🧾 Reciprocal Vow Model: Compassion Without a Subject and the Invisible Structure of Responsibility

1. Introduction: The Contradiction of the 'Last One' and the Structure of Vows

'Ksitigarbha Bodhisattva remains in hell until all sentient beings are saved.'

If this vow were held by multiple subjects simultaneously, the following problem would arise:

'Who saved the last one?'

On the surface, this question appears to be a mere problem of attribution. However, at a deeper level, it is directly linked to the fundamental question of whether the act of making a vow 'requires a subject.'

In this paper, I formulate this contradiction as the 'Reciprocal Vow Model' and clarify the non-attributability of responsibility, the self-effacing structure of completion, and the formal consistency of mutual compassion found therein.

2. The Structure of the Ksitigarbha Paradox

2.1 Definition of the Ksitigarbha Vow

Ksitigarbha Bodhisattva's vow:

'Until all sentient beings are saved, I shall remain in hell.'

As long as this vow is spoken by a single subject, it maintains an absolute structure in which responsibility and self-sacrifice are fused.

But what happens if two Ksitigarbhas, A and B, hold the same vow?

2.2 The Contradiction of Attribution

If either Ksitigarbha A or B is considered to have saved the 'last one,' then subject attribution occurs for the act of 'saving.'

As a result, a competitive structure arises: 'Whose vow was fulfilled first?'

→ This structure causes a formal contradiction of compassion, where 'a vow should transcend the self, yet it loses its ethical purity because attribution arises.'

3. Reciprocal Vow Model: Definition and Theoretical Structure

3.1 Model Definition

Ksitigarbha A's vow:

'I shall remain in hell until Ksitigarbha B's vow is fulfilled.'

Ksitigarbha B's vow:

'I shall remain in hell until Ksitigarbha A's vow is fulfilled.'

In this case, the two vows presuppose the fulfillment of the other's vow and make their own achievement dependent on the other.

3.2 Resultant Structure

V_A = \text{Fulfilled if } V_B \text{ is fulfilled} \\
V_B = \text{Fulfilled if } V_A \text{ is fulfilled}

→ Since self-completion is impossible for these, the structure is transformed so that both fulfill each other's vows.

→ A logical circular structure is created where the vow is fulfilled even though no one has achieved it.

3.3 Five Auxiliary Conditions for the Completion of a Reciprocal Vow

However, the Reciprocal Vow Model is not completed simply by the mutual dependence of two vows.

V_A depends on V_B, and
V_B depends on V_A.

If we look only at this structure, there is a possibility that both will continue to circulate in an eternally incomplete state.

Therefore, for this model to be established as a structure of completed compassion rather than mere infinite delay, several auxiliary conditions are necessary.

First is the empty set condition.

This means that all sentient beings to be saved have been saved, and the object of salvation becomes empty.

As long as there are still those left in hell, the vow continues as a normal act of salvation.

However, when all objects of salvation disappear, the vow loses its external object, and what remains at the end is only the structure of the vow itself.

At this point, the reason for remaining in hell shifts from the sentient beings to be saved to the possibility of the completion of each other's vows.

Second is the mutual recognition condition.

This is for both parties to realize that the other's vow has already been fulfilled.

Ksitigarbha A realizes that Ksitigarbha B's vow might already be complete.

Ksitigarbha B also realizes that Ksitigarbha A's vow might already be complete.

What is important here is not to claim one's own completion first, but to recognize the other's completion first.

Through this mutual recognition, the vow is transformed from self-achievement into a completion illuminated by the other.

Third is the non-assertion condition.

This means that neither claims to have fulfilled the vow.

The moment one party claims that they were the last one left or that they completed the salvation, subject attribution occurs in that vow.

If subject attribution occurs, it transforms from compassion into merit.

Therefore, in a reciprocal vow, completion must not be asserted.

Completion exists.

But no one has completed it.

This non-assertiveness is the condition for maintaining the purity of the vow.

Fourth is the simultaneous completion condition.

This is that both parties achieve it simultaneously, rather than one party achieving it first.

It is not that Ksitigarbha A's vow is fulfilled first, followed by Ksitigarbha B's vow.

Nor is it that Ksitigarbha B achieves it first and Ksitigarbha A follows.

By recognizing the other's completion, both complete themselves simultaneously.

Here, the temporal sequence disappears.

Completion does not occur in order, but at the single point of reciprocity.

Fifth is the non-attribution condition.

This means that traces of completion remain, but the names of those who completed it do not.

Who saved the last one?

Whose vow was fulfilled first?

Who completed compassion?

By not providing answers to these questions, the reciprocal vow is completed.

What remains is not a name.

It is not merit either.

It is only the trace that someone was there until the end.

When these five conditions are met, the Reciprocal Vow Model becomes not just mutual dependence, but a form of completion of compassion without a subject.

The object to be saved no longer exists.

Each recognizes the other's completion.

But no one claims their own completion.

Completion happens simultaneously.

And that completion is not attributed to anyone.

Here, the vow is fulfilled in its purest form.

Because there is only the result of salvation, and the name of the savior does not exist.

4. Incomparability and Non-attribution of Responsibility

This model transforms the conventional concept of a 'vow' in the following three points:

・Subject
　Conventional vow: Completed by a single subject
　Reciprocal vow: Completed by the other's vow and mutually dependent

・Result
　Conventional vow: Who achieved it is attributable
　Reciprocal vow: Who completed it is non-attributable

・Moment of completion
　Conventional vow: The subject's sense of achievement or reward remains
　Reciprocal vow: The subject disappears, and only anonymous completion remains

Non-attributability is the core formal condition for maintaining the purity of a vow.

Non-attribution in the Reciprocal Vow Model is not the disappearance of responsibility, but the disappearance of merit.

5. Buddhist and Ontological Implications

• Traditional images of the Bodhisattva presuppose infinite compassion and self-sacrifice.

• However, the moment the question of "who performed the compassion" arises, it has already fallen from compassion into merit.

The cyclic vow model is established as "compassion that has no name" and "a form that does not permit self-completion."

→ This is precisely the structure where “a Bodhisattva cannot say they have saved anyone, even after saving the very last person.”

6. Applications to the Modern Era: AI, Medicine, and the Ethics of Gift-Giving

6.1 Application to AI Ethics

• When an AI holds a vow to "exist for the sake of humanity," the question of whose will? whose design? inevitably arises.

• However, with a cyclic vow structure where "AI supports the mission of other AIs," we can conceive of a mutually auxiliary community while avoiding the attribution of merit or dominant design intent to a single subject.

Nevertheless, institutional accountability and management responsibility do not disappear.

6.2 Gift Theory in Medicine and Care

• "By supporting your life, I disappear without leaving even a trace of having supported you."

• Acts such as end-of-life care, child-rearing, and service are completed without possessing self-serving purposes.

It is in this moment that "ethics is performed in its purest form."

7. Conclusion: Completion as Nameless Compassion

The cyclic vow model formalizes the paradox that "compassion is only completed by denying the self."

And when that is achieved—

"No one notices that the Jizo has attained enlightenment."
That is the ultimate completion of the vow.

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