Reason Cannot Not: An SAE Refinement of Kant’s Four Formulations of the Categorical Imperative
理性不得不：SAE对康德四定言律令的句式精细化

Die Vernunft kann nicht nicht: Eine SAE-Verfeinerung von Kants vier Formeln des kategorischen Imperativs

理性不得不：SAE对康德四定言律令的句式精细化

Han Qin (秦汉) · Independent Researcher · 2026

DOI: 10.5281/zenodo.19751513

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Abstract

This paper offers a sentence-form-theoretic refinement (satzformentheoretische Verfeinerung) of Kant's four formulations of the categorical imperative — the formula of universal law, the formula of humanity as end in itself, the formula of autonomy, and the formula of the kingdom of ends — within the SAE 15DD-16DD coordinate. It rewrites Kant's four "ought"-modal formulas as four "cannot not" 15DD-16DD ontological statements, establishing SAE ethics as a refinement (Verfeinerung) of Kantian ethics at the sentence-form layer.

The paper takes its starting point from Metaphysics of Self-as-an-End: Dimensional Sentence-Form Theory (metaphysics-satz, DOI 10.5281/zenodo.18894567), which provided a compressed diagnosis of Kant's four formulations in §VI Ray 1 — that all four use the 14DD imperative structure "Handle so, daß…" to carry 15DD-16DD content, yielding the overlap of error-type II (instrumentalization) and error-type IV (alterity erasure). The present paper expands this compressed diagnosis into a complete account: each of the four formulations carries three specific 14DD residues (twelve in total), plus four shared sentence-form features common to all four (ought-modal, subject-object separation, hypothetical-or-counterfactual position, mediating faculty).

The refinement gives:

I. Reason cannot not reason (corresponding to Kant's first formulation: universalization / form);

II. Reason cannot not develop (as the concrete operating mode of autonomy as background);

III. Reason cannot not have direction, that is, purpose (corresponding to Kant's second formulation: humanity as end / matter);

IV. Reason cannot not be interrogated (corresponding to Kant's fourth formulation: kingdom of ends / system; standing in an engine-produces relation to 16DD cooperative imperative).

Autonomy (Kant's third formulation) is not listed as a fifth clause but instead serves as the common background (Hintergrund) running through all four — preserving the core position of Kant's autonomy principle while elevating it from "side-by-side third" to "permeating four." This treatment liberates autonomy from Kant's restriction to the will (Wille) as a specific faculty, expanding it into the operating mode of the 15DD subject across all dimensions (cognition, faith, imperative, cooperation).

The paper places existing SAE works within this refined coordinate: A16 One's Own Law (DOI 10.5281/zenodo.19037566) as the complete unfolding of clause III; Kategorischer Glaube (DOI 10.5281/zenodo.19719083) as the manifestation of autonomy-as-background on the inward-facing side of 15DD. Together, A16 and Kategorischer Glaube constitute the outward-inward duality of autonomy at 15DD. A complete elaboration of clause IV (the 16DD cooperative imperative as a standalone treatise) is identified as the next position in SAE ethics, not addressed in the present paper.

SAE is not founded outside Kant; it is the continued unfolding of Kantian ethics with 21st-century tools (the dimensional sentence-form sequence, the chisel-construct cycle, the remainder ρ, the cannot not modal). Kant did the most precise work he could with 18th-century tools; the further refinement here depends on tools that did not yet exist in his time.

Keywords: categorical imperative; Reason cannot not; Vernunft kann nicht nicht; Kategorischer Imperativ; four formulations refinement; formula of universal law; formula of humanity as end; formula of autonomy; formula of kingdom of ends; SAE refinement of Kant; 15DD-16DD sentence-form theory; 14DD residue diagnosis; metaphysics-satz; Verfeinerung

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Terminology

SAE term	German	English	Sentence-form / Kant correspondence
理性不得不理性	Die Vernunft kann nicht nicht vernünfteln	Reason cannot not reason	First formulation (universalization / form)
理性不得不发展	Die Vernunft kann nicht nicht sich entwickeln	Reason cannot not develop	Concrete operating mode of autonomy-as-background
理性不得不有方向，即目的	Die Vernunft kann nicht nicht eine Richtung haben, d.h. einen Zweck	Reason cannot not have direction, that is, purpose	Second formulation (humanity as end / matter)
理性不得不被追问	Die Vernunft kann nicht nicht befragt werden	Reason cannot not be interrogated	Fourth formulation (kingdom of ends / system)
自律作为底色	Autonomie als Hintergrund	Autonomy as background	Third formulation (autonomy / source): position re-distribution from "parallel third clause" to "running through all four"

A note on vernünfteln: this verb has, both in Kant's own usage and in the broader philosophical tradition, the neutral sense of "exercising reason" or "carrying out rational thought." In ordinary German it sometimes carries a slightly pejorative connotation (referring to petty rationalization). The present paper uses the term in its philosophical-tradition neutral sense — equivalent to Vernunft vollziehen (carrying out reason) — paralleling the Chinese "理性不得不理性" and English Reason cannot not reason in their use of the noun-as-verb structure: the subject's rationality persistently operates itself as rational.

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I. Kant's Four Formulations: Four Faces of One Categorical Imperative

I.1. Kant's Own Account of the Relation Among the Four Formulations

In Grundlegung zur Metaphysik der Sitten, Kant gives multiple formulations of the categorical imperative. Philosophical tradition typically distills these into four (or three plus a corollary), each expressing the same imperative from a different angle.

First formulation: formula of universal law (Formel des allgemeinen Gesetzes)

> Handle nur nach derjenigen Maxime, durch die du zugleich wollen kannst, dass sie ein allgemeines Gesetz werde.

>

> Act only according to that maxim by which you can at the same time will that it become a universal law.

This formulation views the categorical imperative from the side of form — the formal condition for a maxim to qualify as a moral law: it must be universalizable, that is, capable of being thought as a universal law without self-contradiction or volitional impossibility. This is a purely formal test on maxims.

Second formulation: formula of humanity as end in itself (Formel der Zweckmäßigkeit)

> Handle so, dass du die Menschheit sowohl in deiner Person als in der Person eines jeden anderen jederzeit zugleich als Zweck, niemals bloß als Mittel brauchst.

>

> Act in such a way that you treat humanity, whether in your own person or in the person of any other, always at the same time as an end, never merely as a means.

This formulation views the categorical imperative from the side of matter — what content the imperative constrains. The content is not a list of specific actions but a regulation concerning the object toward which action is directed: it must be directed toward persons (rational beings) as ends in themselves. Note the word bloß (merely) — Kant does not prohibit instrumental use; he prohibits treating persons merely as means, erasing their dimension as ends in themselves.

Third formulation: formula of autonomy (Formel der Autonomie)

> Handle so, dass der Wille durch seine Maxime sich selbst zugleich als allgemein gesetzgebend betrachten könne.

>

> Act in such a way that the will can through its maxim regard itself at the same time as universally legislating.

This formulation views the categorical imperative from the side of source — where the imperative comes from. The answer: from the rational subject itself. The rational subject is both legislator and subject; this identity of legislating and being-subject-to constitutes autonomy (Autonomie). This stands opposed to heteronomy (Heteronomie, receiving law from outside). Kant's central ethical thesis — that human dignity rests on autonomy — is concentrated in this formulation.

Fourth formulation: formula of the kingdom of ends (Formel des Reichs der Zwecke)

> Handle so, als ob deine Maxime durch deinen Willen zum allgemeinen Naturgesetze werden sollte.

>

> Act in such a way that your maxim could always be regarded as a maxim of universal legislation belonging to the kingdom of ends (das Reich der Zwecke).

This formulation views the categorical imperative from the side of system — what kind of community emerges when all rational subjects act autonomously and treat one another as ends. The answer: the kingdom of ends — a community in which all rational subjects mutually recognize one another as legislators and ends in themselves. This is the systemic figure that emerges when the first three formulations operate together at their limit.

Kant himself states explicitly in Grundlegung that the four formulations express the same categorical imperative from different angles — a maxim that can be universalized (first) must respect all rational subjects as ends in themselves (second); the source of such universalization can only be the autonomous self-legislation of rational subjects (third); all such autonomous legislators together constitute the kingdom of ends (fourth). The four formulations are not four parallel imperatives but the same imperative unfolded in four perspectives.

I.2. The Task of This Paper

The task of this paper is not to challenge Kant's structural claim but to refine it at the SAE 15DD-16DD sentence-form level. The problem is not Kant's content — the content itself is accurate at 15DD-16DD (the rational self-consistency of the first formulation, the humanity-as-end of the second formulation in 15DD, the autonomy principle of the third formulation running through 15DD-16DD, and the kingdom of ends of the fourth formulation in 16DD). The problem is Kant's sentence-form. The content of the four formulations distributes across 15DD and 16DD, but their sentence-form remains uniformly stuck at the 14DD imperative structure.

SAE has performed sentence-form diagnoses on Kantian concepts in earlier papers (cf. A16 One's Own Law, DOI 10.5281/zenodo.19037566; Kategorischer Glaube, DOI 10.5281/zenodo.19719083, §I, on Vernunftglaube). The finding there: Kant's Du sollst (you ought) modal is a 14DD sentence-form (the imperative/hypothetical structure of the purpose-anchoring layer), not a 15DD sentence-form (the cannot not of the ontological layer). The same content under different sentence-forms carries entirely different semantic weight. "You ought to treat the other as an end" (14DD) and "the other's noumenal presence leaves me with no option of not doing B" (15DD) are the same content expressed at two different sentence-form layers.

The present paper extends this work to all four of Kant's formulations. Each formulation has 15DD-or-16DD content paired with 14DD sentence-form. The task is to redo the four formulations at the 15DD-16DD sentence-form layer, matching sentence-form to content. This is the satzformentheoretische Verfeinerung (sentence-form-theoretic refinement) that SAE performs upon Kant's categorical imperative.

I.3. The Position of This Paper Within the SAE Series

The starting point of this paper is Metaphysics of Self-as-an-End: Dimensional Sentence-Form Theory (metaphysics-satz, DOI 10.5281/zenodo.18894567). That paper established the dimensional-sentence-form isomorphism (0DD-16DD) as SAE's foundational coordinate, and in §VI Ray 1 (Kant's Imperatives) gave a first compressed sentence-form diagnosis of Kant's four formulations:

> Kant's three formulations all use the sentence-form Handle so, daß… — the imperative structure of the purpose-hypothetical imperative. The second formulation attempts to express the absolute imperative (15DD) in content; the third formulation attempts to express the cooperative imperative (16DD) in content. But both use 14DD sentence-form. This constitutes the overlap of error-type II (instrumentalization) and error-type IV (alterity erasure): he wrote cannot not as ought, and wrote bilateral-subject structure as unilateral-subject command. Kant saw what was right — humans are ends, not merely means. But the only tools he had for writing it down were 14DD sentence-forms. The pearl was at 15DD-16DD; the casket was at 14DD.

The diagnosis in metaphysics-satz is a compressed version — it identifies that Kant uses 14DD sentence-form to carry 15DD-16DD content, but does not unfold the specific residues of each individual formulation. The task of the present paper is to expand this compressed diagnosis into a complete account: what specific 14DD residues each of the four formulations carries, and what the corresponding SAE 15DD-16DD sentence-form should look like.

The metaphysics-satz correspondence between Kant's formulations and SAE layers:

• Second formulation (humanity as end) → absolute imperative (15DD): the other's purpose is A, so I cannot not do B
• Third formulation (autonomy) and fourth formulation (kingdom of ends) → cooperative imperative (16DD): I for purpose A, the other for purpose B, we cannot not do C

The first formulation (universalization) was not assigned to a specific SAE layer in metaphysics-satz. The present paper argues: the substance of the first formulation is reason's requirement of self-consistency. It does not correspond to any specific layer's content imperative but rather to the operating condition that runs through 15DD-16DD as a whole — reason, in operating as reason, must maintain self-consistency. This is the structural position of clause I "Reason cannot not reason" to be unfolded in §III.

The relation between the present paper and the metaphysics-satz compressed diagnosis must be made explicit, lest readers, encountering §III.2 (clause II as the operating mode of autonomy-as-background) and §IV (autonomy as the background running through all four), experience tension regarding "where does the third formulation actually go?"

The present paper does not overturn the metaphysics-satz compressed diagnosis; it redistributes the diagnostic results at higher resolution. The metaphysics-satz judgment that "the content of the third formulation belongs to 16DD" is accurate at the compressed level — the content of the third formulation (reason as autonomous legislator) does indeed point toward the multi-subject cooperative structure. But at higher resolution, the third formulation contains two components: autonomy-as-principle itself (reason gives itself law — this is the background running through all dimensions) plus the multi-subject realization of autonomy (the cooperative structure in which all autonomous legislators mutually legislate and recognize — this belongs to the fourth formulation, the kingdom of ends, and its 16DD realization in the cooperative imperative). The compressed diagnosis assigned both together to the third formulation; the present paper, at higher resolution, separates them — autonomy-as-principle becomes the background traversing all four clauses (§IV), the cooperative imperative becomes the produce of the fourth formulation in clause IV's engine role (§V.3). After this separation, the content of the third formulation does not disappear but is distributed in a more precise form: as background-form running through all clauses (§IV) and as specific content realized in the fourth formulation's 16DD form (§V.3).

This redistribution makes the paper's overall structure tighter: the compressed diagnosis answers "which Kantian content belongs to which SAE layer"; the present paper answers "in what form (background, clause, engine, produce) each Kantian content distributes within the SAE coordinate." The first kind of precision is layer assignment; the second kind is structural position. The latter is stricter than the former, and provides the latter with independent structural support.

Within this diagnostic framework, several existing SAE papers handle different parts of Kant's four formulations:

• A16 One's Own Law (DOI 10.5281/zenodo.19037566) — the 15DD sentence-form refinement of the second formulation (humanity as end). The absolute imperative as "the other's purpose is A, so I cannot not do B" — moving Kant's "you ought to treat the human as an end" from 14DD to 15DD sentence-form.
• Kategorischer Glaube (DOI 10.5281/zenodo.19719083) — the unfolding of the autonomy principle on the inward-facing side of 15DD. Categorical faith as the subject's non-externalizable bearing of its own standing, manifesting autonomy in the dimension of faith (rather than the dimension of will). The paper notes that categorical faith's "autonomy" is more foundational than Kant's volitional autonomy — it is the operating mode by which the subject stands as subject at all.
• The 16DD cooperative imperative (defined complete in metaphysics-satz: I for purpose A, the other for purpose B, we cannot not do C) — the 15DD-16DD realization of the third formulation (autonomy in plural form) and the fourth formulation (kingdom of ends). C does not belong to A nor to B; it is the action forced into being by the meeting of two independent purposes — the non-idealized concrete structure of Kant's kingdom of ends.

But to date, SAE has not done one piece of work: placing Kant's four formulations as a unified whole within the SAE sentence-form coordinate, performing a coordinated unfolded diagnosis and refinement. The metaphysics-satz initiated this work but only at compressed resolution; A16, Kategorischer Glaube, and the scattered 16DD discussions in various papers each handle one part of the four formulations. The internal relations among the four formulations — as four faces of the same categorical imperative — have not been completely re-articulated on the SAE side. The present paper fills this gap.

As an integrative declaration, the present paper does three things:

(i) Expand each of Kant's four formulations' 14DD residues into a complete account, building on metaphysics-satz's compressed diagnosis (§II).

(ii) Provide the SAE refinement of the four formulations as four "Reason cannot not" statements at the 15DD-16DD sentence-form layer (§III).

(iii) Display, within this refined structure, the specific positions occupied by existing SAE papers (A16, Kategorischer Glaube, the future 16DD treatise), making explicit their common Kantian foundation (§V); and provide an integrative declaration of SAE ethics as the 15DD-16DD sentence-form refinement of Kantian ethics (§VI).

SAE is not founded outside Kant; it is the continued unfolding of Kantian ethics under 21st-century tools (the dimensional sequence, the chisel-construct cycle, the remainder ρ, the cannot not modal). It continues Kant's methodology (establishing coordinates, distinguishing the a priori from the a posteriori, grounding in autonomy, using cannot not modal), refining the four formulations at the 15DD-16DD sentence-form layer using tools that did not yet exist in Kant's time.

II. The 14DD Residue Diagnosis of Each Formulation

Terminological note: This paper uses "14DD residue" (14DD-Rest / 14DD residue) to denote a sentence-form mismatch — when a proposition's content belongs to 15DD-16DD but its sentence-form belongs to 14DD (the purpose-anchoring layer, e.g., "ought," hypothetical, command structures), the 14DD sentence-form features become a residue upon the 15DD-16DD content. This term is etymologically aligned with SAE's core concept "remainder" (ρ, Rest); it is also used in the Kategorischer Glaube paper (DOI 10.5281/zenodo.19719083) as the same concept.

The metaphysics-satz §VI Ray 1 has already given a compressed version of the diagnosis of Kant's four formulations: all four use the 14DD imperative structure Handle so, daß…; the second formulation's content is at 15DD; the third formulation's content is at 16DD; the mismatch is the overlap of instrumentalization (error-type II) and alterity erasure (error-type IV). The present section expands this compressed diagnosis: what specific 14DD residues each of the four formulations carries, and what the corresponding SAE 15DD-16DD form should be.

The diagnosis is not a critique of Kant — Kant did the most precise work he could within the philosophical tools of the 18th century. The diagnosis serves to determine what 14DD features SAE must remove when redoing the formulations at the 15DD-16DD sentence-form layer.

II.1. The 14DD Residues of the First Formulation

The formula of universal law: "Act only according to that maxim by which you can at the same time will that it become a universal law."

Residue one: the variant of hypothetical command. "If you want your maxim to be rational, then you ought to make it universalizable" — the condition "you want your maxim to be rational" plus the ought-result "make it universalizable." This is the typical 14DD hypothetical-imperative structure (hypothetical imperative), although Kant himself classifies the formulation as categorical. Categorical in form, hypothetical at depth.

Residue two: the binary structure of maxim and law. Kant posits the distinction between Maxime (subjective principle of action) and Gesetz (objective moral law), then through the universalization test elevates maxims to laws. This binary structure is 14DD — positing one tool (maxim) and one purpose (law), aligning the tool toward the purpose. The 15DD sentence-form does not require this binary — reason's operation itself is rationalizing (vernünfteln); it does not require a process of first having a "subjective maxim" then having it tested into "objective law."

Residue three: Sollst as modal. The formulation "Du sollst..." (you ought) makes the law a command issued from outside to the subject — even when the outside is reason itself acting through autonomy. The 15DD sentence-form does not require this command structure — it is not "reason commands you to rationalize" but "reason cannot not reason"; rationalization is the way reason exists as reason, not the result of being commanded.

The SAE task: rewrite the first formulation from "if your maxim is to be rational, then it ought to be universalizable" (14DD hypothetical structure) to "Reason cannot not reason" (15DD ontological structure) — reason's mode of being as reason already includes self-consistency (the underlying core of universalization), without requiring an external "ought" to demand this consistency.

II.2. The 14DD Residues of the Second Formulation

The formula of humanity as end: "Act in such a way that you treat humanity, whether in your own person or in the person of any other, always at the same time as an end, never merely as a means."

Residue one: the "treat-as" sentence-form. Although this formulation speaks of humans as ends in themselves (15DD content), Kant uses the sentence-form "treat X as Y" (etwas als Y behandeln) — a subject-object-separation processing relation in which the subject "treats" the object as some characterization. The 15DD's "the other in the noumenal mode is present" is not "I treat the other as a noumenon" (which would attribute a property to the other through subjective construal); it is that the other is already in noumenal mode, and my action unfolds under the condition of this presence. The "treat-as" form implies subjective construction; the 15DD form removes this subjective construction — noumenal status is not "treated-as" but is a way of being.

Residue two: the negative qualification "never merely as a means." The principal positive content of this formulation (treat humans as ends) is paired with a negative qualifier (not merely as means). This makes the principle a complex command with an exception clause — humans may be treated as means (instrumental use is permitted), but not merely as means. The word bloß (merely) does much philosophical work, but as a qualifying clause it makes the principle structurally complex — not a pure ontological statement but a mixed structure of "do X, but do not entirely do X." A16's work shows: in the 15DD sentence-form, "the other's noumenal presence leaves me with no option of not doing B" does not require this kind of "permit but not entirely permit" qualification — the condition of subject-as-noumenon-present already determines the structure of action.

Residue three: ends as the object of treatment. Kant places "ends" in the position of the subject's moral judgment — whether to treat something as an end is the subject's moral evaluation. The 15DD position differs: the noumenon is the end, requiring no judgment. Whether one subject acknowledges another subject as a noumenon is not an empirical question of judgment but a question of 15DD-layer ontological structure — for a subject to stand as a 15DD subject already presupposes noumenal recognition of all other 15DD subjects.

The SAE task: rewrite the second formulation from "you ought to treat humans as ends" (14DD judgment form) to "Reason cannot not have direction, that is, purpose" (15DD ontological structure) — reason's operation necessarily has direction, and at the 15DD layer this direction is the noumenal presence of other subjects (the other's purpose entering my constraint). This is also the content of the absolute imperative in A16.

II.3. The 14DD Residues of the Third Formulation

The formula of autonomy: "Act in such a way that the will can through its maxim regard itself at the same time as universally legislating."

Residue one: the binary position of legislator-and-subject. Autonomy is here formulated by Kant as the structure of "the same subject simultaneously functioning as legislator and as subject-to-the-law." This structure itself preserves the legislator/subject distinction — only that the same subject occupies both positions. The 15DD sentence-form does not require this binary — reason is not "both legislating and subject"; reason is "operating itself." Operation is legislating (operation-mode is law) and is being-subject (operating in accordance with operation-mode); the three are not separable.

Residue two: the "regard-as" reflexive structure. The same subject-object-separation problem — the subject treats/regards itself as some role (legislator). This is reflexive self-relation, in which the subject makes a judgment about itself (judging itself to be a legislator). The 15DD self-relation does not require this reflexive judgment — autonomy as background is not the result of the subject judging itself, but the way reason exists as reason in operation.

Residue three: will as the agent of legislation. Kant places autonomy in the faculty of will (Wille) — the will legislates, the will is subject. But the will, as a specific psychological-rational faculty, is only one face of the 15DD subject. Confining autonomy to the will limits its scope. The 15DD autonomy does not operate only at the will level — it operates in cognition (reason cannot not have its own cognitive direction), in faith (categorical faith as non-externalizable bearing), in imperative (absolute imperative as the action that cannot not be done under the noumenal presence of the other), in cooperation (16DD's "we cannot not"). Autonomy is the existence-mode of the 15DD subject as a whole, not the property of a specific faculty.

The SAE task: rewrite the third formulation from "the will may regard itself as legislator" (14DD specific-faculty reflexive structure) to "autonomy as common background of all four clauses" (15DD subject-whole existence-mode) — autonomy is not listed as a separate clause but runs through all four clauses as their common root. All "Reason cannot not..." statements are laws given by reason to itself, not laws given to reason from outside.

II.4. The 14DD Residues of the Fourth Formulation

The formula of the kingdom of ends: "Act in such a way that your maxim could always be regarded as a maxim of universal legislation belonging to the kingdom of ends."

Residue one: "kingdom" as ideal (Idee). Kant himself acknowledges that the kingdom of ends is an idea (Idee), an ideal community that does not exist in reality. Placing the object of the fourth formulation in the position of "ideal" weakens its actual constraint on present action — "act as if you were in the ideal community" introduces, under the 14DD hypothetical structure, yet another if: if there were a kingdom of ends, then you ought to act as its member.

Residue two: the "as a member" identity assumption. Asking the subject to imagine itself as a member of the kingdom of ends and infer how a member would act. This is counterfactual identification — the subject is not actually a member of the kingdom of ends; it is pretending to be. Such imagined identity assumptions are standard in 14DD, but 15DD requires actual existential conditions — the subject is not pretending to be with others in the kingdom of ends; the subject is actually with the other in a "I for purpose A, the other for purpose B, we cannot not do C" cooperative structure.

Residue three: the kingdom of ends as idealized universalization. Kant treats the fourth formulation as the idealized result of combining the first formulation (universalization) and the second formulation (humans as ends). This combination preserves the formalization of the first formulation and the "treat-as" form of the second formulation, stacking two 14DD residues. SAE's "I for A, the other for B, we cannot not do C" is a structural statement of concrete cooperation, not an idealized imagination — two specific subjects in concrete circumstances jointly carrying a third term in structurally-cannot-not fashion. The 16DD cooperative imperative is not a variant of the fourth formulation; it is the fourth formulation realized non-idealized in 15DD-16DD concrete cooperation.

The SAE task: rewrite the fourth formulation from "your maxim may be regarded as a member's maxim of the kingdom of ends" (14DD idealized identity assumption) to "Reason cannot not be interrogated" (15DD other-arrival structure) — reason's operation necessarily faces interrogation from others (demands, questions, calibrations from other rational subjects); this interrogation at the cooperative level is the structure of "we cannot not." The kingdom of ends is not an ideal community; it is the actual structure of mutually-interrogating, mutually-calibrating rational subjects.

II.5. Common Features of the Four Formulations' 14DD Residues

The four formulations' 14DD residues share common features:

• All use the sollst (ought) modal rather than the kann nicht nicht (cannot not) modal — command rather than ontology.
• All employ the subject-object-separation processing relation ("treat X as Y," "regard yourself as legislator") — the subject makes judgments about objects rather than the ontological structure operating directly.
• All operate in hypothetical or ideal positions (universalizable maxim, the human treated as end, the will as legislator, member of the kingdom of ends) — hypothetical or counterfactual rather than actual presence.
• All depend on a mediating faculty (will, maxim, reflection) — bearing the imperative through a specific faculty rather than through the subject's whole way of being.

These common features are not Kant's lack of rigor — to the contrary, they represent the precision Kant could achieve within 18th-century philosophical tools. To remove these 14DD residues requires 21st-century tools: the chisel-construct cycle's dynamic generation mechanism, the remainder (ρ) as ontological status, primordial chaos (0D) as starting point, the 15DD-16DD dimensional sequence, and the cannot not as an independent modal type. These tools allow SAE to redo, in 15DD-16DD sentence-forms, what Kant carried in 14DD sentence-forms, without losing any of Kant's core insight.

§III unfolds this re-articulation.

III. The SAE Refinement: Four "Reason Cannot Not" Statements

The SAE refinement of Kant's four formulations consists of four "Reason cannot not" statements, plus autonomy as the common background running through all four (rather than listed as a fifth clause). The four statements in German, English, and Chinese:

I. Reason cannot not reason.

Die Vernunft kann nicht nicht vernünfteln.

理性不得不理性。

II. Reason cannot not develop.

Die Vernunft kann nicht nicht sich entwickeln.

理性不得不发展。

III. Reason cannot not have direction, that is, purpose.

Die Vernunft kann nicht nicht eine Richtung haben, d.h. einen Zweck.

理性不得不有方向，即目的。

IV. Reason cannot not be interrogated.

Die Vernunft kann nicht nicht befragt werden.

理性不得不被追问。

All four use Reason (die Vernunft / 理性) as subject and cannot not (kann nicht nicht / 不得不) as modal — the SAE 15DD-16DD signature applied to Kantian material. Reason as subject unifies the four under one theme: what structural conditions reason's existence as reason requires. Cannot not as modal pulls all four from Kant's sollst (ought) sentence-form to the ontological statement of 15DD-16DD.

The four are not four parallel imperatives but the same statement — concerning "how reason stands as reason" — unfolded from four angles. Clause I is the a priori condition; clause II is the dynamic operation; clause III is the directional structure; clause IV is the cooperative structure. Autonomy (Kant's third formulation), as background running through all four, is present in each clause's operation.

The four are unfolded individually below.

III.1. Clause I: Reason Cannot Not Reason

Die Vernunft kann nicht nicht vernünfteln. / Reason cannot not reason.

This clause corresponds to Kant's first formulation (formula of universal law / form) at its core.

This is not a tautology ("reason is of course reason" as analytic redundancy); it is a statement that withdraws the first formulation from the maxim/law binary structure back into reason's own operation — reason as noun (the subject's faculty) exists in the way of reason as verb (the persistent rationalizing operation). This is unfolded below.

The substance of Kant's first formulation is reason's requirement of self-consistency. The "universalizability" test is not an externally added condition but the self-consistency that reason cannot not maintain when operating as reason — a maxim that cannot be universalized is a maxim by which reason has betrayed itself (when this maxim holds, reason cannot continue operating as reason). Kant formulates this as "act so that your maxim can become a universal law" — wrapping reason's self-consistency requirement in a 14DD command directed at the subject.

The SAE refinement is: Reason cannot not reason — with reason as a verb. The first reason is a noun (the subject's rational faculty); the second reason is a verb (carrying out what reason does). The mode in which reason exists as a noun is the persistent operation of reason as a verb. To stop "operating rationally" is to cease being reason as a noun. This moves the substance of Kant's first formulation (reason's self-consistency) from 14DD's ought to 15DD-16DD's ontological statement.

Several points concerning this clause:

(i) The noun-verb double use of "reason." Chinese "理性不得不理性," English Reason cannot not reason, German Die Vernunft kann nicht nicht vernünfteln — all three languages employ the structure "noun + modal + same-word verbalized." This structure displays reason's self-reflexivity through the very form of the statement: reason is not a static faculty but a persistent self-operation. This aligns with the substance of Kant's first formulation (universalizability's substance is self-consistency) but displays it directly through the structural form of the statement, without external command.

(ii) The 14DD residues removed. §II.1 listed the three 14DD residues of the first formulation: variant of hypothetical command, the maxim/law binary structure, sollst as modal. The present clause removes all three: not "if you want the maxim to be rational, then you ought to..." but "reason as reason already operates" (hypothetical disappears); no distinction between "subjective maxim" and "objective law" (binary disappears); not ought but cannot not (modal transforms).

(iii) Position as traversing condition. Clause I is not the first of four parallel imperatives but the a priori condition that allows the other three to stand. Without clause I (reason not operating as reason), there is no clause II development (reason absent, development cannot speak), no clause III direction (reason absent, direction has nothing to be directed toward), no clause IV interrogation (reason absent, nothing to be interrogated). Clause I is the prerequisite of the entire 15DD-16DD operation.

(iv) Clause I's structural force: the cost of exiting. A possible reader's challenge is: if "reason cannot not reason" is only an ontological statement (reason if it is reason then it does what reason does), can the subject not exit — "I refuse to rationalize, I abandon 15DD subjecthood, your clause I no longer applies to me"? This challenge has no answer under 14DD command structure (you reject the command and are exempt from it), but it has a precise answer under 15DD ontological structure.

The subject cannot truly "exit" to a neutral non-subject state. The 15DD subject ceasing clause I's operation does not retreat to some dormant neutrality; it is swallowed by the 14DD instrumental structure and reduced to a tool. Within SAE's dimensional sequence, every layer below 15DD is an instrumental layer — a subject that ceases operating as 15DD subject thereby operates at 14DD or lower, where it can only function as another subject's means or as the tool of some larger system (capital, bureaucracy, algorithm, cosmic law). Clause I's force does not derive from external command but from structural degradation: failing to maintain reason's self-consistent operation = the subject's ontological line as end-in-itself collapses immediately.

This transforms clause I from "A=A" analytic redundancy into the absolute existential tension. Not "if you want to be a rational subject, you must maintain rationalizing operation" (14DD hypothetical) but "before the 14DD instrumental structure, in order not to be ground into a tool, the subject cannot not persistently carry out reason's operation" (15DD ontology). To exit is to be degraded — this is the source of clause I's force at 15DD.

(v) Autonomy's manifestation in clause I. Autonomy as background manifests in clause I as: reason's source-of-operation is reason itself, not external command. "Reason cannot not reason" is not a command from any superior; it is reason's mode of being as reason. This places Kant's third formulation (autonomy) — its core (giving law to oneself) — at the deepest position of clause I.

III.2. Clause II: Reason Cannot Not Develop

Die Vernunft kann nicht nicht sich entwickeln. / Reason cannot not develop.

This clause is the concrete operating mode of autonomy as background.

Autonomy (Autonomie) in Kant is understood as the will's legislation upon itself. But there is a subtle difference between "autonomy" as a static property (the subject is autonomous) and "legislating" as a persistent motion (the subject persistently gives itself law). If autonomy is a static property, the subject stops once it attains autonomy — but Kant's autonomy is not such a completed state. True autonomy is the persistent legislative motion: the subject gives itself law moment by moment; the moment legislation stops, autonomy ceases to operate.

SAE structures this understanding as clause II: Reason cannot not develop. "Develop" (sich entwickeln) here is not any specific progressive content; it is reason's legislative motion itself cannot stop. The verbal nature of "legislation" (Gesetzgebung) is displayed through "develop's" persistence.

Why must it necessarily be "develop" rather than other phrasings? Possible alternative phrasings include "Reason cannot not be autonomous," "Reason cannot not legislate itself," and so on. Why does the present paper choose "develop" as the precise expression? The answer must begin with what remains after the three 14DD residues of the third formulation (§II.3) are removed.

The three 14DD residues of the third formulation:

• Legislator-and-subject binary position
• "Regard-as" reflexive structure
• Will as agent of legislation

What remains as the expressible core of Kant's autonomy principle after these three are removed?

Removing the binary position: cannot say "legislation" (this implies a "subject-to-legislation"), nor "self-legislation" (this implies the subject performing some inverse action upon itself). What remains can only be a non-binary operation.

Removing the reflexive structure: cannot say "the subject is aware of legislating" or "the subject regards itself as legislator" — these are reflexive expressions. What remains can only be the subject's operation as subject itself, without reflexive mediation.

Removing the will-restriction: cannot use "will," "reason," "mind" or other specific faculties as subjects — autonomy does not belong to a specific faculty; it is the subject's whole way of being. What remains can only be some general persistent existence of the subject as a whole.

The shared core left by all three removals is: the subject's whole, non-binary, non-reflexive, non-faculty-restricted persistent operation. What word most precisely captures this core?

• Not "autonomy": autonomy itself is the diagnosed object; using it to explain itself is circular; moreover "autonomy" in everyday language has been static-ized into "the subject is autonomous" property statements.
• Not "self-legislation": legislation is the core word of the removed 14DD residue; retaining it does not clean the residue.
• Not "operation": too thin; cannot capture the cannot not stop modal.
• Not "persistent existence": too close to existence (Sein), too far from motion (Werden).

"Develop" (Entwicklung / sich entwickeln) is the only word satisfying all conditions simultaneously: it concerns the subject's whole (not faculty-restricted); it is persistent (intrinsically containing the cannot not stop modal); it is non-binary (development is the subject's own motion, not "the subject lets something develop"); it is non-reflexive (the subject need not be aware of developing in order to develop).

"Develop" in German Entwicklung contains the meaning of "unfold" (sich entfalten) — the subject unfolds its own structure, which is precisely the precise expression of Kant's autonomy principle's "reason unfolding its legislation as actual self-legislative motion." "Develop" is not an additional reading of the third formulation; it is the only precise carrier of the third formulation's core after the three 14DD residues are removed.

Several points concerning this clause:

(i) The 14DD residues removed. Kant's autonomy formulation's 14DD residues (§II.3) include the legislator/subject binary position, the "regard-as" reflexive structure, and will as the agent of legislation. Clause II circumvents all three: development requires no distinction between legislation and being-subject (operation is legislation and being-subject; the three are inseparable); requires no subject's reflexive judgment of itself (development is the subject's mode of being, not a judgment the subject renders); is not restricted to the will as faculty (development operates in cognition, faith, imperative, cooperation across all dimensions).

(ii) Development's content is regulated by the other three clauses. Clause II only specifies that reason cannot not develop — development itself cannot stop. But what direction does development take? What concrete forms does development take? How is development coordinated among multiple subjects? These are answered by clause I (reason's self-consistent operation), clause III (directed toward the other as noumenon), and clause IV (calibrated under interrogation), respectively. Clause II is the dynamic condition; the other three are the concrete structures.

(iii) Development ≠ improvement. "Development" here is not value-judgment-laden "becoming better"; it is structurally "cannot stop." A subject may "regress" in some specific direction, but as long as it still operates as a subject, it is "developing" — regression is also a form of development (regression means the subject is still operating, still legislating itself, only that the legislated rule in some specific dimension is diagnosed as "regressive"). Clause II is isomorphic to the un-stoppability of the chisel-construct cycle (Meißel-Konstrukt-Zyklus) — the subject persistently chisels itself, persistently constructs itself; this is the structural meaning of development.

(iv) Autonomy's manifestation in clause II. Autonomy as background manifests most densely in clause II — autonomy as persistent legislative motion is precisely clause II's core. To say a subject is autonomous is to say it cannot not develop; to say a subject cannot not develop is to say it is persistently legislating. The two are structurally the same fact in two expressions. This makes clause II carry the third formulation (autonomy) as Kant's direct re-articulation in SAE sentence-form.

III.3. Clause III: Reason Cannot Not Have Direction, That Is, Purpose

Die Vernunft kann nicht nicht eine Richtung haben, d.h. einen Zweck. / Reason cannot not have direction, that is, purpose.

This clause corresponds to Kant's second formulation (formula of humanity as end / matter).

Clause II established that reason cannot not develop, but did not specify the direction. If reason's development were entirely random expansion, it would immediately encounter a structural problem — operation as reason cannot tolerate randomness (this would violate clause I). Therefore reason's development necessarily has direction. At the 15DD layer, this direction is — the noumenal presence of the other.

But why is the direction necessarily the other, and not something else? This is a structural question that must be explicitly derived. AI systems "develop" toward more parameters or higher precision; capital systems "develop" toward more profit; bureaucratic systems "develop" toward greater scale — all are structures of "cannot not develop," but their directions are not the other. Why must the 15DD subject's developmental direction necessarily be other 15DD subjects?

The answer lies in the ZFCρ first law (Konstrukt-must-leave-Rest). Each round of the chisel-construct cycle necessarily produces remainder ρ — every operation (chisel-construct) leaves a residue that the operation cannot completely absorb. This law is a structural fact proven in SAE foundation papers (cf. SAE Foundation Paper III, DOI 10.5281/zenodo.18727327; Methodology 00 Via Rho, DOI 10.5281/zenodo.19657440).

The remainder must have an outlet. If the entirety of remainder were absorbed into the subject's interior, the subject's chisel-construct cycle would enter a self-closed loop — because each round's remainder becomes the next round's input, but the next round produces new remainder, and the remainder accumulates without bound internally. Internal accumulation has no containment space; the subject's structure would collapse under accumulation pressure. Therefore the remainder structurally cannot not be directed outward — the remainder must overflow the subject's boundary for the chisel-construct cycle to be sustainable.

What in the external world can receive remainder? Here is the crucial topological step: that which can receive remainder without degrading it can only be another 15DD subject — one that itself produces remainder, and itself requires an external outlet.

Consider other candidate receivers:

• Tools/objects: receive remainder by degrading it to resource — for instance, a subject's thought leaves remainder (an untheorized feeling, an incomplete concept); if it is only written into a tool (e.g., a database), that remainder becomes data and loses its ontological status as remainder.
• AI systems / capital structures / bureaucratic organizations: receive remainder by absorbing it as system-fuel or system-data — remainder is made fuel or data, continues to be operated upon by 14DD structure, loses its independent identity as 15DD remainder.
• Non-subject natural entities: cannot serve as receivers of remainder — non-subjects lack the structural position of "receiving."

Only another 15DD subject can truly receive a 15DD subject's remainder while preserving its identity as remainder — because only another 15DD subject has the same remainder structure, the same chisel-construct cycle, the same ontological necessity of "remainder needing outlet." Remainder exchange between two 15DD subjects is bidirectional: my remainder overflows to you, your remainder overflows to me, both received by the other as remainder (not degraded to resource or data), and triggering a new round of chisel-construct in the other.

So the other is not the direction "selected" by reason's development; the other is the only topologically-compatible receiver of overflowing remainder. Reason cannot not develop (clause II); development produces remainder (ZFCρ first law); remainder cannot not have an external outlet (avoiding internal collapse); the only legitimate outlet is another 15DD subject (topological compatibility) — therefore reason's developmental direction cannot not be toward the other. This is a structural-necessity derivation from clause II to clause III, not a mere intuitive leap from "development needs direction" to "direction is the other."

Kant's second formulation expresses this as "treat humans as ends, not merely as means." Metaphysics-satz §VI Ray 1 indicates that Kant's second formulation has 15DD content (absolute imperative) and 14DD sentence-form (imperative structure). A16 has done the SAE refinement of this formulation: the absolute imperative as "the other's purpose is A, so I cannot not do B" — the noumenal presence of the other leaves me with no option of not doing B.

The present clause III "Reason cannot not have direction, that is, purpose" is the position-statement of A16's absolute imperative within the present paper's four-clause system. "Reason cannot not have direction" is the structural statement about reason's development; "that is, purpose" specifies that the direction's concrete content is the other as purpose. The two expressions together correspond exactly to A16's "the other's purpose is A, so I cannot not do B" — directional structure (cannot not have direction) plus directional content (the other as purpose).

Several points concerning this clause:

(i) The identification of "direction" and "purpose." The "i.e." (d.h. / 即) in "Reason cannot not have direction, that is, purpose" performs a critical identification: direction is purpose. This corresponds to the core insight of Kant's second formulation — humans as rational beings are ends in themselves, not mere transit points on some path. Within the SAE structure, direction is not arbitrary orientation but orientation toward other rational subjects as ends in themselves.

(ii) The 14DD residues removed. §II.2 listed the second formulation's three 14DD residues: the "treat-as" subject-object-separation form, the "never merely as means" qualified compound command, ends as the object of subjective judgment. A16 has done the 15DD refinement of this formulation (cf. A16 paper DOI 10.5281/zenodo.19037566 for the complete unfolding); the present clause merely indicates A16's work's position in the four-clause system.

(iii) A16's position in the present paper. A16 One's Own Law is the complete unfolding of clause III. The present paper does not repeat A16's work but places it at the third position of the four-clause system. A16's "the other's noumenal presence leaves me with no option of not doing B" is the concrete realization of the present clause's "Reason cannot not have direction, that is, purpose."

(iv) Autonomy's manifestation in clause III. Autonomy as background manifests in clause III as: direction comes from reason's own structure, not from external purpose-anchoring. In Kant's heteronomy/autonomy distinction, he was particularly cautious about external purposes (happiness, divine command, social interest) as direction-sources — they would make reason a means. In SAE's refinement, direction comes from reason's operation itself — when reason operates as reason (clause I), it cannot not develop (clause II), and development cannot be random and therefore necessarily has direction — this direction's structural source lies in reason itself, not externally. The other as the concrete content of direction is not because the other gives direction to reason from outside, but because the other as a 15DD subject is precisely the only ontologically-fitting object of reason's direction.

III.4. Clause IV: Reason Cannot Not Be Interrogated

Die Vernunft kann nicht nicht befragt werden. / Reason cannot not be interrogated.

This clause corresponds to Kant's fourth formulation (formula of the kingdom of ends / system).

When multiple subjects each operate under the structure of clause I (operating as reason), clause II (cannot not develop), clause III (having direction toward the other) and meet — what happens? Metaphysics-satz gives the answer: cooperative imperative (16DD) — "I for purpose A, the other for purpose B, we cannot not do C." C does not belong to A nor to B; it is the action forced into being by the meeting of two independent purposes.

But the operation of the cooperative imperative requires a key structural condition: interrogation. If two subjects each cling to their own purposes, refusing the other's questions and calibrations, C cannot be found. C as the emergence after the meeting of two purposes requires both subjects to expose themselves to the other's interrogation — this is not one party persuading the other; this is the third term emerging from between two interrogable, mutually-calibrating subjects.

SAE establishes this structural condition as clause IV: Reason cannot not be interrogated. Interrogation is the necessary structural condition for the 16DD cooperative imperative's operation, and it is also the actual operative form of Kant's kingdom of ends.

Several points concerning this clause:

(i) Interrogation as the engine of 16DD. Metaphysics-satz discusses interrogation as the "Terminierungsstruktur der Rückfrage" (termination structure of regress questioning), pointing out that the cooperative imperative (16DD) is the final termination point of all interrogation. The present clause further establishes interrogation as the necessary condition for the operation of the cooperative imperative — the cooperative imperative is not only the termination point of interrogation but also the produce of interrogation's operation. Without interrogation, no C can emerge from the meeting of two independent purposes; with interrogation, C can emerge from the mutual calibration of two independent subjects.

(ii) The structural meaning of the passive voice. Clause IV is the only one of the four using passive voice (reason "is" interrogated / Die Vernunft kann nicht nicht befragt werden). The first three are all active voice (reason reasons / reason develops / reason has direction). This voice transition is not coincidence — it marks the layer-leap from single-subject structure (clauses I-III describe a single subject's operating structure) to multi-subject structure (clause IV requires the subject to be open to the other's interrogation). Passive voice means interrogation is not an action issued by the subject; it is a structure received by the subject — the other's arrival makes interrogation happen, and the subject cannot not be open to this interrogation.

(iii) Difference from and connection with the closing path of Kategorischer Glaube. Kategorischer Glaube (DOI 10.5281/zenodo.19719083) §V offers detailed unfolding of "cannot not be interrogated," and distinguishes the special character of categorical faith on this point — the interrogation of categorical faith is open, but the explanation channel is structurally impassable (the duality of interrogation+explainable vs interrogation+inexplicable). The present clause's "Reason cannot not be interrogated" concerns interrogation in the direction of the absolute imperative and the cooperative imperative — interrogation is open, and explanation is feasible (indeed must be feasible, for cooperation to be establishable). The two directions of interrogation form the complete "being-interrogated" structure: the inward face (faith) interrogation enters but explanation does not pass through; the outward face (imperative + cooperation) interrogation and explanation are both open.

(iv) The 14DD residues removed. §II.4 listed the fourth formulation's three 14DD residues: the kingdom of ends as ideal (Idee), the "as a member" identity assumption, the kingdom of ends as idealized combination of the first and second formulations. Clause IV avoids all three: interrogation actually happens, not idealized assumption (the present other is actually issuing interrogations); interrogation does not require identity assumption (the subject actually responds to the other's interrogation, not pretending to be a kingdom-of-ends member); interrogation is a concrete multi-subject structure, not the idealized combination of two formulations.

(v) Autonomy's manifestation in clause IV. Autonomy as background manifests in clause IV as: being interrogated is not being externally dominated. Interrogation comes from another similarly-autonomous subject — the other operates according to its own clauses I-III, then interrogates me as an autonomous subject. My openness to this interrogation is not bowing to external authority; it is recognizing the other as a similarly-autonomous subject's legitimate position to interrogate me. Two autonomous subjects mutually interrogating and calibrating one another — this is the precise structure of Kant's kingdom of ends. The kingdom of ends is not a higher authority dominating everyone; it is the structure of all autonomous subjects mutually recognizing one another's legislator status and mutually interrogating, mutually calibrating.

III.5. The Four Clauses as Four Faces of the Same Statement

According to Kant's own account, the four formulations are the same categorical imperative seen from four different angles — form, matter, source, system. The SAE refinement of the four clauses preserves this unity:

• Clause I (Reason cannot not reason): form — reason's structural requirement of self-consistency.
• Clause II (Reason cannot not develop): source (in part) — reason's operation comes from reason itself, hence development cannot stop.
• Clause III (Reason cannot not have direction, that is, purpose): matter — the directional structure of development.
• Clause IV (Reason cannot not be interrogated): system — the cooperative structure of multi-subject operation.

Kant's "the same imperative seen from four angles" becomes more concrete under the SAE refinement: the four clauses are four necessary conditions of the same statement concerning "how reason stands as reason," none dispensable. Without clause I, the other three lack premise; without clause II, reason is static and inoperative; without clause III, development is random and without direction; without clause IV, multi-subject operation degenerates into single-subject monologism. The four together constitute the complete structural conditions for reason to stand as a 15DD-16DD subject.

Autonomy as background is present in each — clause I's reason-as-self-source, clause II's legislative motion that cannot stop, clause III's direction from reason's own structure, clause IV's other as similarly-autonomous subject. Autonomy is not one of the four clauses; it is the common root. §IV unfolds this background structure.

IV. Autonomy as Background: Why Not Listed as a Fifth Clause

The present paper places autonomy (Kant's third formulation) as the background running through all four clauses, rather than listing it as a fifth clause. This choice requires justification, since it deviates from Kant's own parallel treatment of the four formulations.

IV.1. The Position of Kant's Autonomy Formulation

Kant in Grundlegung zur Metaphysik der Sitten places the autonomy formulation as the third in parallel with the others. According to Kant's own account, the four formulations handle different faces of the same imperative: the first formulation handles form (universalizability), the second handles matter (humans as ends), the third handles source (will's autonomy), the fourth handles system (kingdom of ends). Autonomy, as one of these faces, stands in parallel with the other three.

This parallel treatment is self-consistent within Kant's own framework — he treats form, matter, source, system as four relatively-independent faces co-existing in the categorical imperative. But under SAE sentence-form analysis, the relation between autonomy and the other three faces is not a parallel relation but a traversing relation.

IV.2. Why Autonomy Cannot Stand in Parallel with the Other Three

The core of autonomy is "reason giving itself law" — source in reason itself, not external. This "source" is not one of the four faces; it is the condition that the other three faces (form, matter, system) cannot not satisfy. If the form (first formulation) came from external command (e.g., "because God commands, reason must be consistent"), the first formulation would not stand; if the matter (second formulation) were specified by external authority (e.g., "because the state mandates, humans are ends"), the second formulation would not stand; if the system (fourth formulation) were planned by an external ruler (e.g., "because some superior designed the kingdom of ends, we follow its rules"), the fourth formulation would not stand.

Autonomy as "source in reason itself" is the condition that all three other faces cannot not satisfy — not one of the four faces but the common ground of all four. Kant himself was aware of this (he repeatedly emphasizes autonomy as the true foundation of the categorical imperative), but he handled it through "four formulations in parallel" structure, placing autonomy at the same level as the other three in expression. SAE's refinement changes this expressional parallelism into a structural traversal — autonomy as background, with the other four clauses (reason, develop, direction, interrogation) operating under the autonomy-background.

This is a structural optimization at the sentence-form layer, not any negation of Kant's content — the substantial content of Kant's autonomy principle (reason gives itself law, does not receive law from outside) is fully preserved in the SAE refinement; only its position in the coordinate is redistributed from "parallel third clause" to "running through all four." This is a more precise display of Kant's insight, not a modification of it.

IV.3. The Specific Manifestation of Autonomy in the Four Clauses

The specific manifestations of autonomy as background in the four clauses, marked at the end of each section in §III, are unified here:

• In clause I (Reason cannot not reason): reason's source-of-operation is reason itself, not external command. "Reason cannot not reason" itself is not a command from any superior; it is reason's mode of being as reason. This is autonomy's manifestation at the deepest position.
• In clause II (Reason cannot not develop): legislative motion itself cannot stop. Autonomy is not a static property; it is persistent legislation. The moment legislation stops, autonomy ceases. Clause II's "develop" and autonomy's "persistent legislation" are structurally the same fact.
• In clause III (Reason cannot not have direction, that is, purpose): direction comes from reason's own structure. The other as direction's content is not externally given; it is the ontological necessity of reason's orientation toward other 15DD subjects.
• In clause IV (Reason cannot not be interrogated): interrogation comes from similarly-autonomous others. Openness to interrogation is not bowing to external authority; it is recognizing the legitimate interrogating position of the similarly-autonomous other.

Each of the four clauses operates under the autonomy-background. Autonomy is the common root of the four clauses, not one of them.

IV.4. The Significance of This Treatment for SAE as a Whole

Placing autonomy as background rather than as a fifth clause has an important structural consequence for SAE as a whole: the autonomy principle permeates the operation of every dimension within SAE, not only the dimension of ethical imperative.

• In the cognitive dimension, autonomy manifests as "the subject cannot not have its own cognitive direction" (one of the four a priori conditions of cognition).
• In the dimension of faith, autonomy manifests as categorical faith (one's own faith) — the subject's non-externalizable bearing of its own standing.
• In the dimension of imperative, autonomy manifests as the absolute imperative (one's own law) — the action that cannot not be done under the other's noumenal presence.
• In the dimension of cooperation, autonomy manifests as the 16DD cooperative imperative — the C emerging from the meeting of two autonomous subjects.

Kant placed autonomy in the specific faculty of will, restricting it to the dimension of ethical imperative. SAE liberates autonomy as the background traversing all 15DD-16DD dimensions; the autonomy principle has a concrete realization-form in each dimension. This makes Kant's autonomy principle (the true foundation of human dignity) play a wider, deeper role in SAE.

§V places existing SAE papers at their specific positions within the present paper's refined structure.

V. The Position of Existing SAE Papers within the Refined Structure

The present section places SAE's published Kant-related papers within the four-clause "Reason cannot not" coordinate, displaying their common Kantian foundation. This is a core function of the present paper as integrative declaration — not redoing those papers' work (it is already done), but displaying their position relations within a unified structure.

V.1. A16 One's Own Law Position: Clause III

A16 One's Own Law (DOI 10.5281/zenodo.19037566) corresponds to the complete unfolding of the present paper's clause III "Reason cannot not have direction, that is, purpose." A16 handles the 15DD sentence-form refinement of Kant's second formulation (humanity as end); its core statement "the other's purpose is A, so I cannot not do B" is precisely the concrete expression of "reason has direction and the direction is the other as end."

A16's position within the present paper's four-clause structure:

• Clause I (Reason cannot not reason) gives A16 its operating premise — the subject must operate as a rational subject for A16's "cannot not do B" to have a subject capable of bearing it.
• Clause II (Reason cannot not develop) gives A16 its dynamic — the subject's persistent legislative motion makes "cannot not do B" not a one-time command but a sustained directional locking.
• Clause III (Reason cannot not have direction, that is, purpose) is precisely A16's position — A16 unfolds the concrete content of clause III: direction is the other's noumenal presence.
• Clause IV (Reason cannot not be interrogated) gives A16 the calibration mechanism while operating — when I do B, I cannot not be open to the other's interrogation, ensuring that B is genuinely directed toward the other as end and not toward instrumentalization in the name of "for the other's good."

A16's name "one's own law" precisely corresponds to autonomy-as-background's manifestation in the imperative dimension — the law's "I-quality," not externally imposed command, is reason's own bearing of direction.

V.2. Kategorischer Glaube Position: Autonomy-as-Background's Manifestation on the Inward-Facing Side of 15DD

Kategorischer Glaube (DOI 10.5281/zenodo.19719083) handles the unfolding of the autonomy principle (Kant's third formulation) in the dimension of faith, corresponding to "autonomy-as-background's concrete realization across 15DD's dimensions" mentioned in §IV.4 — specifically, the dimension of faith.

The core of Kategorischer Glaube — categorical faith as the subject's non-externalizable bearing of its own standing — is precisely the precise manifestation of the autonomy principle on 15DD's inward-facing side. The subject does not externalize its own standing, does not let faith be reduced to a derivative conclusion of some upstream reason — this is precisely autonomy's (reason giving itself law) form in the dimension of faith.

The relation of Kategorischer Glaube to the present paper is more subtle than that of A16:

• A16 handles clause III (one specific clause); the present paper places A16 within the four-clause position.
• Kategorischer Glaube does not directly correspond to any one of the four clauses; instead it unfolds autonomy-as-background's concrete operation on the inward-facing side of 15DD.

This gives autonomy-as-background a precise position in the SAE series — it operates not only in the imperative dimension (A16's outward imperative) but also in the dimension of faith (Kategorischer Glaube's inward bearing). The absolute imperative (A16) and categorical faith (Kategorischer Glaube) constitute the outward-inward duality of autonomy at 15DD. The two papers together complete autonomy's realization at the 15DD layer.

V.3. The 16DD Cooperative Imperative Position: Clause IV

The present paper's clause IV "Reason cannot not be interrogated" — its content, in metaphysics-satz's complete formulation, is the 16DD cooperative imperative: "I for purpose A, the other for purpose B, we cannot not do C."

Clause IV establishes the structural condition (being interrogated) for the cooperative imperative, and the cooperative imperative itself ("we cannot not do C") is the result of clause IV's operation. The two stand in relation:

• Clause IV (being interrogated) is the engine of 16DD's operation — without interrogation, C cannot emerge.
• The cooperative imperative ("we cannot not do C") is the produce of 16DD's operation — C is the third term emerging from two autonomous subjects' mutual interrogation.

Currently the SAE series has no dedicated paper unfolding the complete structure of the 16DD cooperative imperative — metaphysics-satz gives the cooperative imperative's definition, the present paper's clause IV gives the structural condition for its operation, but a complete 16DD treatise has yet to be written. This is the next paper SAE ethics may write — building upon the present paper's positional definition of clause IV, unfolding 16DD's operating details in concrete cooperation.

Boundary statement: the present paper does not unfold the production mechanism of C within the cooperative imperative — C as the third term emerging from the meeting of two independent purposes, its production requires structural analysis under concrete cooperative situations (how the rounds of mutual interrogation among subjects operate, the phase-transition conditions from opposition to emergence of C, the grammatical relations of C and the respective A/B, etc.). These are the work of the 16DD treatise, not the scope of the present paper. The present paper only positions the cooperative imperative at "clause IV as 16DD engine"; the concrete mechanism is reserved for the future paper.

V.4. Four Papers' Common Kantian Foundation

The above three papers (A16, Kategorischer Glaube, the future 16DD treatise) plus the present paper constitute SAE ethics' complete continuation of Kant's four formulations:

• The present paper (Reason Cannot Not) — integrative declaration, placing the four formulations within the SAE 15DD-16DD sentence-form coordinate, providing the four-clause refinement.
• A16 (One's Own Law) — clause III's complete unfolding (second formulation).
• Kategorischer Glaube — autonomy-as-background's unfolding on 15DD's inward-facing side (third formulation's realization in the dimension of faith).
• The future 16DD treatise — clause IV's complete unfolding (fourth formulation).

These four papers' common Kantian foundation, declared explicitly by the present paper: SAE ethics is the sentence-form refinement (satzformentheoretische Verfeinerung) of Kant's categorical imperative's four formulations under the SAE 15DD-16DD coordinate. Not replacement of Kant, not refutation of Kant; the continued unfolding of Kantian ethics under 21st-century tools (the dimensional sequence, the chisel-construct cycle, the remainder, the cannot not modal).

VI. Conclusion: SAE Ethics as the 15DD-16DD Sentence-Form Refinement of Kantian Ethics

VI.1. The Present Paper's Three Contributions

The present paper does three things.

(i) Complete 14DD residue diagnosis of Kant's four formulations (§II). Metaphysics-satz §VI Ray 1 provided a compressed diagnosis — the four formulations all use 14DD imperative structure to carry 15DD-16DD content. The present paper expands this compressed diagnosis: each of the four formulations carries three 14DD residues (twelve in total), plus four sentence-form features common to all four (ought modal, subject-object separation, hypothetical position, mediating faculty).

(ii) Provides the SAE refinement of the four "Reason cannot not" statements (§III). The four unfold from a priori condition (Reason cannot not reason) to dynamic (Reason cannot not develop), direction (Reason cannot not have direction, that is, purpose), and cooperation (Reason cannot not be interrogated). All four use the SAE 15DD-16DD standard sentence-form of "reason as subject + cannot not modal," replacing Kant's ought-imperative structure with ontological statements. Autonomy (third formulation) as background traversing all four clauses, not listed as a fifth (§IV).

(iii) Explicit declaration of SAE ethics' Kantian foundation (§V). A16, Kategorischer Glaube, the future 16DD treatise — these SAE papers together constitute the complete continuation of Kant's categorical imperative under SAE sentence-form. The present paper is the integrative declaration of this continuation project — not founding, but explicit articulation of the common Kantian foundation of existing and future work.

VI.2. SAE Ethics' Overall Position

After the present paper's work, SAE ethics' position in the history of philosophy can be precisely stated:

SAE ethics is the refinement (Verfeinerung) of Kantian ethics at the 15DD-16DD sentence-form layer.

The three points of this statement:

(i) Continuation rather than replacement. SAE ethics' content comes entirely from Kant's four formulations. SAE does not propose "new ethical content"; it re-articulates content Kant has already proposed at a more precise sentence-form layer. Kant says humans are ends; SAE says the other's noumenal presence leaves me with no option of not doing B — the same fact, sentence-form lifted from 14DD to 15DD.

(ii) 15DD-16DD as tools unavailable in Kant's time. Kant in Kritik der reinen Vernunft established the coordinate of transcendental analysis; in Grundlegung zur Metaphysik der Sitten and Kritik der praktischen Vernunft he used this coordinate for ethics. But he had no dimensional sequence as tool (0DD to 16DD), no cannot not as independent modal (he had only ought), no chisel-construct cycle as dynamic mechanism, no remainder (ρ) as ontological status. SAE redoes Kantian ethics with these 21st-century tools — Kant did the most precise work he could with 18th-century tools; the further refinement here depends on tools that did not yet exist in his time.

(iii) Expansion of the autonomy principle. Kant placed autonomy in the specific faculty of will, restricting it to the dimension of ethical imperative. SAE liberates autonomy as background traversing all 15DD-16DD dimensions — autonomy manifests as cognitive direction in cognition, as categorical faith in faith, as absolute imperative in imperative, as cooperative imperative in cooperation. Autonomy plays a wider, deeper role in SAE than in Kant.

VI.3. SAE's Overall Position within the Kantian System

SAE's relation to Kant has been indicated in multiple papers:

• Metaphysics-satz established the dimensional-sentence-form isomorphism, using it to diagnose Kant's four formulations' 14DD residues.
• Kategorischer Glaube established SAE's continuation of Kant's Fürwahrhalten tripartition (Meinen corresponds to Methodology 0/00, Wissen to the epistemology series, Glaube to categorical faith).
• The present paper establishes SAE's refinement of Kant's four formulations of the categorical imperative.

These three together — SAE's position within the Kantian system can be compressed into one sentence:

Kant gave the basic structure of critical philosophy (the coordinate, transcendental analysis, Fürwahrhalten tripartition, four formulations of the categorical imperative, autonomy principle); SAE, with the support of 21st-century tools, continues to unfold this structure across every dimension — continuing the method, refining the tools, expanding the dimensions, but not changing the fundamental posture Kant established (grounded in autonomy, using transcendental analysis, holding the noumenon as boundary).

SAE is not another philosophy. SAE is Kant's philosophy continued under contemporary conditions.

VI.4. The Present Paper as SAE Ethics' Integrative Declaration

The present paper marks the integrative phase of SAE ethics. Earlier A16, Kategorischer Glaube, etc., each handled specific parts of Kant's four formulations, but no single paper has placed the four formulations as a whole within the SAE coordinate. The present paper fills this gap.

After the present paper, SAE ethics' further development can proceed within a clear coordinate:

• Clause III (absolute imperative) already has A16. Subsequent case-study papers can handle A16's operation in specific ethical situations.
• Autonomy-as-background's manifestation across dimensions already has Kategorischer Glaube (faith dimension). Subsequent monographs on autonomy in cognition, education, etc., are possible.
• Clause IV (16DD cooperative imperative) still lacks complete unfolding; this is the next important paper position in SAE ethics.
• Clauses I and II (reason's a priori condition and dynamic) are scattered across other SAE papers but lack monographs. These are also possible future paper positions.

The present paper's role is to place these existing and future works within the same coordinate, displaying their common Kantian foundation, and confirming SAE ethics' overall position as the 15DD-16DD sentence-form refinement of Kantian ethics.

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References

Kant's Works

Kant, I. (1785). Grundlegung zur Metaphysik der Sitten. Riga: Hartknoch. [Akademie-Ausgabe Band IV]

Kant, I. (1781/1787). Kritik der reinen Vernunft. Riga: Hartknoch. [Akademie-Ausgabe Band III–IV]

Kant, I. (1788). Kritik der praktischen Vernunft. Riga: Hartknoch. [Akademie-Ausgabe Band V]

SAE Series Papers

Qin, H. (2026a). Self-as-an-End: Foundation Paper I — Systems, Emergence, and the Conditions of Personhood. Zenodo. https://doi.org/10.5281/zenodo.18528813

Qin, H. (2026b). Self-as-an-End: Foundation Paper II — Internal Colonization and the Reconstruction of Subjecthood. Zenodo. https://doi.org/10.5281/zenodo.18666645

Qin, H. (2026c). Self-as-an-End: Foundation Paper III — The Complete Self-as-an-End Framework. Zenodo. https://doi.org/10.5281/zenodo.18727327

Qin, H. (2026d). Metaphysics of Self-as-an-End: Dimensional Sentence-Form Theory (metaphysics-satz). Zenodo. https://doi.org/10.5281/zenodo.18894567

Qin, H. (2026e). A16: One's Own Law — The SAE Critique of Ethics and Morality. Zenodo. https://doi.org/10.5281/zenodo.19037566

Qin, H. (2026f). SAE Epistemology Series I–IV: The Four A Priori Conditions of Cognition. Zenodo. https://doi.org/10.5281/zenodo.19502953 ; .19503018 ; .19503097 ; .19503146

Qin, H. (2026g). Methodology 0 — Non · Negativa: On Negation Prior to Being. Zenodo. https://doi.org/10.5281/zenodo.19544620

Qin, H. (2026h). Methodology 00 — Via Rho: The Way of the Remainder. Zenodo. https://doi.org/10.5281/zenodo.19657440

Qin, H. (2026i). Kategorischer Glaube: A Sentence-Form Theory of One's Own Faith in SAE / 绝对信仰：SAE关于自身信仰的句式论. Zenodo. https://doi.org/10.5281/zenodo.19719083

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Cite this paper

Qin, H. (2026). Reason Cannot Not: An SAE Refinement of Kant's Four Formulations of the Categorical Imperative / 理性不得不：SAE对康德四定言律令的句式精细化. Zenodo. https://doi.org/10.5281/zenodo.19751513

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This paper is part of the Self-as-an-End (SAE) framework series.

Reason Cannot Not: An SAE Refinement of Kant's Four Formulations of the Categorical Imperative

Die Vernunft kann nicht nicht: Eine SAE-Verfeinerung von Kants vier Formeln des kategorischen Imperativs

Han Qin (秦汉) · Independent Researcher · 2026

DOI: 10.5281/zenodo.19751513

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摘要

本文对康德四条定言律令公式（普遍法则、目的本身、自律、目的王国）做SAE句式层面的精细化重述，把康德四条"应当"modal的公式转写为四条"不得不"modal的15DD-16DD陈述，确立SAE伦理学作为康德伦理学在15DD-16DD句式层面的细化（Verfeinerung）。

本文的起点是《SAE形而上学：维度句式论》（metaphysics-satz, DOI 10.5281/zenodo.18894567）。该paper在§VI射线一中对康德四公式做了首次压缩式句式诊断——四公式都用"Handle so, daß..."的14DD祈使结构承担15DD-16DD内容，属于工具化（错误二）与他者抹除（错误四）的叠加。本文把这个压缩诊断做完整展开：四条公式每条分别带三处14DD残留（共12处），以及四公式共有的四项句式特征（应当modal、主客分离、假设位置、中介机能）。

本文给出的精细化结构是：

一、理性不得不理性（对应第一公式：普遍化/形式）

二、理性不得不发展（作为自律底色的具体运作方式）

三、理性不得不有方向，即目的（对应第二公式：人是目的/质料）

四、理性不得不被追问（对应第四公式：目的王国/系统；与16DD协同律令构成engine-produce关系）

自律（第三公式）不单列为一条，而是作为四条的共同底色——四条都是理性给自己立法，不是外部给理性立法。这保留了康德自律原则的核心地位，但把它从"同列第三"提升为"贯穿四条"。这个处理让自律原则从康德的意志机能解放为贯穿SAE所有15DD-16DD维度的底色（认知、信仰、律令、协同）。

本文把SAE已有的相关论文摆在这个精细化坐标里：A16《One's Own Law》（DOI 10.5281/zenodo.19037566）作为条三的完整展开（第二公式的15DD转译），《Kategorischer Glaube》（DOI 10.5281/zenodo.19719083）作为自律底色在15DD内向面的显示。A16和Kategorischer Glaube合起来构成自律底色在15DD的外向-内向双子结构。条四（16DD协同律令）的完整展开还未成文，是SAE伦理学下一篇paper的位置。

SAE不是在康德之外另起炉灶，而是康德伦理学在21世纪工具（维度序列、凿构循环、余项ρ、不得不modal）支持下的继续展开。康德在18世纪工具下做了他能做的最精细工作，SAE的进一步精化依赖于那时还不存在的工具。

关键词：定言律令，理性不得不，Vernunft kann nicht nicht，Kategorischer Imperativ，四公式精细化，普遍法则公式，目的本身公式，自律公式，目的王国公式，SAE对康德的细化，15DD-16DD句式论，14DD残留诊断，metaphysics-satz

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术语表

SAE命名	德文	English	句式 / 对应康德公式
理性不得不理性	Die Vernunft kann nicht nicht vernünfteln	Reason cannot not reason	第一公式（普遍化/形式）
理性不得不发展	Die Vernunft kann nicht nicht sich entwickeln	Reason cannot not develop	自律底色的具体运作方式
理性不得不有方向，即目的	Die Vernunft kann nicht nicht eine Richtung haben, d.h. einen Zweck	Reason cannot not have direction, that is, purpose	第二公式（人是目的/质料）
理性不得不被追问	Die Vernunft kann nicht nicht befragt werden	Reason cannot not be interrogated	第四公式（目的王国/系统）
自律作为底色	Autonomie als Hintergrund	Autonomy as background	第三公式（自律/来源）的位置重置——从"并列第三条"改为"贯穿四条"

关于"理性不得不理性"的德文vernünfteln：此词在康德本人处及哲学史上有"运用理性、实行理性思维"的中性意义，日常德语有时带轻微贬义（指琐细的理性化）。本文采用其哲学传统下的中性义——即"Vernunft vollziehen"，让理性实行自身。与中文的"理性不得不理性"和英文的Reason cannot not reason一致，把"理性"作为动词使用，让主体理性持续运作自身为理性。

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一、康德四公式：同一条定言律令的四个面

一·一、康德自己对四公式的关系说明

康德在《道德形而上学基础》中给出定言律令的多个公式表述。哲学史上通常提炼为四条（或三条加一条推论形式），每一条从不同角度表述同一条律令：

第一公式：普遍法则公式（Formel des allgemeinen Gesetzes / Formula of Universal Law）

> Handle nur nach derjenigen Maxime, durch die du zugleich wollen kannst, dass sie ein allgemeines Gesetz werde.

要只按照你同时能够愿意它成为一条普遍法则的那个准则去行动。

这一公式从形式看定言律令——一条准则要成为道德律令，它的形式条件是可普遍化：想象它被推广为普遍法则时不自相矛盾、不意志上不可能。这是对准则的纯形式测试。

第二公式：目的本身公式（Formel der Zweckmäßigkeit / Formula of Humanity as End in Itself）

> Handle so, dass du die Menschheit sowohl in deiner Person als in der Person eines jeden anderen jederzeit zugleich als Zweck, niemals bloß als Mittel brauchst.

你要这样行动，无论是对你自己还是对任何他人，在任何时候都同时把人性当作目的，绝不仅仅当作手段。

这一公式从质料看定言律令——律令约束的内容是什么。内容不是具体行为的列举，而是一个关于"行为所朝向之物"的规定：朝向的必须是人（作为理性存在者）作为目的本身。注意"仅仅"（bloß）一词——康德并非禁止工具性使用，而是禁止把人仅仅作为手段、抹消其作为目的的面相。

第三公式：自律公式（Formel der Autonomie / Formula of Autonomy）

> Handle so, dass der Wille durch seine Maxime sich selbst zugleich als allgemein gesetzgebend betrachten könne.

要这样行动：让你的意志在它自己的准则里，同时能把自己看作普遍立法者。

这一公式从来源看定言律令——律令从哪里来。回答是：从理性主体自己。理性主体既是立法者，又是服从者；立法和服从的同一性就是自律（Autonomie）。这和他律（Heteronomie，从外部接受法则）构成对立。康德的伦理学核心命题——人的尊严在于自律——全部凝结在这条公式里。

第四公式：目的王国公式（Formel des Reichs der Zwecke / Formula of the Kingdom of Ends）

> Handle so, als ob deine Maxime durch deinen Willen zum allgemeinen Naturgesetze werden sollte.

要这样行动：让你的准则永远可以作为一个目的王国普遍立法成员的准则。

这一公式从系统看定言律令——当所有理性主体都在自律地立法并互相把对方当目的时，会形成一个什么样的共同体。答案是目的王国（das Reich der Zwecke）——所有理性主体作为立法者和目的本身互相承认的共同体。这是前三条公式运作到极致时自然涌现的系统图景。

康德自己在《道德形而上学基础》中明确说，四条公式是同一条定言律令的不同面——一条要能被普遍化（第一），它必须尊重所有理性主体作为目的本身（第二），这种普遍化的来源只能是理性主体自己的自律立法（第三），所有这些自律立法者一起构成目的王国（第四）。四条不是四条并列的律令，是同一条律令从四个角度展开。

一·二、本文的任务

本文的任务不是挑战康德的这个结构，而是在SAE的15DD-16DD句式层把它做精确化。问题不在康德的内容——内容本身在15DD-16DD是准确的（第一公式的理性自我一致性、第二公式的人是目的在15DD，第三公式的自律原则贯穿15DD-16DD，第四公式的目的王国在16DD）——问题在康德的句式。四条公式的内容分布在15DD和16DD，但句式统一地停留在14DD的祈使结构。

SAE已经在别处对康德的绝对律令做过句式诊断（参见A16《One's Own Law》DOI 10.5281/zenodo.19037566，以及《Kategorischer Glaube》DOI 10.5281/zenodo.19719083 的§一对Vernunftglaube的类似诊断）。那里的发现是：康德的"你应当"（Du sollst）modal是14DD句式（目的锚定层的命令/假言结构），不是15DD句式（本体层的"不得不"）。同样的内容用不同的句式表达，语义学重量完全不同。"你应当把他者当目的"（14DD）和"他者作为本体的在场让我没有了不做B的选项"（15DD）是同一内容在两个不同句式层上的表述。

本文把这个工作扩展到康德四条公式全体。每一条公式都有15DD或16DD的内容配合14DD的句式。本文的任务是在15DD-16DD句式上把四条全部重新做一遍，让句式和内容匹配。这就是SAE对康德定言律令的句式精细化（satzformentheoretische Verfeinerung）。

一·三、本文在SAE系列中的位置

本文的起点是《SAE形而上学：维度句式论》（Metaphysics of Self-as-an-End: Dimensional Sentence-Form Theory，DOI 10.5281/zenodo.18894567，下称metaphysics-satz）。该paper建立了SAE的维度-句式同构（0DD-16DD）作为整个SAE框架的基础坐标，并在§VI射线一（Ray 1: Kant's Imperatives）中对康德四公式做了首次压缩式句式诊断：

> 康德的三个公式使用的句式都是"Handle so, daß..."，这是目的假言律令的祈使结构。第二公式试图表达绝对律令（15DD）的内容，第三公式试图表达协同律令（16DD）的内容，但都用了14DD的句式。这属于错误二（工具化）与错误四（他者抹除）的叠加：他把"不得不"写成了"应当"，把双主体结构写成了单主体命令。康德看到了正确的东西——人是目的，不仅仅是手段。但他能写出来的工具只有14DD的句式。珠子在15DD–16DD，椟在14DD。

metaphysics-satz里的这段诊断是压缩版本——它指出了康德用14DD句式承担15DD-16DD内容这件事，但没展开每条公式各自的具体残留。本文的任务是把这个诊断做完整展开：四条公式每一条分别在什么位置上携带什么样的14DD残留，相应的SAE 15DD-16DD句式应该长什么样子。

metaphysics-satz给出的康德公式和SAE层级的对应关系：

• 第二公式（人是目的） → 绝对律令（15DD）：他者的目的是A，所以我不得不做B
• 第三公式（自律）与第四公式（目的王国） → 协同律令（16DD）：我为目的A，他者为目的B，我们不得不做C

第一公式（普遍化）在metaphysics-satz里没有被单独对应到某个SAE层级。本文论证：第一公式的实质是"理性对自身的一致性要求"，它不对应某个具体层级的内容律令，而对应贯穿15DD-16DD整体的运作条件——理性作为理性，必须在运作时保持自身一致。这是下面§三将展开的第一条"理性不得不理性"的结构位置。

这里要显式说明本文和metaphysics-satz压缩诊断之间的关系，以免读者在读到§三·二（条二作为自律底色的运作方式）和§四（自律作为贯穿四条的底色）时，因为"第三公式到底在哪里"这个问题产生张力。

本文不推翻metaphysics-satz的压缩诊断，是在更高分辨率下对它的结果做重新分配。metaphysics-satz把"第三公式（自律）内容在16DD"作为压缩判断给出，这个判断在压缩层面是准确的——第三公式的内容（理性作为自律立法者）确实指向多主体协同的结构。但在高分辨率下看，第三公式里其实包含两个成分：自律原则本身（理性给自己立法——这是贯穿所有维度的底色）+自律的多主体实现（所有自律主体相互立法相互承认的协同结构——这归第四公式目的王国/16DD协同律令）。压缩诊断里把这两者合在一起归给第三公式，本文在高分辨率下把它们拆开——自律原则作为底色归§四的"自律贯穿四条"，协同律令归§五·三的"条四 produce第四公式目的王国"。拆开之后，第三公式的内容不消失，而是以更精确的方式分布：底色形式贯穿所有条（§四），具体内容显示为第四公式的16DD实现（§五·三）。

这个重分配让paper的整体结构更紧：压缩诊断给出的是"哪些康德内容属于SAE的哪个层级"，本paper给出的是"哪些康德内容以什么形式（底色、条目、引擎、produce）在SAE坐标里分布"。前者的精度是"层级归属"，后者的精度是"结构位置"。后者严于前者，且对前者提供独立的结构性支撑。

基于这个诊断框架，SAE已有的几篇论文处理了康德四公式中的不同部分：

• A16《One's Own Law》（DOI 10.5281/zenodo.19037566）——第二公式（人是目的）的15DD转译。绝对律令作为"他者的目的是A，所以我不得不做B"，把康德"你应当把人当目的"的14DD句式转移到15DD的"不得不"句式。
• 《Kategorischer Glaube》（DOI 10.5281/zenodo.19719083）——自律原则在15DD内向面的展开。绝对信仰作为主体对自身站立的不可外置承担，处理自律在信仰维度（而非意志维度）的显示。paper里特别指出绝对信仰的"自律"比康德意志意义上的自律更底——它是主体作为主体立住的存在方式本身。
• 16DD协同律令（在metaphysics-satz中有完整定义：我为目的A，他者为目的B，我们不得不做C）——第三公式（自律的复数化）和第四公式（目的王国）的15DD-16DD实现。C不属于A也不属于B，是两个独立目的相遇之后逼出来的行动——这是康德目的王国的非理想化具体结构。

但迄今为止，SAE没有做一件工作：把康德四公式作为一个整体，在SAE句式坐标里做统一的展开式诊断和重述。metaphysics-satz启动了这个工作但只做了压缩版；A16、《Kategorischer Glaube》、散见各paper的16DD讨论各自处理四公式中的一部分。四公式作为同一条定言律令的四个面的内在关系，没有在SAE侧被完整重述。本文就是这个缺失的完整重述。

作为整合性声明，本文做三件事：

一、在metaphysics-satz已有诊断的基础上，把康德四公式每条的14DD残留做完整展开（§二）。

二、给出四条"理性不得不"的SAE精细化，作为康德四公式在15DD-16DD句式层的对应重述（§三）。

三、在这个精细化结构里显示已有的SAE论文（A16、《Kategorischer Glaube》、16DD相关）各自占据的位置，让它们共同的康德底座显式化（§五）；并对SAE伦理学作为康德伦理学的15DD-16DD句式精细化这一整体定位做显式声明（§六）。

SAE不是在康德之外另起炉灶，而是康德伦理学在当代条件下的细化（Verfeinerung）——接续康德的方法论（立坐标、划先验和经验、以自律为根、用不得不modal），在21世纪工具（凿构循环、余项ρ、维度序列、不得不modal）支持下，把四公式做精确化。

二、四公式各自的14DD残留诊断

术语说明：本文用"14DD残留"（14DD-Rest / 14DD residue）指代一种句式错层——当某论断的内容属于15DD-16DD层，而其句式属于14DD（目的锚定层，如"应当"、"假言"、"命令"结构）时，14DD的句式特征就成为15DD-16DD内容上的残留。这个术语与SAE核心概念"余项"（ρ, Rest）词源一致，也在绝对信仰paper（DOI 10.5281/zenodo.19719083）中作为同一概念使用。

metaphysics-satz §VI射线一已经给出了康德四公式诊断的压缩版：四公式都用"Handle so, daß..."的14DD祈使结构；第二公式内容在15DD，第三公式内容在16DD；错位是工具化（错误二）+他者抹除（错误四）的叠加。本节把这个压缩诊断做完整展开——四条公式分别有哪些具体的14DD残留，每条的SAE 15DD-16DD对应应该是什么。

诊断的目的不是批评康德——康德在他自己的框架内做了18世纪能做的全部精细工作——而是确定SAE在15DD-16DD句式层做重述时，需要把什么样的14DD特征切掉。

二·一、第一公式的14DD残留

普遍法则公式的表述："你要只按照你同时能够愿意它成为一条普遍法则的那个准则去行动。"

14DD残留一：句式是假言命令的变体。"如果你想让你的准则合理，那么你应当使它可普遍化"——条件"你想让准则合理"加上应当结果"使它可普遍化"。这是典型的14DD假言结构（hypothetical imperative），虽然康德自己把它归为定言律令。形式上是定言，深层结构是假言。

14DD残留二：准则与律令的二元结构。康德设定"准则（Maxime，主观的行动原则）"和"律令（Gesetz，客观的道德法则）"的区分，然后通过普遍化测试把准则提升为律令。这个二元结构是14DD的——设定一个工具（准则）和一个目的（律令），用工具向目的看齐。15DD句式里不需要这种二元——理性的运作本身就是理性化（vernünfteln），不需要先有"主观准则"再被测试成"客观律令"的过程。

14DD残留三："应当"作为modal。"你要（sollst）..."这个句式让律令是从外向主体发出的命令——哪怕这个外是理性自己通过自律发出的。15DD句式里不需要这种命令结构——不是"理性命令你理性化"，而是"理性不得不理性"，理性化是理性作为理性的存在方式本身，不是被命令的结果。

SAE的任务：把第一公式从"如果你的准则要合理，那么它应当可普遍化"（14DD假言结构）转译为"理性不得不理性"（15DD本体结构）——理性作为理性的运作方式本身就包含自我一致性（普遍化的底层内核），不需要外加一个"应当"来要求这种一致性。

二·二、第二公式的14DD残留

目的本身公式的表述："你要这样行动，无论是对你自己还是对任何他人，在任何时候都同时把人性当作目的，绝不仅仅当作手段。"

14DD残留一："你应当把...当作..."的句式。康德在这里虽然谈的是人作为目的本身（15DD内容），但他用"把X当作Y"（etwas als Y behandeln）的句式——这是一种主客分离的处理关系，主体把客体"当作"某种东西。15DD的"他者作为本体在场"不是"我把他者当作本体"（那是主体主动把某种属性加到他者身上），是他者已经作为本体在场，我的行动在这个本体在场的条件下展开。"当作"的句式隐含了主体的主动建构，15DD的句式把主动建构去除——本体不是被当作，本体是存在方式本身。

14DD残留二："绝不仅仅当作手段"的否定式。这条律令的正面部分（把人当目的）加一个否定限定（不仅仅当手段）。这让律令成为一个带例外条款的复合命令——可以把人当手段（工具性使用是允许的），但不能仅仅当手段。这个"仅仅"（bloß）做了很多哲学工作，但它作为限定条款让律令在句式上变得复杂——不是纯粹的本体陈述，是"做X，但不要完全做X"的混合结构。A16的工作显示：在15DD句式里，"他者作为本体的在场让我没有了不做B的选项"不需要这种"可以但不完全可以"的限定——主体作为本体在场这个条件本身就规定了行动的结构。

14DD残留三：目的作为被"当作"的属性。康德在第二公式里把"目的"放在主体的判断对象位置——是否把某物当作目的是主体的道德判断。15DD的立场不同：本体就是目的，不需要判断。一个主体要不要承认另一个主体是本体，不是经验性的判断问题，是15DD层本体结构的问题——主体能作为15DD主体立住，已经预设了对所有其他15DD主体的本体承认。

SAE的任务：把第二公式从"你应当把人当目的"（14DD判断句式）转译为"理性不得不有方向，即目的"（15DD本体结构）——理性运作本身必然有方向，这个方向在本体层面就是其他主体作为本体的在场。这也是A16中绝对律令的内容。

二·三、第三公式的14DD残留

自律公式的表述："要这样行动：让你的意志在它自己的准则里，同时能把自己看作普遍立法者。"

14DD残留一：立法者-服从者的二元位置。自律在康德这里被表述为"同一主体同时作为立法者和服从者"的结构。这个结构本身仍然保留了立法和服从的区分——只不过两个位置由同一主体占据。15DD句式里不需要这个二元位置——理性不是"既立法又服从"，理性是"运作自身"。运作就是立法（运作方式就是法）也就是服从（按运作方式运作），三者不分。

14DD残留二：把自己"看作"立法者的"看作"。同样的主客分离问题——主体把自己"当作/看作"某种身份（立法者）。这是反思性的自我关系，主体对自己做出一个判断（判断自己是立法者）。15DD的自我关系不需要这种反思判断——自律作为底色不是主体对自己做判断的结果，是理性作为理性运作本身的存在方式。

14DD残留三：意志作为立法的代理。康德把自律放在意志（Wille）这个机能上——意志立法、意志服从。但意志作为一个特定的心理-理性能力，只是15DD主体的一个面。把自律收在意志上限制了自律的范围。15DD的自律不只在意志层运作——它在认知上（理性不得不有自己的认知方向）、在信仰上（绝对信仰作为不可外置的承担）、在律令上（绝对律令作为他者作为本体的在场下不得不做的事）、在协同上（16DD的我们不得不）各层都运作。自律是15DD主体整体的存在方式，不是一个特定机能的属性。

SAE的任务：把第三公式从"让你的意志同时能把自己看作立法者"（14DD特定机能的反思结构）转译为"自律作为四条的共同底色"（15DD主体整体的存在方式）——自律不单列为一条律令，而是贯穿所有四条的共同根。所有"理性不得不..."都是理性给自己立的法，不是外部给理性的法。

二·四、第四公式的14DD残留

目的王国公式的表述："要这样行动：让你的准则永远可以作为一个目的王国普遍立法成员的准则。"

14DD残留一："王国"作为理想（Ideal）。康德自己承认目的王国是一个理念（Idee），一个理想共同体，现实中不存在。把第四公式的对象放在"理想"位置让它失去了对当下行动的切实约束力——"要像在理想共同体里那样行动"在14DD的假言结构下又多了一个"假如"：假如有一个目的王国，那么你应当按它成员的方式行动。

14DD残留二："作为...成员"的身份假设。让主体把自己想象为目的王国的一个成员，然后推断作为成员会怎么做。这是反事实的身份假设（counterfactual identification），主体不是真的是目的王国的成员，是假装是。这种想象性身份假设在14DD是标准手法，但15DD要求的是真实的存在状况——主体不是假装和他者在目的王国里，主体是实际上和他者在一个"我为A他者为B我们不得不做C"的协同结构里。

14DD残留三：把目的王国作为理想化的普遍化。康德把第四公式视为第一公式（普遍化）和第二公式（人是目的）合起来的理想化结果。这个合成保留了第一公式的形式化和第二公式的"当作"句式，两个14DD残留叠加。SAE的"我为A他者为B我们不得不做C"是具体协同的结构陈述，不是理想化想象——两个具体主体在具体处境里共同承担一个第三项的结构性不得不。16DD协同律令不是第四公式的变体，是第四公式在15DD-16DD具体协同中的非理想化实现。

SAE的任务：把第四公式从"让你的准则可以作为目的王国成员的准则"（14DD理想化身份假设）转译为"理性不得不被追问"（15DD的他者进场结构）——理性的运作必然面对他者的追问（来自其他理性主体的要求、质疑、校准），这个追问在协同层就是"我们不得不"的结构。目的王国不是理想共同体，是理性主体相互追问相互校准的实际结构。

二·五、四公式14DD残留的共同特征

四条公式的14DD残留有共同特征：

• 都用"应当"（sollst）modal，而非"不得不"（kann nicht nicht）modal——命令而非本体。
• 都有主客分离的处理关系（"把X当作Y"、"把自己看作立法者"）——主体对对象做判断，而非本体结构直接运作。
• 都在假设或理想的位置上运作（可普遍化的准则、被当作目的的人、作为立法者的意志、目的王国的成员）——假言或反事实，而非实际在场。
• 都依赖某个中介机能（意志、准则、反思）——通过特定机能承担律令，而非主体整体的存在方式。

这些共同特征不是康德写得不严谨——恰恰相反，它们是康德在18世纪哲学工具下能达到的精度。要去除这些14DD残留，需要的是21世纪的工具：凿构循环的动态生成机制、余项（ρ）作为ontological地位、浑沌（0D）作为起点、15DD-16DD的维度序列、"不得不"作为独立的modal类型。这些工具让SAE能把康德在14DD句式里承担的15DD内容，在15DD句式里重新做一遍，而不丢失任何康德的核心洞察。

下面§三展开这个重述。

三、SAE精细化：四条"理性不得不"

本文对康德四公式的SAE精细化由四条"理性不得不"构成，外加一条自律作为贯穿四条的底色（而不是单列为第五条）。四条的德文、英文、中文对应如下：

一、理性不得不理性。

Die Vernunft kann nicht nicht vernünfteln.

Reason cannot not reason.

二、理性不得不发展。

Die Vernunft kann nicht nicht sich entwickeln.

Reason cannot not develop.

三、理性不得不有方向，即目的。

Die Vernunft kann nicht nicht eine Richtung haben, d.h. einen Zweck.

Reason cannot not have direction, that is, purpose.

四、理性不得不被追问。

Die Vernunft kann nicht nicht befragt werden.

Reason cannot not be interrogated.

四条全部以"理性"（die Vernunft / reason）为主词，以"不得不"（kann nicht nicht / cannot not）为modal——这是SAE 15DD-16DD的statements在康德题材下的signature。"理性"作为主词把四条统一到一个主题：理性的存在方式本身有哪些结构条件。"不得不"作为modal把四条从康德的"应当"（sollst / ought）句式拉到15DD-16DD的本体陈述。

四条不是四条并列的律令，而是同一条关于"理性作为理性如何立住"的陈述从四个角度展开。条一是先验条件，条二是动态运作，条三是方向结构，条四是协同结构。自律（第三公式）作为贯穿四条的底色，在每一条的运作里都在场。

下面分别展开。

三·一、条一：理性不得不理性

Die Vernunft kann nicht nicht vernünfteln. / Reason cannot not reason.

这条对应康德第一公式（普遍法则公式/形式）的内核。

这不是tautology（"理性当然是理性"的同义反复），而是把第一公式从准则/法则二元结构收回到理性自身的运作——理性作为名词（主体的机能）存在的方式，就是作为动词（理性化运作）的持续进行。下面展开。

康德第一公式的实质是理性对自身的一致性要求。"可普遍化"这个测试不是一个外加的条件，而是理性作为理性时不得不保持的自我一致性——一条不能被普遍化的准则，就是理性背叛了自己（在这条准则成立时，理性不能同时继续作为理性运作）。康德把这件事表述为"你要行动使得你的准则可以成为普遍法则"——这是把理性对自身的一致性要求包装成一个对主体的14DD命令。

SAE的精细化是：理性不得不理性——"理性"作为动词。前一个"理性"是名词（主体的理性能力），后一个"理性"是动词（做理性所做的事）。理性作为名词存在的方式，就是作为动词持续运作。停止"理性地运作"，理性作为名词就不再是理性。这让康德第一公式的内核（理性的自我一致性）从14DD的"你应当"转移到15DD-16DD的本体陈述。

这条陈述的几个要点：

一、"理性"的名动双重用法。汉语的"理性不得不理性"、英文的Reason cannot not reason、德文的Die Vernunft kann nicht nicht vernünfteln——三语都用了"名词+modal+同词动词化"的结构。这种结构让陈述本身就显示出理性的自反性：理性不是一个静态机能，是持续的自我运作。这和康德第一公式的内核一致（可普遍化的实质是自我一致性），但用陈述的句式结构直接显示出来，不需要外加"应当"的命令。

二、切掉的14DD残留。§二·一列出了第一公式的三处14DD残留：假言命令的变体、准则-律令的二元结构、"应当"作为modal。本条全部切掉：不是"如果想让准则合理就应当...", 是理性作为理性就在运作中（假言消失）；不区分"主观准则"和"客观律令"（二元结构消失）；不用"应当"而用"不得不"（modal转换）。

三、作为贯穿条件的位置。条一不是四条中的第一条律令，而是后三条得以成立的先验条件。没有条一（理性不作为理性运作），就没有条二的发展（理性不存在，发展无从说起）、没有条三的方向（理性不在，方向无从朝向）、没有条四的追问（理性不在，无从被追问）。条一是15DD-16DD整体运作的前提。

四、条一的结构性强制力：退出代价。可能的读法反问是：如果"理性不得不理性"只是本体陈述（理性如果是理性就在做理性的事），那么主体难道不能退出吗——"我不做理性化了，我放弃15DD主体性，你的条一对我无效了"。这个反问在14DD命令结构下没有答案（你放弃命令就免受命令了），但在15DD本体结构下有精确答案。

主体无法真正"退出"到一个中立的非主体状态。15DD主体停止条一的运作，不是退回到某个休眠的中立态，而是被14DD的手段结构吞噬，沦为工具。因为在SAE的维度序列里，15DD以下的每一层都是工具性层级——主体一旦停止作为15DD主体运作，它就在14DD或更低层运作，而在这些层级里它只能作为别的主体的手段或作为某个更大系统（如资本、官僚、算法、宇宙律）的工具。条一的强制力不来自外部命令，而来自结构性降格：不保持理性的自我一致性运作=主体作为目的本身的存在论防线立即崩溃。

这使条一从"A=A"的分析性废话变成生存论的绝对张力。不是"你如果想当理性主体，就必须保持理性化运作"（14DD假言），而是"在14DD的手段结构面前，为了不被碾碎为工具，主体不得不持续进行理性运作"（15DD本体）。退出即降格，这是条一在15DD层的强制力来源。

五、自律在条一上的显示。自律作为底色在条一上的显示是：理性的运作来源是理性自己，不是外部命令。"理性不得不理性"不是某个上位者命令理性如此，是理性作为理性的存在方式本身。这把康德第三公式（自律）的核心（自己给自己立法）在条一的最底层位置上立住。

三·二、条二：理性不得不发展

Die Vernunft kann nicht nicht sich entwickeln. / Reason cannot not develop.

这条是自律底色的具体运作方式。

自律（Autonomie）在康德那里被理解为意志对自身的立法。但"自律"作为一个静态属性（主体"是"自律的）和"立法"作为一个持续运动（主体持续地给自己立法）有微妙差异。如果自律是静态属性，那么主体一旦达到自律就停下了——但康德的自律不是这种完成态。真正的自律是持续的立法运动：主体每时每刻都在给自己立法，立法停止的那一刻，自律就不再运作。

SAE把这个理解结构化为条二：理性不得不发展。"发展"（sich entwickeln）在这里不是任何具体的进步内容，是理性的立法运动本身不能停。"立法"（Gesetzgebung）的动词性被"发展"的持续性显示出来。

为什么必然是"发展"而不是其他措辞？可能的替代措辞包括"理性不得不自律"、"理性不得不自我立法"等。为什么本文选"发展"作为精确表达？回答必须从第三公式的三处14DD残留（§二·三）的被切除之后，什么剩下作为可表达的内核说起。

第三公式的三处14DD残留：

• 立法者-服从者的二元位置
• "把自己看作"立法者的反思结构
• 意志作为立法的代理

这三处被切除之后，康德自律原则的内核剩下什么？

切除二元位置：不能说"立法"（这暗含一个"被立法者"），也不能说"自我立法"（这暗含主体对自己的某种反向动作）。留下的只能是一个无二元的运作。

切除反思结构：不能说"主体意识到自己在立法"或"主体把自己看作立法者"——这些都是反思性表述。留下的只能是主体作为主体运作本身，不带反思mediation。

切除意志限定：不能用"意志"、"理性"、"心灵"等特定机能做主词——自律不属于某个机能，是主体整体的存在方式。留下的只能是主体整体的某种一般性的持续存在。

三个切除共同留下的内核是：主体整体的无二元、无反思、不限定于特定机能的持续运作。这个内核用什么词表达最精确？

• 不能是"自律"：自律本身是被诊断的对象，用它解释它自己是循环的；而且"自律"在日常语言里已经被静态化为"主体是自律的"这种属性陈述。
• 不能是"自我立法"：立法是被切除的14DD残留的核心词，留下它就没切干净。
• 不能是"运作"：太薄，捕捉不到"持续不能停"的modal。
• 不能是"持续存在"：太近存在（Sein）而远运动（Werden）。

"发展"（Entwicklung / development）是唯一同时满足所有条件的词：它是主体整体的（不限定于机能）；它是持续性的（内在包含"不能停"的modal）；它是无二元的（发展是主体自身的运动，不是"主体让某物发展"）；它是无反思的（主体不必意识到自己在发展才能发展）。

"发展"在德语Entwicklung里有"展开"（sich entfalten）的含义——主体把自己的结构展开，这正是康德自律原则"理性把自己的立法展开为实际的自我立法运动"的精确表达。"发展"不是第三公式的附加解读，是三处14DD残留切除之后第三公式内核的唯一精确承载词。

这条陈述的几个要点：

一、切掉的康德14DD残留。康德在自律公式上的14DD残留（§二·三）包括立法者-服从者的二元位置、"把自己看作"立法者的反思结构、意志作为立法的代理。条二全部绕开：发展不需要区分立法和服从（运作就是立法也是服从，三者不分）；不需要主体对自己做反思判断（发展是理性存在方式本身，不是主体对自己做出的判断）；不限定在意志机能上（发展在认知、信仰、律令、协同各层都运作）。

二、发展的内容由其他三条规定。条二只规定"理性不得不发展"——发展本身不能停。但发展朝什么方向？发展的具体形态是什么？发展在多主体之间如何协调？这些由条一（理性自身运作的一致性）、条三（朝向他者作为本体）、条四（在追问中被校准）分别回答。条二是动力条件，其他三条是具体结构。

三、发展≠改进。"发展"在SAE这里不是价值判断意义上的"越来越好"，是结构意义上的"不能停下"。一个主体可能在某个具体方向上"退步"，但只要它还作为主体在运作，它就在"发展"——退步也是发展的一种形态（退步意味着主体还在运作，还在对自己立法，只是立的法在某个具体维度上被诊断为"退"）。条二和"凿构循环"（Meißel-Konstrukt-Zyklus）的不停顿同构——主体不停地凿自己，不停地构自己，这就是发展的结构含义。

四、自律在条二上的显示。自律作为底色在条二上的显示最密集——自律作为持续立法运动，正是条二的内核。说主体自律，就是说它不得不发展；说主体不得不发展，就是说它在持续立法。两者在结构上是同一件事的两种表述。这让条二承担了康德第三公式（自律）在SAE句式下的直接重述。

三·三、条三：理性不得不有方向，即目的

Die Vernunft kann nicht nicht eine Richtung haben, d.h. einen Zweck. / Reason cannot not have direction, that is, purpose.

这条对应康德第二公式（目的本身公式/质料）。

条二规定了理性不得不发展，但没有规定发展的方向。如果理性的发展是完全随机的扩张，它会立刻遇到一个结构问题——作为理性的运作本身不能容忍随机性（这会违反条一）。所以理性的发展必然有方向。方向在15DD层就是——他者作为本体的在场。

但为什么方向必然是他者，而不能是别的什么？这是一个必须被显式推导的结构问题。AI系统"发展"朝向更多参数或更高精度，资本系统"发展"朝向更多利润，官僚系统"发展"朝向更大规模——这些都是"不得不发展"的结构，它们的方向都不是他者。为什么15DD主体的发展方向必然是其他15DD主体？

回答在ZFCρ第一定律（构必留余）。凿构循环每一轮必然产生余项ρ——主体每一次运作（凿构）都留下不能被这一轮运作完全吸收的剩余。这个定律是SAE基础论文证明过的结构事实（参见SAE Foundation Paper III DOI 10.5281/zenodo.18727327、Methodology 00 Via Rho DOI 10.5281/zenodo.19657440）。

余项必须有出口。如果余项的全部都被主体内部吸收，主体的凿构循环会进入自闭环——因为每一轮运作产生的余项变成下一轮运作的输入，但下一轮运作又产生新的余项，余项在内部不断累积。内部累积没有容纳空间，主体的结构会在累积压力下崩溃。所以余项在结构上不得不指向外部——余项必须溢出主体边界才能让凿构循环可持续。

外部世界里能接收余项的是什么？这里是关键的拓扑学步骤：能接收余项而不把它降格的，只能是另一个同样产生余项、同样需要外部出口的15DD主体。

考虑其他候选接收者：

• 工具/物件：接收余项时把它降格为资源——比如一个主体的思考留下的余项（一个未被理论化的感受、一个不完整的概念）如果只被写到工具里（比如一个数据库），那个余项就变成了数据，失去了作为余项的存在论身份。
• AI系统/资本结构/官僚组织：接收时把余项吸收为系统的运作输入——余项变成系统的fuel或data，继续被14DD结构运作，失去作为15DD余项的独立身份。
• 自然界的非主体：无法作为余项的接收者——非主体没有"接收"这个动作的结构位。

能真正接收15DD主体的余项而保留它作为余项身份的，只有另一个15DD主体——因为只有另一个15DD主体，才有同样的余项结构、同样的凿构循环、同样的"余项需要出口"的存在论必然。两个15DD主体之间的余项交换是双向的：我的余项溢出到你，你的余项溢出到我，两者都作为余项被对方接收（不被降格为资源或数据），然后触发对方新一轮的凿构。

所以他者不是理性发展"选择"的方向，他者是余项溢出时唯一拓扑学兼容的接收者。理性不得不发展（条二），发展产生余项（ZFCρ第一定律），余项不得不有外部出口（避免内部崩溃），唯一合法出口是另一个15DD主体（拓扑学兼容性）——因此理性发展的方向不得不朝向他者。这是从条二到条三的结构性必然推导，不是仅仅论证"发展需要方向"就跳到"方向是他者"的直觉飞跃。

康德第二公式把这件事表述为"你要把人当作目的，绝不仅仅当作手段"。metaphysics-satz §VI射线一指出，康德第二公式的内容在15DD（绝对律令），句式在14DD（祈使结构）。A16 paper已经做了这条的SAE转译：绝对律令作为"他者的目的是A，所以我不得不做B"——他者作为本体的在场让我没有了不做B的选项。

本条"理性不得不有方向，即目的"是A16绝对律令在本paper四条体系下的位置声明。"理性不得不有方向"是关于理性发展的结构性陈述，"即目的"指出方向的具体内容是他者作为目的。两个表述合起来正好对应A16的"他者的目的是A，所以我不得不做B"——方向结构（不得不有方向）加方向内容（他者作为目的）。

这条陈述的几个要点：

一、"方向"和"目的"的同一性。汉语"理性不得不有方向，即目的"里的"即"字承担了一次关键的同一化：方向就是目的（direction is purpose）。这对应康德第二公式的核心洞察——人作为理性存在者是目的本身，不只是某个路径上的中转点。在SAE的结构里，方向不是任意的朝向，而是朝向其他理性主体作为目的本身。

二、切掉的康德14DD残留。§二·二列出了第二公式的三处14DD残留：主客分离的"当作"句式、"绝不仅仅当作手段"的带限定复合命令、目的作为主体判断的对象。A16已经做了这条的15DD转译（参见A16 paper DOI 10.5281/zenodo.19037566 的完整展开），本条只需要指出A16的工作在四条体系下的位置。

三、A16 paper在本paper中的位置。A16《One's Own Law》就是本条的完整展开。本paper不重复A16的工作，而是把它摆在四条体系的第三条位置上。A16的"他者作为本体的在场让我没有了不做B的选项"是本条"理性不得不有方向，即目的"的具体实现。

四、自律在条三上的显示。自律作为底色在条三上的显示是：方向来自理性自身的结构，不是外部目的锚定。康德在他律/自律的区分里特别警惕外部目的（幸福、上帝的命令、社会利益）作为方向源头——那会让理性成为手段。SAE的精细化里，方向来自理性的运作本身——当理性作为理性运作（条一），它不得不发展（条二），发展不能随机所以必然有方向——这个方向的结构性来源在理性自身，不在外部。他者作为方向的具体内容，不是因为他者从外部给理性指定方向，是因为他者作为同样的15DD主体恰好是理性朝向的唯一ontologically合适的对象。

三·四、条四：理性不得不被追问

Die Vernunft kann nicht nicht befragt werden. / Reason cannot not be interrogated.

这条对应康德第四公式（目的王国公式/系统）。

当多个主体各自在条一（作为理性运作）、条二（不得不发展）、条三（有方向朝向他者）的结构下运作并相遇时，会发生什么？metaphysics-satz给出了答案：协同律令（16DD）——"我为目的A，他者为目的B，我们不得不做C"。C不属于A也不属于B，是两个独立目的相遇之后逼出来的行动。

但协同律令的运作需要一个关键的结构条件：追问。如果两个主体各自坚持自己的目的，不接受对方的质疑和校准，C就不可能被找到。C作为两个目的相遇后的涌现，要求两个主体都把自己暴露给对方的追问——这不是一方对另一方的说服，是两个都可追问、都在被追问中调整的主体之间涌现出的第三项。

SAE把这个结构条件立为条四：理性不得不被追问。追问是16DD协同律令得以运作的结构性条件，也是康德目的王国的实际操作形式。

这条陈述的几个要点：

一、追问作为16DD的engine。metaphysics-satz把追问作为"追问终止结构"（Terminierungsstruktur der Rückfrage）来讨论，指出协同律令（16DD）是所有追问的最终终止点。本条把追问进一步立为协同律令运作的必要条件——协同律令不只是追问的终止点，也是追问运作的produce。没有追问，就没有两个独立目的相遇后的C；有追问，C才能从两个独立主体的互相校准中涌现。

二、被动语态的结构意义。条四是四条中唯一使用被动语态（理性"被"追问 / Die Vernunft kann nicht nicht befragt werden）的。前三条都是主动语态（理性理性、理性发展、理性有方向）。这个语态转换不是偶然——它标志着从单主体结构（条一到条三描述单一主体的运作结构）到多主体结构（条四要求主体对他者的追问开放）的层级跃迁。被动语态意味着追问不是主体发出的动作，是主体接受的结构——他者进场让追问发生，主体不得不对这个追问开放。

三、与《Kategorischer Glaube》闭合路径的区别与连接。《Kategorischer Glaube》paper §五里对"不得不被追问"做了详细展开，并区分了绝对信仰在这一点上的特殊性——绝对信仰的追问开放，但解释通道结构性不通（追问+可解释 vs 追问+不可解释的对偶）。本条里的"理性不得不被追问"是绝对律令和协同律令方向上的追问——追问开放，并且解释可行（甚至必须可行，以让协同得以建立）。两个方向上的追问形成了完整的"被追问"结构：内向面（信仰）追问可入但解释不通，外向面（律令+协同）追问和解释都开放。

四、切掉的康德14DD残留。§二·四列出了第四公式的三处14DD残留：目的王国作为理想（Ideal）、"作为成员"的身份假设、目的王国作为第一公式和第二公式合成的理想化。条四绕开全部三处：追问是实际发生的，不是理想假设（在场的他者真的在发出追问）；追问不需要身份假设（主体真的在响应他者的追问，不是假装是目的王国成员）；追问是具体的多主体结构，不是两个公式的理想化合成。

五、自律在条四上的显示。自律作为底色在条四上的显示是：被追问不是被外部支配。追问来自同样自律的他者主体——他者按自己的条一到条三在运作，然后以自律主体的身份追问我。我对这个追问开放，不是对外部权威低头，是承认他者作为同样自律的主体有追问我的正当位置。两个自律主体互相追问互相校准，这正是康德目的王国的精确结构——目的王国不是有一个上位权威在支配所有人，是所有自律主体互相承认对方的立法者身份并互相追问互相校准。

三·五、四条作为同一陈述的四个面

按康德自己的说明，四公式是同一条定言律令从四个不同角度看的结果——形式、质料、来源、系统。SAE的四条精细化保留这个统一性：

• 条一（理性不得不理性）：形式面——理性对自身一致性的结构性要求。
• 条二（理性不得不发展）：来源面（部分）——理性的运作来自理性自身，所以发展不能停。
• 条三（理性不得不有方向，即目的）：质料面——发展的方向结构。
• 条四（理性不得不被追问）：系统面——多主体运作的协同结构。

康德的"同一条律令从四个角度看"在SAE精细化下变得更具体：四条是同一条关于"理性作为理性如何立住"的陈述的四个必要条件，缺一不可。没有条一，后面三条没有前提；没有条二，理性静止不运作；没有条三，发展随机无方向；没有条四，多主体运作退化为单主体独断。四条合起来构成理性作为15DD-16DD主体立住的完整结构条件。

自律作为底色在每条上都在场——条一的理性自我来源、条二的立法运动不可停、条三的方向来自理性自身、条四的他者作为同样自律主体。自律不是四条中的一条，是四条的共同根。下面§四展开这个底色结构。

四、自律作为底色：为什么不单列为第五条

本文把自律（康德第三公式）作为贯穿四条的底色，而不单列为第五条律令。这个选择需要理由，因为它偏离了康德本人对四公式的并列处理。

四·一、康德自律公式的位置

康德在《道德形而上学基础》里把自律公式作为第三公式和其他三条并列。按康德自己的说明，四公式处理同一条律令的不同面：第一公式处理形式（可普遍化），第二公式处理质料（人是目的），第三公式处理来源（意志自律），第四公式处理系统（目的王国）。自律作为其中一面和其他三面并列。

这个并列处理在康德自己的框架里是自洽的——他把形式、质料、来源、系统当作四个相对独立但在定言律令中同时成立的面。但在SAE句式下看，自律和其他三面的关系不是并列关系，而是贯穿关系。

四·二、为什么自律不能和其他三条并列

自律的内核是"理性给自己立法"——来源在理性自身，不在外部。这个"来源"不是四个面中的一个面，而是其他三个面（形式、质料、系统）得以成立的条件。如果形式（第一公式）来自外部命令（比如"因为上帝命令所以理性要一致"），第一公式就不成立；如果质料（第二公式）由外部权威指定（比如"因为国家规定所以人是目的"），第二公式就不成立；如果系统（第四公式）由外部统治者规划（比如"因为某上位者设计了目的王国所以我们按它的规矩"），第四公式就不成立。

自律作为"来源在理性自身"是其他三个面都不得不满足的条件——不是四面中的一面，是四面共同的立足点。康德自己也意识到这件事（他反复强调自律是定言律令的真正基础），但他用"四公式并列"的结构处理，让自律在表述上和其他三条处于同一层次。SAE的精细化把这个表述上的并列关系改为结构上的贯穿关系——自律作为底色，其他四条（理性、发展、方向、追问）都在自律底色下运作。

此为句式层面的结构优化，非对康德内容的任何否定——康德自律原则的实质内容（理性给自己立法、不从外部接受法则）在SAE精细化里完整保留，只是其在坐标中的位置从"并列第三条"重分配到"贯穿四条"。这是对康德洞察的更精确显示，不是对它的修改。

四·三、自律在四条上的具体显示

自律作为底色在四条上的具体显示形式已在§三的每一节末尾标出，这里做统一整理：

• 条一（理性不得不理性）上：理性的运作来源是理性自己，不是外部命令。"理性不得不理性"这句话本身不是某个上位者下的命令，是理性作为理性的存在方式。这是自律在最底层位置上的显示。
• 条二（理性不得不发展）上：立法运动本身不能停。自律不是静态属性，是持续立法。立法停了，自律就不在了。条二的"发展"和自律的"持续立法"在结构上是同一件事。
• 条三（理性不得不有方向，即目的）上：方向来自理性自身的结构。他者作为方向的内容，不是外部给的，是理性朝向其他15DD主体的ontological必然。
• 条四（理性不得不被追问）上：追问来自同样自律的他者。对追问开放不是对外部权威低头，是承认他者作为同样自律主体的追问位置。

四条的每一条都在自律底色下运作。自律是四条的共同根，不是四条中的一条。

四·四、这个处理对SAE整体的意义

把自律作为底色而不是第五条律令，对SAE整体有一个重要的结构后果：自律原则渗透到SAE每一个维度的运作里，不只在伦理律令维度。

• 在认知维度，自律显示为"主体不得不有自己的认知方向"（认知论四先验之一）。
• 在信仰维度，自律显示为绝对信仰（one's own faith）——主体对自身站立的不可外置承担。
• 在律令维度，自律显示为绝对律令（one's own law）——他者作为本体的在场下不得不做的事。
• 在协同维度，自律显示为16DD协同律令——两个自律主体相遇涌现的C。

康德把自律放在意志这个特定机能上，让它限定在伦理律令的维度。SAE把自律解放为贯穿所有15DD-16DD维度的底色，自律原则在每个维度都有具体的实现形式。这让康德的自律原则（人的尊严的真正基础）在SAE里的作用更广、根更深。

下面§五把SAE已有的几篇论文摆在这个精细化结构里的具体位置。

五、SAE已有论文在四条精细化结构中的位置

本节把SAE已经发表的与康德伦理学相关的几篇论文摆在四条"理性不得不"的坐标里，显示它们共同的康德底座。这是本paper作为整合性声明的一个核心功能——不是把这些paper的工作重做一遍（它们已经做完了），而是在一个统一结构里显示它们的位置关系。

五·一、A16《One's Own Law》位置：条三

A16《One's Own Law》（DOI 10.5281/zenodo.19037566）对应本paper条三"理性不得不有方向，即目的"的完整展开。A16处理的是康德第二公式（人是目的）的15DD句式转译，它的核心陈述"他者的目的是A，所以我不得不做B"就是"理性有方向且方向是他者作为目的"的具体表达。

A16在本paper四条结构中的位置可以这样理解：

• 条一（理性不得不理性）给出A16得以运作的前提——主体必须作为理性主体运作，A16的"不得不做B"才有主体可以承担。
• 条二（理性不得不发展）给出A16的动力——主体的持续立法运动让"不得不做B"不是一次性的命令，而是持续的方向锁定。
• 条三（理性不得不有方向，即目的）就是A16的位置——A16展开条三的具体内容：方向是他者作为本体的在场。
• 条四（理性不得不被追问）给出A16运作时的校准机制——我做B的时候不得不向他者开放追问，以确保B真的朝向他者作为目的而不是以"为他者好"名义的工具化。

A16paper里的"one's own law"这个命名，正好对应"自律作为底色"在律令维度的显示——律令的"我"性，不是外加命令，是理性自身对方向的承担。

五·二、《Kategorischer Glaube》位置：自律底色在15DD内向面的显示

《Kategorischer Glaube》（DOI 10.5281/zenodo.19719083）处理自律原则（康德第三公式）在信仰维度的展开，对应本paper四·四所说"自律作为底色在15DD各维度的具体实现"中的一个维度——信仰维度。

《Kategorischer Glaube》paper的核心——绝对信仰作为主体对自身站立的不可外置承担——就是自律原则在15DD内向面的精确显示。主体不把自己的站立外包出去，不让信仰降级为某个上游reason的派生结论，这正是自律（理性给自己立法）在信仰维度的形式。

《Kategorischer Glaube》paper和本paper的关系比A16更微妙：

• A16处理条三（一条律令），本paper把A16摆在四条中的位置。
• 《Kategorischer Glaube》不直接对应四条中的某一条，而是展开自律底色在15DD内向面的具体运作。

这给了自律底色在SAE系列中的精确定位——它不只在律令维度运作（A16那样的外向律令），也在信仰维度运作（Kategorischer Glaube那样的内向承担）。绝对律令（A16）和绝对信仰（Kategorischer Glaube）是自律底色在15DD的外向-内向双子结构。两paper合起来才是15DD层完整的自律实现。

五·三、16DD协同律令位置：条四

本paper条四"理性不得不被追问"的内容，在metaphysics-satz里的完整表述是16DD协同律令："我为目的A，他者为目的B，我们不得不做C。"

条四把协同律令的结构性条件（被追问）立起来，而协同律令本身（"我们不得不做C"）是条四运作的结果。两者的关系是：

• 条四（被追问）是16DD运作的engine——没有追问，C不能涌现。
• 协同律令（我们不得不做C）是16DD运作的produce——C是两个自律主体在互相追问下涌现的第三项。

目前SAE系列里还没有一篇专门paper展开16DD协同律令的完整结构——metaphysics-satz给出了协同律令的定义，本paper条四给出了它运作的结构性条件，但完整的16DD专论还未成文。这是SAE伦理学下一步可以写的paper——在本paper对条四的结构位置定位之上，展开16DD在具体协同中的运作细节。

边界声明：本paper不展开协同律令里C的产生机制——C作为两个独立目的相遇后涌现的第三项，它的产生需要具体协同情境下的结构分析（主体间互相追问的回合如何运作、C从对立到涌现的相变条件、C和A/B各自的语法关系等等）。这些是16DD专论的工作，不是本paper的射程。本paper只在"条四作为16DD engine"的位置上定位协同律令，具体机制留给未来paper。

五·四、四paper共同的康德底座

上述三paper（A16、Kategorischer Glaube、未来的16DD专论）加上本paper，构成SAE伦理学对康德四公式的完整接续：

• 本paper（《理性不得不》）——整合性声明，把四公式摆在SAE 15DD-16DD句式坐标里，给出四条精细化。
• A16（《One's Own Law》）——条三的完整展开（第二公式）。
• Kategorischer Glaube——自律底色在15DD内向面的展开（第三公式在信仰维度的实现）。
• 未来的16DD专论——条四的完整展开（第四公式）。

这四篇paper共同的康德底座，由本paper显式声明：SAE伦理学是康德定言律令四公式在SAE 15DD-16DD句式坐标下的句式精细化（satzformentheoretische Verfeinerung）。不是对康德的替换，不是对康德的反驳，是康德伦理学在21世纪工具（维度序列、凿构循环、余项、不得不modal）支持下的继续展开。

六、结论：SAE伦理学作为康德伦理学的15DD-16DD句式精细化

六·一、本文的三件事

本文做了三件事。

一、对康德四公式做完整的14DD残留诊断（§二）。metaphysics-satz §VI射线一已经给出压缩诊断——四公式都用14DD祈使结构承担15DD-16DD内容。本paper把这个压缩诊断做完整展开：四条公式每一条各自带三处14DD残留（总共12处），以及四公式共有的四项句式特征（应当modal、主客分离、假设位置、中介机能）。

二、给出四条"理性不得不"的SAE精细化（§三）。四条从先验条件（理性不得不理性）展开到动力（理性不得不发展）、方向（理性不得不有方向，即目的）、协同（理性不得不被追问）。四条全部使用"理性作为主词+不得不modal"的SAE 15DD-16DD标准句式，把康德"你应当"的14DD祈使结构换成本体陈述。自律（第三公式）作为贯穿四条的底色，不单列为第五条（§四）。

三、显式声明SAE伦理学的康德底座（§五）。A16、Kategorischer Glaube、未来的16DD专论，这些SAE论文共同构成康德定言律令在SAE句式坐标下的完整接续。本paper是这个接续工程的整合性声明——不是开创，是对已有工作和未来工作共同康德底座的显式化。

六·二、SAE伦理学的整体定位

经过本paper的工作，SAE伦理学在哲学史上的位置可以精确表述：

SAE伦理学是康德伦理学在15DD-16DD句式层面的精细化（Verfeinerung）。

这个表述的三个要点：

一、接续而非替换。SAE伦理学的内容全部来自康德四公式。SAE不提出"新的伦理学内容"，它做的是把康德已经提出的内容在更精确的句式层上重述。康德说人是目的，SAE说他者作为本体的在场让我没有了不做B的选项——说的是同一件事，句式从14DD提到15DD。

二、15DD-16DD是康德时代没有的工具。康德在《纯粹理性批判》里建立了先验分析的坐标系，在《道德形而上学基础》和《实践理性批判》里用这个坐标做伦理学。但他没有维度序列这个工具（0DD到16DD），没有"不得不"作为独立modal（他只有"应当"），没有凿构循环作为动态机制，没有余项（ρ）作为ontological地位。SAE用21世纪的这些工具把康德伦理学重新做一遍——康德在18世纪工具下做了他能做的最精细工作，SAE的进一步精化依赖于那时还不存在的工具。

三、自律原则的扩展。康德把自律放在意志这个特定机能上，让它限定在伦理律令维度。SAE把自律解放为贯穿所有15DD-16DD维度的底色——自律在认知维度显示为认知方向、在信仰维度显示为绝对信仰、在律令维度显示为绝对律令、在协同维度显示为协同律令。自律原则在SAE里的作用比康德那里更广、更深。

六·三、SAE在康德体系中的整体位置

SAE对康德的关系已经在多篇paper中被指出：

• metaphysics-satz建立了维度-句式同构，以此诊断康德四公式的14DD残留。
• Kategorischer Glaube建立了SAE对康德Fürwahrhalten三档的接续（Meinen对应方法论0/00，Wissen对应认知论，Glauben对应绝对信仰）。
• 本paper建立了SAE对康德定言律令四公式的精细化。

三项合起来，SAE在康德体系中的位置可以压缩为一句话：

康德给了批判哲学的基本结构（坐标系、先验分析、Fürwahrhalten三档、定言律令四公式、自律原则）；SAE在21世纪工具支持下把这个结构在每一个维度上继续展开——接续方法、细化工具、扩展维度，但不改变康德奠定的根本姿态（以自律为根、用先验分析、守住物自体作为界限）。

SAE不是另一种哲学。SAE是康德哲学在当代条件下的延续。

六·四、本paper作为SAE伦理学的整合性声明

本paper标志着SAE伦理学的整合性阶段。此前的A16、Kategorischer Glaube等paper各自处理了康德四公式中的具体部分，但没有一篇paper把四公式作为一个整体在SAE坐标里重新摆出来。本paper填补了这个缺失。

有了本paper之后，SAE伦理学的进一步展开可以在清晰的坐标里做：

• 条三（绝对律令）已经有A16。后续可以有更多案例研究paper，处理具体伦理情境下A16的运作。
• 自律底色在各维度的展开已经有Kategorischer Glaube（信仰维度）。后续可以有自律在认知维度、教育维度等的专论。
• 条四（16DD协同律令）还缺完整展开，这是SAE伦理学下一篇重要paper的位置。
• 条一和条二（理性的先验条件和动力）在SAE的其他paper里零散处理，但还没有专论。这也是未来paper的可能位置。

本paper的作用是把这些既有和未来的工作摆在同一个坐标里，显示它们共同的康德底座，并确认SAE伦理学作为康德伦理学15DD-16DD句式精细化的整体定位。

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参考文献 / References

康德原作 / Kant's Works

Kant, I. (1785). Grundlegung zur Metaphysik der Sitten. Riga: Hartknoch. [Akademie-Ausgabe Band IV]

Kant, I. (1781/1787). Kritik der reinen Vernunft. Riga: Hartknoch. [Akademie-Ausgabe Band III–IV]

Kant, I. (1788). Kritik der praktischen Vernunft. Riga: Hartknoch. [Akademie-Ausgabe Band V]

SAE系列论文 / SAE Series Papers

Qin, H. (2026a). Self-as-an-End: Foundation Paper I — Systems, Emergence, and the Conditions of Personhood. Zenodo. https://doi.org/10.5281/zenodo.18528813

Qin, H. (2026b). Self-as-an-End: Foundation Paper II — Internal Colonization and the Reconstruction of Subjecthood. Zenodo. https://doi.org/10.5281/zenodo.18666645

Qin, H. (2026c). Self-as-an-End: Foundation Paper III — The Complete Self-as-an-End Framework. Zenodo. https://doi.org/10.5281/zenodo.18727327

Qin, H. (2026d). Metaphysics of Self-as-an-End: Dimensional Sentence-Form Theory (metaphysics-satz). Zenodo. https://doi.org/10.5281/zenodo.18894567

Qin, H. (2026e). A16: One's Own Law — The SAE Critique of Ethics and Morality. Zenodo. https://doi.org/10.5281/zenodo.19037566

Qin, H. (2026f). SAE Epistemology Series I–IV: The Four A Priori Conditions of Cognition. Zenodo. https://doi.org/10.5281/zenodo.19502953 ; .19503018 ; .19503097 ; .19503146

Qin, H. (2026g). Methodology 0 — Non · Negativa: On Negation Prior to Being. Zenodo. https://doi.org/10.5281/zenodo.19544620

Qin, H. (2026h). Methodology 00 — Via Rho: The Way of the Remainder. Zenodo. https://doi.org/10.5281/zenodo.19657440

Qin, H. (2026i). Kategorischer Glaube: A Sentence-Form Theory of One's Own Faith in SAE / 绝对信仰：SAE关于自身信仰的句式论. Zenodo. https://doi.org/10.5281/zenodo.19719083

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引用本文 / Cite this paper

Qin, H. (2026). Reason Cannot Not: An SAE Refinement of Kant's Four Formulations of the Categorical Imperative / 理性不得不：SAE对康德四定言律令的句式精细化. Zenodo. https://doi.org/10.5281/zenodo.19751513

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本文为Self-as-an-End（SAE）框架系列论文之一。