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Shannon information and integrated information: message and meaning

T0 review · 3 major / 6 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read This paper argues that the meaning of an experience is the cause–effect structure a conscious system unfolds from its own activity, so meaning is communicated only when sender and receiver unfold similar structures.

desk verdict A clear IIT-based position paper on meaning and communication, undermined only by the undefined notion of structural similarity that carries the central claim. read the letter →

arxiv 2412.10626 v1 pith:3MPINSUB submitted 2024-12-14 q-bio.NC cs.ITmath.IT

Alireza Zaeemzadeh , Giulio Tononi This is my paper · ORCID
classification q-bio.NCcs.ITmath.IT
keywords integratedinformationtheoryΦ-structureintrinsicmeaningShannoncommunicationofconsciousnesscause–effectstructure
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

Where does the meaning of a message live? This paper argues that Shannon information theory, which measures messages in bits and brackets meaning by design, cannot locate it: meaning is not a property of symbols, codes, or computations. The paper's central claim is that meaning is identical to the cause–effect structure—called the Φ-structure—that integrated information theory (IIT) unfolds from a conscious system in a state. If that claim is right, then Alice's experience of a house on fire is the structure of causal distinctions and relations her brain specifies at that moment, and Bob understands her only when her message triggers a structurally similar Φ-structure in his brain. The upshot is that communication of meaning is intrinsic, approximate, and never fully shared.

What carries the argument

The central object is the Φ-structure (cause–effect structure): the set of causal distinctions specified by subsets of units within a complex, together with the relations that bind them, determined from the system's transition probability matrix and its current state. It carries the argument by replacing the picture of meaning as a code with a picture of meaning as a structure: meaning is not read off a symbol but unfolded from a substrate, and communication of meaning becomes a matter of structural similarity between the Φ-folds of sender and receiver.

What would settle it

A direct test would compare two conscious subjects with deliberately different causal architectures: if they can be shown to share the same specific conscious content while their unfolded Φ-folds differ substantially under the IIT formalism, the identity between meaning and Φ-structure fails. Concretely, one could compute Φ-fold similarity for subjects with different connectomes and measure whether their success in communicating a specific percept tracks Φ-fold similarity better than it tracks Shannon mutual information of the transmitted symbols.

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Extended reading notes

Core claim

The paper contrasts two axiomatic uses of probability: Shannon's extrinsic account of messages and IIT's intrinsic account of meaning. It claims that the Φ-structure unfolded from a complex—a maximally irreducible substrate—in its current state fully characterizes, with no additional ingredients, how an experience feels and what it intrinsically means. Within the Φ-structure, each content of experience is a Φ-fold, a sub-structure of distinctions and relations; the feeling of seeing the house on fire is that Φ-fold. Communication of meaning therefore requires that a source complex's Φ-fold trigger a similar Φ-fold in a target complex. Symbol transmission is neither sufficient (a perfect channel can fail to trigger the intended fold) nor necessary (without similar folds, no meaning is carried), and the amount of meaning communicated could in principle be measured by the similarity of source and target Φ-folds.

Load-bearing premise

The load-bearing premise is that Φ-structures from different substrates can be compared by a well-defined similarity measure; the paper itself notes that this is not easy, since it requires unfolding very large structures and finding optimal ways to compare them. Without such a measure, the claim that meaning is communicated when source and target Φ-folds are similar is not yet well-defined.

Editorial extensions

If this is right

  • Standard digital computers, whose wiring cannot support high-Φ complexes, can transmit messages perfectly while communicating no intrinsic meaning; their utterances mean something only when a conscious being interprets them.
  • Because the wiring of each brain differs through development and learning, shared meanings are never identical: communication of meaning is always approximate, and some meanings will be idiosyncratic.
  • Shannon information and integrated information are complementary rather than competing: one quantifies symbol transmission, the other quantifies meaning, and a full account of communication needs both.
  • The amount of meaning successfully communicated can in principle be measured by the similarity of the source and target Φ-folds, not by bit rate, channel capacity, or perceptual richness.

Reading between the lines

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

  • If meaning is identical to Φ-structure, then the claim that digital computers have no intrinsic meaning is an empirical bet about their wiring, not a consequence of the identity itself; a silicon substrate that could support a high-Φ complex would, by the paper's own logic, have meaning.
  • The framework suggests a testable research program: approximate Φ-fold similarity with computable measures and check whether subjective reports of 'getting it' track structural similarity better than mutual information of neural codes.
  • It also implies a strong form of untranslatability: since meanings are absolute structures rather than positions in a semantic space, translation can only maximize overlap between Φ-folds, and some meanings may be untranslatable.
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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 / 6 minor

Summary. This paper contrasts Shannon information theory with integrated information theory (IIT), arguing that Shannon information concerns messages, codes, and extrinsic transmission, whereas IIT treats meaning as an intrinsically defined cause–effect structure (Φ-structure) unfolded from a conscious complex. The authors introduce the notion of a Φ-fold as a sub-structure corresponding to a content of experience, and claim that communication of meaning occurs when a source Φ-fold triggers a similar Φ-fold in a target complex. The paper reviews IIT's axioms and postulates, compares the two frameworks in a table, discusses implications for neuroscience and artificial systems, and includes two supplementary sections on information theory and IIT.

Significance. If the central claim held, the paper would provide a principled distinction between information as message transmission and meaning as consciousness-dependent structure, and would ground a research program for measuring meaning transfer. The paper is clearly written and gives a useful side-by-side comparison of Shannon information and IIT, and it is transparent about the major open problem, namely the absence of a concrete similarity measure for Φ-structures (footnote 14). However, the communication-of-meaning claim is not derived from IIT's axioms; it is an additional definitional step. The paper would be significant as a conceptual proposal, but as it stands the key notion of similarity remains unformalized, so the central conclusion is not yet a testable result. The paper also credits prior and forthcoming work appropriately, and it explicitly acknowledges the computational infeasibility of unfolding large Φ-structures, which is a fair limitation.

major comments (3)
  1. [Communicating integrated information as meaning (Fig. 6 and following text)] The paper's central claim, stated in the abstract and repeated in this section, is that 'for the communication of meaning, the cause–effect structures of sender and receiver must be similar.' However, no formal definition of 'similar' is provided. The text says 'the similarity of the two Φ-folds could be used to measure the amount of meaning communicated,' and footnote 14 concedes that developing ways to compare them optimally is 'not easy.' This is not a minor technicality: without a metric or an equivalence relation on Φ-structures, the claim cannot be evaluated as true or false, and the amount of meaning communicated is undefined. The paper should either supply a candidate similarity measure (or a set of necessary conditions) or explicitly present the communication claim as a conjecture rather than a consequence of IIT.
  2. [Communicating integrated information as meaning, footnote 15] Footnote 15 creates an internal tension with the main claim. It states that 'in IIT's analysis, the meaning of an experience is defined in absolute terms by the distinctions and relations that compose a specific Φ-structure, rather than by its similarity to other Φ-structures,' and it allows for a 'translation' mapping between radically different Φ-structures. If meaning is absolute, then similarity between Φ-structures is an extrinsic relation imposed by the analyst; it is not part of IIT's fundamental explanatory identity ('with no additional ingredients'). The 'it follows' in the abstract therefore does not follow from the axioms and postulates. The paper should clarify how the similarity relation is grounded in IIT or acknowledge that it is a new, extra-theoretical definition.
  3. [Integrated information theory and Information processing vs. information structures] The identification of meaning with the Φ-structure is asserted as IIT's fundamental explanatory identity, not independently demonstrated. The paper states that the Φ-structure 'fully characterizes, with no additional ingredients, how an experience feels—its quality—which defines its intrinsic meaning.' For a paper whose central contribution is a consequence of this identity, this is acceptable as a starting point, but the paper should more clearly separate (i) the IIT-internal definition of meaning from (ii) the new claim about communication of meaning. In particular, the transition from 'meaning is the Φ-structure' to 'communicating meaning requires similar Φ-structures' involves an additional premise about how meaning transfers between systems, which is not part of IIT's postulates. The paper should state this premise explicitly.
minor comments (6)
  1. [Supplementary material II] The notion of a 'Φ-fold' is used throughout the main text but only informally characterized in the supplementary material; a precise definition (e.g., a sub-structure formed by a subset of distinctions and relations) would improve clarity.
  2. [Table I] The capitalization in the final row is inconsistent: 'Meaning Must be provided extrinsically' should be 'Meaning must be provided extrinsically.'
  3. [References] The reference list includes several items marked 'forthcoming' (refs. 13, 14, 52) and an arXiv manuscript (ref. 11) without publication details; please provide updated versions or URLs where possible.
  4. [Supplementary material I] The displayed equation for Shannon entropy appears to be missing the summation sign in the provided text; please ensure all equations are typeset correctly.
  5. [Figure 6] Panel (c) of Figure 6 refers to 'perceptual richness' without defining the term in the caption; a brief definition or a pointer to Supplementary material II would help.
  6. [Information processing vs. information structures] The statement 'information processing can only ever decrease the information transmitted over a channel' is too broad as written; the data-processing inequality applies to specific Markov chains and should be qualified accordingly.

Circularity Check

2 steps flagged · score 7.0 of 10

Central claim reduces to IIT's definitional identity: meaning is the Φ-structure, and 'communication of meaning' is stipulated as triggering a similar Φ-fold; the load-bearing identity is self-cited.

  1. self definitional [Abstract; Section 'Communicating integrated information as meaning' (Fig. 6 discussion)]
    "IIT considers meaning as integrated information and characterizes it as a structure, rather than as a message or code... It follows that, for the communication of meaning, the cause–effect structures of sender and receiver must be similar. ... In short, meaning can only be communicated if a Φ-fold within a Φ-structure specified by a source complex triggers a similar Φ-fold within a Φ-structure specified by a target complex."

    The conclusion is obtained by combining two stipulations: (i) intrinsic meaning is the Φ-structure, and (ii) communication of meaning occurs when a source Φ-fold triggers a similar Φ-fold in the target. The first is IIT's definitional identity; the second is introduced as the 'direct implication' without independent argument. No operational criterion for 'similar' is supplied—footnote 14 concedes that comparing Φ-folds optimally is unsolved. Hence the abstract's 'It follows' is not a derivation from IIT's axioms; it is a restatement of the definition of meaning-communication, with the necessity of structural similarity built into the chosen definition rather than established.

  2. self citation load bearing [Section 'Integrated information theory' (p. 5); Supplementary II (p. 21)]
    "The cause–effect structure (or Φ-structure) unfolded from a complex in its current state fully characterize[s], with no additional ingredients, how an experience feels—its quality—which defines its intrinsic meaning. ... IIT claims that every property of an experience must be accounted for by the Φ-structure specified by its substrate, with no additional ingredients. This is the fundamental explanatory identity of IIT[5]."

    The paper's central derivation assumes the fundamental explanatory identity of IIT—that a Φ-structure fully defines intrinsic meaning—and cites IIT 4.0 [5], a paper by the same research group including the present authors. That identity is exactly the premise that makes the communication conclusion follow. The paper supplies no independent proof, external benchmark, or falsifiable test for it here; it is taken as a postulate of the theory. Thus the chain 'Φ-structure = meaning ⇒ communication requires similar Φ-structures' rests on a load-bearing self-citation that already contains the definitional equation.

full rationale

This is a theory-exposition paper that explicitly builds on IIT rather than testing it; its contrast between Shannon information and IIT is self-consistent and not circular. However, the paper's central claim is presented as a derivation: 'It follows that, for the communication of meaning, the cause–effect structures of sender and receiver must be similar.' The derivation rests on two moves. First, the premise 'meaning = Φ-structure' is imported as IIT's fundamental explanatory identity from a self-authored citation (IIT 4.0), with no independent support in the paper. Second, 'communication of meaning' is stipulated as the source Φ-fold triggering a similar Φ-fold in the target; the same section then says similarity could measure the amount communicated. No formal similarity measure is defined—footnote 14 concedes this is unsolved—so the necessity of similarity is a definitional choice, not a theorem. The paper is transparent about being an IIT-based account, which mitigates the appearance of deception, but the central claim does reduce by construction to the definitional identity plus an added, unformalized similarity criterion. Hence score 7.

Assumptions & free parameters 0 free parameters · 5 assumptions · 3 invented entities

The paper's central claim rests entirely on IIT's postulates and theoretical constructs, all of which are assumed from prior work by the same group. There are no free parameters fitted to data in this paper. The key assumptions are the existence of experience, the validity of the five axioms, the operationalization via cause-effect power, the maximal-existence principle for identifying complexes, and the explanatory identity that Φ-structures fully determine meaning. These are domain assumptions, not standard mathematical facts.

assumptions (5)
  • domain assumption Experience exists (0th axiom).
    Invoked in Supplementary material II: 'Experience exists. Therefore, the substrate of consciousness must be constituted of units that can take and make a difference.' This is the starting point for all of IIT.
  • domain assumption The five axioms of phenomenal existence (intrinsicality, information, integration, exclusion, composition) are irrefutably true of every experience.
    Introduced in the main text 'Integrated information theory' section. These axioms are assumed, not derived, and are then operationalized into postulates.
  • domain assumption Physical existence is cause-effect power, assessed through interventional probabilities.
    0th postulate in the main text: 'Physical existence is defined as cause-effect power of a substrate of units.' This operationalizes the 0th axiom.
  • domain assumption A complex is the set of units that is maximally irreducible, identified by the principle of maximal existence.
    Postulate in Supplementary II: a complex must have higher φs than any overlapping set. This is a background assumption used to identify the substrate of meaning.
  • domain assumption The cause-effect structure (Φ-structure) of a complex in a state fully characterizes experience with no additional ingredients (IIT's explanatory identity).
    This is the central explanatory identity of IIT, invoked in the main text: 'the cause-effect structure... fully characterize[s]... how an experience feels.' The paper provides no independent justification for this identity.
invented entities (3)
  • Φ-structure (cause-effect structure)
    purpose: Defines the intrinsic meaning of an experience as a set of distinctions and relations.
    Theoretical object inherited from IIT 4.0. The paper treats it as the definition of meaning but offers no falsifiable handle outside the theory.
  • Φ-fold
    purpose: Sub-structure of a Φ-structure corresponding to a specific content of experience, used to assess communication of meaning via similarity.
    Introduced as the unit that can be compared between source and target. No formal definition of similarity or measurement method is provided.
  • Complex (maximally irreducible substrate)
    purpose: The set of units whose Φ-structure corresponds to consciousness and meaning.
    Identified through IIT's postulates, but the paper concedes that exhaustive unfolding is computationally infeasible for large systems.

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Cite this review

Pith. "Pith review of Shannon information and integrated information: message and meaning." pith.science (2026). https://pith.science/paper/3MPINSUB

@misc{pith2026241210626,
  author       = {Pith},
  title        = {Pith review of: Shannon information and integrated information: message and meaning},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3MPINSUB}},
  note         = {Machine review of arXiv:2412.10626}
}
read the original abstract

Information theory, introduced by Shannon, has been extremely successful and influential as a mathematical theory of communication. Shannon's notion of information does not consider the meaning of the messages being communicated but only their probability. Even so, computational approaches regularly appeal to "information processing" to study how meaning is encoded and decoded in natural and artificial systems. Here, we contrast Shannon information theory with integrated information theory (IIT), which was developed to account for the presence and properties of consciousness. IIT considers meaning as integrated information and characterizes it as a structure, rather than as a message or code. In principle, IIT's axioms and postulates allow one to "unfold" a cause-effect structure from a substrate in a state, a structure that fully defines the intrinsic meaning of an experience and its contents. It follows that, for the communication of meaning, the cause-effect structures of sender and receiver must be similar.

Figures

Figures reproduced from arXiv: 2412.10626 by the authors.

Figure 1
Figure 1. Communicating meaning. Alice is trying to communicate meaning (conscious contents, such as seeing that the house is on fire) to Bob through a message constituted of symbols. Shannon information theory takes the extrinsic perspective and studies the optimal assignment of symbols and the optimal design of encoding/decoding algorithms. IIT takes the intrinsic perspective of Alice and Bob and studies the intrinsic meani… view at source ↗
Figure 2
Figure 2. Information theory and the communication of symbols. In information theory, the information content of a message is quantified as the minimum number of uniquely decodable symbols (binary digits) assigned to it. In a communication system, unwanted redundancies are removed (source coding) and errors are corrected by adding communication and computation overhead (channel coding). The source-target pair can achieve opti… view at source ↗
Figure 3
Figure 3. IIT and the structure of meaning. IIT defines information as meaning, understood as the content of experience (the feeling is the meaning). It takes the intrinsic perspective of the system and characterizes the meaning of an activity pattern as the Φ-structure unfolded from a complex (a maximally irreducible substrate). The main complex is outlined in blue on the surface of the cerebral cortex (assuming the maximum … view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: Differences between Shannon information and integrated information. (a) Shannon information captures correlations (e.g., between units A and B owing to their common input from unit X). In contrast, integrated information captures cause-effect power—the ability of units…
Figure 5
Figure 5. Figure 5: Information processing and information structures in the brain. [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]
Figure 6
Figure 6. Figure 6: Communicating meaning according to IIT. There is no communication of meaning if (a) the source or the target is not conscious, (b) the symbols are not transmitted successfully, or (c) the symbols do not trigger a similar sub-structure within the Φ-structure of the targ…
Figure 7
Figure 7. Figure 7: Codes and relevant codes [PITH_FULL_IMAGE:figures/full_fig_p019_7.png]

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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. Intrinsic meaning, perception, and matching

    q-bio.NC 2024-12 conditional novelty 6.0 of 10

    Within IIT, perception is formalized as a stimulus-triggered portion of a Φ-structure, and perceptual differentiation and matching quantify how much intrinsic meaning an environment triggers.

Reference graph

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Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.