5.1 Postulates 1–3: The Present, Causal Continuity, and the Cosmological Parameter
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Postulate 1 (Ontological Primacy of the Present): At any stage of cosmic evolution, only the current
hypersurface of reality—the present state of the universe—possesses ontological existence as
presently real. The present is not, however, an isolated instant: it exists as part of a continuous
causal-temporal progression whereby each state emerges through the lawful evolution of immediately
preceding states and in turn contributes to the emergence of subsequent states. Earlier states do
not persist as independently existing regions of spacetime. Their physical consequences continue
within later states through ongoing causal continuity, of which only a subset remains organized as
information-bearing records accessible in present physical systems.
Stated without formalism, the picture is as follows. Write P_n for the entirety of what exists at
generative stage n. Existence at that stage is P_n and nothing besides: P_{n−1} has ceased to exist
as a state and P_{n+1} has not yet been generated. Generation carries P_n to P_{n+1}, at which point
existence is P_{n+1}. The present is accordingly not a distinguished region within a larger existing
whole but the whole of what exists. Two clarifications prevent the obvious misreadings. First, that
P_{n−1} has ceased to exist as a state does not mean it left nothing behind: its causal consequences
are incorporated into P_n, and a subset of them remain organised as records (Postulate 4, §14).
Ceasing to exist and becoming irrelevant are different things. Second, the future is unrealised
rather than hidden: P_{n+1} is not an existing region we are unable to observe but a set of
potential successors of which one is generated.
Postulate 2 (Causal Continuity): The present state of the universe arises as the causal continuation
of immediately prior physical states. Every event in the present is linked through chains of
physical interaction to earlier events within its past light cone. In the emergent-geometric regime,
this causal ordering is represented by relativistic spacetime geometry; more fundamentally, causal
ordering is the primitive structure from which spacetime geometry is reconstructed (Causal
Reconstruction Principle, §10.3). Generative ordering is therefore prior to metric structure, not
derived from it.
Postulate 3 (Cosmological Temporal Parameter): The progression of the present boundary is
parameterized by cosmological time. In the big-bang-origin formulation used here, this is the
maximal proper time elapsed since the initial singularity (§6.1); a surface-relative generalization
for bouncing spacetimes is given in §6.10.1. In the emergent geometric regime, the generation
parameter σ is a monotone relabeling of this function (Appendix A.3). This provides a physically
grounded temporal ordering of successive states of reality and resolves objections based on the
relativity of simultaneity. In FLRW solutions, cosmological time is the familiar cosmic time t,
equal to the proper time along the comoving matter congruence. That is how the parameter is realized
and measured, not what defines it (§6.3). Prior to geometric emergence, σ functions as a pre-
geometric ordering parameter without presupposing proper time. Its use introduces no preferred frame
beyond what is already present in standard cosmology.
Terminology. Throughout this framework, the matter frame denotes the local rest frame of the
cosmological matter distribution: u^μ is the unit timelike eigenvector of T_{μν}, and ρ_c := T_{μν}
u^μ u^ν is the energy density measured in that frame. The matter-frame congruence is the family of
worldlines tangent to u^μ. In FLRW and in single-stream regions it coincides with the maximizing
geodesics that define cosmological time (§6.3). It is not used to define co-presence, and no
postulate requires a physical system to belong to it in order to occupy a generative stage. The
distinction is developed in §9.4.1.
5.2 Postulate 4: Persistence Through Causal Continuity and Records
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Postulate 4 (Persistence Through Causal Continuity and Records): Although earlier states of the
universe no longer exist as independent regions of spacetime, the physical consequences of those
states continue through later states via lawful, continuous transformations of matter, energy,
fields, and information-bearing structures. Certain aspects of those consequences remain organized
as causal records that encode information about past events, while other aspects become distributed,
transformed, or effectively unrecoverable. Such records include radiation fields, particle
distributions, gravitational structures, and cosmological relics, the most extensive of which are
the cosmic microwave background and the neutral hydrogen observed through the 21 cm line (§14). The
signal exists now; the emitting matter existed earlier; the earlier state itself no longer exists.
What remains is not the earlier organization but the continuing propagation of its physical
consequences, one subset of which functions as a causal record.
5.2.1 Persistence and the Truth of the Past
While CTGP holds that earlier states do not persist as independently existing regions of spacetime,
the causal consequences of those states continue propagating within later states through ongoing
physical evolution. Some of those consequences remain organized as causal encodings and records
accessible in the present. This should not be taken to imply that present encodings exhaust all
truths about the past.
CTGP distinguishes between:
(i) ontological persistence, which is limited to present physical structures and their encoded
causal records, and
(ii) truth about past events, which may extend beyond what is currently encoded.
On this view, past events were fully real at their corresponding present stage and remain
determinately true as events that occurred, even if aspects of those events are no longer physically
encoded or recoverable in the present state of the universe.
Present encodings therefore function as partial physical persistence and evidential traces, not as
the total grounding of all past truths.
The grounding objection. A standard objection to presentism asks what makes past-tense statements
true if the past does not exist. CTGP adopts a Lucretian answer (Bigelow 1996). The truthmaker for a
past-tense truth is the present world itself, which instantiates past-tensed properties: the present
universe has the property *having been, at stage σ′, such that p*. These properties are primitive.
They are not grounded in any further fact, whether a present record or an existing past stage, since
no past stage exists to ground them. Nor are they records. Records are categorical physical
structures that carry evidence about the past and can be degraded or erased (§14.6). Past-tensed
properties belong to the present state as a whole and, once acquired, are retained at every later
stage (Definition 17.20). This is the precise sense in which the present lawfully descends from
earlier stages: descent is not a relation to something that still exists but a property the present
has. Since past-tensed properties are properties of Pₙ itself, this account adds no independently
existing past object or historical stage to the present ontology.
This also fixes the status of M(σ). M(σ) is not the truthmaker. It is the formal representation of
the present world’s past-tensed profile, laid out as if its stages co-existed so that the ordinary
semantics of tense can be applied. The ground is the present, and the history is its representation.
CTGP therefore faces neither horn of the usual dilemma: it does not reify M(σ), which would make it
a growing block, and it does not leave past truths ungrounded. The formal semantics (Definition
17.20) indexes earlier stages in the metalanguage; a clause such as “W_σ′ ⊨ φ” is read as tensed — φ
was the case at σ′ — and carries no commitment to existing past stages.
The cost should be stated. Past-tensed properties do not supervene on the present’s categorical
physical configuration, since two present states could agree in every categorical respect while
differing in their pasts. This is the familiar objection that Lucretian properties “cheat” (Sider
2001). CTGP accepts this cost as the formal counterpart of a claim it makes on independent grounds:
records are evidence rather than grounds, and truths about the past outrun what is encoded. If past
truths supervened on present categorical structure, then losing a record would change what happened,
and CTGP denies that (Proposition 17.22). This cost also bears on the explanatory-economy argument
of §3.4: the economy claimed there is unification of the arrows of time under one mechanism, not
parsimony of ontology, and the primitive properties posited here count against the latter. CTGP
therefore does not eliminate past facts; it relocates them into the present, as irreducible past-
tensed properties of what exists now. The ontology is leaner than eternalism in what exists, not in
what is fundamental.
5.2.2 Conservation, Organization, and Recoverability
CTGP distinguishes four separate concepts that are often conflated:
(i) Conservation of physical existence. Matter, energy, fields, and physical processes continue
through lawful transformations. In general relativity this continuity is underwritten by local
conservation laws, ∇μTμν = 0; global conserved quantities follow, by Noether’s theorem, only
where the spacetime has corresponding symmetries. CTGP does not claim that physical existence
disappears when a state ceases to be present.
(ii) Conservation of information. Information may persist in transformed or distributed forms
even when no localized or practically recoverable record remains. Questions regarding the
ultimate conservation of information depend upon the relevant physical domain and remain
distinct from questions of record formation.
(iii) Conservation of organization. Particular arrangements, structures, configurations, and
correlations may cease to exist even while the physical constituents involved continue in
transformed states. CTGP identifies the loss of present existence primarily with the loss of the
earlier state’s specific organization, not with the annihilation of all physical continuity.
(iv) Recoverability of knowledge. The existence of physical consequences does not imply that
those consequences remain sufficient to reconstruct prior states. Ontological persistence and
epistemic accessibility are distinct. Something may continue to exist in transformed or
distributed form while becoming effectively unrecoverable as a coherent record.
Accordingly, CTGP’s claim that earlier states no longer exist refers to the non-persistence of those
states as present ontological organizations, not to the disappearance of all physical continuity
arising from them.