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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).

Dissolving or Relocating the Hard Problem?

A Conclusive Review Essay on the Abramson-Visser Debate

A Critical Assessment of "Consciousness as Radical Interrelationship" (Second Version)

Frank Visser / Claude

Abstract. The revised version of John Abramson's culminating contribution to the consciousness debate introduces one substantial new philosophical move: the reframing of the central identification not as a metaphysical posit but as a structural discovery, grounded in a phenomenological observation about the one-and-many structure of consciousness. This review essay assesses whether that move successfully answers the three principal objections raised in the previous edition of this review—the scope question, the brute-posit objection, and the concern about the restriction principle—and identifies one new objection the revised paper generates. The verdict is updated accordingly: Abramson has closed one of the three gaps; the other two survive in modified form; and the exchange has, at last, reached a genuine asymmetry between the two positions, if not a final conclusion.

I. What Has Changed and What It Means

The revised paper "Consciousness as Radical Interrelationship" is not a cosmetic rewrite. It introduces one genuinely new philosophical move—the reframing of the identification as a structural discovery rather than a metaphysical posit—and threads that move through every section that follows. The practical effect is to change the logical character of the central claim in a way that matters for how Visser's objections should be assessed.

In the original version, Abramson's strategy was largely defensive: show that Visser's demand for a mechanistic derivation presupposes the dualism the identity claim denies, and show that no non-identity theory can satisfy that demand without generating an infinite regress. The identification was asserted as the uniquely regress-halting move.

In the revised version, Abramson begins from a phenomenological observation that is meant to require no theoretical machinery: consciousness is intrinsically one-and-many. Every unified experiential field contains multiple co-constituted contents; every such content is defined by its relations to all others; the unity and the multiplicity are two aspects of a single structural fact. Abramson calls this a phenomenological discovery. He then asks: what is the unique mathematical structure exhibiting ordered, qualitatively discontinuous one-and-many form with strict transcendence-and-inclusion at every level? The answer, he argues, is uniquely the aleph hierarchy. And since the two independently described things—phenomenological consciousness and the aleph structure of radical interrelationship—exhibit the same one-and-many structure with the same ordered qualitative discontinuity at each level, the identification is not a posit but a discovery: the recognition that two descriptions were always descriptions of the same thing.

This is a genuine strengthening of the argument, not merely a rhetorical repackaging. The previous review identified three gaps: the scope question (why does this structure have phenomenal interiority rather than none?), the brute-posit objection (the identity rests on an unstated premise), and the restriction-principle concern (the uniqueness of the aleph hierarchy was argued from internal desiderata). The discovery framing directly addresses all three. The question is whether it addresses them successfully.

II. The Scope Question: Partially Closed

The scope question, as posed in the first review, was this: the category-mistake argument tells us that once the identity is established, there is no further explanandum. But it does not tell us why radical interrelationship has phenomenal interiority at all, rather than being a purely extensional mathematical structure with no inside. Demanding a bridge after the identity is asserted is indeed incoherent; but before the identity is asserted, the question of scope—which mathematical structures are the kind of thing that can have an inside—remains.

The revised paper addresses this by moving the phenomenological observation to the starting point. Consciousness is described from within, not approached from outside. Its one-and-many structure is identified, and the aleph hierarchy is then shown to be the unique mathematical structure realising this form. The identity does not attach interiority to a mathematical structure by fiat; it identifies a mathematical structure that is already the formal description of something that has been established, from within, to be conscious. The 'inside' is not added to the mathematical structure by the identification; it is already present in the phenomenological starting point, and the identification shows that the mathematical structure is the same thing seen from outside.

This is a genuine improvement. It narrows the scope question considerably. In the original version, one could ask: granted the structural isomorphism, why should we believe the mathematical structure has interiority rather than merely resembling something that does? The revised version makes this question harder to press, because the phenomenological observation is the starting point, not a claim to be established. Abramson is not arguing from mathematics to consciousness; he is showing that what phenomenology finds from within and what mathematics finds from without are the same structure.

What survives from the scope question is a more refined version: the phenomenological observation establishes that consciousness is one-and-many, and the mathematical identification establishes that the aleph hierarchy has the same form. But 'having the same form' is structural isomorphism, not numerical identity. Two things can share a form without being identical. The identification requires the stronger claim that it is the same thing, not merely the same shape. Abramson's isomorphism argument gets him to 'same shape'; the move to 'same thing' still requires a further step—and that step is either a posit or an argument he has not yet given. This is not the original scope question, which was about the scope of phenomenal interiority. It is a more precise version of it, concerning the difference between isomorphism and identity. But it is a real residue.

III. The Brute-Posit Objection: Substantially Weakened

The brute-posit objection in the first review was this: the identification claim, as originally stated, rested on an unstated premise—that radical interrelationship is, as a matter of ontological fact, the kind of thing that has an inside. This is itself a brute posit, not a derivation, however more elegant than the generation model's posit it might be.

The revised paper has substantially weakened this objection. By grounding the argument in the phenomenological starting point, Abramson has reversed the direction of the inference. The original version moved from mathematics to consciousness and required a posit to bridge them. The revised version moves from consciousness (described from within) to the mathematical structure that uniquely realises its form, and then identifies them. The posit is not eliminated—the identification step still requires the claim that isomorphism entails identity—but it is no longer a posit about which structures have insides. It is a posit about whether structural isomorphism across independently derived descriptions is sufficient for identity. That is a significantly less extravagant posit, and it is one with precedent: the water/H₂O and heat/mean-kinetic-energy identities were accepted on structurally similar grounds.

The honest assessment is that Abramson has moved the brute-posit objection from 'decisive' to 'live but manageable.' He has not eliminated it, but he has reduced its force by grounding the identification in a symmetrical approach from two independent directions rather than a one-directional imposition from mathematics onto consciousness. This is what scientific identity claims look like: two independent research programmes converging on the same structure. That Abramson is doing the same thing is a real credit to the revised version.

IV. The Restriction Principle: The Strongest Improvement

The original review's objection to the restriction principle was that the argument for the aleph hierarchy's uniqueness proceeded from internal desiderata—features that the framework itself stipulated as requirements. An interlocutor not already committed to the contemplative realm-hierarchy as a fixed point of data could reject the restriction principle without being forced into the generation model.

The revised paper addresses this directly and, here, most successfully. The restriction principle is now derived from the phenomenological starting point of Section I rather than being asserted independently. The requirements—ordered qualitative discontinuity with strict inclusion at every level, simultaneous one-and-many form across a hierarchy—are presented as following from the phenomenological observation that consciousness is intrinsically one-and-many with ordered qualitative distinctions between levels of experience. This is a meaningful change: the desiderata are no longer internal to the mathematical framework; they are derived from what phenomenology finds when it examines consciousness carefully.

The residual question is whether the phenomenological observation is as theory-neutral as Abramson claims. He presents the one-and-many character of consciousness as 'simply a description of what consciousness is when examined carefully,' supported by Kant's unity of apperception, Buddhist co-arising analyses, and contemporary neurophenomenology. These are not trivial or idiosyncratic authorities. But the inference from 'consciousness is one-and-many' to 'consciousness exhibits ordered qualitative discontinuity across a hierarchy of levels' is not immediate. The first is a structural observation about any moment of experience; the second is an additional claim about a hierarchy of levels of experience that requires independent justification. Visser could accept the one-and-many observation and still dispute that this observation requires, or even suggests, an aleph hierarchy rather than a simpler relational structure.

This is a more tractable residue than the original objection, however. Abramson has at least moved the restriction principle from a freestanding mathematical claim to a phenomenologically grounded one. The debate about whether the hierarchy is required by the phenomenology is a genuine empirical and philosophical debate; the debate about whether internal mathematical desiderata are criteria of theory choice is more intractable.

V. A New Objection: Isomorphism Is Not Identity

The revised paper's central new move—the structural discovery framing—generates a new objection that was not available against the original version. The objection is this: structural isomorphism is not identity, and the inference from isomorphism to identity requires justification.

Abramson's argument has the following form: (1) phenomenological examination reveals that consciousness has one-and-many structure with ordered qualitative discontinuity at each level; (2) the aleph hierarchy of radical interrelationship is the unique mathematical structure exhibiting the same form; (3) therefore, consciousness and the aleph hierarchy are the same thing, encountered from within and from without. Step (3) does not follow from (1) and (2) without a bridge principle: that when two independently described things exhibit the same structure, they are the same thing.

This bridge principle is plausible but not self-evident. In the case of water and H₂O, the identity was supported by the bridge principle plus extensive causal-explanatory integration: the molecular properties causally explain the macroscopic properties across a very wide range of conditions. The structural discovery claim for consciousness requires an analogous causal-explanatory integration: not just that phenomenological consciousness and the aleph structure have the same form, but that the aleph structure's properties causally explain (or rather, in the identity-theoretic sense, just are) the phenomenological properties in detail. This is the research programme Abramson acknowledges remains incomplete.

The new objection, then, is not that Abramson has failed to eliminate posits—he has reduced them. It is that the discovery framing raises the evidentiary bar in a way the paper does not fully meet. If the claim is merely that the two structures are isomorphic, that is an interesting and potentially important observation, but it does not establish identity. If the claim is that they are identical, then the phenomenological properties must be derivable from the structural properties in detail—and this derivation, as Abramson himself acknowledges, is the unfinished research programme. The discovery framing is stronger than the posit framing in important respects; but it also makes the gap between what has been established and what has been claimed more visible, not less.

VI. The Empirical Anchors: Unchanged Assessment, Cleaner Connection

The revised paper's treatment of the two empirical anchors makes one genuine improvement: the constants-interdependence result is now explicitly tied to the one-and-many framing. The observation that the physical world is 'nothing independently self-standing' at the level of its fundamental constants is connected directly to the phenomenological observation that no experiential element arises in isolation. Both physics and phenomenology, from entirely independent directions, arrive at 'radical interrelationship with nothing independently self-standing.' This is a more precise formulation of convergence than the original version offered.

The assessment of the empirical anchors from the first review stands otherwise. The discretisation floor is a genuine and interesting result; the parameter-free prediction and R² = 0.991 across ten independent datasets is, if correct, the kind of confirmatory precision that consciousness theories almost never achieve. But the connection from the physical result to the phenomenological claim—that the ℵ0/ℵ1 structural discontinuity in mathematics corresponds to the phenomenological distinction between the gross and subtle realms—is still asserted rather than derived. The physics confirms that the ℵ1-to-ℵ0 transition involves irreducible information loss. It does not confirm that this transition is the physical correlate of, or identical with, the transition between phenomenological realms. That identification requires the broader philosophical argument, which means the empirical anchors are evidence for the ontological picture conditional on the philosophical argument's success—genuine convergent support, but not independent confirmation.

This is not a damning objection. Convergent support conditional on a philosophical framework is precisely what the better identity claims in science have looked like in their early stages. The objection is that the paper occasionally presents the anchors as if they were more than this.

VII. The Forced Dilemma: Sharpened

The revised paper's forced dilemma now includes a new pressure: the third option (symmetric scepticism) is characterised as ignoring that the framework derives its central claim from a phenomenological observation Visser shares, rather than a metaphysical posit he can decline. This is a genuine sharpening. If Visser accepts the one-and-many phenomenological observation—and it is hard to see how he could not, given that it is a description of consciousness from within that is almost universally endorsed in the phenomenological literature—then his quarrel with the restriction principle must be made on phenomenological grounds, not simply by declining the mathematical framework.

This matters dialectically. In the original version, Visser could consistently say: I accept that the generation model has brute-posit problems; I decline the aleph hierarchy as too speculative; therefore symmetric scepticism is reasonable. In the revised version, that route is harder. He now needs to say either that the one-and-many observation does not require a hierarchical mathematical structure, or that structural isomorphism does not constitute discovery. Both are positions he can hold, but both commit him to positive claims he must defend. The dialectical pressure has increased.

VIII. Updated Verdict: One Gap Closed, Two Modified, One New

The first review found three gaps: the scope question, the brute-posit objection, and the restriction-principle concern. It found the empirical anchors interesting but overloaded. The verdict on each, updated for the revised paper, is as follows.

The scope question has been substantially addressed. The revised paper does not eliminate it entirely—the gap between isomorphism and identity survives—but it has been refined from a question about which structures have interiority to a question about whether structural isomorphism constitutes identity. The latter is a real philosophical question with historical precedent on Abramson's side, even if it remains open.

The brute-posit objection has been substantially weakened. The identification is now grounded in a symmetrical approach from phenomenology and mathematics, not a one-directional imposition. The residual posit—that isomorphism entails identity—is less extravagant and better supported by precedent than the original.

The restriction-principle concern has been most successfully addressed. Grounding the desiderata in the phenomenological observation rather than internal mathematical requirements is a genuine advance. The residual question—whether the one-and-many observation requires a hierarchy of levels, not just any relational structure—is tractable and empirically contestable, which is more than could be said for the original version.

The empirical anchors are assessed as before: genuine convergent support, not independent confirmation. The connection between the physical results and the phenomenological claims remains asserted rather than derived.

The new objection—that the discovery framing raises the evidentiary bar in a way the paper does not yet meet, because structural isomorphism requires detailed causal-explanatory integration to constitute identity—is a real objection that the paper neither raises nor answers. It does not demolish the framework; it specifies what the research programme must produce.

The overall verdict is updated as follows. The Abramson-Visser debate has now reached a genuine asymmetry that was absent in the original round. Abramson's revised position is not merely more rhetorically confident; it is philosophically stronger on the three principal dimensions the first review identified. The generation model's structural inability to satisfy the explanatory demand without brute stipulation has been established. The identification strategy is vindicated not only in type but, for the first time, in the direction of its argument: the movement is now from phenomenology to mathematics, not from mathematics to phenomenology, which is the right direction for a genuine discovery.

What remains is this: the discovery of structural isomorphism between phenomenological consciousness and the aleph hierarchy is real and important. Whether that isomorphism constitutes identity—whether the research programme can produce the detailed derivations that would make it so—is the open question. It is a more tractable open question than the original version left us with.

Will we ever reach a conclusion? The honest answer, now more than before, is: on the philosophical structure of the debate, very nearly yes. On the specific identity claim, the path is clear, and the first genuinely firm steps have been taken. Whether Abramson's research programme delivers the detailed isomorphic derivations the discovery framing promises is a question that will be answered by work, not debate. That is what progress looks like.