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REVIEW 3 major objections 4 minor 1 cited by

Structural constraints to compare phenomenal experience

T0 review · 3 major / 4 minor · reviewed 2026-08-09 · deepseek-v4-flash

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Pith's one-line read Modelling experiences as layered coloured networks ordered by potential and actual composition forces quantitative comparisons to be partial: levels of consciousness are rankable by counting actual compositions, but phenomenal contents at…

desk verdict The paper's central formal claim is false: Definition 3.1 yields a preorder, not a poset, so the advertised incomparability of same-level phenomenal contents does not follow. read the letter →

arxiv 2502.02154 v2 pith:2QXPMCS3 submitted 2025-02-04 q-bio.NC

J. Díaz-Boils , N. Tsuchiya , CM. Signorelli This is my paper · ORCID
classification q-bio.NC
keywords AnimalConsciousnessStructuralismSubjectiveexperiencePosetMultilayernetworkPartialorder
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper asks how far quantitative comparison of conscious experiences can go. It models each experience as a coloured multigraph (a layer), allows layers to be combined either in parallel ($\otimes$, potential composition) or merged ($\odot$, actual composition), and orders the resulting chains by the rule that a configuration is larger when its layer set is contained in another's and no actual composition in the smaller chain corresponds to a potential composition in the larger one. The main result is that this ordered structure yields only partial comparability: levels of consciousness, defined by counting actual compositions $\odot$, are comparable, but phenomenal contents at the same level—such as $G \otimes H \otimes K$ versus $G \otimes K \otimes H$—are not. The authors conclude that even under the optimistic assumption that all experiences are quantitatively comparable, absolute rankings of experiences, especially across species, do not follow from the mathematics; evolution may instead produce different, partly incomparable modes of experience.

What carries the argument

The central object is a poset (partially ordered set) of experiential layers built from coloured multigraphs. Each layer is a graph whose edges carry colours representing aspects or modalities of experience, and layers are assembled into chains using two operations: $\otimes$ (potential or parallel composition, non-commutative) and $\odot$ (actual or merged composition, commutative, with priority over $\otimes$). The partial order on chains is defined componentwise: a chain $x$ is $\leq y$ exactly when $x$'s layer set is contained in $y$'s and no position where $x$ uses $\odot$ has $y$ using $\otimes$. The maps $f_j$, which convert a single $\otimes$ into $\odot$ at position $j$, are order-preserving and generate upward trajectories; the count of $\odot$ appearances then defines levels, while the non-commutativity of $\otimes$ leaves same-level configurations incomparable.

What would settle it

A concrete falsifier would be a reliable empirical demonstration that two experiences with the same number of actual compositions—for example, $G \odot H \otimes K$ and $G \otimes H \odot K$—are nonetheless consistently ranked by subjects as more or less intense or complex, using a measurement that does not itself presuppose the model's ordering convention.

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Extended reading notes

Core claim

Under the assumption that experiences are quantitatively comparable and can be described by layers, the paper's central discovery is that an ordered structure for comparing them leads only to partial comparison. In the poset of layer concatenations, experiences are comparable only when one chain's layer set is contained in the other's and no position has the smaller chain using actual composition ($\odot$) while the larger uses potential composition ($\otimes$). As a direct consequence, levels of consciousness—the horizontal strata in the poset where every chain has the same number of $\odot$ appearances—are comparable, while phenomenal contents on the same level are mathematically incomparable. The same partiality applies inter-species: configurations with more layers but fewer actual compositions, such as $G \otimes H \otimes K \otimes L$, cannot be ordered against configurations with fewer layers but more actuality, such as $G \odot H \otimes K$, so a larger evolutionary repertoire does not automatically imply a 'bigger' conscious experience.

Load-bearing premise

The load-bearing premise is the modelling convention that actual composition ($\odot$) is phenomenologically more intense and more complex than potential composition ($\otimes$); if real experiences do not consistently respect that ordering, the poset, the level-counting by $\odot$, and all derived incomparability claims lose their foundation.

Editorial extensions

If this is right

  • Levels of consciousness can be partially ordered by the number of actual compositions $\odot$, so claims like 'awake is higher than deep sleep' have a formal footing in the model.
  • Phenomenal contents at the same level cannot be ranked by the model in terms of complexity or intensity; any such ranking would require additional structure beyond the poset.
  • Inter-species comparisons are only partial: more experiential layers do not automatically make a species' conscious experience larger, because actuality ($\odot$) and potentiality ($\otimes$) trade off.
  • The poset constrains experiential trajectories: application of $f_j$ always increases experience, while the inverse relation $g_j$ is non-deterministic, so reverse transitions are underdetermined.
  • If the arguments hold, models of consciousness that assume an absolute scalar of experiential richness must either drop that assumption or add extra mathematical structure to justify it.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A natural empirical extension is to test whether human subjects can consistently rank experiences that the model declares incomparable (same number of $\odot$ but different orderings); a reliable ranking would indicate the model is missing a dimension.
  • The non-determinism of the inverse mappings suggests a formal parallel with dissociative or attentional phenomena, where moving from a unified experience to its parts does not uniquely determine which parts will be attended to.
  • One could import a metric or geometric structure onto the poset to make same-level contents comparable; the paper's framework then becomes a scaffold for comparing such extra assumptions.
  • The inter-species conclusion could sharpen debates on animal consciousness: instead of asking which species has 'more' consciousness, one should ask which experiential maxima each species attains within its own layer structure.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper proposes a multilayer network formalization of conscious experience, with two composition operations: ⊗ (potential/parallel, non-commutative) and ⊙ (actual/unified, commutative). It defines a relation ≤ on chains of layers (Definition 3.1), asserts that this relation is a partial order (Lemma 3.2), and uses it to argue that experiences are only partially comparable: levels of consciousness (counted by occurrences of ⊙) are comparable, while phenomenal contents at the same level are not. The partiality is then applied to intra-species and inter-species comparisons, with implications for animal consciousness and evolutionary debates.

Significance. The paper addresses a timely and important question: whether phenomenal experiences can be quantitatively compared, and it attempts to formalize partial comparability within a single mathematical structure. Its explicit acknowledgment of the modeller's role and its minimal-assumption approach are strengths, as is the ambition to connect a formal framework to debates on animal consciousness. However, the central mathematical claim is not currently supported: the proposed relation ≤ is not a partial order, and the paper's own conclusion about same-level incomparability is contradicted by Definition 3.1. The intended construction may be repairable, but as written the formal foundation fails. No machine-checked proofs or reproducible code are provided; the key lemma is stated without proof.

major comments (3)
  1. [Definition 3.1, Lemma 3.2] The relation ≤ is not antisymmetric, so (G⊗C,≤) is not a poset. Let G, H, K be distinct layers and set x = G⊗H⊗K and y = G⊗K⊗H. Both chains have index set {1,2,3} and all operations are ⊗, so Definition 3.1 gives x ≤ y and y ≤ x. Since ⊗ is explicitly non-commutative (Section 2.2), x ≠ y. Thus Lemma 3.2 is false, and the paper's statement in Section 3.2 that 'every two chains of layers living on the same level ... although not comparable using ≤' is contradicted by the definition. This also invalidates the central conclusion of Section 4.1 that phenomenal contents at the same level are not comparable. The proof of Lemma 3.2 is omitted; the counterexample shows why it cannot be supplied as stated.
  2. [Section 3.2, Example 3.7] The claim that configurations at the same level are 'mathematically not comparable' is not a consequence of the stated definition; it is a property of the stipulated relation, and the stipulated relation actually makes same-level permutations comparable in both directions. The intended result may be obtainable by modifying Definition 3.1, for instance by requiring that the ordered sequence of layers on the left is a prefix of the ordered sequence on the right, but such a change must be made and all subsequent examples and propositions must be rechecked. As written, the central theorem is unsupported.
  3. [Section 3.1] The convention that ⊙ is 'more complex' or 'phenomenologically more intense' than ⊗ is a modeling stipulation with no independent empirical support. The paper acknowledges this, but the entire ordering, the counting of levels by occurrences of ⊙, and all derived comparability claims depend on it. If this priority is not accepted, the partial order and its consequences do not follow from the multilayer structure alone. The authors should state explicitly that the results are conditional on this stipulation and, if possible, indicate what empirical or phenomenological data could test it.
minor comments (4)
  1. [Definition 2.4] The notation V(G⊙H):=V(G)⊔V(H) together with p=|V(G)∩V(H)| is inconsistent; if V(G) and V(H) overlap, disjoint union would duplicate shared vertices rather than identify them, so the formula for the number of vertices is unclear.
  2. [Section 2.1] The paper identifies the layer (G,colG) with G but then writes G∈G⊗C; G⊗C is defined as a set of multilayers, so the terminology 'layer' and 'multilayer' is used inconsistently.
  3. [Example 3.7] The diagram uses arrows labeled f1 and f2, but some edges, for example from K⊗H⊗G, have two f2 arrows, which is confusing; a precise definition of the arrows in the diagram would improve readability.
  4. [References] The reference list contains an unattached bibliographic entry ('A.M.S. Colloquium Publications, vol. 25, Revised Edition, New York, 1948.') that appears to be a leftover from template text.

Circularity Check

1 steps flagged · score 6.0 of 10

Central 'partial comparability' result is encoded in the definition of ≤, not derived from the assumption of comparability.

  1. self definitional [Section 3.1, Definition 3.1; Section 3.2 (levels by ⊙ count); Section 4.1]
    "By convention we say that G ⊗ H ⊗ K ≤ G ⊙ H ⊗ K ... Therefore, layers of experience interacting through G⊙H are considered more 'complex', in the sense of unitary and actual experiences, than interaction G ⊗ H. ... This definition allows us to compare different chains of experiential layers. However, this comparison is partial. ... levels of consciousness are comparable (by counting the appearance of⊙) while phenomenal contents at the same level are not."

    The claimed 'result' that comparison is only partial is built into the stipulated relation ≤, not derived from the abstract assumption of comparability. Definition 3.1 chooses, by convention, that ⊙ is more complex than ⊗ and that inequality holds only when no ⊙-position faces a ⊗-position; the incomparability of G⊙H⊗K and G⊗H⊙K is exactly the failure of that condition in the two directions. Likewise, levels are defined as the number of ⊙, so 'levels are comparable by counting ⊙' is a tautology. The conclusion thus reduces to the definitional input. Separately, Lemma 3.2 is unproved and e.g. G⊗H⊗K and G⊗K⊗H are mutually ≤ under the definition, so the specific incomparability claim is not even entailed by the definition (a correctness issue, not circularity).

full rationale

The paper is transparent that it is constructing a formal model: layers, ⊗, ⊙, and the convention that ⊙ ranks above ⊗ are all stipulated, and the authors explicitly say that structural and mathematical choices constrain experiential comparison. However, the central advertised finding — that assuming quantitative comparability leads to only partial comparison — is not a consequence forced by that assumption. It is a direct property of the particular partial order Definition 3.1 constructs: the relation is chosen so that some pairs are comparable and others are not. The same-level content incomparability is presented as a substantive result, but for chains such as G⊙H⊗K and G⊗H⊙K it follows immediately from the two 'no ⊙/⊗' conditions failing in opposite directions. The level comparability by counting ⊙ is also definitional, since Section 3.2 defines levels by the number of ⊙ occurrences. This is a self-definitional reduction of the central claim, warranting a moderate-to-high circularity score. The self-citations to the authors' prior multilayer work [19, 20, 25, 24] are background and not load-bearing; the core definitions appear in the paper itself. No fitted empirical predictions are made, so there is no fitted-input circularity. Independently, the formal argument is at risk because Lemma 3.2 is asserted without proof and fails for permuted all-⊗ chains under the stated definition, but that is a correctness concern, not a circularity one.

Assumptions & free parameters 1 free parameters · 6 assumptions · 2 invented entities

The central argument rests on a small set of domain assumptions about representing experience as multilayer networks and composing them with two operations. The only invented entities are the layer representation and the actuality-potentiality distinction, neither of which has an external falsifiable handle. The crucial ordering convention, that ⊙ is more complex than ⊗, is an ad hoc stipulation that carries the entire conclusion.

free parameters (1)
  • number of layers d and e, colour set C, graph configurations = undefined (modeller's choice)
    Section 3.1 sets d=e for intra-species and d<e for inter-species comparison; the concrete layers and colours are instantiated by the researcher (Section 2.1). These choices determine which comparisons are available.
assumptions (6)
  • domain assumption Experiences can be represented as coloured multigraphs (layers) with nodes, edges, colours, and multiplicity.
    Section 2.1 states that experiences are modeled as a network in a multigraph. This is the foundational representational premise.
  • domain assumption Layers compose via two operations: non-commutative tensor ⊗ (potential or parallel) and commutative merge ⊙ (actual or unified).
    Introduced in Sections 2.2 and 2.3 without empirical derivation; the operations define how layers combine.
  • ad hoc to paper ⊙ is assigned priority over ⊗ and makes a layer more complex or phenomenologically more intense.
    Section 3.1 says by convention G⊙H is considered more complex and that experiencing in actuality is more intense than experiencing in potentiality. This convention generates the whole order.
  • ad hoc to paper Definition 3.1's comparison rule: x≤y iff layers of x are a subset of layers of y and no position changes from ⊙ to ⊗.
    This rule is stipulated, not derived, and is what makes the order partial.
  • ad hoc to paper d=e corresponds to intra-species comparison and d<e to inter-species comparison.
    Section 3.1 interprets the case d=e as comparison within a species and d<e as comparison between species. This is an interpretive stipulation.
  • ad hoc to paper The pair (G⊗C, ≤) is a poset (Lemma 3.2).
    Stated without proof. The antisymmetry property fails for permutations, so this is an unverified assumption.
invented entities (2)
  • Layer of experience (coloured multigraph)
    purpose: Minimal unit representing a phenomenal experience; combinations of layers produce richer experiences.
    Introduced as the basic ontology of the model; there is no external measurement or falsifiable handle that identifies a layer independently of the modeller's choice.
  • Experiential actuality vs potentiality (⊙ vs ⊗)
    purpose: Distinguishes unified, occurring experiences from separated, potential ones; used to define the ordering.
    A conceptual distinction with no independent operationalization; it is the basis of the more-complex convention.

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Cite this review

Pith. "Pith review of Structural constraints to compare phenomenal experience." pith.science (2026). https://pith.science/paper/2QXPMCS3

@misc{pith2026250202154,
  author       = {Pith},
  title        = {Pith review of: Structural constraints to compare phenomenal experience},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2QXPMCS3}},
  note         = {Machine review of arXiv:2502.02154}
}
read the original abstract

This article defines a partial order structure to study the relationship between levels and contents of conscious subjective experience in a single mathematical set-up. We understand phenomenal structure as extrapolated relationships among experiences, instead of fixed properties of specific experiences. Our mathematical account is based on multilayer network theory. Multilayer theory is a generalization of graph and network theory, widely used in several scientific domains. This structure is also the underlying conceptual and mathematical structure of most current models of conscious experience. From our simple set of assumptions, yet rigorous analysis, we conclude that assuming the comparison and quantification among phenomenal experiences yield only partial comparison, rather than commonly assumed absolute comparability. This has implications for evolutionary and animal consciousness: evolution may encompass diverse modes of experiencing, not necessarily implying larger ones on an absolute scale. Our characterization elucidates structural constraints on experiential comparisons imposed by assumptions and choices made by modellers as active participants in the scientific process. In summary, in light of our phenomenological intuitions, it might be right that some experiences carry qualitative aspects that make them incompatible or non-comparable with other experiences, quantitatively speaking. Some experiences are comparable (e.g. at some experiential levels), but others are not. These results have direct implications for consciousness science, evolution and animal consciousness.

Figures

Figures reproduced from arXiv: 2502.02154 by the authors.

Figure 1
Figure 1. Examples of layers of experience and their composition. Nodes without edges represent undefined configurations, while coloured edges represent aspects of experience. They can range from specific qualities, cognitive processes, to locations in space and others. According to each case, a modeller may need different numbers of nodes, edges and colours to represent all the allowed phenomenal configurations. A) Layers of… view at source ↗

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. On the utility of toy models for theories of consciousness

    q-bio.NC 2025-07 conditional novelty 3.0 of 10

    A consciousness researcher makes the case that toy models help clarify, test, and compare theories of consciousness, using IIT and GWT as case studies.

Reference graph

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Reviewed August 9, 2026 · model on record in the stance chip above.