The Structural Indistinguishability Model of Transcendence (RETM): A Relational Framework for Information-Based Underdetermination

Abstract

Claims that some domain of inquiry has reached, or is bounded by, a "transcendent" limit recur across religious discourse, popular science communication, and specialist debates about the foundations of physics, mathematics, and mind. Such claims are typically treated as reports about the world: a boundary is said to exist, and the inquirer is said to have detected it. This article introduces the Structural Indistinguishability Model of Transcendence (RETM), a conceptual-theoretical framework that instead treats transcendence as a relational state of an assessment situation rather than a free-standing property of an object in the world. RETM defines this situation as a quintuplet Ω = ⟨A, τ, D, M, t⟩ — an agent or system A, a task τ, the data D available to A, the model or inferential framework M through which D is interpreted relative to τ, and the time t at which the assessment occurs. Within this relational unit, the article distinguishes three variables that are routinely conflated in transcendence-talk: structural indistinguishability (Ts), a formally assessable property of underdetermination between rival hypotheses given D and M; experienced uncertainty (Te), the phenomenological state of A; and selected resolution (Tr), the practical or doxastic move by which A closes the gap between Ts and action. It further distinguishes a relational boundary (Br), an independently assessable limit of what M can resolve given D, from textual boundary language (Bx), the explicit discursive claim that such a limit has been reached. Cognitive load (K) is introduced as a moderator of the mapping from Ts to Te and Tr, not as a necessary condition for underdetermination itself. Building on these distinctions, the article proposes an eight-type taxonomy of transcendence claims (ontological, epistemic, phenomenological, cognitive, information-structured, systemic, narrative, and social/identity-bound), an audit method for detecting unlicensed type-shifts between these categories, and a symmetry requirement (IPC-symmetry) for applying this audit evenhandedly across religious, secular, and scientific claims. RETM is presented explicitly as a research program rather than a validated general theory, and the article closes with a set of falsification criteria intended to make the framework's core commitments empirically answerable rather than merely programmatic.

1. Introduction

Across strikingly different domains of discourse, inquirers arrive at a common rhetorical move: having reached the limit of what current data, methods, or concepts can settle, they describe that limit as though it were a feature of reality itself, independent of the inquiry that produced it. A theologian points to the difficulty of explaining the origin of physical law and infers a transcendent cause. A popular-science account of quantum indeterminacy or consciousness slides from "we do not currently have a mechanism" to "there is, in principle, no mechanism." A political or ideological community, confronted with evidence that complicates a cherished narrative, declares the matter to lie beyond what evidence could ever adjudicate. In each case, a gap between available information and a desired conclusion is bridged by boundary language — "beyond," "ultimately," "in principle unknowable" — that asserts more than the evidential situation licenses.

This move is not confined to religious apologetics, where it has long been recognized and named (the "god of the gaps" pattern is only its best-known instance). It recurs, structurally identically, in secular and scientific registers: in speculative popular science, in political rhetoric, and in ordinary reasoning under uncertainty. What these instances share is not their content but their form: an inference from a state of not-knowing to a claim about what cannot, even in principle, be known or be otherwise. The present article argues that this form deserves a domain-general name and a domain-general diagnostic apparatus, because the error it risks — treating an artifact of a particular inquiry (its data, its model, its moment) as a property of the world independent of any inquiry — is the same error wherever it occurs, and is best exposed by a vocabulary that does not already presuppose which domain's claims are suspect.

The Structural Indistinguishability Model of Transcendence (RETM) is offered as such a vocabulary. Its central methodological commitment is that transcendence is not, and cannot coherently be treated as, an independent object in the world available for direct inspection. It is instead a relational state that holds, or fails to hold, of a specific assessment situation: some agent, addressing some task, with some data, through some model, at some time. Changing any one of these five elements can change whether, and in what sense, a "beyond" is truthfully asserted. A claim that a question lies beyond the reach of inquiry is therefore always, on this framework, elliptical for a claim about a particular Ω — and the central diagnostic task is to make that ellipsis explicit and to check whether it is warranted.

RETM does not take a position on whether mind-independent limits to knowledge or to nature exist; that would itself be an ontological claim of exactly the kind the framework is built to scrutinize before endorsing. Its ambition is narrower and, we think, more tractable: to provide a formal vocabulary for distinguishing the structural fact of underdetermination from the experience of uncertainty and from the decision to treat a matter as settled or unsettleable, and to provide a method for auditing arguments that move between these without justification. The framework is offered in a spirit of methodological naturalism: it examines transcendence-claims as objects of study — as things people say, under identifiable conditions, with identifiable structure — without presupposing either that any given claim is true or that it is false.

The remainder of the article proceeds as follows. Section 2 introduces the Ω-quintuplet as RETM's unit of analysis and explains why treating transcendence relationally, rather than as a standalone predicate, is the framework's foundational move. Section 3 develops the formal core of the model: the three-way distinction between structural indistinguishability, experienced uncertainty, and selected resolution; the boundary variables Br and Bx; and the moderating role of cognitive load K. Section 4 presents an eight-type taxonomy of transcendence claims. Section 5 develops two epistemological safeguards — an audit method built around type signatures and bridge premises, and a symmetry requirement for applying that audit across domains. Section 6 outlines applications, and Section 7 states the framework's status as a research program together with explicit falsification criteria. Section 8 concludes.

2. The Unit of Analysis: The Ω-Quintuplet

RETM's foundational move is to relocate the subject of analysis. Ordinary usage treats "transcendence" as a predicate that can apply to an object or a domain — "X transcends explanation," "Y is beyond human understanding" — as though the property picked out were intrinsic to X or Y, available for detection independent of who is asking, with what resources, and when. RETM replaces this with a relation defined over a five-element tuple:

Ω = ⟨A, τ, D, M, t⟩

where A denotes the system or agent conducting the assessment (an individual reasoner, a scientific community, an institution, or an artificial system); τ denotes the task or question under consideration; D denotes the data available to A in connection with τ; M denotes the model, theory, or inferential framework through which A interprets D relative to τ; and t denotes the time at which the assessment is made.

Each element does real work. A matters because capacity, training, and prior commitments differ across agents, and a limit for one agent need not be a limit for another operating on the same data. τ matters because a body of data may be more than adequate for one question and radically insufficient for another; "transcendence" is never with respect to inquiry in general but always with respect to some specific task. D matters because it is a bounded, revisable set — what counts as available evidence at one point can expand, contract, or be reinterpreted. M matters because the same data can support radically different conclusions depending on the model brought to bear on it; underdetermination, as developed below, is defined jointly over D and M, not over D alone. And t matters because none of A, τ, D, or M are fixed: an inquiry that is genuinely stuck today may not be stuck after a new instrument, a new theorem, or a new theoretical framework becomes available.

The central claim that motivates this construction is that transcendence should be understood as a state of Ω — formally, as a function T(Ω) — rather than as a property of some referent external to Ω. This is a methodological rather than a metaphysical thesis. It does not assert that nothing exists independently of inquiry; it asserts only that the label "transcendent," when responsibly used, tracks a relation between an inquiry and its object, not the object considered apart from any inquiry. A claim of the form "X is transcendent" is, on this view, always incomplete until it specifies, at least implicitly, whose assessment, of what task, on what data, through what model, and at what time is being reported. Making this specification explicit is the first step of the audit method developed in Section 5, and it is often sufficient by itself to reveal that a claim asserted in the categorical, ontological register ("X is unknowable") is actually warranted, if at all, only in the narrower, relational register ("X is not resolvable by A's current M given A's current D").

Two clarifications forestall likely misreadings. First, treating transcendence as relational does not trivialize it into mere subjectivity: Ω-relational states are, as Section 3 shows, subject to independent, checkable criteria (via Br) and are not simply whatever an agent happens to feel or say. Second, the relational treatment is symmetric across "sizes" of A: it applies equally to an individual struggling with a single question and to an entire scientific field assessing the foundations of its discipline. What changes across these cases is the content of A, τ, D, and M, not the applicability of the framework.

3. The Formal Core

3.1 Structural Indistinguishability, Experienced Uncertainty, and Selected Resolution

RETM's central diagnostic distinction separates three variables that ordinary transcendence-talk routinely collapses into one another.

Structural indistinguishability (Ts) is a property of the assessment situation Ω, holding when the available data D, interpreted through the admissible model space M, fail to discriminate between two or more rival hypotheses relevant to τ. Where a hypothesis space contains competing candidates that are empirically equivalent given D — indistinguishable in their predictions, their fit, or their explanatory adequacy under M at t — Ts(Ω) obtains. This is, in essence, a generalized underdetermination thesis in the tradition of Duhem and Quine, reframed as a variable that can be locally assessed for a given Ω rather than asserted globally of theory as such. Because it is defined over checkable relations between D, M, and a hypothesis space, Ts is in principle open to independent evaluation: through formal results (e.g., proofs of empirical equivalence, non-identifiability of parameters, undecidability), through statistical measures of model comparability, or through explicit demonstration that rival models fit D equally well.

Experienced uncertainty (Te) is, by contrast, a state of A: the phenomenological or psychological register of not-knowing, confusion, doubt, or (on the positive side) a sense of mystery or awe. Te is not defined over D and M directly but over A's internal state in response to τ, D, and M as A represents them. Crucially, Te can diverge from Ts in both directions. An agent may experience high uncertainty in a situation of low structural indistinguishability — for instance, a non-expert confronting a well-resolved scientific question may feel lost despite the matter being settled by expert consensus grounded in a determinate D and M. Conversely, an agent may experience unwarranted confidence in a situation of genuine structural indistinguishability, mistaking one arbitrarily privileged hypothesis for the resolved answer.

Selected resolution (Tr) names the further step by which A moves from an assessment (however experienced) to a working stance: adopting a prior, deferring to authority, suspending judgment, invoking an auxiliary premise, or making a decision to treat the matter as closed for practical purposes. Tr is not a discovery about the world; it is an action A takes, and different agents facing an identical Ts may select different Tr — one might suspend judgment, another might adopt a provisional working hypothesis, a third might make what is frankly a leap sanctioned by considerations external to D and M (a pragmatic commitment, a decision procedure, or, in explicitly non-evidential domains, a faith commitment). RETM does not evaluate the rationality of any particular Tr in general; it insists only that Tr be recognized as a selection, not mistaken for a further disclosure of Ts.

The diagnostic payoff of the three-way distinction is this: a very large class of problematic transcendence-claims can be redescribed as arguments that report a Tr, or an intensified Te, while claiming the epistemic warrant that would only attach to an independently assessed Ts — and, further, that illicitly promote that Ts-level warrant into an ontological conclusion about Br (see below) without a licensing bridge. Making the three variables terminologically distinct is what allows this pattern to be named and checked rather than merely felt to be suspicious.

3.2 Boundary Variables: Relational Boundary (Br) versus Textual Boundary Language (Bx)

A second distinction separates the boundary as independently assessed from the boundary as asserted.

The relational boundary (Br) is the limit of what M can resolve given D for τ at t, considered as an object of independent assessment: it is checkable in principle by means external to the bare assertion that a limit exists — formal undecidability or incompleteness results, measurement-theoretic limits (e.g., resolution, sensitivity, or sampling bounds), statistical power calculations, or demonstrations of non-identifiability. Because Br is tied to the actual capabilities of A's D and M, it should in principle respond to changes in those capabilities: a Br grounded in current instrumentation should shift, or be shown not to shift, when instrumentation improves.

Textual boundary language (Bx) is, by contrast, the explicit discursive claim that a boundary has been reached or crossed — the actual sentence asserted: "this cannot be known," "science will never explain this," "we have reached the edge of what is knowable." Bx is a feature of a text or utterance, assessable by ordinary methods of argument analysis, and it is produced under all the usual pressures that shape assertion generally: rhetorical goals, audience expectations, genre conventions, and motivated reasoning.

RETM's methodological requirement is that Bx never be treated as self-certifying evidence for Br. The two can, and frequently do, come apart: Bx can overrun Br (a confident claim of unknowability where the actual structural situation is merely unresolved-for-now, or where relevant Br has not even been assessed), and Bx can underrun Br (a hedge or a disclaimer that understates a genuinely robust Br, for instance where a real formal limit is downplayed for rhetorical effect). The audit method in Section 5 is largely a procedure for checking Bx claims against independently assessed Br before treating a transcendence-claim as licensed by the evidential situation it purports to describe.

3.3 Cognitive Load (K) as Moderator

Cognitive load (K) denotes the resource demand placed on A at t — working-memory demand, time pressure, emotional arousal, unfamiliarity or expertise deficit, and the various pressures associated with motivated reasoning. RETM assigns K a specific and limited role: K moderates the mapping from Ts to Te and from Ts (together with Te) to Tr; it is not treated as a necessary condition for Ts itself.

This distinction matters because it is tempting, and partly correct, to explain transcendence-talk as an artifact of limited cognitive resources. RETM accepts that K raises the probability that Te is reported, and raises the probability that Tr collapses prematurely into strong Bx claims — under time pressure, emotional load, or expertise deficit, agents are more likely to convert a provisional "I do not currently know" into a categorical "this cannot in principle be known." But RETM denies that K is what generates structural indistinguishability itself: Ts can hold for an idealized reasoner with unlimited working memory and no time pressure, wherever D and M jointly and formally fail to discriminate between rival hypotheses (as in genuine cases of empirical equivalence or non-identifiability). Treating K as a moderator rather than a necessary condition keeps the model's structural core (Ts) independent of any particular agent's psychology, while still giving the framework resources to explain why Te and Tr so often diverge from Ts in predictable, load-dependent ways. This separation is also what makes the framework's central claims answerable to evidence at all: Section 7 returns to it as one of RETM's stated falsification points.

4. The Taxonomy: Eight Types of Transcendence

RETM distinguishes eight ideal types of transcendence-claim, individuated by the source and target of the boundary being invoked. Each type is assigned a type signature κ, used in the audit method of Section 5. The types are not mutually exclusive in practice — a single claim often functions as more than one type simultaneously — but distinguishing them analytically is what allows the audit method to detect illegitimate movement between them.

1. Ontological transcendence (κ = ontic). Claims about what exists beyond the reachable domain of inquiry, asserted independently of any particular inquirer's epistemic situation — for instance, traditional metaphysical claims that some reality lies beyond the natural or physical order as such. This is the register in which the highest-stakes inferential errors occur, because ontic conclusions are the ones most often illegitimately supported by premises that are, on inspection, merely epistemic (κ = epistemic) or experiential (κ = experiential).

2. Epistemic transcendence (κ = epistemic). Limits on what can currently be known given available methods, data, or theory — underdetermination of theory by evidence, formal limitative results (e.g., Gödelian incompleteness within a specified formal system), or measurement limits. This is the type most directly formalized by Ts, and the type within which most legitimate, well-licensed transcendence-claims properly belong.

3. Phenomenological transcendence (κ = experiential). Experiences that exceed an agent's capacity to represent or articulate them in available concepts or language — reports of mystical or peak experience, the aesthetic sublime, or certain altered states. Claims of this type describe a limit on representation or articulation by a particular A, not (without further argument) a limit on what exists or on what could in principle be known by some other means.

4. Cognitive transcendence (κ = cognitive-capacity). Limits arising from the processing capacity of a particular agent or system, independent of the objective informational situation — working-memory limits, lack of relevant expertise, or the bounded rationality of a given reasoner. This type is closely coupled to K and is often what is actually being reported when Bx claims are made under load.

5. Information-structured transcendence (κ = informational). Limits that are strictly a function of the structure of available data — degrees of freedom insufficient to identify a parameter, compression or encoding limits, signal-to-noise constraints, or sampling limitations. This type is the most directly and precisely formalizable instance of Ts, since it can often be stated as an explicit property of D (e.g., a demonstrable non-identifiability result).

6. Systemic transcendence (κ = institutional/systemic). Limits that emerge from the architecture, rules, or organization within which A operates — disciplinary boundaries, institutional mandates, methodological conventions that exclude certain classes of question by design rather than by evidential necessity. A question can be systemically "beyond" a given institution's remit without being beyond inquiry as such.

7. Narrative transcendence (κ = narrative/symbolic). Boundaries constructed through storytelling, myth, or symbolic framing, in which a "beyond" is posited as part of a meaning-making structure rather than as the output of an evidential assessment — creation narratives, hero's-journey framings of the unknown, and similar symbolic constructions. Narrative transcendence can be entirely legitimate on its own terms (as meaning-making rather than as description) while becoming illegitimate the moment it is redeployed as though it were an epistemic or ontic finding.

8. Social/identity-bound transcendence (κ = social-identity). Boundaries invoked primarily to protect group belonging or identity commitments, where the transcendence-claim functions as a marker of in-group loyalty rather than as an assessment of Ts — the pattern most closely associated with identity-protective cognition (IPC). Claims of this type are frequently dressed in the vocabulary of another type (most often epistemic or ontic) while functioning, on analysis, as type 8; detecting this mismatch between professed and functional κ is one of the audit method's principal tasks, and is the focus of the symmetry requirement in Section 5.2.

5. Epistemological Safeguards

5.1 The Audit Method

RETM proposes a four-step audit procedure for evaluating any argument that invokes a transcendence-claim, whatever its domain.

Step 1 — Identify premises. The argument is decomposed into its constituent premises and its conclusion, in the ordinary manner of argument reconstruction.

Step 2 — Assign type signatures (κ). Each premise, and the conclusion, is assigned a type signature drawn from the eight-type taxonomy of Section 4 (or, where a premise straightforwardly reports Ts, Te, Tr, Br, or Bx as such, tagged directly with that variable). This step forces explicit attention to what kind of claim is actually being made at each point in the argument — epistemic, ontic, experiential, and so on — independent of the vocabulary in which it happens to be phrased.

Step 3 — Check for type-shifts. The argument is scanned for points at which the type signature changes between a premise and the conclusion it is meant to support — paradigmatically, a shift from an epistemic premise ("current methods cannot explain X") to an ontic conclusion ("X has a cause outside the natural order"), or from a social-identity-functioning premise dressed as epistemic to an ontic conclusion. Such shifts are not automatically illegitimate; they are flagged as requiring justification.

Step 4 — Require a bridge premise (β) for any type-shift. Wherever Step 3 detects a shift in κ, the argument is required to supply an explicit bridge premise β that independently justifies the move — for instance, a stated and defended reason why, in this particular case, epistemic limits should be taken to track ontic limits. An argument that shifts type signature without such a bridge premise is flagged as an audit failure: a silent type-shift. This does not establish that its conclusion is false, only that the argument as given does not license it; supplying an adequate β, where one exists, would repair the argument, and the absence of an available β is itself informative.

The audit method is domain-general by design. It applies identically to a theological argument moving from epistemic gaps to ontic conclusions, to a popular-science account moving from "we lack a mechanism" to "there is no mechanism even in principle," and to a political argument moving from "the evidence on this point is disputed" to "the matter is beyond what evidence could settle."

5.2 Methodological Symmetry (IPC-Symmetry)

The audit method is only a safeguard if it is applied evenhandedly. RETM therefore states, as a second-order methodological requirement, that the same analytical threshold be applied to religious, secular-ideological, and scientific transcendence-claims alike — a requirement termed IPC-symmetry, after its connection to identity-protective cognition. No claim is exempted from Steps 1–4 merely because it is phrased in the vocabulary of science, and no claim is subjected to a stricter threshold merely because it is phrased in religious or traditional vocabulary.

This requirement follows directly from the taxonomy of Section 4: because type 8 (social/identity-bound) claims are frequently dressed in the vocabulary of type 1 or type 2 regardless of the domain in which they arise, a rigorous audit must check the functional κ of a claim — what work it is actually doing, including what social or identity-protective function it serves — and not merely its professed κ. Symmetry is what guards against the common failure mode of applying the audit rigorously to claims from a disfavored (outgroup) source while suspending it for claims from a favored (ingroup) source, a failure mode that is itself a paradigm instance of identity-protective cognition operating on the analyst rather than on the claim under analysis.

6. Applications and Falsifiability

6.1 Applications

RETM's vocabulary is intended for direct application to at least three recurring problem areas.

Pattern detection. Apophenia — the perception of meaningful pattern in what is in fact noise, and its socially amplified forms such as conspiratorial reasoning — can be redescribed within RETM as a case in which Te is reported as high (or, more precisely, a spurious pattern is reported as confidently detected) while the actual Ts, properly assessed, is low or the relevant Br has not been independently established. The framework offers a vocabulary for separating "a pattern is genuinely present and Ts is low" from "a pattern is asserted (high Bx) without Br having been assessed at all."

Communicating scientific uncertainty. Scientists and science communicators regularly need to distinguish "we do not yet know" (an epistemic, provisionally assessed Br, in principle revisable as D and M improve) from "this cannot be known" (a categorical ontic or epistemic-in-principle claim, requiring a much stronger and rarer form of warrant). RETM's Br/Bx distinction, together with the audit method, offers a disciplined way of checking which of these is actually licensed by the state of a given field before it is asserted in either direction.

Identity-protective cognition. The framework offers a way of analyzing how group-protective reasoning manufactures Bx claims that are disconnected from any independently assessed Br in order to defend a community's identity commitments — a pattern with applications in political psychology, science communication research, and the study of religious and ideological communities alike, subject always to the symmetry requirement of Section 5.2.

6.2 Status as a Research Program

RETM is presented here as a research program in the sense associated with Lakatos, rather than as a validated general theory. Its hard core consists of the Ω-relational thesis (Section 2) and the Ts/Te/Tr distinction (Section 3.1); its protective belt consists of auxiliary and revisable commitments, including the specific moderating role assigned to K (Section 3.3) and the eight-type taxonomy (Section 4). The distinction matters because it clarifies which parts of the framework are meant to be defended by revising auxiliary claims in light of evidence, and which parts would, if abandoned, constitute abandonment of the program itself.

Correspondingly, RETM is offered together with explicit conditions under which its central claims would be considered falsified or in need of substantial revision:

• If Br, once operationalized through independent measures (formal undecidability or non-identifiability results, measurement-theoretic bounds, model-comparison statistics), fails to respond to independent changes in system capability — that is, if improving A's data or model does not move the assessed Br in the predicted direction — the relational-boundary construct is falsified.
• If Ts and Te are found to be empirically inseparable across all tested conditions — if no dissociation between structural indistinguishability and experienced uncertainty is ever observed — the framework's central diagnostic distinction collapses and requires abandonment or fundamental revision.
• If K is shown to be a necessary condition for structural underdetermination — that is, if Ts is found to be zero in every case where K is zero — then K's proposed status as a moderator rather than a necessary condition is falsified, and the model of Section 3.3 requires revision.
• If the eight-type taxonomy fails to achieve inter-rater reliability above chance when independent coders assign type signatures to real-world transcendence-claims, the taxonomy is inadequately specified and requires revision or reduction.
• If the audit method, when tested against unaided reasoning in controlled conditions, fails to reduce the rate of undetected type-shift errors, its claimed value as an epistemological safeguard is undermined.

These criteria are offered as a starting specification rather than an exhaustive one; a central task for future work is to operationalize each of Br, Ts, Te, K, and κ-assignment with enough precision to make these tests actually runnable.

7. Conclusion

This article has proposed that transcendence-claims — the recurring inference from a state of not-knowing to a claim about a boundary in the world — are best understood not as reports about free-standing objects but as states of a relational assessment situation, formalized as the quintuplet Ω = ⟨A, τ, D, M, t⟩. Within this relational unit, RETM distinguishes structural indistinguishability (Ts) from experienced uncertainty (Te) and from selected resolution (Tr); distinguishes an independently assessable relational boundary (Br) from the discursive claim that a boundary has been reached (Bx); and treats cognitive load (K) as a moderator of the path from Ts to Te and Tr rather than as a necessary condition for underdetermination itself. Building on these distinctions, the article has proposed an eight-type taxonomy of transcendence-claims, an audit method built around type signatures (κ) and bridge premises (β) for detecting unlicensed movement between them, and a symmetry requirement for applying that audit evenhandedly to religious, secular, and scientific claims alike.

Throughout, the framework has been offered under a commitment to methodological naturalism and ontological neutrality: nothing in RETM asserts or denies that mind-independent limits to knowledge or to nature exist. Its claim is narrower — that whatever the truth of such matters, the inference from a particular inquiry's current state to a categorical claim about the world requires a license that is very often missing, and that a shared, domain-general vocabulary makes that missing license easier to notice, in one's own arguments no less than in others'. RETM is offered explicitly as a research program rather than a settled result, with stated conditions under which its central constructs would be falsified. Future work should aim to operationalize Br, Ts, and κ-assignment with sufficient precision for empirical testing, to examine the Ts/Te dissociation experimentally, and to assess the taxonomy's reliability and the audit method's practical value across the domains — religious, secular, and scientific — to which it is intended to apply.