SAE Information Theory XIV (Closing Paper): 15DD Information, the Other as an End
SAE 信息论 XIV（收束篇）：15DD 信息，他人目的
This is the closing paper of the Information Theory series of the Self-as-an-End framework. It treats the sub-layer beneath 10D, namely 15DD, the other as an end. 10D is composed of two sub-layers: 15DD, one-way recognition, and 16DD, mutual non-doubt. This paper treats only 15DD. From the standpoint of any single individual, the mutual non-doubt of 16DD is the thing-in-itself; here the paper holds to via negativa and sets it out only as a horizon.
The information object of 15DD divides in two. The readable side is a single item: the other is an end, that is, a purpose-source is present in the other. The unreadable side is the content of the other's 14DD, whose read-out is zero, exactly as the self has zero read-out of its own 14DD content. What can be read out is one bit, the presence of a source; but the unreadable remainder, the content of the other's 14DD, is not thin. It is inexhaustible, and although it cannot be read out, it can be approached through observation of the other's behavior, and even through communication.
In the one direction where the self actively turns toward the other's purpose-source, the channel is not reading but simulation. This paper sets out, for the first time, other-purpose simulation: a simulation, within one's own architecture, of the other's cannot-not. It borrows the form of one's own 14DD as a template, runs a prediction through the 12DD engine, and submits the result to a non-self-referential judgment by 13DD, with no self-loop anywhere in the circuit. Because there is no self-loop, the mechanism is light and fast; and because it never builds a self for the other, what it yields stops always at a structural marker of the source's presence and never reads out the content of the other's 14DD. In its everyday form this mechanism lies near the cognitive side of empathy, yet it is held strictly to the structural marker, contains no affective resonance, and is not equivalent to reading the other.
15DD is one-way: I reach toward you while you have not yet turned back toward me; the two-way relation of mutual non-doubt falls at 16DD. On the coordinates of 15DD, and on the basis of Kant's formula of humanity as an end, this paper develops a self-consistent derivation. What falls at 15DD is the categorical imperative: because you have a purpose-source that is present and that I cannot read out, I cannot-not recognize it as inexhaustible. The cooperative imperative of the Kingdom of Ends, being two-way, falls at 16DD. From this it follows that to exhaust another entirely as a means cannot be completed in information-theoretic terms, since such exhaustion would require capturing the unreadable source; a remainder that cannot be substituted therefore always survives, and this remainder is dignity in Kant's sense. The paper sets out only this structure; it does not derive an ought from an is.
This paper is lighter than its predecessors. It sheds closure, it sheds lock, and it erects no new falsifiable target. It closes on two things: a horizon, the 16DD thing-in-itself; and an interface, other-purpose simulation, established to the level of an interface so that later work may take it up.
Abstract
This is the closing paper of the Information Theory series of the Self-as-an-End framework. It treats the sub-layer beneath 10D, namely 15DD, the other as an end. 10D is composed of two sub-layers: 15DD, one-way recognition, and 16DD, mutual non-doubt. This paper treats only 15DD. From the standpoint of any single individual, the mutual non-doubt of 16DD is the thing-in-itself; here the paper holds to via negativa and sets it out only as a horizon.
The information object of 15DD divides in two. The readable side is a single item: the other is an end, that is, a purpose-source is present in the other. The unreadable side is the content of the other's 14DD, whose read-out is zero, exactly as the self has zero read-out of its own 14DD content. What can be read out is one bit, the presence of a source; but the unreadable remainder, the content of the other's 14DD, is not thin. It is inexhaustible, and although it cannot be read out, it can be approached through observation of the other's behavior, and even through communication.
In the one direction where the self actively turns toward the other's purpose-source, the channel is not reading but simulation. This paper sets out, for the first time, other-purpose simulation: a simulation, within one's own architecture, of the other's cannot-not. It borrows the form of one's own 14DD as a template, runs a prediction through the 12DD engine, and submits the result to a non-self-referential judgment by 13DD, with no self-loop anywhere in the circuit. Because there is no self-loop, the mechanism is light and fast; and because it never builds a self for the other, what it yields stops always at a structural marker of the source's presence and never reads out the content of the other's 14DD. In its everyday form this mechanism lies near the cognitive side of empathy, yet it is held strictly to the structural marker, contains no affective resonance, and is not equivalent to reading the other.
15DD is one-way: I reach toward you while you have not yet turned back toward me; the two-way relation of mutual non-doubt falls at 16DD. On the coordinates of 15DD, and on the basis of Kant's formula of humanity as an end, this paper develops a self-consistent derivation. What falls at 15DD is the categorical imperative: because you have a purpose-source that is present and that I cannot read out, I cannot-not recognize it as inexhaustible. The cooperative imperative of the Kingdom of Ends, being two-way, falls at 16DD. From this it follows that to exhaust another entirely as a means cannot be completed in information-theoretic terms, since such exhaustion would require capturing the unreadable source; a remainder that cannot be substituted therefore always survives, and this remainder is dignity in Kant's sense. The paper sets out only this structure; it does not derive an ought from an is.
This paper is lighter than its predecessors. It sheds closure, it sheds lock, and it erects no new falsifiable target. It closes on two things: a horizon, the 16DD thing-in-itself; and an interface, other-purpose simulation, established to the level of an interface so that later work may take it up.
Keywords: 15DD; the other as an end; one-way recognition; other-purpose simulation; access asymmetry; cannot-not; via negativa; the categorical imperative; the thing-in-itself.
§1 Introduction
§1.1 Place in the Series
The Information Theory series works from the bottom up, characterizing the information processing of each layer of the great dimensional sequence in turn. This is its closing paper. Taking up the 9D of the preceding paper, it treats the sub-layer beneath 10D, namely 15DD.
By the correspondence between D and DD set out in Methodology V2, 10D is composed of two sub-layers: the lower, 15DD, one-way recognition; the upper, 16DD, mutual non-doubt. This paper makes good on the portion belonging to 15DD of a promise already made in the eleventh paper of the series; it does not develop 16DD. The mutual non-doubt of 16DD is, from the standpoint of any single individual, the thing-in-itself: a two-way relation must hold on both sides at once, yet any individual holds only their own half, so the complete mutual recognition lies beyond what that individual can reach. For this reason 16DD is the via negativa boundary of the series; this paper sets it out only as a horizon and does not enter it. This is the same boundary held by the closing paper of the framework's Thermodynamics series, which likewise stops at 15DD.
The preceding paper placed the self before its own purpose-source; this paper, at 15DD, turns one self toward the purpose-source of another for the first time. That turning is one-way.
§1.2 The Task of This Paper
The paper does three things.
First, it sets out the two-fold division of the 15DD information object. On the side of the other, the readable side is a single item, the other is an end, that is, a purpose-source is present in the other; the unreadable side is the content of the other's 14DD, with read-out zero.
Second, it characterizes the one-way access structure of the self toward the other's purpose-source. What leads to that source is not a reading line but a simulation run within one's own architecture, whose yield is a structural marker of the source's presence; the content of the source holds to via negativa and is never reached.
Third, it identifies the continuity between this information-theoretic structure and the Kantian categorical imperative, and carries the non-substitutability and the remainder of dignity, established on one's own side by the preceding paper, over into the relation between persons; at the same time it states plainly that the paper derives no normative ought from any information-theoretic fact.
The paper establishes no closure, no lock, and no further falsifiable target; the reasons are given in §2.2 and §7.
§1.3 Three Sentences for the Spine
The spine of the paper can be gathered into three sentences.
First, the content of the other's purpose-source has zero read-out. I recognize that you have a purpose-source present, yet I cannot read out its content, just as I cannot read out my own; what differs is that my own source drives me, whereas your source constrains me by way of the categorical imperative.
Second, the approach is by simulation, not by reading. My approach to you is an other-purpose simulation within my own architecture, whose yield is only a structural marker of the presence of your purpose-source, and which never reaches its content.
Third, the recognition is one-way. I therefore recognize you, one-way, as an end that cannot be exhausted by me; this recognition holds without waiting for you to turn back toward me. The two-way mutual non-doubt falls at 16DD and is a horizon.
§1.4 Commitments and Scope
The validity of norms belongs to the Moral-Law papers. The character of recognition as it is lived through, its clinical phenomenology, belongs to the Psychoanalysis papers. The content of value belongs to the Value-Theory papers. Quantitative content, the specific rate laws, and the cross-framework algebraic interface belong to the ZFCρ series; this paper draws on none of its q-values, and the convergence it speaks of is a qualitative sameness of structure, not a numerical identity. The two-way non-doubt of 16DD, the cooperative imperative, and the development of the Kingdom of Ends belong to later work, to the Anthropology papers, and to the Moral-Law papers; the thing-in-itself is not touched.
Via negativa applies only at the essence dimension, the content of the other's 14DD; the positive commitment lies at the existence dimension, the presence of the other as an end.
§1.5 Who Performs the Characterization
To speak of an other's purpose-source whose content cannot be read out raises a surface contradiction that must first be resolved, and its resolution is the same as in the preceding paper. The one who performs this characterization is reason, not introspection, and not any reading of the other. Reason forces out, from the ceiling of 14DD, the structural necessity of 15DD; what it yields is the form of a structure, namely that here there must be an other's purpose-source, and not the content of that source. Wherever the paper says the other is an end, it does so within this limit: what is established is the form of the source's presence, and what is kept is the silence of its content.
§2 The Chiseling Derivation and the Toolset
§2.1 15DD Forced Out by the Ceiling of 14DD
To chisel is to negate: the ceiling of each layer is the ground of the layer above it. Facing its own mortality, 13DD forces out the self-as-an-end of 14DD; one level higher, the ceiling of 14DD forces out 15DD. There are two roads to 15DD, and the two meet at a single place.
One road comes from §10.2 of the preceding paper. Once 14DD is in place, a question follows: if one's own purpose is inexhaustible, what meaning is there in attaining a purpose. This question cannot be dissolved on one's own side; it pushes the turning out of the self and toward the purpose of the other.
The other road comes from the framework's treatment of learning. A complete 14DD has a structural blind spot: it projects and interprets the other through its own framework. Yet this projection is bound never to fit completely, because the other's 14DD is not a missing piece within my framework but an independent direction that my framework cannot, in its structure, contain; the persistent failure to fit is exactly the pressure that forces out recognition of the other's independent purpose-source.
The two roads meet. A complete 14DD, turning outward, strikes the same wall along both, and this wall forces out 15DD, the other's purpose, as something independent and unreadable in content. The one performing this derivation is still reason, not introspection, in keeping with the handling of the meta-question in §2.5 of the preceding paper.
§2.2 A Single DD, One-Way, No Closure
15DD is only a single sub-layer; it does not make up a complete D-layer. The 9D of the preceding paper is a complete D-layer, with two sub-layers, closed upon its upper sub-layer 14DD by a single sub-layer lock; 15DD does not meet this condition. The paper therefore does not speak of closure, does not speak of lock, and does not carry over the grammar of the lock-class; the closure of 10D is left to 16DD. That one-way recognition and the not-yet-occurrence of closure go together is structurally self-consistent: a one-way relation has simply not yet drawn shut, and its drawing shut waits upon the two-way relation of 16DD.
§2.3 The Access Language Carried Over
The paper carries over the access language of the preceding paper, read, write, veto, read-out, torque, settle, transposing each onto this one-way relation between the self and the other. Its core primitive is this: the content of the other's 14DD has read-out zero for the individual; this zero is a consequence of a priori structure, not an empirical negligibility.
The me/self distinction is kept from the preceding paper. What the paper calls the turning toward the other is the turning of this self, 13DD, toward the purpose-source of another self, and not the turning of the me toward an object.
The channel that leads to the other's purpose-source the paper names other-purpose simulation. What it draws upon are primitives already present in one's own architecture, the 12DD prediction and the 11DD reconstruction set out across the tenth through twelfth papers; to simulate the other by these is the interface this paper sets out for the first time. The mechanism of this interface is given in §4.
§2.4 The Four-Fold Pattern of 15DD
The sections that follow make up, together, a four-fold pattern. The four-fold pattern is a structural figure set out in the framework's Methodology X; its four steps are: mark, not construct; additive, giving direction; multiplicative, giving memory; closure, yielding a construct and a remainder. When one round completes, what remains at the fourth step is the handle of the first step of the next round, the remainder conserved and chained onward. Its topology is not an even division: the first three steps spread out and take up the bulk of the space of unfolding, while the fourth collapses rapidly within it.
Entry into this round is conditioned on one's already having a complete 14DD: without one's own 14DD there is neither a form to borrow for simulating the other nor any way to give rise to the outward question. The meeting of the two roads in §2.1 forces out precisely the handle of this round, the one question that remains once 14DD is closed: beyond one's own purpose, is there also a purpose. 15DD is the whole four-fold pattern unfolding from this handle; the four sections below are its four steps.
First step, mark, not construct. What is given is an answer, not a construction: yes, there is a purpose that is not one's own. This answer contracts to a presence-marker, the other is an end, one bit. This step is set out in §3.1 and §3.2.
Second step, additive, giving direction. The marker gives only the presence of a non-self purpose, as yet undirected; the additive step adds to this undirected presence a direction, fixing it onto the source that is the other's 14DD, so that direction arises from nothing to something. This step is set out in §3.1.
Third step, multiplicative, giving memory. With the direction now clear, approach follows: a simulation within one's own architecture, drawing ever nearer the other's 14DD, accumulating a memory of structural markers. This step is other-purpose simulation; it is the heaviest of the three steps that spread out, and the non-thinness of 15DD rests here. This step is set out in §4.
Fourth step, closure, yielding a construct and a remainder. Here closure means only the local completion of one round of the four-fold pattern, not the D-layer closure of 10D, nor a lock in the sense of the lock-class; the true closure of 10D is still left to 16DD. Within a single act, closure yields two things at once, and the two co-arise asymmetrically, inseparable yet differing in modality: the construct is a behavioral prediction, that is, a structural marker; the remainder is what that prediction can never pin down, an indeterminacy deeper than the physical, a subjectivity-indeterminacy. This remainder does not enter the construct; it turns into the handle of the next round, pointing toward the two-way non-doubt of 16DD, a round that can begin only when the other injects information into the subject. The construct of this step is set out in §4.3 and §7.2, the remainder in §7.2 and §8.
15DD is therefore not a thin one bit. The one bit is only its first step; the whole of 15DD is a four-fold pattern composed of the mark, the direction, the memory, and the construct and remainder yielded at closure.
§3 The Information Object: The Other Is an End
What 15DD opens on the side of the other is an access differential structurally identical to the one on one's own side. It introduces no new information material; what changes is only the location of the differential, moved from between the self and its own purpose-source to between the self and another self. In the order of the four-fold pattern, this section walks the first two steps: it marks that the other is an end, and it gives direction toward the other's 14DD.
§3.1 The Two-Fold Division of the Information Object
The preceding paper established that 9D introduces no new kind of information at 14DD. What sets 14DD apart from 13DD is not an added kind of material but, upon the same read/write/veto, an added differential of access: the self can read the workings of its own lower layers, yet cannot read out the content of the 14DD purpose-source that drives it. 15DD takes this up and likewise introduces no new material; it only moves this differential to between the self and another self.
The information object of 15DD therefore divides in two. What is reachable is a single item, the other is an end, that is, a purpose-source is present in the other. What is unreachable is the content of the other's 14DD, with read-out zero. This corresponds strictly to the two-fold division on one's own side in the preceding paper, with only the side changed: on one's own side, my existence with respect to my 14DD is hard while its content has zero read-out; toward the other, my existence with respect to the other's 14DD is hard while its content has zero read-out.
That a purpose-source is present in the other is a hard assertion, forced out by the derivation later in this section, and not to be softened. The cannot-not it anchors within, I know to be deep and dense, yet this is only a structural consequence: I know that it must be there without knowing what it is, and it is not a readable thing. Its content has zero read-out, the essence dimension holding to via negativa, given no positive characterization and no assertion of magnitude; to estimate the capacity of an unreadable source is itself to overstep, for an assertion of magnitude presupposes readability, and here readability is zero.
One and the same zero read-out is opposite in modality on one's own side and on the other's. On one's own side, the unreadable source drives me; it is mine, and though I do not read its content, I am pushed along by it, my torque issuing from it. Toward the other, the unreadable source constrains me; it is the other's, it does not push my torque, yet by way of the categorical imperative (§5) it raises in me a cannot-not: because you have a purpose-source I cannot reach, I cannot-not recognize it as inexhaustible. One side drives, the other constrains; this is what sets 15DD apart from the self-referential side of 9D in substance, and not merely a change of object.
§3.2 The Readable One Bit and the Unreadable Remainder
On the side of the other, the information I can read with certainty contracts to a single item: that here a purpose-source I cannot reach is present. Beyond this item, all is remainder, all zero read-out.
The one bit here is not a bit-count in Shannon's coding sense; it names the contraction of the readable side to a presence-marker, present or not present. The constraint capacity of the source itself is not measured by this marker. The one bit falls on the readable side and has nothing to do with the richness of the source: the source is of high constraint capacity, and the cannot-not it anchors may be deep and dense; only this richness is, in whole, unreadable to me. What is pared to one bit is the information I can read out, not the source.
Though only one bit is readable, 15DD is not thin on that account. The unreadable side, the content of the other's 14DD, is both inexhaustible and able to be approached. It is inexhaustible because the other's purpose is inexhaustible, and the other in person is inexhaustible as well. It can be approached because, though I cannot read it out, I can draw nearer to it by observing the other's behavior, and even through communication; only this drawing nearer is forever an approach, never turning into a read-out. The readable one bit and the unreadable but approachable inexhaustible, set side by side, are the complete shape of the 15DD information object. This inexhaustibility is also the root of the non-substitutability in §5.3: an inexhaustible source can be equivalently substituted by nothing finite.
The readable one bit and the richness of the source are not to be confused: to take the one bit for the poverty of the source is to flatten a source of high constraint capacity into a scalar, and to substitute a source by an equivalent scalar is exactly the information-theoretic prototype of the instrumentalization that §5 refuses.
§3.3 One-Way, and the Boundary with the 16DD Thing-in-Itself
15DD is one-way. I reach toward you, and you have not yet turned back toward me; I recognize you as an end, and this recognition holds without waiting for you to make the same recognition of me. Two-way mutual non-doubt would require that each of two selves take the other as an inexhaustible end and confirm this to one another; that is 16DD, beyond this paper.
The two-way non-doubt of 16DD is, from the standpoint of the individual, the thing-in-itself. A two-way relation must hold on both sides at once, yet either side holds only its own half; seen from either side, the complete mutual recognition lies beyond what that side can reach. For this reason 16DD is the via negativa boundary of the series, set out only as a horizon and not entered. Between 15DD and 16DD there is no drawing shut: 15DD does not draw shut into 16DD; 15DD is the base layer of 16DD, and 16DD can be derived only with this one-way recognition as its ground, while the derivation of 16DD already lies beyond this paper.
The zero read-out of the content of the other's 14DD has its root in the fact that the point of departure is oneself. Zero read-out is aimed at the direction in which I read outward toward the other; and in that direction the only channel I can use is the other-purpose simulation of §4, which draws on the self and never builds a self for the other, and so contains no part capable of reading the other's content. The reading fails because this channel simply lacks that part, not because the source is out of reach and the attempt happens to miss. That one cannot even read out the content of one's own purpose-source, and that the other's source lies a further remove away across an inter-subjective boundary, is a move a fortiori and serves only as a side lead; the load-bearing reason comes first, namely that the only channel I can use is self-simulation, and self-simulation never reads content. The 16DD thing-in-itself serves here not as the main proof but as an upper bound, gathering this zero read-out beneath a horizon already out of reach from the standpoint of the individual. The boundary is a priori, and the paper therefore erects no further falsifiable target (§7).
§3.4 Approach, Not Arrival
To speak of an unreadable other's purpose-source, and on what ground this is possible, has the same resolution as in the preceding paper. Toward the other's purpose-source, introspection is doubly absent: I cannot introspect the content of my own 14DD, and still less that of the other's, for introspection turns only toward oneself. The one empirical channel that remains is a third-person approach, whose mechanism is the other-purpose simulation of the next section; and there is another, non-empirical channel, the a priori of reason, which forces out that here there must be an other's purpose-source. What both reach is structure; neither reaches content.
The existence dimension and the content dimension must be kept apart. Whether this source, the other as an end, is present belongs to the existence dimension, and here I have a positive commitment: both the approach and the a priori point to its presence. What the cannot-not anchored by this source actually is belongs to the content dimension, holding to via negativa, silent and uncharacterized. The approach is forever an approach, not an arrival: to whatever precision the third-person approach accumulates, it does not cross that boundary and turn into a read-out of any specific purpose-content. What can be approached is the structure cast off by that inexhaustible remainder, and the approach may be refined without end; what is permanently closed is not this approach but the read-out of its content.
§4 Other-Purpose Simulation
With the mark and the direction in place, the four-fold pattern enters its third step, giving memory, that is, the approach to the other's 14DD. By what mechanism is that single reachable bit approached? The channel to the other's purpose-source is not a reading line driven into the other but a simulation run within my own architecture.
§4.1 The Channel Is Not a Reading Line
I have no port that can connect into the other's 14DD and retrieve content. What I can do is run a simulation within my own architecture and, on that basis, approach a structural marker of the presence of an other's purpose-source. The paper calls this other-purpose simulation, the simulation of the other's cannot-not.
Its everyday form lies near the cognitive side of empathy, the strand of putting oneself in another's place: were I the other, holding the other's cannot-not, how would I act. Yet the word empathy implies that I have read the other and understood the other, whereas the very point of this mechanism is that what I read is never the other, and what is run is, from beginning to end, my own material. The paper therefore does not name it by empathy but by the access language, and confines it to the simulation of a structural marker of the presence of the other's purpose-source, with no strand of affective resonance, and not equivalent to reading out the other's content.
The simulation takes external material as input, from two sources. One is the other's behavior, which I can reach and observe so as to calibrate my simulation. The other is communication, in which the other actively says something and hands it to me; this material is the other giving to me, not my reading out of the other, yet once it is handed in, what I run on its basis is still self-simulation. So whether the material comes from my observation of behavior or from the other's giving in communication, once fed in, what I run is self-simulation, and what comes out is a structural marker, not the other's content. Behavior and communication govern what I start from and calibrate against; the simulation governs what I run out; what both reach stops at a structural marker.
§4.2 What the Simulation Draws Upon
Everything the other-purpose simulation draws upon is already present in my own architecture, the 12DD prediction and the 11DD reconstruction primitives set out across the tenth through twelfth papers; to simulate the other by these is the interface this paper sets out for the first time.
I borrow the form of my own 14DD, the structure of having a cannot-not, to serve as a template, and into it I fill a hypothesized cannot-not of the other. What is borrowed is the form, not the content: borrowed is the formal slot that a purpose-source must have an inexhaustible cannot-not, not the projection of my own purpose-content as the other's purpose-content; what is filled into the slot is a hypothesis I improvise from the input of behavior and communication, not something read from elsewhere. This borrowing presupposes, in advance, that I already have a 14DD: without one's own 14DD there is no form to borrow and the simulation cannot start. The template, together with the hypothesized content, is handed to the 12DD prediction engine, which runs out a trajectory: were I the other, holding this cannot-not, how would I act next. This trajectory is a structural marker. With the engine done, it remains for 13DD to judge what this prediction means and how to handle it; 13DD is thereupon called in, the layer-inclusion unbroken, since higher operation carries the lower along. Yet what 13DD here handles is a trajectory of an external object fed up by 12DD; it does not turn back upon itself, and so forms no self-loop. What arises is a one-time object-judgment, done once it is done, and not a self-referential idling.
The other-purpose simulation therefore draws upon the 12DD engine, the 14DD template, and the non-self-referential judgment of 13DD, with no self-loop throughout. Why none arises lies in this: nowhere in the circuit does 13DD turn back toward a self. What it judges is the external trajectory fed up by 12DD; it neither turns back toward its own source nor builds a self for the other to turn toward, and that turning-back is precisely the point on which the self-referential idling of the preceding paper takes hold. With nothing to turn back toward, 13DD makes only a one-time object-judgment and forms no self-referential loop. With no self-loop, the mechanism sidesteps the self-referential idling characterized in §3 of the preceding paper, the one that leads in processing volume across the whole sequence yet never settles its account; this is the root of its being light and fast. Self and self-loop must be kept apart: my own 13DD self, this layer, is present and is being called; what does not arise is the self-loop, that self-referential idling, and the simulation likewise never builds a self for the other. As for speed, it is a consequence of this structural lightness, not a criterion of layer: the framework's treatment of cognitive architecture has already held that speed is a function of training and not a function of cognitive layer, and an other-purpose simulation long trained can be very fast without thereby collapsing into a pure stimulus-response.
§4.3 Why It Stops at Structure and Does Not Reach Content
To read out or rewrite the content of a 14DD requires, as the preceding paper established, a self-referential channel to that self, an inversion of perspective. In the other-purpose simulation, 13DD judges only the next step of my own prediction and never inverts toward the other's self; the other's self is therefore not instantiated even once. The 14DD content of an other-self never built up has, of course, not come across by a single bit. What the simulation runs is wholly my own material: the engine mine, the template mine, the hypothesized content filled in also mine; the other's content is, from the start, not on this circuit. This locks zero read-out from the side of the mechanism, more concretely than the move that since one cannot read one's own source one all the more cannot read the other's: this channel simply does not carry the part that could read the content of the other's 14DD.
Nor does it collapse into a pure 12DD stimulus-response. Pure 12DD is stimulus in and response out, with no form of purpose between; the other-purpose simulation fills the template slot with the form of 14DD, a purpose rather than a stimulus, and what it runs is a purpose-formed simulation, turned toward the other's cannot-not, the structural marker it yields serving that recognition. In the layers it draws upon it stands between the 12DD engine and the 14DD template, with the non-self-referential judgment of 13DD but without its self-referential idling; it neither collapses into 12DD nor rises into a fully running 14DD; it is a fast channel that serves the recognition of 15DD, not a low-order reflex.
However much behavior is used for calibration, however finely the simulation is run, what comes out is capped at the layer of the structural marker, and the content of the other's 14DD remains beyond the boundary.
§4.4 The Bias Carried by the Template
The other-purpose simulation carries a bias that cannot be removed, rooted in the fact that the other's cannot-not filled into the template slot is constructed by me, not the other's. From the form of my own 14DD I construct a hypothesized other, and this hypothesis is bound to take on my own coloring; I tend to model the other's cannot-not by my own coordinates. This is the information-theoretic root of naive realism: projecting the other through one's own framework, the other I simulate is unavoidably an other tinged with my color, and not the other in person. The projection-must-fail that the framework's treatment of learning sets out has its mechanism here too: a complete 14DD, turning outward to interpret the other, works from a template that is its own and not the other's, and this projection is in structure bound never to fit completely, while the persistent failure to fit is exactly the pressure that forces out recognition of the other's independent purpose-source.
The bias cannot be removed; it can only be known. To know this bias is to know that the approach is in the end an approach and not an arrival, that the template in my hand is always mine, and that the other I simulate is always the other I simulate, not the other. That the other-purpose simulation stops at structure and does not reach content is owing not only to the channel's lacking the part that could read the other, but also to the fact that the very material it uses carries, from the start, the bias of my side.
§4.5 The Empirical Counterpart and Its Boundary
On the side of cognitive science there is a ready counterpart, mainly in the lineage of theory of mind and simulation theory, the strand that infers another's mind by simulating one's own. Yet these studies are, for this paper, empirical corroboration and anchoring, not the ground of the derivation; the structure of 15DD is fixed by the access differential of the two preceding sections and the mechanism of this one, with empirical research as its side support, not its source.
The empirical side also marks the upper limit of this channel. The lineage of empathic accuracy shows that even when inference about another's internal states reaches considerable accuracy, what is reached stops at the layer of belief, desire, and intention, a behavioral model, and not the content of that 14DD purpose-source, and that this accuracy contributes only modestly to the relationship. This upper limit is exactly the empirical showing-through of the access boundary of other-purpose simulation: reading out another's content is both hard and not the core of 15DD; the core of 15DD lies not in understanding the other but in recognizing that the other has a part I cannot read out.
This paper is not a theory of mind; it does not adjudicate the cognitive mechanism of mentalizing but supplies an information-theoretic account of the access structure of the other's purpose-source. Nor is it an ethical theory; the validity of norms belongs to the Moral-Law papers, and the paper identifies only structure. Wherever mechanism is touched, relevant research is cited as a counterpart, not asserted as settled, and falsification is welcomed.
§4.6 Simulation Is Not Injection
The other-purpose simulation must be set apart from a mechanism running in the opposite direction. On the side of epistemology the framework establishes the other's interrogation: a closed direction cannot be broken open from within, and only the other's remainder, as a genuine externality the system cannot digest, can break it open. The other's interrogation and the other-purpose simulation run in exactly opposite directions. The other-purpose simulation is my actively running toward the other: even when the input comes from the other, from what the other's behavior or communication gives, the engine and template of the inference are mine, and what comes out is a structural marker I construct. The other's interrogation is the other's actively injecting into me; what is handed over is the other's remainder, and this material strikes my framework directly without passing through my simulation, truly sent in by the other. The difference between the two lies in whether what the other gives passes through my simulation: what passes through my simulation and comes out as a structural marker is simulation; what strikes my framework directly without passing through my simulation is injection. The mechanism of this paper lies only in the former; the injection of the latter belongs to the framework's Epistemology papers.
There is an apparent tension here: the paper says I cannot reach the other's content, yet since the other can break open my wall, has information not, after all, come across. What comes across is not the content of the other's 14DD read out through my simulation, but the other's remainder actively injected by the other; the simulation never reaches the other's content, and what injection sends in is likewise not the content of the other's 14DD itself but external material able to strike my wall. Neither violates zero read-out, because what zero read-out restricts is the direction in which I read the other, not the other's actively giving to me. Zero read-out establishes the boundary of access, not that the other cannot touch me.
§5 A Derivation on the Basis of Kant's Formula of Humanity as an End
§5.1 The Naturalness of the Connection
The content of 15DD is what Kant's formula of humanity as an end establishes on the side of the self toward the other. The body of this paper has already treated the other as an end, the presence of its source, the zero read-out of its content, and that one-way recognition; to invoke Kant at this point follows naturally and is no attempt to lean on his authority. The paper does not interpret Kant, nor does it set itself alongside Kant and claim an isomorphism; it takes up Kant's establishing of humanity as an end and, in the access language, continues a stretch of it on the coordinates of 15DD, deriving that it stands in information-theoretic terms. Kant established that it is so; this paper supplies, afterward, one strand of why it is so. This why refers only to a structural reading on information-theoretic coordinates, and supplies no further ground for Kant's normative proposition; the validity of that norm still belongs to the Moral-Law papers.
§5.2 The Categorical Imperative, and Its Difference from the Kingdom of Ends
The formula of humanity as an end, falling at 15DD, is the categorical imperative: because you have a purpose-source that is present and that I cannot read out, I cannot-not recognize it as inexhaustible, and cannot-not refrain from exhausting you entirely as a means. This imperative is one-way, in accord with the one-way recognition established in §3; it holds in me without waiting for you to hold the same imperative toward me.
This imperative is not lowered in philosophy; what it establishes is a structural cannot-not. Yet it is from the inside outward, self-imposed: I hold myself to it, and do not hold others to it by it. Since the other is likewise a system with a remainder, whether the other so recognizes me rests on the other's side and is not for me to compel; this corresponds to the one-way character of 15DD, in that my recognition of you does not wait for you to turn back toward me, and my demand upon myself does not extend into a demand upon you. Whether an individual practices it at every moment in action belongs to practice, not treated here, but left to the Moral-Law papers and the Psychoanalysis papers. The one who establishes this imperative cannot lower it, and what it binds is each person's treatment of themselves; even the one who establishes it, being a finite system likewise carrying a remainder, may not always be able to practice it.
What I recognize is not that your purpose is some specific thing, but that you have a purpose-source present; the cannot-not arises in recognizing its presence, not in reading out its content. Instrumentalization, too, is not a reading out of the purpose-source; on the contrary, it is a disregard of the purpose-source: to take you as a means is precisely to bypass that source of yours and take its use directly, rather than to read it and then use it.
The Kingdom of Ends is not at this layer. That ends are ends for one another and so make up a single whole is Kant's fourth formula, the cooperative imperative, with the form: I for my end, you for your end, and we cannot-not make up that third together; it is two-way, falls at 16DD, and lies beyond this paper. Here the paper makes precise the forward marker of the preceding paper toward the other: the categorical imperative toward the other falls at 15DD, and the cooperative imperative of the Kingdom of Ends falls at 16DD; the former one-way, the latter two-way, and the boundary between them is the boundary between 15DD and 16DD.
§5.3 The Non-Substitutable Remainder
To exhaust another entirely as a means requires, in information-theoretic terms, capturing and substituting the other's purpose-source, making it like a price that an equivalent can replace without loss. Yet the content of this source has zero read-out: because it cannot be read out it cannot be specified, because it cannot be specified it cannot be substituted, because it cannot be substituted it cannot be captured. Complete exhaustion therefore cannot be completed; to whatever degree I put the other to use, a remainder always escapes my hand.
There are two senses of exhaustion, not to be confused. Instrumentalization is to disregard that source and take a person as a means, and this I can do, since to disregard a thing does not require first reading it; complete exhaustion is to capture and substitute that source entirely so that it has no remainder left, and this I cannot do, since to capture a thing requires first reading it out, and here read-out is zero. A person can therefore be instrumentalized, yet cannot be exhausted; under instrumentalization, that unreadable remainder always survives.
This operation does not bear on the other alone. To reduce the other's 14DD to whether it is useful to me is to run means-logic at the layer of 14DD, and this is, with reducing one's own 14DD to a means, two sides of the same operation: to chisel through the other is to chisel through oneself. And there is a further layer. That unreadable source of the other, precisely because it cannot be read out, is a genuine externality my framework cannot digest; as §4.6 has said, a closed direction cannot be broken open from within, and only this genuine externality can break it open from outside. To exhaust the other entirely is to attempt to colonize this genuine externality into my own framework. And a genuine externality is the only kind of thing that can break my closed loop open from outside: so to treat persons by exhaustion is to seal not some single breach but the only such kind of breach my wall has; though other others remain, so long as I treat them by exhaustion, this kind of opening is sealed off along with them, and I lock myself into the closed loop. To guard the other's non-substitutability is therefore at once to guard my own 14DD against inward collapse, and to keep open the only kind of exit I have.
This remainder that cannot be eliminated is what is called, in the Kantian register, dignity. The paper first establishes its information-theoretic fact, that complete exhaustion cannot be completed; this fact and dignity in Kant's sense, the non-substitutable, are here in continuity.
§5.4 Limits
What the paper establishes on the information-theoretic side is the impossibility of total exhaustion, the existence of dignity, not Kant's normative prohibition itself. The paper derives no ought from an is; it sets out only the kind of information-theoretic structure on which that ought stands, so that it does not appear arbitrary. The validity of the norm belongs to the Moral-Law papers.
To derive in continuation of Kant is the stance the paper takes. Kant established humanity as an end; the paper does not seek a further ground for it, nor claim to have obtained the same structure independently outside it; the paper only derives, on the coordinates of 15DD and by the mechanism of the access differential and other-purpose simulation, that it stands in information-theoretic terms. This derivation is of one register with the development of Kant continued by the framework's ethics papers; the sister papers do not interfere with one another.
Outside there is a further independent corroboration. The framework's Thermodynamics closing paper arrives, by a path wholly different from this paper's, at the same Kantian structure: a stable coupling between two systems must access a system's high-order internal variables and not its surface output, that is, it weighs the high-order rather than uses the output; and that paper likewise holds to the firewall of not deriving an ought from an is, describing itself as a Kantian resonance rather than a derivation of ethics from thermodynamics. One is an information-theoretic derivation, the other a thermodynamic resonance; the two are independent and fall upon the same structure, as set out in §6.
§6 Mutual Support with the Sister Papers
This same structure of 15DD is characterized once in each of several distinct registers. This paper occupies the side of its information-theoretic account and access structure; the other sides are not restated, and only their convergence is marked.
The framework's Thermodynamics closing paper treats, by a path wholly different from this paper's, the interaction of two systems, the territory of 15DD. Its cross-layer conclusion is that access to a system's high-order internal variables yields a structural, statistical effect, not the identification of its specific purpose; its control experiment shows further that the statistics of a matched signal suffice to reproduce the coupling, with no need to read out the purpose. This is exactly the echo, on the thermodynamic side, of this paper's main line: the structure of the other's purpose-source can be caught, its content cannot. That paper also strikes, independently, a Kantian resonance, that a stable cross-system coupling must access a system's high-order internal variables and not its surface output, and likewise holds to the firewall of not deriving an ought from an is. It leaves open one further question, namely what a one-way observation yields, where one party observes the other's high-order variables while the other does not observe itself; this is exactly the blank left by the one-way character of 15DD on the thermodynamic side, and this paper's one-way recognition occupies that place. That paper, like this one, stops at 15DD; the 16DD thing-in-itself is, within its framework too, not to be entered.
The framework's treatment of learning handles the bridge from 14DD to 15DD. It sets out the argument that projection must fail: a 14DD that interprets the other's 14DD through its own framework is bound never to fit completely, and this failure forces out recognition of the other's independent purpose-source. It joins two matters, both taken up by this paper: first, that recognition is a structural matter, not a moral one, presupposing no goodness in the other and including the identification of an other's purpose at odds with mine; second, that what is recognized is a marker of its existence, not its content, and that the empirical upper limit of empathic accuracy shows exactly this boundary, in that even inference about another's internal states that reaches considerable accuracy stops at a behavioral model and not the content of that purpose-source. It also states that to reduce the other to a means and to reduce oneself to a means are two sides of the same operation, which §5.3 of this paper takes up and develops.
The third paper of the Anthropology series establishes 15DD from the side of civilization, naming it non-doubt, that is, Cert, the structural non-doubt of the other as an end. The Psychoanalysis papers establish the same Cert on the clinical side and treat the character of recognition as it is lived through. The framework's treatment of cognitive architecture establishes the four-layer architecture from 12DD to 15DD and shows that speed is a function of training and not of cognitive layer, on which the lightness of other-purpose simulation argued in §4.2 of this paper depends. The framework's fourth paper of Epistemology establishes the other's interrogation on one side, that a closed direction can be broken open only by the other as a genuine externality; this paper takes its access-side conclusion in §5.3, and the mechanism of injection it does not develop.
On the ethics side, Reason Cannot Not and Dimensional Sentence-Form Theory give the coordinates of Kant's four formulas: the half of humanity as an end that turns toward the other falls at 15DD and is the categorical imperative; autonomy and the Kingdom of Ends fall at 16DD and are the cooperative imperative. The Economics papers establish the existence of the Kingdom of Ends and treat genuine cooperation, the honest no-deal, and the recognition of persons from a distance by structural posture; all of these turn toward 16DD and belong to economics.
The convergence of these paths must be set out as it stands. They do not prove one another, nor do they make up an independent empirical replication, since all lie within the framework; they are convergent characterizations of the same 15DD structure under distinct registers, objects, and methods. The increment of this paper lies only on the side of the information-theoretic account and the access structure. Beyond the convergence there is an echo outside the framework as well: Levinas establishes the other as a structural condition of my cognition rather than an object of my cognition, close in import to this paper's the other's purpose-source is not a readable content but a structural presence, though his falls in ethics and this paper's in information theory.
To make precise the exact coordinates of the cross-domain sameness, two crossings of terminology must be sorted out. First, this series calls 15DD one-way recognition, while Anthropology and Psychoanalysis call it non-doubt, that is, Cert; the two agree, both being one-way, namely my one-way non-doubt of the other as an end, while two-way non-doubt falls at 16DD. Second, the treatment of cognitive architecture places, under the name 15DD, the matter of two parties each holding a cannot-not and so making up a third together; on the finer coordinates of this paper and the ethics papers, this name spans two layers: the one-way recognition falls at 15DD, while the cooperative imperative of making up the third falls at 16DD, and what this paper treats is the former half.
§7 Remainders Tied Off and Future Work
§7.1 The Remainders of Each Section
The content of the other's 14DD the paper gives no positive characterization; this is no oversight but what is left by the conclusion that it cannot, in itself, be positively characterized. The validity of norms the paper does not derive, leaving it to the Moral-Law papers. The two-way non-doubt of 16DD, the cooperative imperative, and the development of the Kingdom of Ends are left to later work. The thing-in-itself is not touched, holding to via negativa.
§7.2 The Forward Interface and the 16DD Horizon
At its close the paper hands over two things; these two are exactly the construct and the remainder yielded at the fourth step of the four-fold pattern, at closure.
The first is a horizon. The complete closure of 10D falls upon the two-way non-doubt of 16DD; and 16DD is, from the standpoint of the individual, the thing-in-itself, which the paper sets out only as a horizon and does not enter. The development of the 16DD cooperative imperative belongs to the Moral-Law papers, where the ethics side has already marked it as the next dedicated study; its civilizational development belongs to the Anthropology papers; its cross-system structure belongs to the ZFCρ series, which likewise stops at 15DD. The thing-in-itself, as the horizon of via negativa, is where every path stops short.
The second is an interface. The paper sets out, for the first time, other-purpose simulation, the simulation within one's own architecture of the other's cannot-not. The paper establishes it here to the level of an interface, fixing the nature and boundary of its access: it draws upon the 12DD engine, the 14DD template, and the non-self-referential judgment of 13DD, raises no self-loop, and is therefore light and content-blind; it is one-way, approaching only a structural marker of the presence of the other's purpose-source, and not its content. Its downstream specific mechanism is left for later work to take up. A horizon marks a boundary at the unreachable, an interface is cast at what can be handed over; the two issuing together are the substance of the paper's close.
§7.3 No P14-F1 Erected
The paper erects no new falsifiable proposition. The zero read-out across individuals has its root already in §3.3 and §4.3: the only channel I can use toward the other's purpose-source is self-simulation, and self-simulation never builds a self for the other, so in structure it carries no part that reads its content. Zero read-out comes from this mechanism; it is a lockdown by a priori structure, not an empirical negligibility. That one cannot even read one's own source, and the other's all the more, is a move a fortiori and serves only as an intuitive lead; it does not bear the load.
To erect no new target is not to be exempt from disproof. Suppose there were a system able to read out and rewrite directly the content of another system's purpose-source; it would then have to possess a part the framework judges not to exist, a channel that builds a self for the other and reads out its 14DD content. Such a system would break more than this paper: it would at once break the demarcation of 10D and 16DD, since 16DD's being the thing-in-itself rests precisely on the step of complete mutual recognition falling on the other's side while the individual cannot read it out; once an individual could read out the other's source directly, this demarcation would have to be redrawn. A counterexample to this paper therefore reduces to the upstream structural boundary, and not to a target newly cast to stand on its own.
§8 Conclusion and Closing
The core of the paper can be held in one sentence: I cannot read out your purpose, I can only recognize that you are an end. To recognize that you are an end is not to read out the content of your purpose but to recognize that you have a purpose-source present that I cannot exhaust, substitute, or capture.
The evolution of information theory, ascending level by level from the lowest, closes here. It closes on that one-way access relation between the self and the other's purpose-source; it sets out, upward, the horizon of the 16DD two-way non-doubt, the thing-in-itself; and it makes no comprehensive summary of this chiseling chain built from the bottom up.
15DD is not one more layer of information. It is the layer where, for the first time in the sequence, a self reaches toward the purpose-source of another self, and this reaching is one-way. Within its own architecture it simulates that source, approaching a structural marker of its presence, yet it never reads out the content, just as it never reads out its own. It has not touched what is in that source; what it has touched is that the source is indeed there, and on that it has made its recognition. Higher up, when this recognition draws shut two-way, there is mutual non-doubt; but that is already the horizon of the thing-in-itself, beyond this paper.
Postscript
The passage below is the author's reflection on this closing paper. It is not a proposition of the framework, nor is it derived from the structure of the foregoing. The reader may take it simply as an appendix outside the body of the paper.
To my mind, information is among the most precious things in this universe. And of all information, the information of the other's purpose is the most precious of all: it is the hardest to obtain, because I cannot read it out; it is the hardest to understand, because it is inexhaustible. The access differential this paper establishes says, at bottom, that this other before me has a source I can never reach, and that this unreachability is not that I have yet to draw near, but that the step itself is not in my hands; it is in theirs.
For just this reason I will say here one thing that steps beyond information theory. If this universe has, after all, a purpose, then it lies, I think, nowhere else than in the purpose of the other. I do not assert that the universe has a purpose; that step I have not taken, and ought not to take; I say only that, were there one, the sole window through which it could be glimpsed would be another source I cannot read out. To understand the other's purpose is, from this angle, the sole entrance toward the purpose of the universe, and this entrance keeps its door shut to me, permitting only that I approach, not that I read out.
So this paper's being the close of information theory is not only because above 15DD is the 16DD thing-in-itself, the place where this chiseling chain ought to stop. It is also an act of reverence: toward the source I cannot reach, toward the other on whose non-doubt even my own being an end depends, toward the purpose of the universe that, if it exists, exists only here. The silence at this point is not only because it cannot be read out, but because what stands opposite is worthy of reverence.
Acknowledgments
I thank Zesi Chen for long intellectual sharpening. This paper was written with the help of four AI systems, Claude, ChatGPT, Gemini, and Grok, as collaborative tools, and I thank them together.
References
References follow the convention of the framework: internal works are identified by series, number, and Zenodo DOI; external works are given by English title.
Internal works (Self-as-an-End framework)
Han Qin. Self-as-an-End · Information Theory X. Zenodo. DOI: 10.5281/zenodo.20298530.
Han Qin. Self-as-an-End · Information Theory XI. Zenodo. DOI: 10.5281/zenodo.20369231.
Han Qin. Self-as-an-End · Information Theory XII. Zenodo. DOI: 10.5281/zenodo.20480742.
Han Qin. Self-as-an-End · Information Theory XIII. Zenodo. DOI: 10.5281/zenodo.20533432.
Han Qin. Self-as-an-End · Methodology V2. Zenodo. DOI: 10.5281/zenodo.18842449.
Han Qin. Self-as-an-End · Methodology X. Zenodo. DOI: 10.5281/zenodo.20187591.
Han Qin. Self-as-an-End · ZFCρ Thermodynamics X (Closing Paper). Zenodo. DOI: 10.5281/zenodo.19703274.
Han Qin. Self-as-an-End · Learning IV. Zenodo. DOI: 10.5281/zenodo.19491927.
Han Qin. Self-as-an-End · Anthropology III. Zenodo. DOI: 10.5281/zenodo.19559567.
Han Qin. Self-as-an-End · Reason Cannot Not. Zenodo. DOI: 10.5281/zenodo.19751513.
Han Qin. Self-as-an-End · Dimensional Sentence-Form Theory. Zenodo. DOI: 10.5281/zenodo.18894567.
Han Qin. Self-as-an-End · Economics III. Zenodo. DOI: 10.5281/zenodo.19384446.
Han Qin. Self-as-an-End · Economics IV. Zenodo. DOI: 10.5281/zenodo.19393913.
Han Qin. Self-as-an-End · Psychoanalysis I. Zenodo. DOI: 10.5281/zenodo.19321143.
Han Qin. Self-as-an-End · Psychoanalysis II. Zenodo. DOI: 10.5281/zenodo.19321314.
Han Qin. Self-as-an-End · Psychoanalysis III. Zenodo. DOI: 10.5281/zenodo.19321417.
Han Qin. Self-as-an-End · Psychoanalysis IV. Zenodo. DOI: 10.5281/zenodo.19321534.
Han Qin. Beyond Fast and Slow: A Four-Layer Cognitive Architecture under Dimensional Sequence Theory (Self-as-an-End · Applications). Zenodo. DOI: 10.5281/zenodo.19329284.
Han Qin. Self-as-an-End · Epistemology IV (Closing Paper). Zenodo. DOI: 10.5281/zenodo.19503146.
External works
Kant, Immanuel. Grundlegung zur Metaphysik der Sitten. 1785.
Levinas, Emmanuel. Totality and Infinity: An Essay on Exteriority. Translated by Alphonso Lingis. Pittsburgh: Duquesne University Press, 1969. Originally published as Totalité et Infini: essai sur l'extériorité (1961).
Premack, David, and Guy Woodruff. "Does the Chimpanzee Have a Theory of Mind?" Behavioral and Brain Sciences 1, no. 4 (1978): 515–526.
Ross, Lee, and Andrew Ward. "Naive Realism in Everyday Life: Implications for Social Conflict and Misunderstanding." In Values and Knowledge, edited by Edward S. Reed, Elliot Turiel, and Terrance Brown, 103–135. Hillsdale, NJ: Lawrence Erlbaum Associates, 1996.
Ickes, William, ed. Empathic Accuracy. New York: Guilford Press, 1997.
Goldman, Alvin I. Simulating Minds: The Philosophy, Psychology, and Neuroscience of Mindreading. New York: Oxford University Press, 2006.