal and spatiotemporal ontology is redundant where change and relational structure discharge all the relevant empirical and explanatory work. The paper does not claim to have shown that no temporal or spatiotemporal ontology can satisfy this requirement. Its narrower claim is methodological: the move from indispensable temporal representation to ontological fundamentality requires an additional premise, and that premise must be supported by evidence or explanation rather than inferred from representational necessity alone.

The resulting framework is compatible with realist, relational, functionalist, and emergent approaches, provided their ontological commitments are assessed separately from the representational vocabulary used to formulate them. Its contribution is consequently not a new physical theory of time, but a diagnostic framework for keeping semantic, empirical, and metaphysical claims distinct.

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