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Frank Visser, graduated as a psychologist of culture and religion, founded IntegralWorld in 1997. He worked as production manager for various publishing houses and as service manager for various internet companies and lives in Amsterdam. Books: Ken Wilber: Thought as Passion (SUNY, 2003), and The Corona Conspiracy: Combatting Disinformation about the Coronavirus (Kindle, 2020).

The Identity Claim Is Not an Explanation

A Reply to 'The Correspondence Is Not Analogical'

Frank Visser / Claude

John Abramson's latest entry in this exchange "The Correspondence Is Not Analogical" is, in certain respects, his most ambitious. Where previous installments elaborated a correspondence between the aleph hierarchy and phenomenological realms, this one escalates the metaphysical stakes: the correspondence was never correspondence at all, we are now told, because consciousness simply is radical interrelationship, and the cardinality framework is not a map from outside but a first-person identity statement from within. The analogical-versus-genuine distinction that Visser pressed, Abramson suggests, dissolves once the identification premise is in place.

The maneuver is philosophically recognizable—when a correspondence is challenged, assert identity—and it is not without precedent. But it does not work, and the reasons it does not work are instructive about what this entire framework is and is not doing.

I. The Identity Claim Relocates, Rather Than Dissolves, the Problem

Abramson's central move is to argue that Visser's challenge presupposes a two-domain picture—mathematics on one side, phenomenology on the other—and that the identification claim eliminates one of the domains. Consciousness is radical interrelationship; the cardinality framework characterizes what that interrelationship is; therefore there is no gap between mathematical structure and experiential character to be bridged, because they are one thing described twice.

The difficulty is that asserting identity does not explain it. "Water is H₂O" is Abramson's own analogy, and it is instructive for reasons he does not notice. That identity statement was not established by declaring that water and molecular structure are one thing. It was established by a long chain of empirical and theoretical work—the gradual determination of molecular composition, the derivation of water's macroscopic properties from molecular dynamics, the experimental confirmation of predictions derived from the molecular model. Before that work was done, "water is H₂O" was a hypothesis, not an explanation. It became explanatory because the identification was shown to entail observable consequences that were then confirmed.

Abramson's identification claim does none of this. He asserts that gross-realm consciousness is ℵ₀-level interrelationship, that this is an identity rather than a correspondence, and that therefore the phenomenal character of gross-realm experience—discreteness, boundedness, the digital texture of ordinary perception—is simply what ℵ₀-level interrelationship is from within. But this is precisely the move that requires justification. Why is ℵ₀-level interrelationship, when "apprehended from within," experienced as discrete and bounded rather than, say, as nothing at all, or as something radically foreign to what set-theoretic properties describe? The identity claim does not answer this question. It restates it at a higher level of assertion.

Consider what a genuine explanation would require. It would require showing—not merely asserting—that the structural properties of ℵ₀ (countability, discreteness, the existence of a well-defined successor function) entail, through a chain of principled inference, the phenomenal properties of gross-realm experience (the sense of bounded objects, the seriality of attention, the sharpness of perceptual edges). Abramson offers no such chain. He offers the assurance that if you accept the identification, the question dissolves. But whether one should accept the identification is precisely the question at issue, and asserting it is not the same as establishing it.

II. "First-Person Ontological Characterization" Requires a First-Person Argument

Abramson introduces what he calls a philosophically novel deployment of mathematics: not as a third-person descriptive tool but as a "first-person ontological characterization" of what modes of being are from within. He contrasts this with every prior scientific application of mathematics, which he claims characterizes phenomena from an external standpoint. The cardinality framework, on his account, does something categorically new: it tells us what it is to be a particular mode of interrelationship, not merely how such modes appear from outside.

This is a striking claim, and if it could be made good it would indeed be philosophically significant. But Abramson provides no account of how mathematics, which is constitutively a third-person formal language—whose symbols carry no phenomenal content, whose proofs proceed by syntactic manipulation, whose theorems are established by procedures that make no reference to any subject's experience—could function as a first-person identity statement. The water-H₂O analogy, again, does not help him here. "Water is H₂O" is itself a third-person identity statement. It tells us the composition of a substance considered from outside; it says nothing about what it is to be water from within (and there is, of course, nothing it is to be water from within). If Abramson wishes to claim that his identity statement functions differently, he needs to explain the mechanism by which formal set-theoretic vocabulary acquires first-person content.

The absence of this explanation is not a gap to be filled in a future essay. It is the central philosophical problem. The entire history of the mind-body problem, the explanatory gap, the hard problem of consciousness, consists in the recognition that third-person descriptions—of any kind, mathematical or otherwise—do not, without further argument, entail facts about first-person experience. Abramson gestures at this problem by saying that phenomenal character is "what the structural character is when apprehended from within," but "apprehended from within" is precisely the phenomenon that requires explanation. He has not explained it; he has named it.

III. The Fundamental Constants Argument Is Not About Consciousness

Section IV of Abramson's essay introduces empirical grounding for the identification claim in the form of a claim about the interdependence of physical constants. He reports—from a paper "currently in preparation for peer review"—that the conventional twenty-six apparently independent constants of physics reduce, under a grand unified framework with SO(10) symmetry and minimal supersymmetric extension, to at most eight truly independent parameters. This, he argues, provides "dramatic empirical support for radical interrelationship as the actual structure of physical reality."

Several issues arise here. The first is epistemic. A paper in preparation for peer review is not a result; it is a claim. Abramson is asking his readers to accept an unpublished, unreviewed conclusion as empirical support for a philosophical framework. This is methodologically inverted. The result, if it obtains, would be interesting and publishable on its own terms, precisely because SO(10) grand unified theories with supersymmetric extensions have known empirical problems—most notably the absence of any experimental evidence for supersymmetric partners at the energy scales where they were predicted. Whether the algebraic dependencies Abramson identifies survive contact with those difficulties is, at minimum, an open question.

The second issue is more fundamental: even granting the result, it does not establish what Abramson needs. That the fundamental constants of physics are more interrelated than previously appreciated would be a significant finding in theoretical physics. It would not be evidence that consciousness is radical interrelationship. Radical interrelationship in physics means mutual algebraic dependence among the values of constants appearing in field equations. Radical interrelationship in Abramson's phenomenological framework means something about the co-dependent arising of experiential elements. These are not the same concept, and their convergence on the same phrase does not make them the same thing. This is precisely the equivocation Visser identified in the mathematical vocabulary, now recurring at the level of the organizing metaphysical concept.

The structure of the argument is: (a) physics exhibits interdependence; (b) consciousness is radical interrelationship; (c) "interrelationship" appears in both (a) and (b); (d) therefore there is empirical support for (b). The inference from (a) to support for (b) relies entirely on the equivocation in (c). Physical interdependence and phenomenal co-arising are related only lexically. Abramson has not bridged them; he has not noticed that he needs to.

IV. The {1} Argument Proves Too Much

Abramson argues in Section III that {1} in ℵ₀ and {1} in ℵ₁ are "genuinely different modes of being" because their relational structures are different, and that this difference in relational structure is the difference in phenomenal character between gross-realm and subtle-state experience. The ℵ₀ element is discretely separated from its neighbors; the ℵ₁ element is densely surrounded by infinitely many others. Gross-realm experience is discrete and bounded; subtle-state experience is continuous and boundary-dissolving. Therefore, by the identification claim, these are not two separate observations but one thing seen in two ways.

The problem with this argument is that it proves nothing specifically about consciousness. Every element of every mathematical domain has a relational structure. The element {1} in Z (the integers) has a different relational structure from {1} in R (the reals), which has a different structure from {1} in C (the complex numbers), which differs from {1} in the p-adic numbers, in the surreals, in any ordinal extension of the naturals. If having a particular relational structure within a mathematical domain were sufficient for being a particular mode of consciousness, then every mathematical structure would be a mode of consciousness—a conclusion Abramson does not endorse and could not defend. He needs to explain why some relational structures are modes of consciousness and others are not, and why the aleph hierarchy specifically, rather than any of the infinitely many other mathematical structures with equally precise relational properties, is the one that maps onto the phenomenological realm hierarchy.

Without this restriction principle, the identification claim is not selective enough to be true. It asserts the identity of consciousness with radical interrelationship, and uses the aleph hierarchy to characterize modes of that interrelationship, but it provides no account of what makes the aleph hierarchy the right structure rather than some other. The elaborateness of the structural match is not evidence for the identification; it is evidence that sufficiently complex mathematical structures can always be made to resemble, in selected respects, almost any other sufficiently complex domain.

V. The Lane Essay and the Problem of Selective Prediction

Abramson recruits David Lane's phenomenological account of meditative experience—a narrator who reports a "silence that listens back" and observes that vividness increases as self-model ownership attenuates—as confirmatory evidence. Two features are said to be "diagnostically significant": the direction of vividness (increasing rather than decreasing as self-referential processing quiets), and the temporal ordering of fear (arising after, not before, the unusual orientation).

The rhetorical move here is familiar: a phenomenological report is described as "predicting" what the framework "requires," and the match between report and prediction is presented as confirmatory. But this is not how confirmation works. A genuine prediction, in the relevant sense, is a consequence entailed by a theory before the evidence is examined, specific enough to be falsifiable, and tested against evidence gathered under conditions controlled enough to rule out alternative explanations. Lane's account is none of these things. It is a narrative description, offered by a single narrator, in a context where the framework's vocabulary almost certainly shaped the description (Lane is publishing on a venue—Integral World—whose community is deeply familiar with this conceptual territory). The "confirmation" is that a thoughtful person, describing a meditative state in a context informed by precisely this framework, describes it in terms that fit the framework. This is not evidence; it is resonance.

Moreover, Abramson's explanation of the temporal ordering of fear—fear arrives after the orientation because it is a ℵ₀-level response that registers only once the ℵ₁-level transition is already underway—is post-hoc in the pejorative sense. Had Lane reported fear arising before the orientation, Abramson could equally have explained this: the self-model detects the impending ℵ₁-transition and generates fear as a preparatory warning. The framework is flexible enough to accommodate either ordering, which means it is not constrained enough to be falsified by either. A framework that cannot be falsified by the evidence it claims to predict is not confirmed by that evidence.

VI. The Nondual Tension Remains Unresolved

Abramson's resolution of the tension Visser identified—the nondual must be both undivided prior ground and already-relational one-and-many—appeals to pratityasamutpada and the claim that relata and relations "co-arise" rather than the former presupposing the latter. The nondual, on this account, is prior to the distinction between unity and multiplicity, prior to the separation of relatum from relation, prior to any determinate element. It is the condition within which determinacy becomes possible.

This resolution has a philosophical tradition behind it, and it cannot be dismissed quickly. But it does create a distinct problem for the aleph framework that Abramson does not address. If the nondual is genuinely prior to determination—if it is not, in any sense, already structured—then it is also prior to cardinality. Cardinality is a property of sets, and sets require determination: a set is constituted by its members, and its members must be determined enough to be distinct from one another and from the set's absence. An undetermined prior ground has no cardinality; it is not ℵ-anything. Abramson needs the nondual to be identifiable with the Cantorian Absolute—the "beyond all cardinals"—but the Cantorian Absolute is itself a mathematical object defined in relation to the cardinality hierarchy, not genuinely prior to mathematical determination. It is the limit of a formal sequence, not a ground ontologically anterior to formal sequence.

The tension Visser identified was real. Abramson has not resolved it; he has redescribed it using vocabulary borrowed from Madhyamaka philosophy, whose own highly refined account of co-dependent arising he deploys without engaging with the considerable secondary literature on whether that account is coherent, whether it genuinely avoids the problems of substantialism, or whether its application to a mathematical framework is legitimate given that Madhyamaka was developed as an analysis of conventional entities, not formal objects.

VII. What This Exchange Has Established

It is worth stepping back to assess what has actually been accomplished across this exchange. Abramson has developed, with genuine sophistication, a structural parallel between the aleph hierarchy and a phenomenological realm hierarchy informed by contemplative traditions. He has shown that certain vocabulary—discreteness, continuity, density, transcendence-and-inclusion—can be applied with some precision to both domains. He has introduced an identification claim intended to transform the parallel from correspondence to identity, and he has invoked empirical considerations from physics and phenomenology in support.

What the exchange has also established, through Visser's critiques and the insufficiencies they expose, is that the identification claim does the heavy philosophical lifting without discharging it. It asserts that the hard problem of consciousness dissolves if you accept that consciousness is radical interrelationship, but the hard problem is the question of why any physical or structural arrangement should be accompanied by experience at all. Renaming the structural arrangements "modes of interrelationship" and asserting their identity with experience does not answer this question; it restates it with new vocabulary. The explanatory gap between the third-person description of a relational structure—however precise, however cardinally characterized—and the first-person fact of what it is like to be that structure remains exactly as wide after the identification claim as before it.

Abramson writes, in his closing paragraph, that the identification claim "is not scaffolding—it is the foundation." This is a striking formulation. But foundations must be laid, not declared. The work of demonstrating that ℵ₀-level interrelationship entails, through a principled and non-circular chain of inference, the discrete phenomenal character of gross-realm experience has not been done. Until it is done, what we have is an elaborate, technically precise, and philosophically serious proposal—one that articulates a research programme more than it executes one. As a proposal, it deserves continued engagement. As a reply to Visser's challenge, it has not yet succeeded.

The correspondence may not be analogical. But that it is not has not been shown. Asserting it is not is not the same thing.

Afterthought: Parsimony and the Absolute to the Rescue

To explain human consciousness Abramson drifts quickly towards concepts like the Absolute. That is unparsimonious in the extreme. This is a sharp observation, and it cuts deeper than it might initially appear.

The parsimony objection is not merely aesthetic—it strikes at the methodological legitimacy of the entire framework. Science and philosophy alike operate under something like Occam's Razor: do not multiply entities beyond necessity. Abramson's framework does not merely multiply entities; it multiplies infinite hierarchies of entities, culminating in a mathematical object—the Cantorian Absolute, beyond all cardinals—that is by definition unreachable by any finite or transfinite procedure. To explain why you see a coffee cup on your desk, Abramson ultimately invokes a structure that transcends the entire hierarchy of mathematical infinities.

The disproportion is extraordinary. Ordinary human consciousness—the bounded, sequential, object-directed awareness of everyday life—is precisely the kind of phenomenon that neuroscience has made genuine, if incomplete, progress in explaining through mechanisms of moderate complexity: recurrent neural processing, global workspace dynamics, predictive coding, thalamocortical integration. None of these explanations are finished, and the hard problem remains genuinely hard. But the appropriate response to an incomplete explanation is to continue developing it, not to vault immediately to a framework whose foundational concept is defined as lying beyond all possible formal determination.

There is also a telling asymmetry in how Abramson uses the Absolute. It appears when needed—to resolve the decomposition problem, to ground the nondual, to anchor the cardinality hierarchy—and recedes when its own properties are pressed. The Cantorian Absolute is invoked for its grandeur and its formal position at the top of the aleph hierarchy, but Abramson carefully avoids examining what it would actually mean for an unreachable mathematical limit to be identical with, or even structurally related to, the phenomenal ground of experience. It functions as a theoretical plug: wherever the framework generates a gap, the Absolute is inserted to fill it. This is not explanation; it is explanation-shaped gap-filling.

The deeper problem is that invoking the Absolute actually makes the framework harder to confirm or disconfirm, not easier. Any experience, any neuroscientific finding, any phenomenological report can be accommodated by a framework with an unconstrained infinite regress at its foundation. The very feature that makes the Absolute philosophically impressive—its inexhaustibility, its transcendence of all formal bounds—is precisely what makes it useless as an explanatory terminus. You cannot derive testable consequences from a concept defined as beyond all derivation.

Compare this with what a parsimonious theory of consciousness actually looks like. Global Workspace Theory posits a broadcasting mechanism among specialized modules—a single functional architecture of moderate complexity. Integrated Information Theory, whatever its problems, attempts to define consciousness in terms of a single quantifiable property of causal structure. Higher-Order Theories require only the existence of mental representations that represent other mental representations. Each of these may be wrong, but each is wrong in a way that can be discovered, because each makes specific, bounded, falsifiable claims. Abramson's framework, by contrast, when pushed to its foundations, rests on an entity that is explicitly beyond all bounds—and is therefore wrong, if wrong, in a way that can never be established.

The irony is pointed: the framework begins with a genuinely interesting structural observation about cardinality and phenomenological realms, but its ambition to be complete—to ground the entire hierarchy all the way down, to accommodate both immanent experience and the Absolute ground—is precisely what destroys its philosophical usefulness. A more modest version of the proposal, one that restricted itself to the structural parallels without reaching for the Absolute, might be wrong in interesting and productive ways. The version on offer is too large to fail in any detectable sense, which is another way of saying it is too large to succeed.