Towards a Mathematical Structure of Global Phenomenal Consciousness

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Review: Entropy MS4269644

Whatever model one chooses to investigate as an explanation of consciousness, the proximate goal from a scientific standpoint should be to identify the physical constraints that model predicts and devise experimental methods to test for their presence or absence. But this is difficult for theories where the production of experiential states (i.e. qualia) is supposed to be a direct output of integrative processes acting across the cortex (most theories in other words) because we have no physical model for how diffuse, connectomal mechanisms could give rise to such states. Representational theories are an example, because there is no way to understand what a representation is in mechanistic terms. In consequence I think that many like myself gravitate by default to physicalist models, where sensations map to EM field effects or similar, because there we do have some handle on the constraints. I therefore think the authors are doing exactly what is needed in trying to pin down more precisely what a connectionist/integrative model of consciousness requires if it is to unify the qualia of experience in real time.

Hence I applaud what the authors are trying to do in this paper, and in particular the focus on identifying constraints. But I do have two problems with the paper as it stands.

(1) I am not able to assess the more technical/mathematical parts of the argument, so I cannot judge the paper fully, leaving this at best a partial review. Partly this is my own lack of suitable background and knowledge, and indeed most papers in Entropy are beyond my ability to fully comprehend. On the other hand, as a representative of those in the field who want to see the combination problem solved, and would like to understand that solution, there may be a better way for the authors to get their key points across and make them accessible to a wider readership. So I am suggesting here an expansion of the section explaining in plain language how their form of analysis is relevant and how it works. I realize the authors have tried to do this with their figures and relevant text. For me, however, it just does not come across, a matter perhaps of their methods being too different from what I am familiar with. 

(2) On the parts I can assess, what stands out for me is the authors’ conviction that consciousness is necessarily unified in real time, which I read as a belief that this is accomplished in a computational way by connectomal processes. But this not the only way to view the combination problem, which means this analysis, though valid for one set of models, may be solving something that is a non-problem for others models. In the alternative camp I would place those who see the cortex as silent, so that consciousness need not map to cortical processing in all cases or even in any case [see Merker (2007) Consciousness without a cerebral cortex, Behav. Brain Sci. 30:63; Earl (2019) The structure of mind and the role of consciousness, J. Psychol. Behav. Sci. 7:84; and for experimental support Berridge & Kringelbach (2015) Pleasure systems in the brain, Neuron 86:646]. In a recent email exchange with Dr. Berridge, I asked how far he would go currently in supposing that sensations could be both produced and act locally (essentially a non-integrative model of consciousness), and my impression is that he sees no reason to reject the idea that much of consciousness could simply be assembled in a non-integrative way (the constitutive option) as opposed to being unified through integrative processes. The leads me to suggest that the present authors are going unnecessarily far out on a limb with such statements as (line 65) “... conjoint phenomenology always possesses an additional phenomenal quality of unity that renders the experience irreducible to its parts.” Vision and the binding problem are typically used in support of this argument, but this is not universally accepted, not by Merker for example, so far as I recall his comments on the subject, nor by DiLollo (2012, The feature-binding problem is an ill-posed problem, Trends Cogn. Sci. 16:317), though I cannot say I fully understand his objection either. The point, however, is that using conscious vision as an explanatory target is a double-edged sword – it is both the most demanding of percepts to explain for any theory, but is also so different qualitatively from the rest of conscious experience that we have no guarantee that models of consciousness based on the properties of the visual percept will apply to any other category of contents.

The alternative to a consciousness that achieves unity through integrative processes is one assembled constitutively from the output of individual hotspots, meaning modular entities, and these could be located elsewhere than the cortex - in the thalamus according to Merker or even more basally (for some forms of affect) according to Berridge & Kringelbach. There is a recent theory paper exploring this option by Lacalli (2025, Scaling up from sentience, Front. Psychol. 16:1648930) that explores some of the implications, but the relevant point for this review is that a hotspot-based model gives you a clear experimental target, to localize the hotspot in question and examine its structure and activity, which then will ideally reveal the relevant constraints. With regard to the present MS, all I am saying here is that I think, to be comprehensive, the authors should include at least some caveats on their view, that seeking to explain what one might call computational (real-time, integrative) unity, is an attempt to solve a problem that for some categories of theory is simply not much of an issue.

 

Author Response

Thank you very much for a close reading of our manuscript and for your thoughtful comments. Please see attached for our responses.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This is a stimulating paper that makes a useful contribution to addressing an important issue in the scientific study of consciousness. The issue is how to systematically describe the contents of experience in such a way that hypotheses about part-whole relations can be tested empirically and quantitatively. Precisely formulating how elementary “aspects” of experience are combined into larger more complex “broad” experiences is a fundamental problem for consciousness science. It is also arguably a prerequisite for solving the (also fundamental) phenomenal binding problem: to understand how the physical substrate of consciousness implements its complex irreducible unity.

In the present manuscript the authors apply a “sheaf-theoretic” framework from mathematical category theory to operationally define the contents of experience, from isolated “narrow” qualia to “broad” combinations of qualia. Their framework for specifying conscious contents combines (i) relationships among the parts of individual complex experiences with (ii) relationships among different experiences. Their formulation represents a testable hypothesis about the specific form that part-whole relationships take in human experience. Whether or not this specific formulation is supported by detailed experimentation, it provides a clear reference point for empirical investigation.

The manuscript is well-written and does a good job of introducing category and sheaf theory, which was unfamiliar to me.

I do have a number of questions and suggestions for clarifying and strengthening the argument.

I think the most substantial weakness is some ambiguity about the concrete operational/experimental procedures for “local observations” to measure how people are experiencing narrow vs broad qualia. This part of the paper, towards the end, gets sketchier. A revision should clarify when observations of isolated aspects of experience are to be sampled using attentional instructions applied to the same stimulus (as in the example case with two visual gratings), vs by using different stimuli that attempt to isolate specific narrow qualia. Both approaches appear to be approximations and their limitations should be discussed.

Other comments:

It would be helpful to mention the meaning of “sheaf” as a bound bundle earlier in the exposition. The term was obscure to me until I realized that binding was the whole point.

p4 line 118 “the neurophenomenological research program…often relies on…predetermined experiential dimensions.” This makes it sound like the present proposal will evade this limitation, but according to my understanding it does not. The limitation is acknowledged on p25 at lines 778-780: “It is yet unclear …how empirical measures can be specified for arbitrary partitions of experience.”

p7 lines 244-245: “hypothesized to be mirrored”—this is a venerable hypothesis going back to Spinoza, Leibniz, Whitehead, Russell, (Chalmers, 1997), and others. The single Tononi 2019 citation does not do justice to this history, which should at least be mentioned in the Discussion if not cited here. “The order and connection of ideas is the same as the order and connection of things”—proposition seven of book two of Spinoza’s Ethics on pg 35 of (Spinoza, 2005). Although the neural/physical substrate of conscious unity is not the main focus of the present article, it is part of its motivation, so it would be appropriate to note approaches to this problem. E.g., (Chalmers, 2017, Cleeremans et al., 2000, Feldman, 2013, Revonsuo and Newman, 1999, Treisman, 1998). (Wiest, 2025) defends a specific biophysical proposal regarding how this “mirroring” (aka “isomorphism”) of phenomenal and physical properties could be true under our contemporary physical theory. Models like this might constrain the form that part-whole relations could take. A little more about the logic the different researchers have applied to constraining the psycho-physical relationship would be appreciated. E.g., p10 line 323 “must be…more similar…” and the mention of reference 34 on page 24 are disconnected asides but could be part of a brief section that treats this issue a little more systematically.

p9 lines 286-287 “complete descriptions of individual phenomenal experiences are unattainable”—this is understood as a consequence of the quantum nature of consciousness in (Georgiev, 2020). “Quantum information” about a system’s state is inaccessible “from the outside.”

p13 lines 407-408 “it is plausible that this subsumptive relationship is transitive”—it occurs to me to wonder if this would rule out indefinite narrow qualia. For example, in Borges’ (very) short story Argumentum Ornithologicum, he describes imagining a flock of birds in which the precise number of birds is indeterminate. Can the present formulation allow for such a thing?

p14 line 426 “capture relative proximity relations between elements without requiring a metric distance.” This is obscure to me. Do we still get a quantification of the proximity—i.e., a number? So what’s the distinction?

p17 line 488-9 “dissimilarities between…this trial and…all other trials.” This definition of the dissimilarity matrix seems to mean that the “qualia measures” will vary from experiment to experiment. This seems like a major problem if this formalism is to be used for comparing results across different experimental contexts.

p17 line 513 “project”—this word calls to mind the literature using quantum-like measurement projection operators to represent specific questions and judgments (Pothos and Busemeyer, 2022, Tsuchiya et al., 2025). This connection might be mentioned since the 2^nd author on the present manuscript has contributed to this literature. In other words, the quantum-like formalism might complement or implement the attentional “restriction operators” defined more abstractly in the present article.

p19-22. Binding by gluing. The idea that global coherence of an experience might be tested or produced by local matching is concrete and plausible. However, given the mention of contextuality, I wonder if the present model could capture nonlocal contextual effects, in which matching is necessary among noncontiguous parts. Can the authors comments on this here or in the Discussion? Are such effects already demonstrated in the literature?

p22 line 678 “part-to-part”—although the focus of the present study was part-to-whole relationships, I would appreciate a bit more discussion of the extent to which the present formalism can capture part-to-part relationships that are implicit or explicit in the broad experience, like “visual object A is bigger than B” or “A is to the left of B.”

p23-24 lines 710-716. This paragraph mentions a major limitation of the present proposal, but does not discuss it adequately. Specifically, the difficulties inherent in trying to measure narrow vs broad qualia. “Most existing works measure” narrow qualia because the qualia space grows exponentially as new dimensions of complexity are added. How to measure similarity among such complex broad experiences is a major challenge not addressed in the present paper. Whether I am misunderstanding the situation or not, this needs further discussion and clarification.

p24 line 752 “local observations”—it’s not clear to me what these local observations are. They could reflect attention to local visual features, or presentation of isolated “narrow” stimuli, or variations I’m not thinking of. If different experimenters make different choices the results will be difficult to compare. Perhaps this should be discussed in the limitations section.

Relatedly, it would be helpful to make the author’s notion of qualia measurements a bit more concrete. Might the example include some numbers representing measured values, or a few sentences explaining how those measured values would be acquired?

References cited:

CHALMERS, D. 2017. The Combination Problem for Panpsychism. In: BRÜNTRUP, G. & JASKOLLA, L. (eds.) Panpsychism. Oxford University Press.

CHALMERS, D. J. 1997. The Conscious Mind : in Search of a Fundamental Theory, New York, Oxford University Press.

CLEEREMANS, A., CHALMERS, D., CLEEREMANS, A., KOCH, C., MERIKLE, P. & WILKEN, P. 2000. The unity of consciousness: Binding, integration, and dissociation - Brussels, Belgium, June 29-July 2, 2000. Consciousness and Cognition, 9, S1-S2.

FELDMAN, J. 2013. The neural binding problem(s). Cogn Neurodyn, 7, 1-11.

GEORGIEV, D. D. 2020. Inner privacy of conscious experiences and quantum information. Biosystems, 187.

POTHOS, E. M. & BUSEMEYER, J. R. 2022. Quantum Cognition. Annu Rev Psychol, 73, 749-778.

REVONSUO, A. & NEWMAN, J. 1999. Binding and consciousness. Conscious Cogn, 8, 123-7.

SPINOZA, B. 2005. Ethics Penguin Classics.

TREISMAN, A. 1998. Feature binding, attention and object perception. Philos Trans R Soc Lond B Biol Sci, 353, 1295-306.

TSUCHIYA, N., BRUZA, P., YAMADA, M., SAIGO, H. & POTHOS, E. M. 2025. Quantum-like Qualia hypothesis: from quantum cognition to quantum perception. Frontiers in Psychology, 15.

WIEST, M. C. 2025. A quantum microtubule substrate of consciousness is experimentally supported and solves the binding and epiphenomenalism problems. Neuroscience of Consciousness, niaf011 10.1093/nc/niaf011.

Author Response

Thank you very much for taking the time to read our manuscript closely and for providing detailed comments. Please see attached for our responses.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors have addressed my concerns and made useful additions to the MS, not least in the treatment of phenomenal versus feature binding. There is still much here that is beyond my immediate expertise to judge, but the paper is definitely, for me, one worthy of future more detailed study.  

Author Response

Comments: The authors have addressed my concerns and made useful additions to the MS, not least in the treatment of phenomenal versus feature binding. There is still much here that is beyond my immediate expertise to judge, but the paper is definitely, for me, one worthy of future more detailed study.

Response: We thank the reviewer for their encouraging remarks and thoughtful feedback throughout the review process.

Reviewer 2 Report

Comments and Suggestions for Authors

The authors have admirably addressed my suggestions in their revision, by adding substantive discussion and reference to relevant literature. The new “Intuitively” summary paragraphs are helpful. I just have a few suggestions for improving the revised version.

I strongly recommend that the authors choose a different term to articulate the important distinction between phenomenal binding and functional or computational forms of binding. Unfortunately, the authors refer to computational binding as “feature binding.” This was not present in the original submission and it is unfortunate for at least two reasons. First, phenomenal binding necessarily includes feature binding. The consciously experienced visual field is composed of visual “features” whether they are joined into “objects” or not. The authors’ main example illustrates this by embodying a visual field with two distinct features: the local grating stimuli. “Feature binding” is a poor choice of term in this context because it could refer to conscious or unconscious binding of features, as in the references cited by the authors (which I appreciate). Those results make it clear that feature binding can also occur consciously.

Second, in the context of discussing the approach to studying broad/complex experiences vs narrow/simpler experiences, defining “feature binding” solely in functional terms is like fighting with both hands tied behind your back. Why? Because the natural way to approach complexity is in terms of the simplest combinations of…features! This is what is done in the central concrete example in the paper, so it seems really unhelpful to disallow the use of the word “feature” when discussing combining elementary experiences.

This distinction between functional binding for information processing purposes and phenomenal binding for complex conscious experiences is made across multiple neuroscientific taxonomies of binding (e.g., Plate, 2007:775; Hirstein, 2012:57-58; Revonsuo & Tarkko, 2002:4). Although Feldman 2013 does contrast visual “feature binding” with phenomenal binding aka the unity of consciousness, this is not a helpful example to follow as I explained above. Some alternative references supporting a different nomenclature (i.e. phenomenal binding vs functional/computational binding) are:

Hirstein, W. (2012). Mindmelding: Consciousness, neuroscience, and the mind's privacy. Oxford University Press.

Plate, J. (2007). An analysis of the binding problem. Philosophical Psychology, 20(6), 773-792.

Revonsuo, A., & Tarkko, K. (2002). Binding in dreams-the bizarreness of dream images and the unity of consciousness. Journal of Consciousness Studies, 9(7), 3-24.

Revonsuo, A.; Newman, J. (Jun 1999). "Binding and consciousness". Conscious Cogn. 8 (2): 123–7. doi:10.1006/ccog.1999.0393. PMID 10447994. S2CID 32430180.

Percy C, Agarwal G. The phenomenal binding problem for neural networks. Conscious Cogn. 2026 Mar;139:104003. doi: 10.1016/j.concog.2026.104003. Epub 2026 Feb 3. PMID: 41637896. https://pubmed.ncbi.nlm.nih.gov/41637896/

Chronological comments:

p4. Footnotes: I hope you will choose another term besides feature binding here. Even though your ref 22 supports this, your refs 24 and 25 show that feature binding CAN BE CONSCIOUS. Similarly, binding features into objects requires a computational solution but it also raises a phenomenal binding problem when the object is perceived or imagined consciously.

p15. The experienced visual field is an example of phenomenal feature binding even if you don’t call it that—this will introduce unnecessary cognitive dissonance and confusion in the reader if you insist on using “feature binding” to refer exclusively to functional or computational binding.

p24, p26, p27. The additions regarding contextuality or “disunity” are helpful. On the other hand, given that you are proposing a criterion for contextuality, it would also be helpful to cite and compare to other proposed contextuality criteria (in the Discussion), as in these papers:

BASIEVA, I., CERVANTES, V. H., DZHAFAROV, E. N. & KHRENNIKOV, A. 2019. True Contextuality Beats Direct Influences in Human Decision Making. Journal of Experimental Psychology-General, 148, 1925-1937.

BRUZA, P. D., FELL, L., HOYTE, P., DEHDASHTI, S., OBEID, A., GIBSON, A. & MOREIRA, C. 2023. Contextuality and context-sensitivity in probabilistic models of cognition. Cognitive Psychology, 140.

Author Response

We are grateful to the reviewer for taking the time to thoroughly review our manuscript again and for their helpful and constructive feedback. Please see attached for our responses to the comments.

Author Response File: Author Response.pdf