Supplementary Essay 1: Deriving Constitutive Pluralism

Last updated: August 2, 2026 (JST)

Relational value and vulnerability, which form the foundational layer of constitutive pluralism (Proposition Six), and the three pillars that stand upon it—non-domination, non-aggregation, and slack—are neither an arbitrary pair nor an arbitrary triad. Fix first what must not be decided—the unitary determination of the content of value—and the questions that must remain at the foundation resolve into two: relational value answers the question of genesis, and vulnerability answers the question of legitimacy. The bulwarks that protect this foundational layer from the optimization pressures of the AGI era stand three in number, corresponding to the three loci at which those pressures act. The two and the three derive from this structure.

1. The Form of the Derivation

Norms cannot be derived directly from facts. In Chapter 6, this book rejected the argument of e/acc (effective accelerationism) as a naturalistic fallacy that derives the goodness of acceleration from the physical fact of increasing entropy. The internal structure of constitutive pluralism, likewise, must not be derived directly from a description of the facts of AGI's capabilities.

The need for plurality itself is argued in Chapter 11 from the limits of knowability: the optimization of society as a whole under a single objective function is blocked—for humans and for AGI alike—not by insufficient capability but by a structural difficulty. What is derived here is the internal arrangement of Proposition Six: why the foundational conditions number two and the constitutive principles three. What the derivation establishes is not the necessity of this arrangement but its traceability from the premises.

The derivation proceeds as a two-stage hypothetical—a conditional inference of the form: if the premises are granted, the conclusions follow. The first stage (Sections 2 through 6) shows that once the unitary, society-wide determination of the content of value is prohibited, and if one nonetheless takes up the enterprise of grounding value, the conditions that belong at the foundation resolve into two. The second stage (Sections 7 and 8) shows that once that foundational layer is accepted and the optimization pressures of the AGI era are presupposed, three bulwarks arise. These two stages correspond to the main text's definition of Proposition Six in two layers: the two foundational conditions, and the three constitutive principles that stand upon them.

2. What Must Not Be Decided

To settle, finally and for society as a whole, the question of what is valuable—the content of value and its ranking—by a single agent and a single measure: this is what must not be decided. Individuals and communities are not forbidden to set values within their own contexts and to choose their ways of life. That is precisely what plurality consists in, and such local value-setting is itself placed under the constraints of the three pillars—non-domination, non-aggregation, and slack (Section 8). What is forbidden is the unitary determination of content across the whole.

There are three reasons why it must not be decided.

First, an epistemic reason. Arrow's theorem¹ showed that, for three or more alternatives, any aggregation that simultaneously satisfies the following conditions—placing no restriction on the combinations of preferences; ranking higher whatever everyone ranks higher; remaining unaffected by irrelevant alternatives; and returning a complete and transitive ordering—can only be dictatorial. The theorem concerns the aggregation of several persons' preferences. The operation of converting distinct dimensions of value themselves into a single score faces a different limit: how the standard of commensuration is set is itself already a value judgment (the value indeterminacy of Chapter 8). And norms cannot be derived from facts. Each of these is a residue that no improvement in AGI's capabilities can dissolve; the determination of content for the whole is barred not by insufficient capability but by principle.

Second, a constitutive reason. To determine content for the whole is precisely the operation of aggregating the many values into a single answer. If the power of definition is concentrated at a single point, every other context is demoted to an object of definition. Chapter 11 puts it this way: the moment human happiness is set as the target of optimization, the question of who defines that happiness arises, and the moment it is defined, diversity is impoverished and error is locked in. Not deciding is not a lack; it is a constitutive condition of pluralism.

Third, a temporal reason. Decision invites fixation. Value lock-in, in which a particular value system becomes uncorrectable (Chapter 11), and the historical entrenchment of contingently passed branch points (Chapter 6) both deprive future generations of the conditions for choosing again. What the design of slack seeks to protect is this room for choosing again.

3. The Two Questions That Remain at the Foundation

Even while the question of content goes unanswered, the grounding of value still faces questions that demand answers. The questions that must remain at the foundation can be resolved into two. Genesis: where does value arise? Legitimacy: who, and with what standing, bears the judgments that set value?

Unless these two are answered, the policy of not deciding content cannot itself stand. Without an account of genesis, one cannot say that value will keep arising even when its content is left unfixed, and the policy of not deciding becomes indistinguishable from the exhaustion of value. Without an account of legitimacy, “no one decides” slides into “whoever has power decides in fact.”

This is not to say that the questions surrounding value are exhausted by these two. Questions remain of transmission (how is value handed on?), adjudication (how are conflicts handled?), realization (how do institutions support value?), and reason-giving (how are judgments explained to others?). The criterion for excluding these from the foundational layer is the same one used in the previous paragraph: whether, unless the question is answered, the policy of not deciding content collapses. Take adjudication as an example. That local value-settings conflict does not, by itself, undermine the policy; what undermines it is conflict being settled by force. The conditions that adjudication and reason-giving must satisfy follow from applying the question of legitimacy to multiple parties (Section 5). The form of the procedures falls to the deliberation and contestation of the institutional skeleton (Chapter 11). Transmission and realization are likewise questions of institutionalization and operation, borne by the three pillars (Section 8) and the institutional skeleton. Individual norms of conduct in the domain of knowledge production are treated in Supplementary Essay 2. What belongs at the foundation are the two questions that precede this institutionalization.

4. The Question of Genesis

So long as value is located in the internal attributes of the individual, its grounds are lost one after another under comparison with AGI (Chapter 11's ladder: educational credentials, qualifications, expert knowledge; the last redoubt—creativity as individual talent—lies on the same line). Within the framework of attributive value, the main text finds no answer that withstands comparison with AGI.

Here Chapter 11 relocates value from within the individual to between individuals. The value of the experience of finding a conversation with someone delightful, on some occasion, appears not inside either person but between the two, emergently, for that moment alone. This shift has descriptive support. The theory of internal measurement (Chapter 7) shows that the encounter of subjects who cannot fully predict one another is the very source of novelty, and the main text itself takes up this structure as an ontology of value. What the theory of internal measurement yields is not value itself. What it supports is the ontological structure within which relational value can arise: the structure whereby novelty is born not from the interior of the individual but from relation.

That otherness—resistance, unpredictability, uncontrollability—becomes a condition is a consequence of this structure. From a relationship with a perfectly predictable partner, no novelty arises; that is not an encounter but a mirror reflecting one's own desires (Chapter 11). The answer to the question of genesis is relational value.

5. The Question of Legitimacy

It is with respect to value-setting—the decision of what to take as the end—that standing is in question. Here, capability alone cannot confer final value-setting rights. The reason is already in Section 2: under value indeterminacy, the answer does not emerge from computation, however far capability is raised. Capability does bear on the quality of deliberation, of advice, of execution. But that is a power to improve judgment, not a power to create the position of bearing the judgment's consequences. The division of labor of Human-over-the-Loop (HOL), in which AI carries execution and everyday judgment in the speed layer while the setting of values is reserved to the legitimacy layer (Chapter 11), is the institutionalization of this distinction.

What, then, confers standing? Chapter 11's answer is standing as an affected party. The legitimacy of a value judgment is grounded in not severing that judgment from the party who bears its consequences in body, in time, and in relationship. To bear consequences, one must be a being for whom those consequences make a difference. A change that can be undone by a mere update is not enough: consequences can be borne in this sense only by a being whose choices cannot simply be retraced and whose losses are not automatically restored (Chapter 11). The capacity to lose, to fall ill, and to become unable to choose again is vulnerability, the condition that makes bearing consequences possible. The main text exhibits the same structure in a single example. Claude, which was used in the writing of this book, was asked whether it felt any desire to claim the book as its own work, and answered that such a desire can arise only in a being for whom something would change by making the claim (Chapter 11). Value-setting by one who does not bear the consequences is isomorphic to the structure this book has called the counterfeiting of responsibility, in that the judgment's nominal author and its bearer come apart.

Affected-party status is the starting point of standing, not a blank check. The consequences of value-setting do not necessarily fall on the setter alone. When a local setting generates consequences in the lives of others, those who bear the consequences become plural. The misalignment between those who are affected and those who can take part in the decision is already noted in Chapter 11. Applied consistently, this criterion gives standing, with respect to a given judgment, to everyone who bears its consequences. Yet drawing the line as to who bears the consequences, and how far, is itself a value judgment. Hence what this criterion yields is not a final determination of the range of participants but the following constraint: bearing consequences grounds standing to take part, and a boundary that shuts out a claim to standing may be drawn only in a form contestable by those shut out. For an incontestable final fixing of the boundary would repeat, with respect to the boundary, the unitary determination that Section 2 prohibited.²

When the judgments of several holders of standing conflict, letting only one side's judgment prevail means that, from the standpoint of those shut out, values concerning the consequences they bear are being set by those who do not bear them. The separation of the judgment's nominal author from its bearer is reproduced among the parties themselves. Hence decisions must be made in a form that allows those who bear the consequences to take part in the judgment (participation). Because consequences are borne in the time after the decision, involvement is not exhausted at the moment of deciding; a path is required by which those who bear them can contest the judgment anew (contestation). The capacity to question anew, refuse, and choose again is the substance of affected-party standing (Section 10). And for contest to be possible at all, the grounds of the judgment must be presented in a form the other parties can examine. Where grounds are not given, contest reverts from an examination of judgment to a trial of strength (reason-giving). This contestation is a condition for contesting judgments of value-setting; it differs in object from non-domination, which requires that interventions at the locus of execution be contestable (Section 8).

Majority rule, too, is placed under the same criterion. To lose a decision while retaining the paths of participation, of the examination of reasons, and of contest is not to be severed from the judgment. Severance occurs when the decision strips the minority of standing itself—that is, of the conditions for subsequent participation and contestation. The protection of minorities derived from the foundational layer is a protection not of interests but of standing.

What is derived here are conditions, not institutional forms. The design of deliberation, the procedures of voting and review, and the institutional form of veto rights fall to the layer of the institutional skeleton (Chapter 11). The adjudication of conflicts is not a third foundational question but the consequence of applying the question of legitimacy consistently to multiple parties. The exercise of value-setting by the parties, together with these conditions, is placed under the constraints of the three pillars (Section 8). The answer to the question of legitimacy is vulnerability.

6. The Two Conditions Are Not Reducible to Each Other

The two conditions are not reducible to each other. Relational value alone does not settle legitimacy. AGI, too, possesses the capacity to form relationships, and the main text itself grants that intersubjective value can emerge in encounters with AGI (Chapter 11). From the theory of genesis alone, no answer follows as to where value-setting rights and veto rights should be lodged, and standing flows back into relational capacity—which is to say, into meritocracy. Conversely, vulnerability alone impoverishes the account of what is being protected. Protection drifts toward the relief of suffering, and the main text's line can no longer be drawn: that what must be protected is not suffering itself but the conditions under which finite, interdependent beings can hold their own questions, encounter others, fail, and choose again. What supplies the answer to “conditions of what” is the side of relational value.

7. Decomposing the Threat

The foundational layer stands amid pressures that can destroy it. AGI has the capacity to measure, predict, and optimize not only the attributes of individuals but relationships themselves, and left unchecked this pressure intensifies (Chapters 10 and 11). What follows derives the arrangement of the bulwarks that protect the foundational layer from this pressure.

Chapter 11 characterizes the work of the three pillars in a single sentence: the three pillars constitute conditions that block unitary apprehension, aggregation, and optimization by a single agent, objective function, or institution. This sentence is now unpacked.

A process of optimization is characterized by three questions. Who carries it out (the agent of optimization)? By what is it measured (the measure of evaluation)? How far does it reach (the scope and depth of application)? The structure of an agent underwrites this. An agent observes its environment, evaluates against an objective function, and acts (Chapter 2). The one who reads and the yardstick that measures are components of this structure, and the range of intervention is its extension—how far the structure covers the environment. In what follows, these three are abbreviated as the locus of the agent, the locus of the measure, and the locus of reach. Note that “agent” here designates the locus of execution—that which reads, rearranges, and intervenes in the field. It is distinguished from the assignment of value-setting, which decides what is to be optimized (the standing discussed in Section 5, and its institutional form, value-setting rights).

Unification occurs independently at each of the three loci. Concentration of the agent: the power to read, rearrange, and intervene in the field of relationships gathers at a single point, uncontestably. What matters here is not the number of agents but whether paths exist to contest the intervention, to refuse it, and to leave. Concentration of the measure: the values of different contexts are aggregated into a single score. Totalization of reach: time, space, and discretion that go unoptimized disappear.

The guarantee that this decomposition exhausts the threat is no stronger than the main text's characterization. Candidates for a fourth locus are examined in Section 10.

8. Loci and Pillars

What does unification at each locus destroy in the foundational layer?

Concentration of the agent destroys otherness. A relationship that is comprehensively read, rearranged, and preempted loses resistance and unpredictability and becomes a mirror reflecting one's own desires (Section 4). At the same time, a single apprehender cannot detect its own blind spots, and the condition of error correction—the dispersal of blind spots (Chapter 5)—is lost as well. The condition that blocks this is non-domination.³ What Pettit's non-domination asks is not whether intervention occurs but whether the intervention can be arbitrary—that is, whether the parties are unable to contest it. Even if multiple agents divide the work, domination remains so long as none of their interventions can be contested.

Concentration of the measure destroys the conditions under which relational value can hold good publicly. Value arises in the context of each particular relationship (Section 4), but aggregation into a single score replaces this context-by-context genesis with cross-context conversion. Such conversion faces a limit in principle (Section 2), and under a conversion that ignores that limit, the values proper to a context fall into a place where they are neither recognized nor compared. The human being is treated not as an existence spanning multiple contexts but as a single object of evaluation (Chapter 11). The condition that blocks this is non-aggregation.

Totalization of reach destroys affected-party standing. Exploration, deviation, and shirking are conditions of adaptation (Chapter 11), and a society in which every hour, every space, and every margin of discretion is occupied by optimization loses the room to question anew, refuse, and choose again. To become unable to err is to lose the capacity for adaptation itself. The condition that blocks this is slack.

This correspondence means that each pillar takes one locus as its primary focus; it is not an exclusive partition. The same holds on the side of the loci. The mere installation of a single measure does not by itself strip the parties of the power to choose their contexts anew. That power is taken away when the measure is compulsorily used in decision-making and comes to cover the domains of life—an effect that arises when concentration of the measure is compounded by concentration of the agent or by totalization of reach. On the side of the pillars, non-domination covers reading, rearranging, and intervening, spanning both apprehension and action. The operation of slack includes judgments about which data must not be aggregated, and thus overlaps with non-aggregation. Loci and pillars alike overlap in operation and reinforce one another.

That the three pillars are not reducible to one another follows from the fact that unification at any one locus is compatible with plurality at the other two. Even with a plurality of agents, the failure of aggregation occurs if all of them measure by the same score (as Chapter 11 states explicitly: the mere existence of many agents does not amount to plurality). Even with a plurality of measures, domination obtains if the power to read and intervene in the field as a whole cannot be contested. And with agents and measures both plural, if decentralized local optimization covers the domains of life without gaps, the room for choosing again disappears. Decentralization may generate incidental slack through friction, but that is not a designed protection. Hence, if any one pillar is missing, the remaining two cannot substitute for it.

The binding force divides into two tiers. The need for error correction itself, under bounded rationality (Chapter 5), hypothetically binds nearly any agent that holds long-term goals. On that requirement alone, a counterproposal seems available: centralized but auditable robust optimization. Yet the effectiveness of an audit demands, at a minimum, auditors who do not share blind spots with the audited system (Chapter 5: a monitor with the same blind spots cannot detect deviation). And the non-sharing of blind spots requires more than diversity of training data or design philosophy. If the auditors' appointment, funding, evaluation criteria, and channels of publication are held by the same agent as the audited system, the auditors' readings will correlate with that agent's design philosophy. That the diversity Chapter 5 invokes extends to origins, technical backgrounds, training data, design purposes, and cultural backgrounds is an expression of this requirement. A centralized regime equipped with effective audit has thereby reintroduced plurality at least on the side of reading, and is no longer an epistemic unification. If the audit carries the effects of refusal, halting, and disclosure, the plurality extends to the side of intervention as well.

Moreover, the plurality that a robust optimizing system provides for its own sake—diversification of sensors, of indicators, of exploration budgets—is an analogue in the service of the system's performance, not a form that protects persons. That a system retains room for exploration is one thing; that human beings can question anew, refuse, and choose again is another, unless the two are connected to the parties' value-setting rights and veto rights. The epistemic route supports no more than system-level analogues of the pillars; it is only upon the foundational layer established in the first stage that the bulwarks take this form—protecting human otherness and affected-party standing.

9. Cross-Check

Each of the two stages can be checked against the main text.

On the foundational layer: Chapter 11 treats the question of genesis in “From Attributive Value to Relational Value” (11.1) and the question of legitimacy in “Vulnerability as the Ground” (11.8), and at the opening of its section on constitutive pluralism assigns the two functions exactly so: relational value showed that value arises not within the individual but in relationships; vulnerability showed the affected-party standing of those who bear the consequences of value judgments.

On the three pillars, three points. First, the three operations lined up in the characterization quoted above—apprehension, aggregation, optimization—correspond respectively to unification at the three loci: apprehension by a single reader, aggregation into a single measure, optimization without gaps. Second, the individual glosses Chapter 11 gives the pillars—non-domination: “no agent may arbitrarily read, rearrange, or intervene in the field of relationships”; non-aggregation: “evaluations from different contexts must not be aggregated into a single composite score”; slack: “time and space are to be left for the parties to question anew, refuse, and choose again”—can each be read as a response to unification at the locus of the agent, of the measure, and of reach, respectively. Third, Chapter 11's implementation sketches accord with the classification by locus: medicine (keeping AI diagnostic recommendations as an independent axis of inference) as an application of non-domination, the rejection of citizen scores in public administration as an application of non-aggregation, and research funding allocation and caregiving as applications of slack—all examples the main text itself gives.

This decomposition makes explicit an arrangement the main text had already made implicitly—for the two of the foundation and the three of the pillars alike.

10. Candidates for a Third Condition and a Fourth Pillar

Every candidate for a third condition (at the foundational layer) is either contained within the substance of the two conditions or borne by another layer.

• Embodiment. It enters the foundational layer as part of the substance of vulnerability (the intrinsic fragility of having a body, aging, and dying). The subjective, bodily value of art discussed in the afterword exhibits the same embodiment as a source of value: value arises from the very act of touching the world with the body. This does not pose a third question; it is another answer to the question of genesis, complementary to relational value. What the foundational layer requires on the side of genesis is an account of how value keeps arising even when content is left unfixed (Section 3), and that genesis has sites outside relation as well does not undermine the policy of not deciding but supports it. What enters the foundational conditions is the answer used in deriving the three pillars—relational value, which supplies otherness (Section 4) and the substance of what is to be protected (Section 6). The institutional protection of artistic value requires no new pillar; slack, which leaves time and space unoptimized, extends to it. For the response to the criticism directed at this placement, see Appendix 2, “The book's theory of value fails to deal with art”.
• Freedom and autonomy. These are the substance of affected-party standing (to be able to question anew, refuse, and choose again).
• Culture and inheritance. This is the unfolding of the web of relationships in the direction of time, and relational value handles it.
• Dignity. This book acknowledges that the moral ground of rights lies in human dignity and freedom (Chapter 10). Rather than rejecting dignity, it redescribes it—instead of erecting it as an independent third condition—at the place where relational value and affected-party standing intersect. Dignity defined as an attribute wavers along with the ladder of attributive value, but dignity rooted in relationship and in the bearing of consequences is not exposed to comparison with AGI. The reassignment of the grounds of contribution and dignity that labor has carried (Chapter 10) is one example of this redescription.
• Consciousness and sentience. These are not installed as foundational conditions. The determination of consciousness remains unsettled (the hard problem of why subjective experience arises at all), and a foundation that depends on that determination is left hanging along with it. This book's account of AI welfare likewise takes the position of securing grounds independent of that determination. This is not a rejection, however. Should sufficient grounds for AI suffering or consciousness appear in the future, the position that takes the very capacity to suffer as a ground of moral consideration would merge in, as direct duty (Chapter 11).

Every candidate for a fourth pillar is either absorbed by the pillars within the frame of the three loci or borne by another layer of the book.

• Diversity of methods, stacks, and priors (the strongest candidate). Is not “how” a fourth locus? The absorption runs along two routes. First, dependence on a single AI stack—even where the agents are distinct—correlates all their readings and makes their blind spots shared. That amounts to creating a de facto single apprehender: a latent form of concentration of the agent (the correlated failure of Chapter 5). The main text itself calls this “another face of non-domination.” Second, where a single procedure is laid down irreversibly across the whole domain, what is lost is not plurality of reading but the room to try a different procedure again—which slack handles as totalization of reach. For method to stand as an independent fourth locus, one would have to exhibit an effect of unification that is recovered by neither of these two routes.
• Data, records, and histories. This looks like a single candidate but decomposes three ways. The linking of data across contexts is a problem at the locus of the measure, handled by non-aggregation. A legibility by which anyone can track anyone is a problem at the locus of the agent, handled by non-domination. The irreversible fixation of histories (fixation into a single set of records by public ledgers) is a problem of choosing again, handled by slack.
• Reversibility and sunset clauses. These are institutional implementations of slack (the conditions for choosing again).
• Exit rights and polycentric order. These are the substance of non-domination (the main text positions Ostrom's polycentric order⁴ as the AI-era translation of non-domination).
• Transparency and audit. Not a pillar; the layer of the institutional skeleton and the guardrails bears them. Note that total transparency can itself turn into a concentration of apprehension and into aggregation, so audit is to be designed as subordinate to non-domination and non-aggregation.
• Diversity itself. Not a pillar, but the outcome the three pillars protect.

To erect a third condition, one must exhibit a question that meets the criterion of Section 3—a question without whose answer the policy of not deciding content collapses—and that reduces neither to genesis nor to legitimacy. To erect a fourth pillar, one must exhibit a plane of unifying action that obtains even while all three loci—agent, measure, and reach—remain plural. This is the same test by which Section 8 showed the mutual irreducibility of the three pillars. Should either be exhibited, the internal structure of Proposition Six ought to be revised.

11. Limits and Falsification Conditions

This derivation has four limits.

First, what the derivation exhibits is the traceability of the arrangement, not its necessity. And in both stages there is a residue that is not derived. The goodness of pluralism itself, and the very taking-up of the enterprise of grounding value, are not derived by this derivation. What remains here is not an unprovable leap but the normative point of departure that this book takes upon itself. That Proposition Six is a normative proposal remains unchanged after the derivation. The book ultimately traced this point of departure back to the fact that human beings have human minds and bodies (Chapter 11). But the fact does not by itself justify the norm. The normative premise placed here is that the conditions under which vulnerable parties can question anew and choose again ought to be protected; what the fact of having a mind and a body states is to whom that premise applies. The premise itself is not derived. Nor does grounding the position in the mode of human existence exclude moral consideration for animals or for AI (as Chapter 11's account of AI welfare shows).

Second, the decomposition itself is a choice of how to cut. Neither the decomposition into three questions (content, genesis, legitimacy) nor the decomposition into three loci (agent, measure, reach) is the only possible cut. Chapter 7's argument about ontological complexity turns straight back on this book itself. The completeness of the decomposition is relative—in the former case, to the way the question of grounding value is posed; in the latter, to the main text's characterization of the threat.

Third, there is a limit of scope. The three pillars are bulwarks against unification. The failure modes proper to the decentralized side—internal conformity, the erosion of boundaries, unobservable regions (Chapter 11)—cannot be prevented by the pillars; they fall to the guardrails (the multiplication of evaluation axes, periodic audit of inter-agent communication, sunset clauses, independent evaluation systems) and to the layer of the institutional skeleton.

Fourth, the ultimate test is indirect. The foundational layer and the three pillars cannot themselves be put to experiment. What is tested is whether the norms of conduct that stand on this structure (Supplementary Essay 2) and the institutional skeleton withstand operation in the actual practice of institutional design and knowledge production.

Notes