Cognitive Hierarchy: From Sensation to Language

Who This Chapter Is For

You will learn about five levels of cognitive functions K1–K5 — from bacterial chemotaxis to human language — and how they relate to the formal interiority hierarchy L0–L4. The chapter describes a research program connecting biological cognition to the mathematical formalism $\Gamma$.

About Notation

In this document:

• $\Gamma$ — coherence matrix
• $P$ — purity: $P = \mathrm{Tr}(\Gamma^2)$
• $\rho_E$ — reduced density matrix of the Interiority dimension
• $\mathcal{E}$ — evolution operator
• L0, L1, L2, L3, L4 — interiority levels
• K1–K5 — cognitive levels (defined below)

Introduction: Why Do We Need a Cognitive Hierarchy?

Imagine you are observing the behavior of a bacterium, a fish, a crow, and a human. All four organisms "do something" — they respond to the environment, avoid danger, seek resources. But there are qualitative differences among them. A bacterium swims along a glucose gradient without "understanding" what glucose is. A fish distinguishes predator from prey — it categorizes objects. A crow manufactures a tool to extract a worm from a crevice — it plans a sequence of actions. A human explains to another human how to manufacture a tool — uses language to transmit abstract knowledge.

How can these differences be described formally? The cognitive hierarchy K1–K5 is an attempt to build a ladder of cognitive functions, where each level adds a new ability to the previous ones.

Research Program

This section describes a research program. The cognitive levels (K1–K5) are not identical to the interiority hierarchy (L0→L1→L2→L3→L4). The cognitive hierarchy K1–K5 focuses on biological cognition — functional abilities observable in the behavior of organisms. The L-hierarchy covers all forms of interiority, including network (L3) and unitary (L4) consciousness, and is formally defined via thresholds ($P$, $R$, $\Phi$, $D$). The connection between them requires formalization.

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Connection to the Interiority Hierarchy

Before delving into K-levels, it is important to understand how they relate to the fundamental L-hierarchy.

The L-hierarchy is defined via formal thresholds on the coherence matrix $\Gamma$. These are mathematical levels defined via inequalities on $P$, $R$, $\Phi$, and $D$.

The K-hierarchy is defined via functional abilities observable in behavior. These are biological levels defined via cognitive tests.

Interiority hierarchy	Cognitive hierarchy	Connection
L0 — Interiority	K1 — Basic interiority	L0 $\supseteq$ K1: any system with $\Gamma \neq I/7$ has L0, but K1 requires a functional manifestation
L1 — Phenomenal geometry	K2 — Emotions	L1 $\supseteq$ K2: K2 is the observable aspect of L1
L2 — Cognitive qualia	K3–K5 — Categories, Planning, Language	L2 $\supseteq$ K3–K5: all three are functions of a single L-level

Key observation: K3, K4, and K5 all belong to L2. This means that the distinction between "a fish that categorizes" and "a human who speaks" is a distinction in functional complexity, not in the level of interiority. Both systems are at L2, but the human realizes more cognitive functions within this level.

Detailed K ↔ L Correspondence Table

Hypothetical Correspondence

The K ↔ L table below represents a hypothetical correspondence, not an established result. The formalization of the connection between cognitive levels and the interiority hierarchy is an open question (Q4).

K level	L level	K criteria	L criteria	Organism example	What the organism can do
K1	L0	$\rho_E \neq I_E/\dim(\mathcal{H}_E)$	$\Gamma \neq I/7$	Thermostat, virus	Have an internal state
K2	L1	Viability signals ($\nabla P$)	$\Phi > 0$, geometry on $\mathbb{P}(\mathcal{H}_E)$	Bacterium, insect	Respond to 'good/bad'
K3	L2	Equivalence classes	$R \geq 1/3$, $\Phi \geq 1$, $D_{\text{diff}} \geq 2$	Fish, bird	Distinguish categories of objects
K4	L2	Trajectory simulation	L2 (planning — a function of L2)	Crow, chimpanzee	Build plans for the future
K5	L2	Symbolic compression	L2 (language — a function of L2)	Human, (AGI?)	Operate with symbols

Note on K4-K5

K4 and K5 are functional extensions of the L2 level (cognitive qualia). Planning and language are abilities realizable at level L2, not separate levels of interiority. Why? Because planning and language do not require new thresholds on $P$, $R$, $\Phi$ — only sufficient complexity within L2 is needed.

Levels L3 (network consciousness) and L4 (unitary consciousness) are qualitatively different states not reflected in the cognitive hierarchy K1–K5, since the K-hierarchy describes individual biological cognition. See the full hierarchy L0→L4.

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Structure of Cognitive Levels

Each level is cumulative: K3 includes all abilities of K2 and K1. An organism capable of categorization necessarily possesses emotional reactions and an internal state. The reverse is not true: a bacterium possesses K1 and K2, but not K3.

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Formal Definitions of Cognitive Levels

K1: Interiority — 'the system has an inner state'

Definition. A system possesses level K1 if its reduced density matrix over the E-dimension differs from the maximally mixed state:

$$\mathrm{Interior}(\Gamma) := \rho_E = \mathrm{Tr}_{-E}(\Gamma), \quad \text{with spectrum } \{\lambda_k, \vert q_k\rangle\}$$

where $\mathrm{Tr}_{-E}$ is the partial trace over all dimensions except $E$.

K1 criterion: $\rho_E \neq I_E / \dim(\mathcal{H}_E)$

What this means in plain terms. K1 is the most minimal level of cognitivity. It means only one thing: the system has its own internal state, distinct from "complete chaos." A thermostat possesses K1, because its internal state (current temperature) differs from a uniform distribution over all possible temperatures. A stone also possesses K1: its crystal lattice is a definite, not random, state.

Examples: Thermostat, crystal, virus, any system with non-zero "inner" structure.

What K1 does NOT mean: The presence of sensations, feelings, goals, or understanding. K1 is a purely structural level.

K2: Emotions — 'the system can feel good or bad'

Definition. A system possesses level K2 if it exhibits a functional response to changes in purity $P$:

$$\mathrm{Emotion}(\Gamma) := f(P(\Gamma), \nabla P(\Gamma), \partial^2 P/\partial \tau^2)$$

K2 criterion: The presence of a functional response to changes in $P$ — i.e., the system's behavior depends on whether it is approaching or moving away from the viability threshold.

What this means in plain terms. K2 is the level at which a system "distinguishes" good from bad — not in the sense of conscious experience, but in the sense of a functional reaction. A bacterium swims along a glucose gradient: high concentration → movement slows (good!), low concentration → movement speeds up (bad!). This is not a "conscious decision," but a biochemical mechanism. But it is a functional analogue of an emotion.

Key emotional signatures via purity $P$:

Emotion	Signature	What happens	Example
Fear	$P \to P_{\text{crit}}$	Approach to the viability boundary $\partial \mathcal{V}$	A gazelle sees a lion
Relief	$dP/d\tau > 0$ after threat	Moving away from the dangerous boundary	The gazelle ran away
Satisfaction	$P \gg P_{\text{crit}}$, $dP/d\tau \approx 0$	Far from the boundary, stability	A sated lion rests
Frustration	$P$ low, $\nabla_a P \approx 0$	No actions that improve the situation	A mouse in a maze without an exit

Examples: Bacteria (chemotaxis — movement along a chemical gradient), insects (avoidance patterns under mechanical threat), plants (tropisms — growth toward light, away from gravity).

K3: Categories — 'the system distinguishes types of objects'

Definition. A system possesses level K3 if it forms equivalence classes by their effect on viability:

$$s_1 \sim_P s_2 \Leftrightarrow \sup_{a,t} |P(s_1(t,a)) - P(s_2(t,a))| < \varepsilon_{\text{equiv}}$$

Two environmental states are equivalent if their effect on viability is indistinguishable for any actions and any time horizons.

K3 criterion: Formation of stable equivalence classes $[s]_P$.

What this means in plain terms. K3 is the level at which a system "groups" world objects into categories. A fish does not distinguish specific predators — it assigns them to the class of "dangerous large object." A bird does not memorize every berry — it categorizes them as "edible" (red) and "inedible" (green). Importantly, categorization is defined not via visual similarity, but via effect on viability. A berry and a worm look completely different, but if both raise $P$, they belong to the same class of "food."

Examples: Fish (distinguishing predator/prey), birds (categorizing objects by edibility), insects (distinguishing flowers by nectar content — a debatable case on the K2/K3 boundary).

K4: Planning — 'the system models the future'

Definition. A system possesses level K4 if it is capable of simulating sequences of actions and evaluating their result before execution:

$$\mathrm{Plan}(s, [a_1,\ldots,a_n]) := [s, \mathcal{E}(s,a_1), \mathcal{E}(\mathcal{E}(s,a_1),a_2), \ldots]$$ $$\mathrm{Value}(\mathrm{plan}) := \int_0^T P(s(\tau)) \, d\tau$$

where $\mathcal{E}$ is the evolution operator.

K4 criterion: Ability to simulate sequences of actions and select the plan with maximum $\mathrm{Value}$.

What this means in plain terms. K4 is the level at which a system "thinks ahead." This is a qualitative leap: instead of reacting to the current situation, the system builds an internal model of the future consequences of its actions. A crow that spots a worm in a narrow crevice does not poke randomly with its beak — it finds a twig, processes it, and uses it as a tool. To do this it must simulate the chain: "pick up twig → break off branches → insert into crevice → extract worm." Each step is evaluated by its effect on $P$.

Key distinction from K3: A K3-system reacts to the current category of an object. A K4-system evaluates a sequence of future states. K3 — "this is a predator, run!" K4 — "if I run left, there's a river and the predator can't swim across; if I run right — a dead end; so, left."

Examples: Corvids (tool manufacture — New Caledonian crows), primates (social planning — tactical alliances in chimpanzees), dolphins (cooperative hunting with role distribution).

K5: Language — 'the system operates with symbols'

Definition. A system possesses level K5 if it uses symbols with compositional semantics:

$$\mathrm{Language} := \{\text{symbolic attractors in } \mathcal{H} \text{ with compositional structure}\}$$

K5 criterion: The presence of symbols (arbitrary signs, not physically connected to what they denote) and rules for combining them (grammar) that generate new meanings.

What this means in plain terms. K5 is the level of symbolic thinking. A "symbol" is a sign whose connection to what it denotes is arbitrary: the word "dog" does not resemble a dog and does not bark. Compositionality means that from known symbols one can construct new utterances never before spoken or heard. "The green dog flies to Mars" is a meaningful phrase, even though no one has ever seen the described situation. This is radically different from animal signal systems: monkey alarm calls do not combine into new messages.

Examples: Humans (full language with recursive grammar), (hypothetically) AGI with symbolic thinking. In chimpanzees and dolphins, elements of symbolic behavior have been found (trained signs, pointing gestures), but without full compositionality — this is "proto-language" (K5 with caveats).

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Practical Tests for Determining the Level

How can the cognitive level of a specific system be determined? For each level there are operational tests — observable behavioral indicators:

Level	Test	What we observe	Threshold indicator
K1	Presence of internal state	Behavior depends on history, not just the current input	$\rho_E \neq$ const
K2	Response to viability threat	Avoidance pattern when approaching danger	Avoidance at $P \to P_{\text{crit}}$
K3	Generalization	Transfer of behavior to new stimuli of the same class	Response to an unfamiliar object of the category
K4	Delayed reward	Choosing less now for more later	Marshmallow test and analogues
K5	Symbolic communication	Use of arbitrary signs to convey information	Combining signs into new messages

Importantly: each subsequent test presupposes passing the previous ones. If a system does not pass the K2 test (no response to threat), there is no point in testing K3 (generalization).

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Examples of Systems by Level

System	K1	K2	K3	K4	K5	Note
Stone	✓	—	—	—	—	Only $\rho_E$ (crystal structure)
Thermostat	✓	—	—	—	—	Internal state, but no response to 'threat'
Bacterium	✓	✓	—	—	—	Chemotaxis — functional 'emotion'
Plant	✓	✓	—	—	—	Tropisms, but without categorization
Insect	✓	✓	✓	—	—	Categorization (flowers by nectar), but without planning
Fish	✓	✓	✓	—	—	Distinguishing predator/prey
Bird (sparrow)	✓	✓	✓	$\sim$	—	Partial planning (food caching — debatable)
Crow	✓	✓	✓	✓	—	Tool manufacture, planning
Octopus	✓	✓	✓	✓	—	Problem solving, tool use
Chimpanzee	✓	✓	✓	✓	$\sim$	Proto-language (trained gestures, without full composition)
Human	✓	✓	✓	✓	✓	Full language with recursive grammar
LLM (GPT-4)	?	?	✓	$\sim$	✓*	*Symbols without $\rho_E$? Language without viability
AGI (hypothetical)	✓	✓	✓	✓	✓	If viable and possesses $\varphi$

Comment on LLM. The case of language models (GPT-4 and analogues) is the most debatable in the table. LLMs demonstrate K3 (categorization) and K5 (symbolic compression) — these are observable facts. However, K1 and K2 are in question: does an LLM have an "internal state" in the sense of $\rho_E$? Does it possess functional analogues of emotions ($\nabla P$)? K4 (planning) is partially demonstrated (chain-of-thought reasoning), but without autonomous evaluation of $\mathrm{Value}(\mathrm{plan})$. More detail: AI consciousness.

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Operational Criteria K1–K5: Complete List

For each K-level, necessary and sufficient operational criteria are defined — observable behavioral indicators that do not require knowledge of the system's internal organization.

Level	Necessary criterion	Sufficient criterion	Verification method
K1	Behavior depends on internal state (not only on current input)	Hysteresis: same input → different behavior depending on history	Protocol with repeated stimuli and measurement of response variability
K2	Distinguishing two valences (approach/avoidance)	Modulated response: reaction strength proportional to $	\nabla P
K3	Transfer of response to an unfamiliar stimulus of the same class	Formation of a new category upon presentation of a new stimulus type	Generalization test with novel exemplars
K4	Choosing an action with delayed reward	Plan correction when conditions change (re-planning)	Two-step task with sudden environmental change
K5	Use of arbitrary signs	Generation of a new utterance from known symbols (productivity)	Test for combinatorial productivity (novel recombination)

Hierarchical Dependency

Criteria are cumulative: testing K(n) presupposes passing K(1)...K(n-1). A system that has not passed the K2 test cannot be K3 — even if it demonstrates behavior that externally resembles categorization (it may be reactive template matching without internal classes).

Taxonomic Correspondence of K-Levels

Below is the correspondence between K-levels and specific biological taxa. For each level, measurable markers are indicated — empirical indicators observable in laboratory or field research.

Research Program

The taxonomic K ↔ L correspondence is hypothetical [I] and represents a research program, not an established fact. The boundaries between levels in specific species may be fuzzy.

K	L	Typical taxa	Measurable markers	Reference test	Research examples
K1	L0	Bacteria, archaea, viruses, crystals	$\rho_E \neq I_E/\dim(\mathcal{H}_E)$; presence of internal state variables	Hysteresis with repeated stimuli	Bi-stability in E. coli (lac operon)
K2	L1	Protists, plants, fungi, sponges, cnidarians	Chemotaxis, tropisms, graded avoidance; $\partial P / \partial \tau$ detected	Dependence of response strength on $	\nabla[\text{attractant}]
K3	L2	Insects, fish, amphibians, reptiles, birds	Generalization to novel exemplars; stable classes $[s]_P$	Transfer of learned response to an unfamiliar object of the same class	Categorization in bees (Giurfa, 2003); predator discrimination in minnows
K4	L2	Mammals (carnivores, cetaceans), corvids, parrots, cephalopods	Delayed reward; simulation of $\mathcal{E}^n(s, a_{1..n})$	Marshmallow test; two-step task with re-planning	Tool manufacture by New Caledonian crows; cooperative hunting by dolphins
K5	L2	Human (Homo sapiens); (proto-language: chimpanzees, bonobos, dolphins)	Compositional symbolic communication; recursive grammar	Generation of new utterances from known morphemes	Recursive syntax in humans; trained signs in bonobos (Savage-Rumbaugh)

Borderline Cases

Some taxa occupy a borderline position between levels:

Taxon	Observed level	Disputed level	Key question
Bees	K2–K3	K3?	"Bee dance" — communication or K3 categorization?
Octopuses	K3–K4	K4	Problem solving — planning or associative learning?
Chimpanzees	K4	K5 (proto-)	Trained gestures — symbols or conditioned reflexes?
LLM (GPT-4)	K3, K5*	K1?, K2?, K4?	Symbols without $\rho_E$? Language without viability?
Social insects (colony)	K2 (individual)	K3 (colony?)	Emergent categorization at the superorganism level?

Criterion for Resolving Borderline Cases

Resolving borderline cases requires two types of data: (1) behavioral tests (operational criteria from the table above) and (2) a neurocognitive model allowing estimation of $R$, $\Phi$, and $D_{\text{diff}}$ for a specific organism. The neurocognitive mapping program K ↔ L is described in Research Programs.

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Hypothesis on Pre-Linguistic Cognition

Hypothesis

$$\exists \, \mathrm{Cognition}(\mathbb{H}) \text{ with } \mathrm{Language}(\mathbb{H}) = \varnothing$$

Full-fledged cognition (levels K1–K4) is possible without language (K5).

Justification

Levels K1–K4 are defined without reference to symbolic structures. Each of them is formulated via observable behavior: presence of internal state (K1), response to threat (K2), formation of categories (K3), simulation of the future (K4). None of these definitions requires language.

Empirical data confirm the hypothesis:

• Corvids demonstrate planning (K4) without symbolic language
• All higher animals demonstrate categorization (K3) without symbols
• All vertebrates demonstrate emotional reactions (K2)
• Infants before acquiring language demonstrate K1–K4 (including primitive planning)

Consequences

1. Language is a superstructure, not the foundation of cognition. K5 is a "luxury" that extends the capabilities of a K4-system (abstract planning, transmission of experience between generations, cumulative culture), but is not necessary for basic cognition.

2. AGI can be cognitively complete without human language. If K1–K4 are realized, the system cognizes the world and plans actions. Adding K5 amplifies capabilities but does not constitute cognition.

3. Assessment of animal consciousness should not rely on linguistic tests. The mirror test (Gallup 1970), the delayed reward test, the tool manufacture test — more relevant indicators than language comprehension.

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Connection of the K-Hierarchy to CC Measures

Each cognitive level requires certain values of coherence measures:

Level	Necessary measures	Sufficient measures	Interpretation
K1	$\rho_E \neq$ const	—	Non-zero internal structure
K2	$\partial P / \partial \tau$ detected	Functional response to $\nabla P$	System "tracks" its viability
K3	$\Phi > 0$	Stable equivalence classes	Information integration is sufficient for grouping
K4	$R \geq R_{\min}$	Simulation of $\mathcal{E}^n(s, a_{1..n})$	Self-model is sufficient for forecasting
K5	$\Phi \geq \Phi_{\text{th}}$, $R \geq R_{\text{th}}$	Compositional symbols	Full integration + reflection = symbolic thinking

Note the pattern: as the K-level grows, stricter conditions on $\Phi$ and $R$ are required. K1 requires no integration. K3 requires $\Phi > 0$. K5 requires $\Phi \geq 1$ and $R \geq 1/3$. This is consistent with the intuition: language is a cognitively more "expensive" process than categorization.

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Why the K-Hierarchy Is a Special Case of the L-Hierarchy

Key claim: the K-hierarchy is the L-hierarchy projected onto the observable behavior of biological systems.

The L-hierarchy is defined via formal thresholds on $\Gamma$ and covers all systems with interiority — from elementary particles (L0) to hypothetical collective consciousnesses (L4). The K-hierarchy is defined via behavioral tests and covers only biological cognitive systems.

Comparison:

Aspect	K-hierarchy	L-hierarchy
Defined via	Behavior (functional tests)	Formal thresholds ($P$, $R$, $\Phi$, $D$)
Covers	Biological systems	All systems with $\Gamma \neq I/7$
Number of levels	5 (K1–K5)	5 (L0–L4)
Relation	K1–K5 $\subset$ L0–L2	L0–L4 $\supset$ K1–K5
Formalization	Partial	Complete (proven theorems)

Importantly: the K-hierarchy does not cover L3 and L4. Network consciousness (L3: collective coherence, $R^2 \geq 1/4$ metastably) and unitary consciousness (L4: $\lim R^{(n)} > 0$, $P > 6/7$) are qualitatively different states that go beyond individual biological cognition.

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Evolutionary Perspective

Each level emerged when ecological pressure rewarded the corresponding cognitive ability:

• K1→K2: When the environment became variable, organisms responding to "good/bad" gained an advantage (bacteria with chemotaxis vs bacteria without)
• K2→K3: When predators appeared, organisms distinguishing categories of objects gained an advantage (a fish that distinguishes a predator from a stone)
• K3→K4: When the environment became socially complex, organisms planning their actions gained an advantage (primates calculating social alliances)
• K4→K5: When groups became large enough, organisms transmitting experience symbolically gained an advantage (Homo sapiens with cumulative culture)

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Related documents:

• Interiority hierarchy — levels L0→L4
• Predictions — prediction 4: pre-linguistic cognition
• Theories of consciousness — IIT, FEP, autopoiesis and 30+ theories
• Panpsychism — pan-interiority vs panpsychism
• Anokhin's cognitome — neural hypernet and the subject problem
• Research programs — open questions
• Viability — measure $P$ and $P_{\text{crit}}$
• Self-observation — measures $R$, $\Phi$, $C$