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.
