Intentionality

Bridge from the previous chapter

In the preceding chapters we examined what is experienced (qualia), how it is experienced (emotions), when it is experienced (subjective time). Now comes the most fundamental question: about what is the experience? Consciousness is always directed toward something — an object, a thought, a feeling. This directedness is called intentionality and receives in UHM a precise mathematical expression: a morphism in the category $\mathbf{Hol}$ that preserves experiential content.

On notation

• $\Gamma$ — coherence matrix, $\gamma_{ij}$ — its elements
• $\mathbf{Hol}$ — category of Holonomies
• $\varphi$ — self-modelling operator
• $R$ — reflection measure, $R_{\text{th}} = 1/3$
• $\Phi$ — integration measure
• Full notation table — in Notation

Chapter roadmap

1. Philosophical history — from Brentano to Searle
2. Definition — intentionality as a CPTP morphism with the E-condition
3. Threshold — why intentionality requires L2
4. Types — apperceptive, evidential, teleological, affective, immanent
5. Composition — closure theorem (subcategory $\mathbf{Int} \subset \mathbf{Hol}$)
6. Self-consciousness — the identity intentional act
7. L0–L4 hierarchy — from absence of directedness to identity
8. Intentional cone — the set of reachable states
9. Connection to No-Zombie — why absence of intentionality does not equal absence of experience

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Philosophical History: The Directedness of Consciousness

Brentano (1874): intentionality as the criterion of the mental

Franz Brentano in "Psychology from an Empirical Standpoint" (1874) formulated a thesis that became one of the foundational claims of the philosophy of mind:

"Every mental phenomenon is characterized by what the medieval scholastics called the intentional (or mental) inexistence of an object, and which we, though in somewhat ambiguous terms, would call the relation to a content, the direction toward an object."

What does this mean in plain language? Every conscious state is directed toward something:

• You see an apple (perception directed toward an object)
• You think about a problem (thinking directed toward a content)
• You desire ice cream (desire directed toward a thing)
• You fear the dark (fear directed toward a situation)

A stone is directed toward nothing. A river is not "about" anything. But consciousness is always about something — that is its defining property. Brentano proposed using intentionality as the criterion of distinction between the mental and the physical.

Husserl (1900): noesis and noema

Edmund Husserl, Brentano's student, developed his idea into a systematic phenomenology. He introduced two key concepts:

• Noesis (noesis) — the act of consciousness, the "how" of its directedness (perception, recollection, judgement…)
• Noema (noema) — the content of the act, the "toward what" of consciousness (object, thought, value…)

Every act of consciousness is a pair (noesis, noema). One cannot have a noesis without a noema (consciousness without an object) or a noema without a noesis (object without consciousness).

Husserl also introduced the concept of the horizon of intentionality: when you see an apple, you see not only its front side — you expect it to have a back side, that it is heavy, that it is edible. This "horizon" is the invisible but essential background of every act of consciousness.

Searle (1983): intentionality and speech acts

John Searle in "Intentionality" (1983) linked intentionality to conditions of satisfaction: every intentional state sets a condition under which it is "satisfied" (a belief is true or false, a desire fulfilled or not, an intention realised or not).

Searle also proposed the famous "Chinese Room" argument (1980): a computer program can simulate understanding Chinese, but does not possess intentionality — it does not "understand" in the sense that a human understands. For Searle, intentionality is a biological phenomenon belonging to certain neural systems.

UHM position: intentionality as a morphism

UHM offers a formalisation that combines the intuitions of all three thinkers:

Philosopher	Idea	Formalisation in UHM
Brentano	Consciousness is always directed	Morphism $f: \Gamma_A \to \Gamma_B$ in the category $\mathbf{Hol}$
Husserl	Noesis/noema, horizon	Noesis = morphism $f$; noema = $\Gamma_B$; horizon = intentional cone $\mathcal{I}(\Gamma)$
Searle	Conditions of satisfaction, biological grounding	E-compatibility = condition of satisfaction; $R \geq 1/3$ = biological threshold

The key distinction of UHM from all three: intentionality is not binary (present/absent), but graded — from complete absence (L0) through proto-intentionality (L1) to full intentionality (L2) and meta-intentionality (L3).

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Motivation

Intentionality is a fundamental property of consciousness: its directedness toward an object. Consciousness is always consciousness of something (Brentano, Husserl). In UHM, intentionality receives a formal expression as a morphism in the category of Holonomies $\mathbf{Hol}$.

An everyday analogy. A torch always shines somewhere — it has a direction. Consciousness is like a torch: it cannot simply "be" without an object of illumination. Intentionality is the "beam" of the torch. In the UHM formalism: the morphism $f: \Gamma_A \to \Gamma_B$ is the "path of the beam" from one state to another, and this path must not "switch the torch off" (must not impoverish the E-sector).

But why is intentionality formally a morphism rather than, say, a function or a relation? Because:

1. Morphisms compose: from "I see an apple" and "the apple is red" it follows "I see a red apple" — a chain of intentional acts forms a new act
2. Morphisms preserve structure: an intentional act does not destroy the object (a CPTP channel preserves normalisation and positivity)
3. There exists an identity morphism: self-consciousness is the "directedness toward oneself", $\mathrm{id}: \Gamma \to \Gamma$

These are precisely the axioms of a category. Intentionality is not an accidental property attached to consciousness, but a structural invariant of the category $\mathbf{Hol}$.

Definition of Intentionality (D.1)

Definition D.1 (Intentionality) [D]

Intentionality is a CPTP morphism $f$ in the category $\mathbf{Hol}$ satisfying the condition of E-compatibility:

$$f: \Gamma_A \to \Gamma_B, \quad f \in \mathrm{Mor}_{\mathbf{Hol}}(\Gamma_A, \Gamma_B)$$

with the additional condition:

$$\mathrm{rank}(\rho_E^{(B)}) \geq \mathrm{rank}(\rho_E^{(A)})$$

where $\rho_E^{(X)} = \mathrm{Tr}_{-E}(\Gamma_X)$ is the reduced experience matrix of system $X$.

Interpretation: The intentional act $f$ "directs" system $A$ toward system $B$ in such a way that experiential content is not impoverished.

Let us unpack the definition part by part.

What is a CPTP morphism?

CPTP stands for "Completely Positive Trace-Preserving". This is the class of transformations that are physically realisable:

• Trace-Preserving: $\mathrm{Tr}(f(\Gamma)) = \mathrm{Tr}(\Gamma) = 1$. Normalisation is preserved — "probabilities remain probabilities".
• Completely Positive: $f$ maps admissible states to admissible states, even when the system is part of a larger system. This guarantees that the transformation is "physical" — it does not create negative probabilities.

In Kraus representation:

$$f(\Gamma) = \sum_m K_m \Gamma K_m^\dagger, \quad \sum_m K_m^\dagger K_m = I$$

where $K_m$ are Kraus operators compatible with the $\Omega^7$ structure (see Category Hol).

What is E-compatibility?

The condition $\mathrm{rank}(\rho_E^{(B)}) \geq \mathrm{rank}(\rho_E^{(A)})$ means: the rank of the reduced experience matrix does not decrease. What does this mean informally?

$\rho_E = \mathrm{Tr}_{-E}(\Gamma)$ is what the Interiority ($E$) measurement "sees" when all other dimensions are "traced out" (averaged). The rank of $\rho_E$ is the number of "independent directions" in E-space along which there is nonzero content. The higher the rank, the richer the experience.

E-compatibility guarantees: an intentional act does not impoverish experience. It may enrich (rank grows) or preserve (rank unchanged), but not diminish.

Analogy. If $\Gamma$ is a picture of the world, then an intentional act is "pointing the lens" at a part of the picture. The condition $\mathrm{rank}(\rho_E^{(B)}) \geq \mathrm{rank}(\rho_E^{(A)})$ guarantees that when pointing the lens the picture does not lose detail — it may acquire new detail, but not lose it. The CPTP channel formalism ensures that the "lens" is physically realisable (preserves positivity and normalisation).

Numerical example. Suppose before the intentional act: $\rho_E^{(A)}$ has rank 3 (three independent "directions" of experience). After the act "I notice the red colour of the apple": $\rho_E^{(B)}$ has rank 4 — a new direction (colour) has been added. E-compatibility is satisfied: $4 \geq 3$. If after the act the rank had fallen to 2, this would not be an intentional act — it would be "forgetting", "repression", a destruction of experience.

Threshold of Intentionality (C.1)

Statement C.1 (Threshold of intentionality) [C]

Condition: The threshold $R_{\text{th}} = 1/3$ is a theorem [T] ($K = 3$ from the triadic decomposition).

Intentionality in the full sense (an "about-something" directed structure) requires level L2:

$$R(\Gamma) \geq R_{\text{th}} = \frac{1}{3}, \quad \Phi(\Gamma) \geq \Phi_{\text{th}} = 1$$

Below L2 there exist proto-intentional processes: morphisms $f \in \mathrm{Mor}_{\mathbf{Hol}}$ without a condition on $\mathrm{rank}(\rho_E)$. These are "reactive" directedness (tropisms, reflexes), lacking an "about-something" structure.

Why intentionality requires L2

Intentionality presupposes distinguishing subject from object: "I see an apple". This requires:

1. A model of the subject — "who directs". This is provided by the self-modelling operator $\varphi$, creating an inner "map of self" $\varphi(\Gamma)$.

2. A model of the object — "what is directed at". This is provided by sufficient accuracy of the self-model, enabling the system to distinguish "self" from "not-self".

The quality of the self-model is measured by the reflection measure:

$$R = \frac{1}{7P(\Gamma)} \geq \frac{1}{3}$$

When $R < 1/3$ (equivalently $P > 3/7$) the system is too far from the dissipative attractor $I/7$ to structure the subject–object distinction that is constitutive of intentionality. Master definition: Self-observation.

Numerical example: three beings.

Entity	$R$	$\Phi$	Level	Directedness	Experience
Thermostat	$0.02$	$0.3$	L0	None	Reacts to temperature, but is not "directed" at anything
Amoeba	$0.15$	$1.5$	L1	Proto-intentionality	Moves toward food, but there is no "I" and no "food as object"
Human	$0.50$	$2.1$	L2	Intentionality	"I see an apple" — there is a subject, an object, an act

For the human: $R \approx 0.5$ means $P \approx 1/(7 \times 0.5) \approx 2/7$ — the system is near the critical threshold, in the Goldilocks zone. For the amoeba: $R \approx 0.1$ ($P \approx 1.4$, but for physical systems $P \leq 1$, so $R \geq 1/7 \approx 0.14$) — reflection is minimal, the subject–object distinction is blurred. For the thermostat: $R$ is close to $1/7$ — reflection at the lower bound.

Types of Intentionality (I.1)

Interpretation I.1 (Sectoral types of intentionality) [I]

Different types of intentionality are determined by which sectors of the coherence matrix dominate in the morphism $f$. This is an interpretation — a mapping of formal sectors onto phenomenological types.

Table of types

Type	Dominant sector	Formal characteristic	Phenomenology	Example
Apperceptive	$A \to E$	$\gamma_{AE}$ ↑ under $f$	Discrimination enters interiority	"I see a red apple"
Evidential	$L \to E$	$\gamma_{LE}$ ↑ under $f$	Logical coherence in interiority	"I understand the proof"
Teleological	$D \to U$	$\gamma_{DU}$ ↑ under $f$	Directed change toward unity (goal)	"I strive toward a solution"
Affective	$D \to E$	$\gamma_{DE}$ ↑ under $f$	Process acting on interiority	"I feel joy"
Immanent	$E \to O$	$\gamma_{EO}$ ↑ under $f$	Interiority directed toward the ground	"I experience presence" (meditation)

Let us examine each type in detail.

Apperceptive intentionality

Definition. Apperceptive intentionality is the directedness of attention toward an object. The term "apperception" was introduced by Leibniz (1714) to denote conscious perception, in contrast to unconscious "petites perceptions".

$$f_{\text{appc}}: \Gamma \to \Gamma', \quad \text{where } |\gamma'_{AE}| > |\gamma_{AE}|$$

Mechanism. The morphism $f_{\text{appc}}$ strengthens the coherence between Articulation ($A$, discrimination) and Interiority ($E$, experience). Subjectively: "I see/hear/feel this". Articulation "selects" the object from the background; Interiority "receives" what has been selected into experience.

Analogy. A spotlight ($A$) illuminates part of the scene, and that part "enters" consciousness ($E$). Before the act of attention the whole scene is illuminated uniformly (low $\gamma_{AE}$). After the act — a bright beam picks out the object (high $\gamma_{AE}$).

Numerical example. Before the act of attention: $|\gamma_{AE}| = 0.08$ (background perception). After directing attention to the apple: $|\gamma'_{AE}| = 0.25$ — a threefold amplification. At the same time, by normalisation, the other $|\gamma_{AX}|$ ($X \neq E$) decrease: the "spotlight" of attention focuses, withdrawing resources from the periphery. $|\gamma_{AS}|$ falls from $0.15$ to $0.08$ — structural discrimination weakens in favour of experience. For more detail see Attention and memory.

Evidential intentionality

Definition. Evidential intentionality is directedness toward understanding — the experience of the "self-evidence" of a logical connection.

$$f_{\text{evid}}: \Gamma \to \Gamma', \quad \text{where } |\gamma'_{LE}| > |\gamma_{LE}|$$

Strengthening of the link between Logic ($L$) and Interiority ($E$). Subjectively: "I understand this". The coherence $\gamma_{LE}$ is "evidence" (qualia #16).

Analogy. If apperception is a spotlight, then evidence is a magnifying glass: it does not merely show the object, but reveals its inner logic. The "aha!" moment — when scattered facts fall into a chain — is a sharp jump in $|\gamma_{LE}|$.

Numerical example. A student reads a theorem's proof. On the first reading: $|\gamma_{LE}| = 0.05$ — "I see the formulas but do not understand". On the third reading: $|\gamma_{LE}| = 0.15$ — "I'm beginning to see the logic". The "aha!" moment: $|\gamma_{LE}|$ jumps to $0.30$ — "I've got it!". Simultaneously $|\gamma_{EU}|$ (synthesis) rises — the separate steps of the proof cohere into a single whole.

Teleological intentionality

Definition. Teleological intentionality is directedness toward a goal — the experience of "I am striving toward…".

$$f_{\text{tel}}: \Gamma \to \Gamma', \quad \text{where } |\gamma'_{DU}| > |\gamma_{DU}|$$

Strengthening of the link between Dynamics ($D$) and Unity ($U$). Subjectively: "I want/intend to achieve this". The coherence $\gamma_{DU}$ is "teleology" (qualia #15).

Analogy. Teleological intentionality is a compass: it indicates the direction of movement. Dynamics ($D$) — the energy of movement; Unity ($U$) — the destination. When $\gamma_{DU}$ is high, movement is meaningful — the system "knows where it is going".

Numerical example. A marathon runner. At the 30th kilometre: $|\gamma_{DU}| = 0.22$ — "I'm running toward the finish, the goal is clear". Dynamics ($\gamma_{DD} = 0.20$) is high but purposeful — directed toward unity. At "the wall" (35th km): $|\gamma_{DU}|$ drops to $0.08$ — "why am I running? I can't remember". Dynamics are the same, but the connection to the goal is lost — pure suffering without meaning. If the runner "breaks through the wall": $|\gamma_{DU}|$ recovers to $0.18$ — "second wind", the goal is visible again.

Affective intentionality

Definition. Affective intentionality is directedness toward a feeling — the experience of "I feel…".

$$f_{\text{aff}}: \Gamma \to \Gamma', \quad \text{where } |\gamma'_{DE}| > |\gamma_{DE}|$$

This is the bridge to the emotion taxonomy: affective intentionality is an act in which Dynamics ($D$) acts on Interiority ($E$), generating an emotional experience.

Analogy. Apperception — "I see"; evidence — "I understand"; affection — "I feel". If apperception is a spotlight and evidence a magnifying glass, then affection is a resonator: events ($D$) resonate in experience ($E$), as a blow to a tuning fork generates sound in the body of a violin.

Immanent intentionality

Definition. Immanent intentionality is the directedness of Interiority ($E$) toward the Ground ($O$) — the experience of "presence", "being as such".

$$f_{\text{imm}}: \Gamma \to \Gamma', \quad \text{where } |\gamma'_{EO}| > |\gamma_{EO}|$$

This is the most "deep" type of intentionality — directedness not toward an external object, but toward the ground of experience itself. In meditative traditions it is described as "pure presence", "awareness of awareness".

Analogy. Ordinary intentionality is a torch illuminating external objects. Immanent intentionality is a torch turned toward its own source of light. Not "I see an apple", but "I experience the very act of seeing". Not the content of consciousness, but consciousness as such.

Numerical example. A meditator in objectless shamatha practice: $|\gamma_{EO}| = 0.20$, $|\gamma_{AE}| = 0.05$ (apperception almost zero — no external object), $|\gamma_{DE}| = 0.03$ (dynamics minimal — "thoughts have quieted"). The sole bright coherence is $\gamma_{EO}$: experience is directed toward its own ground.

Composition of Intentional Acts (T.1)

What is a subcategory and why does closure matter

Before stating the theorem, let us explain the key concepts.

A category is a mathematical structure consisting of objects and morphisms (arrows between objects). $\mathbf{Hol}$ is a category whose objects are coherence matrices $\Gamma \in \mathcal{D}(\mathcal{H})$ and whose morphisms are CPTP channels compatible with the $\Omega^7$ structure.

A subcategory $\mathbf{Int} \subset \mathbf{Hol}$ is a "part" of the category $\mathbf{Hol}$: the same objects but fewer morphisms (only E-compatible ones).

Closure (of the subcategory under composition) means: if $f$ and $g$ are morphisms in $\mathbf{Int}$, then $g \circ f$ is also a morphism in $\mathbf{Int}$. Why does this matter?

If closure failed, successive intentional acts could destroy intentionality: "I see an apple" ($f$) + "the apple is red" ($g$) would not yield "I see a red apple" ($g \circ f$). Consciousness would be unable to build chains of reasoning, plans, perceptions. Closure guarantees: thinking is possible — every step of reasoning preserves directedness.

Theorem T.1 (Closure of composition) [T]

Let $f: \Gamma_A \to \Gamma_B$ and $g: \Gamma_B \to \Gamma_C$ be intentional morphisms (E-compatible CPTP channels). Then $g \circ f: \Gamma_A \to \Gamma_C$ is an intentional morphism.

Proof.

1. $g \circ f$ is CPTP, since the composition of CPTP channels is a CPTP channel (closure of the CPTP class).
2. $g \circ f \in \mathrm{Mor}_{\mathbf{Hol}}$, since $\mathbf{Hol}$ is a category (morphisms are closed under composition).
3. E-compatibility: $\mathrm{rank}(\rho_E^{(B)}) \geq \mathrm{rank}(\rho_E^{(A)})$ and $\mathrm{rank}(\rho_E^{(C)}) \geq \mathrm{rank}(\rho_E^{(B)})$, hence $\mathrm{rank}(\rho_E^{(C)}) \geq \mathrm{rank}(\rho_E^{(A)})$. $\square$

Corollary. Intentional morphisms form a subcategory $\mathbf{Int} \subset \mathbf{Hol}$:

$$\mathrm{Ob}(\mathbf{Int}) = \mathrm{Ob}(\mathbf{Hol}), \quad \mathrm{Mor}_{\mathbf{Int}} \subset \mathrm{Mor}_{\mathbf{Hol}}$$

Analogy. If you look at a painting ($f$: directing attention) and then begin to analyse it ($g$: transition to understanding), the resulting act $g \circ f$ — "I see and understand the painting" — is also intentional. Consciousness can build chains of directed acts, and each intermediate step preserves or enriches experience. This property is essential for the CC theorems on cognitive dynamics.

Numerical example. A chain of three intentional acts:

Act	Type	$\mathrm{rank}(\rho_E)$ before	$\mathrm{rank}(\rho_E)$ after	E-compatibility
$f_1$: "I notice the apple"	Apperceptive	2	3	3 $\geq$ 2
$f_2$: "I see that it is red"	Apperceptive	3	4	4 $\geq$ 3
$f_3$: "I understand it is ripe"	Evidential	4	4	4 $\geq$ 4
$f_3 \circ f_2 \circ f_1$	Composition	2	4	4 $\geq$ 2

The Identity Intentional Act

The identity morphism $\mathrm{id}_\Gamma: \Gamma \to \Gamma$ is trivially intentional. Phenomenologically this is self-consciousness: the directedness of consciousness toward itself.

In the presence of the self-modelling operator $\varphi$:

$$\varphi: \Gamma \to \varphi(\Gamma) \approx \Gamma$$

Self-consciousness is an intentional act whose "object" is the system itself. The accuracy of self-consciousness is determined by the reflection measure:

$$R = \frac{1}{7P(\Gamma)}$$

At $R = 1$ ($P = 1/7$, $\Gamma = I/7$) the system is at the point of complete chaos. At small $R$ ($P \to 1$) the system is "frozen" in a single state. For reflective consciousness (L2+), $R \geq 1/3$ is required, i.e. $P \leq 3/7$. Master definition: Self-observation.

Numerical example. In an ordinary state a human: $R \approx 0.4$–$0.6$. Self-consciousness is substantial, but far from perfect — much remains "off-screen" (the unconscious). For an experienced meditator in samadhi: $R \to 0.9$ — self-consciousness approaches complete transparency, yet even then, by the theorem on incomplete transparency, at least 3 channels remain opaque.

Intentionality and the L0–L4 Hierarchy

Let us return to Brentano: he regarded intentionality as a binary property — either present or absent. UHM shows that directedness is graded:

Level	Type of directedness	Formal characteristic	Example	Husserlian parallel
L0	No directedness	Only $\Gamma \in \mathcal{D}(\mathcal{H})$, no morphisms	A stone	—
L1	Proto-intentionality	Morphisms in $\mathbf{Hol}$ without E-condition (tropisms)	Amoeba moves toward food	Leibniz's "petites perceptions"
L2	Intentionality	Morphisms in $\mathbf{Int}$ at $R \geq 1/3$ (directed experience "about something")	"I see an apple"	Noesis + noema
L3	Meta-intentionality	Intentionality directed at another's intentionality	"I understand that you see an apple"	Intersubjectivity
L4	Identity	$\varphi(\Gamma) = \Gamma$ — subject and object coincide	Pure self-consciousness	"Absolute consciousness"

Numerical example: L3 (meta-intentionality). Two people, Alice and Bob. Alice sees that Bob is looking at an apple. For Alice:

• $R_{\text{Alice}} \geq 1/3$ — she is aware of herself
• She models $\Gamma_{\text{Bob}}$ — she has a "model of Bob"
• She "sees" Bob's intentional act ($f_{\text{Bob}}: \Gamma_{\text{Bob}} \to \Gamma_{\text{apple}}$)
• This requires SAD $\geq 2$ — two levels of self-modelling: "I know that he knows"

For more detail see the interiority hierarchy.

The Intentional Cone

Consider the set of all states $\Gamma'$ reachable from a given $\Gamma$ via intentional morphisms:

$$\mathcal{I}(\Gamma) := \{\Gamma' \in \mathrm{Ob}(\mathbf{Hol}) : \exists f \in \mathrm{Mor}_{\mathbf{Int}}(\Gamma, \Gamma')\}$$

This set is called the intentional cone — it describes everything that the given system "can direct its consciousness at" from the current state.

Properties of the intentional cone [I]

1. Non-emptiness: $\Gamma \in \mathcal{I}(\Gamma)$ (the identity morphism — self-consciousness is always available)
2. Transitivity: If $\Gamma' \in \mathcal{I}(\Gamma)$ and $\Gamma'' \in \mathcal{I}(\Gamma')$, then $\Gamma'' \in \mathcal{I}(\Gamma)$ (from the closure of composition, Theorem T.1)
3. Boundedness: A CPTP channel cannot increase the purity $P$, so $P(\Gamma') \leq P(\Gamma)$ (without regeneration). This restricts the intentional cone
4. Expansion through regeneration: The regenerative term $\mathcal{R}[\Gamma, E]$ (evolution equation) can expand the cone, since $\mathcal{R}$ is not a CPTP channel in the standard sense

Properties 1–2 are consequences of the category structure. Property 3 follows from the properties of CPTP. Property 4 is an interpretation, depending on the formalisation of $\mathcal{R}$.

Analogy. The intentional cone is like the "reach zone" of a torch with a given battery charge.

• Without recharging (without regeneration $\mathcal{R}$): the cone is limited. Each new act of attention consumes coherence ($P$ does not grow), and sooner or later the "battery dies". A tired person by evening cannot concentrate on anything — his intentional cone has narrowed.
• With recharging (with regeneration): the cone expands. After sleep and rest (restoring $P$) a person can "reach" more distant and complex objects of thought.

Numerical example. A student with $P = 0.38$. His intentional cone includes reading a textbook ($P$ drops slightly), solving problems ($P$ drops faster), but not proving an open problem ($P$ would fall below $P_{\text{crit}}$ — that is beyond the cone). After coffee and 10 minutes of rest ($P$ restores via $\mathcal{R}$) the cone expands — now a more difficult problem is within reach.

Zero Intentionality and Philosophical Zombies

A system with $R < R_{\text{th}}$ does not possess intentionality in the full sense, but this does not make it a "zombie". According to the No-Zombie theorem, for $\Gamma \in \mathcal{D}(\mathcal{H})$ the system always possesses interiority (L0). The absence of intentionality means only the absence of a directed "about-something" structure, not the absence of experience as such.

This is the key distinction of UHM from traditions that identify consciousness with intentionality:

Position	No intentionality =	UHM
Early Husserl	No consciousness	No: there is L0/L1 interiority without intentionality
Analytic philosophy	No mental	No: the mental is broader than intentionality
Searle	No biological consciousness	No: L0 belongs to any $\Gamma \in \mathcal{D}(\mathcal{H})$
UHM	No "about-something" structure	Yes, but experience (interiority) is preserved

Analogy. A newborn infant experiences the world (L1) but has not yet learned to direct consciousness: there is no "I see this", only a "stream of sensations". This is not a "zombie" — it is pre-intentional experience. Or imagine yourself in the moment of waking: for the first fractions of a second you experience (light, warmth, sounds), but are not yet directed at anything specific. This is an L1 state: interiority without intentionality.

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What we learned

1. Intentionality has a rich philosophical history (Brentano, Husserl, Searle) and receives in UHM a precise formalisation: a CPTP morphism in $\mathbf{Hol}$ with the E-compatibility condition: $\mathrm{rank}(\rho_E^{(B)}) \geq \mathrm{rank}(\rho_E^{(A)})$
2. The threshold L2 ($R \geq 1/3$, $\Phi \geq 1$) is necessary for the subject–object structure
3. 5 types of intentionality (apperceptive, evidential, teleological, affective, immanent) are determined by the dominant sector of $\Gamma$, each with unique phenomenology and numerical examples
4. Intentional morphisms are closed under composition — they form the subcategory $\mathbf{Int} \subset \mathbf{Hol}$ (Theorem T.1 [T]), making thinking possible as a chain of acts
5. The intentional cone $\mathcal{I}(\Gamma)$ defines the "horizon" of reachable states — it expands through regeneration
6. Absence of intentionality does not equal absence of interiority — the No-Zombie theorem guarantees L0 (minimal interiority) for any viable $\Gamma$

Bridge to the next chapter

We have completed the section "Structure of Experience": qualia, emotions, time, intentionality. We now move to the section "States of Consciousness" — how the $\Gamma$-profile changes during sleep, meditation, psychedelics, anaesthesia. The first chapter — Altered States of Consciousness — describes four classes of ASC as trajectories in $\Gamma$-space.

Related Documents

• Category Hol — definition of $\mathbf{Hol}$ and morphisms
• Self-observation — $\varphi$ and $R$
• Interiority theory — $\rho_E$ and experiential content
• Interiority hierarchy — levels L0–L4
• Qualia structure — types of qualia $\gamma_{AE}$, $\gamma_{LE}$, $\gamma_{DU}$
• Emotion taxonomy — $\gamma_{DE}$ as affective intentionality
• Categorical formalism — CPTP channels and Kraus representation
• Theorems of Coherence Cybernetics — applied consequences of categorical structure
• Attention and memory — the mechanism of coherence redistribution