Pith. sign in

REVIEW 4 major objections 6 minor 90 references

Intrinsic meaning, perception, and matching

T0 review · 4 major / 6 minor · reviewed 2026-08-10 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Perception is a structured interpretation produced by a complex's intrinsic connectivity, not a transfer of information from the stimulus.

desk verdict A useful conceptual extension of IIT undermined by an inconsistent definition of relation perception value. read the letter →

arxiv 2412.21111 v2 pith:E72QS7MQ submitted 2024-12-30 q-bio.NC

William G. P. Mayner , Bj{o}rn Erik Juel , Giulio Tononi This is my paper · ORCID
classification q-bio.NC
keywords integratedinformationtheoryintrinsicmeaningperceptionΦ-structureperceptualdifferentiationmatchingconsciousnesscause-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

The paper extends integrated information theory (IIT) to answer how intrinsic experience relates to the external world. It claims that a stimulus acts only as a trigger: the felt meaning of a perception is fully determined by the cause-effect structure of the complex, not by what the stimulus represents. From this, the paper builds measures of triggering coefficient, perceptual richness, and perceptual differentiation, and shows in two small sensory-hierarchy models that a system's wiring, not the stimulus, decides what a percept means. If the account holds, the meaningfulness of an environment to an organism can be quantified by how rich and diverse the triggered intrinsic structures are.

What carries the argument

The central machinery is the $\Phi$-structure of IIT, decomposed into distinction $\Phi$-folds (a distinction plus its relations), together with three new quantities built from it: the triggering coefficient $t(x,m)$, which normalizes how strongly a stimulus caused a mechanism's state; perceptual richness $P$, the sum of $\varphi$-values weighted by triggering coefficients; and perceptual differentiation $D_p$, the union of perceptual structures over a stimulus sequence. Matching $M$ is the maximum expected gap between perceptual differentiation for environmental versus random stimulus sequences. These quantities carry the argument by linking intrinsic meaning to extrinsic triggers without letting the stimulus itself supply meaning.

What would settle it

Compute the complete $\Phi$-structure, rather than a sampled subset, for a small system (about six to eight units) exposed to the same segment, centered-odd, and noise environments, and check whether the matching ranking of the two systems reverses; if the ranking changes when the omitted distinctions and relations are included, the reported matching is an artifact of the partial computation.

Watch

Extended reading notes

Core claim

The paper claims that perception should be regarded as a structured interpretation of a state of the complex, where the stimulus merely sets the state and the meaning is supplied by the complex's intrinsic cause-effect structure (the $\Phi$-structure). It defines a triggering coefficient that measures how much a stimulus caused each subset's state, then weights the components of the $\Phi$-structure by this coefficient to obtain a perceptual structure and a perceptual richness value. The paper further defines perceptual differentiation as the richness of the union of perceptual structures triggered by a sequence of stimuli, and matching as the maximum expected difference between differentiation for environmental sequences and for random sequences. In the simulated sensory-hierarchy systems, the same stimulus can trigger different perceptual structures in different systems even when the triggered activity pattern is identical, and each system shows higher matching to the environment whose causal features its wiring was designed to detect.

Load-bearing premise

The demonstrations rely on computing only a hand-picked subset of the distinctions and relations that make up the full cause-effect structure, because computing all of them is infeasible even for the paper's small model, and on assuming the system is maximally irreducible; if the omitted parts or the maximality assumption changed the numbers, the claimed matching results could differ.

Editorial extensions

If this is right

  • Perception should be treated as the triggered portion of a system's $\Phi$-structure, so a stimulus contributes no meaning of its own; it only selects which intrinsic distinctions and relations are expressed.
  • Perceptual richness quantifies how much intrinsic meaning a single stimulus triggers, and can be large or small independently of how much Shannon information the stimulus carries.
  • Perceptual differentiation over a sequence of stimuli measures how meaningful an environment is to a particular complex, not how complex the environment is in itself.
  • In well-adapted systems, high matching will tend to track causal features of the environment relevant to the organism, though not through a simple isomorphism.
  • The same physical activity pattern can carry different meanings in systems with different causal connectivity, so activity patterns alone do not determine experience.

Reading between the lines

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

  • Beyond the paper: if this account is right, measures of neural differentiation could serve as a proxy for meaningfulness even with no ground-truth labels, allowing researchers to search stimulus spaces for inputs that maximize differentiation in order to infer what an organism finds meaningful.
  • Beyond the paper: the formalism predicts that scrambling temporal structure should reduce perceptual differentiation only for systems whose connectivity has internalized those temporal regularities, so differentiation loss under scrambling could index how much of an organism's meaning is temporal.
  • Beyond the paper: the intrinsic-meaning stance implies that two systems with identical input-output behavior but different internal causal structure can have different percepts, a contrast with purely functionalist accounts that could be tested if causal-structure fingerprints were compared with reported experience.
  • Beyond the paper: because matching is defined against a uniform random baseline, the logic extends naturally to active perception, predicting that agents sampling their environment to maximize differentiation will seek stimuli that resonate with their intrinsic meanings.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 6 minor

Summary. This manuscript extends Integrated Information Theory (IIT) to perception. It defines connectedness and a triggering coefficient that quantify how strongly a stimulus at the sensory interface causes the state of subsets of a complex, and then defines perceptual structures, perceptual richness, perceptual differentiation, and matching. Using two small hierarchical model systems (B1, a segment detector; B2, a centered-odd detector) placed in environments that generate segment or centered-odd statistics, the authors illustrate that the same stimulus can trigger different perceptual structures in different systems, that perception is an interpretation whose meaning is intrinsic, and that perceptual differentiation and matching can quantify how meaningful an environment is to a complex. The manuscript is explicit about several limitations: the Φ-structure is only partially unfolded, the system is assumed to be a complex without full exclusion analysis, and the temporal delay τ is a free parameter.

Significance. If the formalism were correct, this would be a substantial contribution: it would give IIT-based, quantity-bearing notions of perceptual content, differentiation, and environment-system matching, and it would make a sharp philosophical claim that meaning is intrinsic and not representational except under additional adaptive assumptions. The paper has genuine strengths: the mathematical objects are defined with care, the model systems are fully specified through transition probability matrices, the computations are exact where performed, and the authors candidly flag the computational infeasibility of full Φ-structure unfolding and the use of a representative subset. However, the central quantitative measure is internally inconsistent as written, and the reported values of perceptual richness, differentiation, and matching therefore do not yet support the paper's main quantitative claims. The matching demonstrations also follow largely from the hand-designed detector properties of B1 and B2, so they illustrate the framework but do not independently test the adaptive claim.

major comments (4)
  1. [§2.3.2, Eqs. (10)–(14)] The perception value of a relation is defined twice, inconsistently. Eq. (10) gives p(x,r(d)) = t(x,r(d)) φr(d), while Eq. (12), described as a general expression, gives p(x,c) = t(x,c) φc/|c|, with |c|=|d| for a relation of degree |d|. For any relation with |d|>1 these definitions differ by a factor of |d|. This is not a cosmetic issue: Eq. (13) defines perceptual richness as a sum over all components, and the reported Φ-structure contains 54,432 relations, many of degree greater than 1, with the text stating that relations contribute significantly to perceptual richness (§3.4). Consequently the numerical values of P, Dp, and matching in Figs. 4, 7, and 8 are ambiguous. Moreover, Eq. (11) and Eq. (14) do not follow from Eq. (13) under either convention: the equality in Eq. (11) would require the triggering coefficients of all relations incident to a distinction to equal the triggering coefficient of that distinction, and Eq. (14) similarly requires t(x,d) to be constant across the distinctions bound by each relation. The authors need to choose one definition, correct Eqs. (11) and (14), and recompute the reported values.
  2. [§2.2.2 and S1 Text] The central quantitative results are computed on a hand-selected representative subset of the Φ-structure, not on the full Φ-structure. The manuscript states in S1 Text that 'the exponential time complexity of the IIT analysis makes exhaustive unfolding of the entire Φ-structure impractical' and that only mechanisms with connected motifs and relations up to degree 3 were computed; it also assumes, for the demonstration, that the system is maximally irreducible. Because Φ, perceptual richness, perceptual differentiation, and matching are defined as sums over all components of C(y), the values reported in Figs. 4, 7, and 8 are not the values of the quantities defined in Eqs. (13), (16), and (19)-(21). No sensitivity analysis or error bounds are provided. The paper should either compute the quantities on the full structure for a smaller system, prove bounds that make the subset representative, or explicitly reframe all reported numbers as heuristic estimates of the formal quantities.
  3. [§3.8, Fig. 8] The matching demonstration is largely built into the construction of the systems and environments. B1 is designed to detect segment patterns, B2 to detect centered-odd patterns, and environments E1 and E2 are designed to generate those patterns frequently. The finding that B1 matches E1 better than E2, and B2 matches E2 better than E1, is therefore a direct consequence of the design, not an independent test of the claim that matching reflects adaptation. This is acceptable as a proof of principle, but the paper's abstract and §2.5 state that in adaptive systems matching reflects 'the matching between intrinsic meanings and causal processes in an environment.' To support that claim, the manuscript would need at least one demonstration in which the system's connectivity is itself generated by an adaptation process (e.g., evolution or learning) under the environmental statistics, rather than hand-wired to the target features.
  4. [§2.3.1 and §3.1] The temporal delay τ is a free parameter, and all simulations fix τ=5 elementary timesteps. Because connectedness in Eq. (5) conditions on ∂S at t-τ, the triggering coefficients, perceptual richness, and matching all depend on τ. The authors note that τ should be chosen to maximize efficacy, but no maximization over τ is reported and no sensitivity analysis is given for the matching values in Fig. 8. The manuscript should either specify a principled way to select τ, show that the qualitative matching results are robust across a range of τ, or explicitly limit the claims to the chosen τ.
minor comments (6)
  1. [§2.2.3, Eq. (3)] Equation (3) contains an extra closing parenthesis: 'Φd(C(d(m))))' should read 'Φd(C(d(m)))'.
  2. [§2.4, Eqs. (17)–(20)] The notation for differentiation capacities is overloaded: D(S) in Eq. (17), Dmax(S) in Eq. (18), and D(∂S,S) in Eq. (20) use the letter D for conceptually different objects. Please rename to avoid ambiguity, for example D_ext, D_int, and D_cap.
  3. [§2.4 and §2.5] Eq. (16) defines differentiation as a sum of φ values, while Eq. (19) defines perceptual differentiation using maximum perception values over the sequence. The relationship between these two notions, and particularly why the component-wise maximum is the right choice for union perception, is motivated only in words; a brief formal justification would help.
  4. [§3.8, Fig. 8] The two-way ANOVA reports the interaction and post-hoc p-values but no effect sizes and no confidence intervals for the pairwise differences. Reporting these would make the claims much easier to assess, especially because the sample size is only n=32 trials.
  5. [References] References [21] and [22] appear to be the same paper (Mensen et al., 2018, 'Differentiation Analysis of Continuous Electroencephalographic Activity Triggered by Video Clip Contents'); one of them should be removed or replaced with a different source.
  6. [General numerical consistency] The text in §3.4 says the awake state specifies a Φ-structure with higher structure integrated information than the all-'OFF' dreaming state in Fig. 2, but the visualizations in Figs. 2 and 4 display scalar values (e.g., 420.34 in Fig. 2B and 385.52 in Fig. 4B) that are not explicitly reconciled with the stated Φ values in the text. Please clarify whether these displayed quantities are the full Φ, the sum of the selected distinction Φ-folds, or something else.

Circularity Check

2 steps flagged · score 6.0 of 10

Central claims are definitional and by-construction: 'meaning' is stipulated to equal the Φ-structure, and B1/B2 matching is built into the model design; Eqs. (10) and (12) are additionally inconsistent.

  1. self definitional [Section 2.2.2; Section 2.3.2 (Eqs. 8-13)]
    "By the explanatory identity of IIT, these account in full, with no additional ingredients, for the quality (or feeling) of an experience, which is the same as its intrinsic meaning (“the meaning is the feeling”)."

    The paper defines intrinsic meaning as the Φ-structure (feeling) via the explanatory identity, citing only the authors' own prior/future work ([3,4]). It then defines perceptual richness P as the sum of triggering-coefficient-weighted φ values (Eqs. 8-13) and asserts that P quantifies the intrinsic meaning triggered by a stimulus. Since 'intrinsic meaning' was stipulated to be the Φ-structure, the claim that P quantifies it is an unpacking of P's definition, not a derived result. No independent measure of meaning is given against which P could be tested, so the central 'quantification' cannot fail: it is true by definition (or by acceptance of the self-cited identity).

  2. fitted input called prediction [Section 3.1; Section 3.8 and Fig. 8 caption]
    "We designed two model systems, 'B1' and 'B2' (Fig. 1), that, by construction, detect different stimulus features. ... As expected, B1 matches better to E1 and B2 matches better to E2, reflecting that the each system has, by construction, 'internalized' aspects of the stimulus statistics that in turn reflect causal processes in their 'matching' environments."

    B1 was constructed with detectors for segment patterns and B2 for centered-odd patterns; E1 was built from segment generators and E2 from centered-odd generators. The matching statistic M (Eq. 21) is the excess of perceptual differentiation Dp for environmental sequences over uniform noise, and Dp is the sum of perception values p=t·φ, which are large precisely for the patterns each system was designed to detect. The ordering M(B1,E1)>M(B1,E2) and M(B2,E2)>M(B2,E1) is therefore entailed by the design choices before any simulation. The paper's own caption admits the result is 'by construction,' so this is a consistency check of the definitions, not an independent test of the claim that perceptual differentiation measures environmental meaningfulness.

full rationale

The paper is an extension of IIT, and much of its mathematical scaffolding is transparent definition-building: connectedness, triggering coefficients, perceptual richness, differentiation, and matching are all explicitly defined, and the B1/B2 simulations are presented as illustrations rather than as tests against external benchmarks. No circularity attaches to the use of PyPhi or to the uniform-stimulus prior; these are stated modeling choices. Two load-bearing steps are nevertheless circular in the sense used here. First, the paper stipulates, citing the authors' own prior work, that 'the meaning is the feeling' and that the Φ-structure accounts 'in full' for the feeling/meaning of an experience; perceptual richness is then defined as the triggering-weighted sum of φ values and asserted to quantify the intrinsic meaning triggered. Because meaning was stipulated to be the Φ-structure, that assertion is analytic, not an empirical finding. Second, the central demonstration of 'matching' is entailed by the model construction: B1 and B2 were built as segment and centered-odd detectors, and E1 and E2 were built from the corresponding generators; the paper's own caption says the result holds 'by construction.' The simulations therefore confirm the definitions rather than provide independent evidence that perceptual differentiation tracks environmental meaningfulness. In addition, though this is a correctness issue rather than circularity, the formalism is internally inconsistent as written: Eq. (10) defines p(x,r(d)) = t(x,r(d)) φr(d), while Eq. (12) defines p(x,c) = t(x,c) φc/|c|, which differs by a factor |d| for relations; Eq. (11) does not follow, and the reported P, Dp, and matching values are not uniquely determined by the stated equations. The partial unfolding of the Φ-structure is disclosed in S1 Text and is a computational limitation, not a circular step. Overall, the central quantitative claims are partially circular and partially ill-defined, so the score is 6.

Assumptions & free parameters 3 free parameters · 4 assumptions · 2 invented entities

The central claim depends on IIT's axioms and on the hand-designed model systems. The quantitative results rely on a partial Φ-structure and on model parameters chosen to produce the desired behavior. No external benchmarks or empirical data are used.

free parameters (3)
  • Temporal delay τ = 5 timesteps in simulations
    Free parameter in connectedness; should be chosen to maximize stimulus efficacy (Section 2.3.1).
  • Model connection weights and activation thresholds (B1/B2) = g factors 1.5, 1, 0.75, 0.5; probabilities 0.99, 0.01; connection strengths 1.0, 0.5, 0.25, 0.1
    Hand-chosen to make B1 detect segments and B2 detect centered odds (S1 Text); these choices drive the matching results.
  • Representative subset of mechanisms and purviews = Not numeric
    The set of distinctions and relations computed is selected by the authors based on prior work and preliminary search, not the full Φ-structure (S1 Text).
assumptions (4)
  • domain assumption IIT axioms and postulates (intrinsicality, information, integration, exclusion, composition) and the explanatory identity that a Φ-structure fully accounts for experience, so meaning equals feeling.
    The entire framework rests on IIT's claim that Φ-structures account for quality and meaning; this is not proven in the paper (Section 2.2).
  • ad hoc to paper The system under analysis is a maximally irreducible complex at the chosen grain.
    The paper assumes the 13-unit system is maximally irreducible without evaluating φs across all subsets and grains (Section 3.2).
  • domain assumption Uniform prior over sensory interface states is the correct intrinsic perspective.
    Connectedness and triggering coefficient use Pr(x)=1/|Ω∂S| rather than observed stimulus statistics (Section 2.3.1).
  • standard math Causal marginalization of background units and Markovian, conditionally independent dynamics of binary units.
    Standard IIT assumptions formalized in Eq. (2).
invented entities (2)
  • Perceptual structure
    purpose: The portion of a Φ-structure weighted by triggering coefficients, representing the intrinsic meaning triggered by a stimulus.
    Defined mathematically within IIT; no independent falsifiable handle yet, only illustrative simulations.
  • Perceptual differentiation and matching
    purpose: Measures of the richness and diversity of triggered meanings and of how well an environment resonates with a complex.
    Proposed as quantitative measures; no empirical validation, and the matching demonstration is by construction.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Intrinsic meaning, perception, and matching." pith.science (2026). https://pith.science/paper/E72QS7MQ

@misc{pith2026241221111,
  author       = {Pith},
  title        = {Pith review of: Intrinsic meaning, perception, and matching},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/E72QS7MQ}},
  note         = {Machine review of arXiv:2412.21111}
}
read the original abstract

Integrated information theory (IIT) argues that the substrate of consciousness is a maximally irreducible complex of units. Together, subsets of the complex specify a cause-effect structure, composed of distinctions and their relations, which accounts in full for the quality of experience. The feeling of a specific experience is also its meaning for the subject, which is thus defined intrinsically, regardless of whether the experience occurs in a dream or is triggered by processes in the environment. Here we extend IIT's framework to characterize the relationship between intrinsic meaning, extrinsic stimuli, and causal processes in the environment, illustrated using a simple model of a sensory hierarchy. We argue that perception should be considered as a structured interpretation, where a stimulus from the environment acts merely as a trigger for the complex's state and the structure is provided by the complex's intrinsic connectivity. We also propose that perceptual differentiation - the richness and diversity of structures triggered by representative sequences of stimuli - quantifies the meaningfulness of different environments to a complex. In adaptive systems, this reflects the "matching" between intrinsic meanings and causal processes in an environment.

Figures

Figures reproduced from arXiv: 2412.21111 by the authors.

Figure 1
Figure 1. The substrate models and their dynamics. (A) [PITH_FULL_IMAGE:figures/full_fig_p012_1.png] view at source ↗
Figure 2
Figure 2. A Φ-structure and its intrinsic meaning in a disconnected state. (A) Illustration of the Φ-structure specified by the B1 system in its current state, when disconnected from the environment. Subsets of the system (mechanisms) that specify an irreducible cause–effect pair (a distinction) are plotted as the lowest cluster of points (brown labels), superimposed on the substrate. The causes of each distinction are shown … view at source ↗
Figure 3
Figure 3. Connectedness and triggering coefficients. (A) [PITH_FULL_IMAGE:figures/full_fig_p017_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: Perception: perceptual structures and perceptual richness. [PITH_FULL_IMAGE:figures/full_fig_p019_4.png]
Figure 5
Figure 5. Figure 5: Perception as interpretation. The same stimulus can trigger different perceptual structures in different systems. Importantly, this can happen even when the activity pattern in both systems is the same. (A) B1 and B2 are presented with the stimulus 00100000, which cont…
Figure 6
Figure 6. Figure 6: Perception and representation. (A) The B1 system is exposed to the segment environment E1 and detects the 3-segment pattern in the stimulus. (B) In the ‘2-segment’ environment E1b, the 3-segment generator is replaced with a 2-segment generator. With two 2-segment gener…
Figure 7
Figure 7. Figure 7: Perceptual differentiation. (A) A sequence of stimuli is presented to the system. (B) Each stimulus triggers a Φ-structure composed of distinctions and relations. (C) When the φ values of these components are weighted by their associated triggering coefficients, we obt…
Figure 8
Figure 8. Figure 8: Matching in different environments. (A) B1 and B2 are exposed to the segment environment E1 (top) and to uniform noise (bottom). n = 32 trials of sequences of k = 4 stimuli were sampled from each. (B) Perceptual richness P triggered in B1 by each environmental stimulus…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

90 extracted references · 47 canonical work pages

  1. [1]

    Integrated Information Theory (IIT) 4.0: Formulating the Properties of Phenomenal Existence in Physical Terms

    Albantakis L, Barbosa L, Findlay G, Grasso M, Haun AM, Marshall W, et al. Integrated Information Theory (IIT) 4.0: Formulating the Properties of Phenomenal Existence in Physical Terms. PLOS Computational Biology . 2023;19(10):e1011465. doi:10.1371/journal.pcbi.1011465. 21As pointed out in [71], a complex of high Φ has additional advantages with respect to...

    doi:10.1371/journal.pcbi.1011465 2023

  2. [2]

    Shannon information and integrated information: message and meaning

    Zaeemzadeh A, Tononi G. Shannon Information and Integrated Information: Message and Meaning. arXiv:241210626 [q-bioNC]. 2024;doi:10.48550/arXiv .2412.10626

    work page Pith review arXiv doi:10.48550/arxiv.2412.10626 2024

  3. [3]

    Only What Exists Can Cause: An Intrinsic View of Free Will

    Tononi G, Albantakis L, Boly M, Cirelli C, Koch C. Only What Exists Can Cause: An Intrinsic View of Free Will. arXiv:220602069 [q-bioNC]. 2022;doi:10.48550/arxiv .2206.02069

    arXiv doi:10.48550/arxiv.2206.02069 2022

  4. [4]

    On Being; forthcoming

    Tononi G. On Being; forthcoming

  5. [5]

    Consciousness and the Fallacy of Misplaced Objectivity

    Ellia F, Hendren J, Grasso M, Kozma C, Mindt G, P Lang J, et al. Consciousness and the Fallacy of Misplaced Objectivity . Neuroscience of Consciousness. 2021;2021(2):niab032. doi:10.1093/nc/niab032

    doi:10.1093/nc/niab032 2021

  6. [6]

    What Caused What? A Quantitative Account of Actual Causation Using Dynamical Causal Networks

    Albantakis L, Marshall W, Hoel E, Tononi G. What Caused What? A Quantitative Account of Actual Causation Using Dynamical Causal Networks. Entropy An International and Interdisciplinary Journal of Entropy and Information Studies. 2019;21(5):459. doi:10.3390/e21050459

    doi:10.3390/e21050459 2019

  7. [7]

    Information Flows in Causal Networks

    Ay N, Polani D. Information Flows in Causal Networks. Advances in Complex Systems. 2008;11(01):17–41. doi:10.1142/S0219525908001465

    doi:10.1142/s0219525908001465 2008

  8. [8]

    Causality

    Pearl J. Causality . Cambridge university press; 2009

    2009

Show all 90 references
  1. [9]

    Quantifying Causal Influences

    Janzing D, Balduzzi D, Grosse-Wentrup M, Sch ¨olkopf B. Quantifying Causal Influences. The Annals of Statistics. 2013;41(5):2324–2358. doi:10.1214/13-AOS1145

    2013 doi

  2. [10]

    IIT Wiki; 2024

    Hendren J, Grasso M, Juel BE, Tononi G, et al. IIT Wiki; 2024. https://www.iit.wiki/

    2024

  3. [11]

    PyPhi: A Toolbox for Integrated Information Theory

    Mayner WGP , Marshall W, Albantakis L, Findlay G, Marchman R, Tononi G. PyPhi: A Toolbox for Integrated Information Theory . PLoS computational biology . 2018;14(7):e1006343

    2018

  4. [12]

    Why Does Space Feel the Way It Does? Towards a Principled Account of Spatial Experience

    Haun A, Tononi G. Why Does Space Feel the Way It Does? Towards a Principled Account of Spatial Experience. Entropy . 2019;21(12):1160. doi:10.3390/e21121160

    2019 doi

  5. [13]

    Why Does Time Feel the Way It Does? Towards a Principled Account of Temporal Experience

    Comolatti R, Grasso M, Tononi G. Why Does Time Feel the Way It Does? Towards a Principled Account of Temporal Experience. arXiv:241213198 [q-bioNC]. 2024;doi:10.48550/arXiv .2412.13198

    2024 doi arXiv

  6. [14]

    A Measure for Intrinsic Information

    Barbosa LS, Marshall W, Streipert S, Albantakis L, Tononi G. A Measure for Intrinsic Information. Scientific Reports. 2020;10(1):18803. doi:10.1038/s41598-020-75943-4

    2020 doi

  7. [15]

    System Integrated Information

    Marshall W, Grasso M, Mayner WGP , Zaeemzadeh A, Barbosa LS, Chastain E, et al. System Integrated Information. Entropy . 2023;25(2):334. doi:10.3390/e25020334

    2023 doi

  8. [16]

    A New Causal Power Theory

    Korb KB, Nyberg EP , Hope L. A New Causal Power Theory . In: Causality in the Sciences. Oxford: Oxford University Press; 2011

    2011

  9. [17]

    Contextual Word Similarity and Estimation from Sparse Data

    Dagan I, Marcus S, Markovitch S. Contextual Word Similarity and Estimation from Sparse Data. In: Proceedings of the 31st Annual Meeting on Association for Computational Linguistics. ACL ’93. USA: Association for Computational Linguistics; 1993. p. 164–171. January 3, 2025 39/47

    1993

  10. [18]

    Normalized (Pointwise) Mutual Information in Collocation Extraction

    Bouma G. Normalized (Pointwise) Mutual Information in Collocation Extraction. Proceedings of GSCL. 2009;30:31–40

    2009

  11. [19]

    Measuring Stimulus-Evoked Neurophysiological Differentiation in Distinct Populations of Neurons in Mouse Visual Cortex

    Mayner WGP , Marshall W, Billeh YN, Gandhi SR, Caldejon S, Cho A, et al. Measuring Stimulus-Evoked Neurophysiological Differentiation in Distinct Populations of Neurons in Mouse Visual Cortex. eNeuro. 2022;9(1). doi:10.1523/ENEURO.0280-21.2021

    2022 doi

  12. [20]

    EEG Differentiation Analysis and Stimulus Set Meaningfulness

    Mensen A, Marshall W, Tononi G. EEG Differentiation Analysis and Stimulus Set Meaningfulness. Frontiers in Psychology . 2017;8:1748. doi:10.3389/fpsyg.2017.01748

    2017

  13. [22]

    Differentiation Analysis of Continuous Electroencephalographic Activity Triggered by Video Clip Contents

    Mensen A, Marshall W, Sasai S, Tononi G. Differentiation Analysis of Continuous Electroencephalographic Activity Triggered by Video Clip Contents. Journal of Cognitive Neuroscience. 2018;30(8):1108–1118. doi:10.1162/jocn a 01278

    2018 doi

  14. [23]

    Integrated Information and State Differentiation

    Marshall W, Gomez-Ramirez J, Tononi G. Integrated Information and State Differentiation. Frontiers in Psychology . 2016;7. doi:10.3389/fpsyg.2016.00926

    2016

  15. [24]

    Stimulus Set Meaningfulness and Neurophysiological Differentiation: A Functional Magnetic Resonance Imaging Study

    Boly M, Sasai S, Gosseries O, Oizumi M, Casali A, Massimini M, et al. Stimulus Set Meaningfulness and Neurophysiological Differentiation: A Functional Magnetic Resonance Imaging Study. PLOS ONE. 2015;10(5):e0125337. doi:10.1371/journal.pone.0125337

    2015 doi

  16. [25]

    Complex Cells as Cortically Amplified Simple Cells

    Chance FS, Nelson SB, Abbott LF. Complex Cells as Cortically Amplified Simple Cells. Nature Neuroscience. 1999;2(3):277–282. doi:10.1038/6381

    1999 doi

  17. [26]

    Recurrent Excitation in Neocortical Circuits

    Douglas RJ, Koch C, Mahowald M, Martin KAC, Suarez HH. Recurrent Excitation in Neocortical Circuits. Science. 1995;269(5226):981–985. doi:10.1126/science.7638624

    1995 doi

  18. [27]

    Intracortical Multiplication of Thalamocortical Signals in Mouse Auditory Cortex

    Li Ly , Li Yt, Zhou M, Tao HW, Zhang LI. Intracortical Multiplication of Thalamocortical Signals in Mouse Auditory Cortex. Nature Neuroscience. 2013;16(9):1179–1181. doi:10.1038/nn.3493

    2013 doi

  19. [28]

    Tuned Thalamic Excitation Is Amplified by Visual Cortical Circuits

    Lien AD, Scanziani M. Tuned Thalamic Excitation Is Amplified by Visual Cortical Circuits. Nature Neuroscience. 2013;16(9):1315–1323. doi:10.1038/nn.3488

    2013 doi

  20. [29]

    Recurrent Interactions in Local Cortical Circuits

    Peron S, Pancholi R, V oelcker B, Wittenbach JD, ´Olafsd ´ottir HF, Freeman J, et al. Recurrent Interactions in Local Cortical Circuits. Nature. 2020;579(7798):256–259. doi:10.1038/s41586-020-2062-x

    2020 doi

  21. [30]

    Primate Neocortex Performs Balanced Sensory Amplification; 2022

    Pattadkal JJ, Zemelman BV , Fiete I, Priebe NJ. Primate Neocortex Performs Balanced Sensory Amplification; 2022

    2022

  22. [31]

    V oltage-Dependent Block by Mg2+ of NMDA Responses in Spinal Cord Neurones

    Mayer ML, Westbrook GL, Guthrie PB. V oltage-Dependent Block by Mg2+ of NMDA Responses in Spinal Cord Neurones. Nature. 1984;309(5965):261–263. doi:10.1038/309261a0

    1984 doi

  23. [32]

    Magnesium Gates Glutamate-Activated Channels in Mouse Central Neurones

    Nowak L, Bregestovski P , Ascher P , Herbet A, Prochiantz A. Magnesium Gates Glutamate-Activated Channels in Mouse Central Neurones. Nature. 1984;307(5950):462–465. doi:10.1038/307462a0. January 3, 2025 40/47

    1984 doi

  24. [33]

    The Life Cycle of Ca2+ Ions in Dendritic Spines

    Sabatini BL, Oertner TG, Svoboda K. The Life Cycle of Ca2+ Ions in Dendritic Spines. Neuron. 2002;33(3):439–452. doi:10.1016/S0896-6273(02)00573-1

    2002 doi

  25. [34]

    Single Spine Ca2+ Signals Evoked by Coincident EPSPs and Backpropagating Action Potentials in Spiny Stellate Cells of Layer 4 in the Juvenile Rat Somatosensory Barrel Cortex

    Nevian T, Sakmann B. Single Spine Ca2+ Signals Evoked by Coincident EPSPs and Backpropagating Action Potentials in Spiny Stellate Cells of Layer 4 in the Juvenile Rat Somatosensory Barrel Cortex. Journal of Neuroscience. 2004;24(7):1689–1699. doi:10.1523/JNEUROSCI.3332-03.2004

    2004 doi

  26. [35]

    A New Cellular Mechanism for Coupling Inputs Arriving at Different Cortical Layers

    Larkum ME, Zhu JJ, Sakmann B. A New Cellular Mechanism for Coupling Inputs Arriving at Different Cortical Layers. Nature. 1999;398(6725):338–341. doi:10.1038/18686

    1999 doi

  27. [36]

    Top-down Dendritic Input Increases the Gain of Layer 5 Pyramidal Neurons

    Larkum ME, Senn W, L ¨uscher HR. Top-down Dendritic Input Increases the Gain of Layer 5 Pyramidal Neurons. Cerebral cortex. 2004;14(10):1059–1070. doi:10.1093/cercor/bhh065

    2004 doi

  28. [37]

    What Can Neurons Do for Their Brain? Communicate Selectivity with Bursts

    Balduzzi D, Tononi G. What Can Neurons Do for Their Brain? Communicate Selectivity with Bursts. Theory in Biosciences. 2013;132(1):27–39. doi:10.1007/s12064-012-0165-0

    2013 doi

  29. [38]

    Relations between the Statistics of Natural Images and the Response Properties of Cortical Cells

    Field DJ. Relations between the Statistics of Natural Images and the Response Properties of Cortical Cells. Journal of the Optical Society of America A, Optics and image science. 1987;4(12):2379–2394. doi:10.1364/josaa.4.002379

    1987 doi

  30. [39]

    Receptive Fields, Binocular Interaction and Functional Architecture in the Cat’s Visual Cortex

    Hubel DH, Wiesel TN. Receptive Fields, Binocular Interaction and Functional Architecture in the Cat’s Visual Cortex. The Journal of physiology . 1962;160(1):106–154. doi:10.1113/jphysiol.1962.sp006837

    1962 doi

  31. [40]

    The Organization of Behavior: A Neuropsychological Theory (Reprint, Ebook)

    Hebb D. The Organization of Behavior: A Neuropsychological Theory (Reprint, Ebook). New York: Psychology Press; 2002

    2002

  32. [41]

    UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction

    McInnes L, Healy J, Melville J. UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction. arXiv:180203426v3 [cs, stat]. 2020

    2020

  33. [42]

    How Do Phenomenal Objects Bind General Concepts with Particular Features?; forthcoming

    Grasso M, et al. How Do Phenomenal Objects Bind General Concepts with Particular Features?; forthcoming

  34. [43]

    Dreaming and the Brain: From Phenomenology to Neurophysiology

    Nir Y , Tononi G. Dreaming and the Brain: From Phenomenology to Neurophysiology . Trends in cognitive sciences. 2010;14(2):88–100. doi:10.1016/j.tics.2009.12.001

    2010 doi

  35. [44]

    Delusional Confusion of Dreaming and Reality in Narcolepsy

    Wamsley E, Donjacour CEHM, Scammell TE, Lammers GJ, Stickgold R. Delusional Confusion of Dreaming and Reality in Narcolepsy . Sleep. 2014;37(2):419–422. doi:10.5665/sleep.3428

    2014 doi

  36. [45]

    Consciousness and Sleep

    Tononi G, Boly M, Cirelli C. Consciousness and Sleep. Neuron. 2024;112(10):1568–1594. doi:10.1016/j.neuron.2024.04.011

    2024 doi

  37. [46]

    Hierarchical Models of Object Recognition in Cortex

    Riesenhuber M, Poggio T. Hierarchical Models of Object Recognition in Cortex. Nature Neuroscience. 1999;2(11):1019–1025. doi:10.1038/14819

    1999 doi

  38. [47]

    The Distinct Modes of Vision Offered by Feedforward and Recurrent Processing

    Lamme V A, Roelfsema PR. The Distinct Modes of Vision Offered by Feedforward and Recurrent Processing. Trends in Neurosciences. 2000;23(11):571–579. doi:10.1016/s0166-2236(00)01657-x

    doi

  39. [48]

    A Quantitative Map of the Circuit of Cat Primary Visual Cortex

    Binzegger T, Douglas RJ, Martin KAC. A Quantitative Map of the Circuit of Cat Primary Visual Cortex. The Journal of neuroscience: the official journal of the Society for Neuroscience. 2004;24(39):8441–8453. doi:10.1523/JNEUROSCI.1400-04.2004. January 3, 2025 41/47

    2004 doi

  40. [49]

    Topology and Dynamics of the Canonical Circuit of Cat V1

    Binzegger T, Douglas RJ, Martin KAC. Topology and Dynamics of the Canonical Circuit of Cat V1. Neural networks: the official journal of the International Neural Network Society . 2009;22(8):1071–1078. doi:10.1016/j.neunet.2009.07.011

    2009 doi

  41. [50]

    Cortical Hierarchy , Dual Counterstream Architecture and the Importance of Top-down Generative Networks

    V ezoli J, Magrou L, Goebel R, Wang XJ, Knoblauch K, Vinck M, et al. Cortical Hierarchy , Dual Counterstream Architecture and the Importance of Top-down Generative Networks. NeuroImage. 2021;225:117479. doi:10.1016/j.neuroimage.2020.117479

    2021

  42. [51]

    Weight Consistency Specifies Regularities of Macaque Cortical Networks

    Markov NT, Misery P , Falchier A, Lamy C, V ezoli J, Quilodran R, et al. Weight Consistency Specifies Regularities of Macaque Cortical Networks. Cerebral cortex. 2011;21(6):1254–1272. doi:10.1093/cercor/bhq201

    2011 doi

  43. [52]

    An Energy Costly Architecture of Neuromodulators for Human Brain Evolution and Cognition

    Castrillon G, Epp S, Bose A, Fraticelli L, Hechler A, Belenya R, et al. An Energy Costly Architecture of Neuromodulators for Human Brain Evolution and Cognition. bioRxiv : the preprint server for biology . 2023;doi:10.1101/2023.04.25.538209

    2023 doi

  44. [53]

    A Blueprint of Mammalian Cortical Connectomes

    Goulas A, Majka P , Rosa MGP , Hilgetag CC. A Blueprint of Mammalian Cortical Connectomes. PLOS Biology . 2019;17(3):e2005346. doi:10.1371/journal.pbio.2005346

    2019 doi

  45. [54]

    Integrated Information Theory: From Consciousness to Its Physical Substrate

    Tononi G, Boly M, Massimini M, Koch C. Integrated Information Theory: From Consciousness to Its Physical Substrate. Nature Reviews Neuroscience. 2016;17(7):450–461. doi:10.1038/nrn.2016.44

    2016 doi

  46. [55]

    Local and Long-Distance Organization of Prefrontal Cortex Circuits in the Marmoset Brain

    Watakabe A, Skibbe H, Nakae K, Abe H, Ichinohe N, Rachmadi MF, et al. Local and Long-Distance Organization of Prefrontal Cortex Circuits in the Marmoset Brain. Neuron. 2023;111(14):2258–2273.e10. doi:10.1016/j.neuron.2023.04.028

    2023 doi

  47. [56]

    Sleep-Dependent Synaptic Down-Selection (II): Single-Neuron Level Benefits for Matching, Selectivity, and Specificity

    Hashmi A, Nere A, Tononi G. Sleep-Dependent Synaptic Down-Selection (II): Single-Neuron Level Benefits for Matching, Selectivity, and Specificity. Frontiers in Neurology . 2013;4. doi:10.3389/fneur.2013.00148

    2013

  48. [57]

    Multiple Transmitter Receptors in Regions and Layers of the Human Cerebral Cortex

    Zilles K, Palomero-Gallagher N. Multiple Transmitter Receptors in Regions and Layers of the Human Cerebral Cortex. Frontiers in neuroanatomy . 2017;11:78. doi:10.3389/fnana.2017.00078

    2017

  49. [58]

    Why Does Consciousness Fade in Early Sleep? Annals of the New York Academy of Sciences

    Tononi G, Massimini M. Why Does Consciousness Fade in Early Sleep? Annals of the New York Academy of Sciences. 2008;1129:330–334. doi:10.1196/annals.1417.024

    2008 doi

  50. [59]

    The Effects of Sleep Stages and Time of Night on NREM Sleep ERPs

    Yang CM, Wu CS. The Effects of Sleep Stages and Time of Night on NREM Sleep ERPs. International journal of psychophysiology: official journal of the International Organization of Psychophysiology . 2007;63(1):87–97. doi:10.1016/j.ijpsycho.2006.08.006

    2007 doi

  51. [60]

    Apical Drive—A Cellular Mechanism of Dreaming? Neuroscience and biobehavioral reviews

    Aru J, Siclari F, Phillips WA, Storm JF. Apical Drive—A Cellular Mechanism of Dreaming? Neuroscience and biobehavioral reviews. 2020;119:440–455. doi:10.1016/j.neubiorev .2020.09.018

    2020 doi

  52. [61]

    Representations and Decodability of Diverse Cognitive Functions Are Preserved across the Human Cortex, Cerebellum, and Subcortex

    Nakai T, Nishimoto S. Representations and Decodability of Diverse Cognitive Functions Are Preserved across the Human Cortex, Cerebellum, and Subcortex. Communications Biology . 2022;5:1245. doi:10.1038/s42003-022-04221-y

    2022 doi

  53. [62]

    A New No-Report Paradigm Reveals That Face Cells Encode Both Consciously Perceived and Suppressed Stimuli

    Hesse JK, Tsao DY . A New No-Report Paradigm Reveals That Face Cells Encode Both Consciously Perceived and Suppressed Stimuli. eLife. 2020;9:e58360. doi:10.7554/eLife.58360. January 3, 2025 42/47

    2020 doi

  54. [63]

    Can the Macro Beat the Micro? Integrated Information across Spatiotemporal Scales

    Hoel EP , Albantakis L, Marshall W, Tononi G. Can the Macro Beat the Micro? Integrated Information across Spatiotemporal Scales. Neuroscience of Consciousness. 2016;2016(1):niw012. doi:10.1093/nc/niw012

    2016 doi

  55. [64]

    Black-Boxing and Cause-Effect Power

    Marshall W, Albantakis L, Tononi G. Black-Boxing and Cause-Effect Power. PLOS Computational Biology . 2018;14(4):e1006114. doi:10.1371/journal.pcbi.1006114

    2018 doi

  56. [65]

    Laws of Organization in Perceptual Forms

    Wertheimer M. Laws of Organization in Perceptual Forms. In: A Source Book of Gestalt Psychology . Kegan Paul, Trench, Trubner & Company; 1938

    1938

  57. [66]

    Eye and Brain: The Psychology of Seeing

    Gregory RL. Eye and Brain: The Psychology of Seeing. World University Library . World University Library; 1966

    1966

  58. [67]

    Handbuch Der Physiologischen Optik

    von Helmholtz H. Handbuch Der Physiologischen Optik. Allgemeine Encyklopadie Der Physik. Leipzig : V oss; 1867

  59. [68]

    The Logic of Perception

    Rock I. The Logic of Perception. Cambridge: MIT Press; 1983

    1983

  60. [69]

    Hierarchical Bayesian Inference in the Visual Cortex

    Lee TS, Mumford D. Hierarchical Bayesian Inference in the Visual Cortex. JOSA A. 2003;20(7):1434–1448

    2003

  61. [70]

    A Complexity Measure for Selective Matching of Signals by the Brain

    Tononi G, Sporns O, Edelman GM. A Complexity Measure for Selective Matching of Signals by the Brain. Proceedings of the National Academy of Sciences of the United States of America. 1996;93(8):3422–3427. doi:10.1073/pnas.93.8.3422

    1996 doi

  62. [71]

    Integrated Information Theory of Consciousness: An Updated Account

    Tononi G. Integrated Information Theory of Consciousness: An Updated Account. Archives italiennes de biologie. 2012;150:56–90

    2012

  63. [72]

    The Human Imagination: The Cognitive Neuroscience of Visual Mental Imagery

    Pearson J. The Human Imagination: The Cognitive Neuroscience of Visual Mental Imagery . Nature Reviews Neuroscience. 2019;20(10):624–634. doi:10.1038/s41583-019-0202-9

    2019 doi

  64. [73]

    Sleep and the Price of Plasticity: From Synaptic and Cellular Homeostasis to Memory Consolidation and Integration

    Tononi G, Cirelli C. Sleep and the Price of Plasticity: From Synaptic and Cellular Homeostasis to Memory Consolidation and Integration. Neuron. 2014;81(1):12–34. doi:10.1016/j.neuron.2013.12.025

    2014 doi

  65. [74]

    Sleep and Synaptic Down-Selection

    Tononi G, Cirelli C. Sleep and Synaptic Down-Selection. European Journal of Neuroscience. 2020;51(1):413–421. doi:10.1111/ejn.14335

    2020 doi

  66. [75]

    Sleep-Dependent Synaptic Down-Selection (I): Modeling the Benefits of Sleep on Memory Consolidation and Integration

    Nere A, Hashmi A, Cirelli C, Tononi G. Sleep-Dependent Synaptic Down-Selection (I): Modeling the Benefits of Sleep on Memory Consolidation and Integration. Frontiers in Neurology . 2013;4. doi:10.3389/fneur.2013.00143

    2013

  67. [76]

    A Survey of Neurophysiological Differentiation across Mouse Visual Brain Areas and Timescales

    Gandhi SR, Mayner WGP , Marshall W, Billeh YN, Bennett C, Gale SD, et al. A Survey of Neurophysiological Differentiation across Mouse Visual Brain Areas and Timescales. Frontiers in Computational Neuroscience. 2023;17. doi:10.3389/fncom.2023.1040629

    2023

  68. [77]

    The Global Neuronal Workspace Model of Conscious Access: From Neuronal Architectures to Clinical Applications

    Dehaene S, Changeux JP , Naccache L. The Global Neuronal Workspace Model of Conscious Access: From Neuronal Architectures to Clinical Applications. In: Dehaene S, Christen Y , editors. Characterizing Consciousness: From Cognition to the Clinic? Research and Perspectives in Neu...

    2011

  69. [78]

    New Labels for Old Ideas: Predictive Processing and the Interpretation of Neural Signals

    Cao R. New Labels for Old Ideas: Predictive Processing and the Interpretation of Neural Signals. Review of philosophy and psychology . 2020;11(3):517–546. doi:10.1007/s13164-020-00481-x. January 3, 2025 43/47

    2020 doi

  70. [79]

    A Mathematical Theory of Communication

    Shannon CE. A Mathematical Theory of Communication. The Bell System Technical Journal. 1948;27(3):379–423. doi:10.1002/j.1538-7305.1948.tb01338.x

    1948

  71. [80]

    Is Coding a Relevant Metaphor for the Brain? Behavioral and Brain Sciences

    Brette R. Is Coding a Relevant Metaphor for the Brain? Behavioral and Brain Sciences. 2019;42. doi:10.1017/S0140525X19000049

    2019 doi

  72. [81]

    The Brain from inside Out

    Buzs ´aki G. The Brain from inside Out. Oxford University Press; 2019

    2019

  73. [82]

    Meaning and Reference

    Putnam H. Meaning and Reference. The journal of philosophy . 1973;70(19):699–711. doi:10.2307/2025079

    1973 doi

  74. [83]

    Representational Similarity Analysis - Connecting the Branches of Systems Neuroscience

    Kriegeskorte N, Mur M, Bandettini P . Representational Similarity Analysis - Connecting the Branches of Systems Neuroscience. Frontiers in systems neuroscience. 2008;2:4. doi:10.3389/neuro.06.004.2008

    2008 doi

  75. [84]

    Conceptual Spaces: The Geometry of Thought

    G ¨ardenfors P . Conceptual Spaces: The Geometry of Thought. The MIT Press; 2000

    2000

  76. [85]

    Dissociating Artificial Intelligence from Artificial Consciousness

    Findlay G, Marshall W, Albantakis L, David I, Mayner WG, Koch C, et al. Dissociating Artificial Intelligence from Artificial Consciousness. arXiv:241204571 [csAI]. 2024;doi:10.48550/arXiv .2412.04571

    2024 doi arXiv

  77. [86]

    Evolution of Integrated Causal Structures in Animats Exposed to Environments of Increasing Complexity

    Albantakis L, Hintze A, Koch C, Adami C, Tononi G. Evolution of Integrated Causal Structures in Animats Exposed to Environments of Increasing Complexity. PLoS Computational Biology . 2014;10(12). doi:10.1371/journal.pcbi.1003966

    2014 doi

  78. [87]

    Beyond the Information given: Studies in the Psychology of Knowing

    Bruner JS. Beyond the Information given: Studies in the Psychology of Knowing. W. W. Norton, Incorporated; 1973

    1973

  79. [88]

    Upper Bounds for Integrated Information

    Zaeemzadeh A, Tononi G. Upper Bounds for Integrated Information. arXiv: 230509826 [q-bioNC]. 2023

    2023

  80. [89]

    A Catalog of Boolean Concepts

    Feldman J. A Catalog of Boolean Concepts. Journal of Mathematical Psychology . 2003;47(1):75–89. doi:10.1016/S0022-2496(02)00025-1

    2003 doi

  81. [90]

    ¨Uber formal unentscheidbare S ¨atze der Principia Mathematica und verwandter Systeme I

    G ¨odel K. ¨Uber formal unentscheidbare S ¨atze der Principia Mathematica und verwandter Systeme I. Monatshefte f ¨ur Mathematik und Physik. 1931;38(1):173–198. doi:10.1007/BF01700692

    1931 doi

  82. [91]

    G ¨odel’s Incompleteness Theorems

    Raatikainen P . G ¨odel’s Incompleteness Theorems. In: Zalta EN, editor. The Stanford Encyclopedia of Philosophy. spring 2022 ed. Metaphysics Research Lab, Stanford University; 2022. S1 T ext The substrate model and its units The two substrate models used in this work each com...

    2022

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.