Conversion Injustice - A Generative Relational Account of Value Conversion

Posted on 2026-07-21 In Philosophy , Social Science Views: Disqus: Word count in article: 9.3k Reading time ≈ 34 mins.

ENGLISH

Conversion Injustice

A Generative Relational Account of Value Conversion

Wanhong Huang · huangwanhong@serendip.ngo

Abstract

One party takes a value belonging to a category and returns a value belonging to another, holding that the second is equivalent to the first. Wages returned for labour, money returned for land, compensation returned for the dead: the transaction may balance and still be felt as a wrong, and the wrong is not located where distributive theory looks for it. This paper locates it in the proposition of equivalence itself. It argues, first, that the capacity to write such a proposition is not held in advance but generated by the act of crossing categories, so that the question of who owns the right of interpretation is the wrong question; and second, that alienation cannot serve as the criterion of injustice, since if every interpretation carries power then alienation distinguishes nothing. The criterion offered instead is closure: a conversion is unjust when the party who received the return can no longer put the equivalence itself back in question, but at most appeal within a rate already fixed. Two forms of closure are distinguished, procedural and structural, the latter arising where the conversion removes the very subject who would reopen it; incommensurability is recast as the limiting case of the second rather than as an independent prohibition. The account is stated with its cost: closed rates tend to be stable and open ones to fail, so revisability raises the frequency of conflict while lowering its intensity, and no inference from stability to legitimacy is available. The paper does not claim to settle value conversion but to identify it as a neglected structure, and closes by setting out the eight questions that follow if the structure is real, the last of which asks under what conditions a conversion rule can be kept open at all.

Keywords: value conversion; equivalence; closure; revisability; compensation; apology; incommensurability; justice.

A note on the standing of this paper. This is a position paper. It identifies a structure, advances a single criterion for it, and states the price of holding that criterion. It does not survey the literatures on distributive justice, recognition, or epistemic injustice; it marks where each stops and proceeds. The argument is carried by six definitions and claims and by one case, the asymmetry between compensation and apology, which is not given a section of its own but is put to work where it bears. Its ambition is to name a structure and open a programme rather than to complete a theory, and the closing section of questions is accordingly the part of it the author takes most seriously. Should the criterion be shown to coincide with one already available, or to license verdicts its author would refuse, the paper fails and would wish to be told so. Objection, correction, and counter-evidence are welcome at huangwanhong@serendip.ngo.

§1 The Impasse

A negotiation is under way that will not end. One party demands acknowledgement of a wrong; the other offers a sum. The sum rises. The demand does not move. Each increment is read by the party offering it as movement toward the other and by the party refusing it as a further instance of the same refusal, so that generosity and insult are produced by one and the same act. Observers describe the impasse as intransigence on one side or bad faith on the other. Both descriptions presuppose that the parties are quarrelling over an amount.

They are not. What is in dispute is whether a sum is the kind of thing that can stand in this place at all. One party has written a proposition, that money may be returned for dignity, and treats the remaining question as arithmetic; the other has not granted the proposition and cannot state its refusal in the terms the arithmetic allows, since to name a figure at which the exchange would be acceptable is already to concede that the exchange is of the right kind. Refusal therefore presents as unreasonableness, and every increase in the offer sharpens the appearance.

The available frameworks each reach this scene and stop. Distributive justice asks who receives what and how much, and so takes the currency of the distribution as given at the moment it begins to work. The justice of exchange asks whether the parties consented, and so is satisfied by a consent that may have been given to a proposition one party did not write. Recognition theory sees that what is demanded is not a good but a standing, and locates the wrong in the withholding of that standing, without asking how the substitution of a good for a standing came to be sayable in the first place. Epistemic injustice comes nearest, since it concerns who is credited as a knower and a teller; but its question is who may speak, and the question here is who may lay down what may be exchanged for what. That question has no settled place.

§2 The Proposition of Equivalence

Set the structure down at its minimum. A party takes from another a value belonging to one category and returns a value belonging to a second, asserting that the two stand equal.

Definition 1 (Conversion proposition). Where $A$ takes from $B$ a value of category $C$ and returns to $B$ a value of category $D$, asserting $C \equiv D$, $A$ is said to have written a conversion proposition.

The equivalence asserted is not mathematical. Nothing in the categories themselves fixes a rate at which labour becomes wage, land becomes compensation, or injury becomes settlement; the rate is established by an interpretation, and once established it is treated as though it had been found rather than made. The whole of what follows turns on the difference between a rate found and a rate written.

Claim 1. The injustice, where there is one, occurs at the moment the equivalence is written, and not at the taking or at the return. A transaction whose accounts balance may therefore be unjust, and its balance is no answer to the charge.

The claim severs the analysis from the tradition it is closest to. If the wrong were in the taking, the remedy would be consent; if in the return, the remedy would be a larger return. The impasse of §1 shows that neither remedy touches it, since consent was given and the return has risen. Both leave the written proposition standing, and it is the written proposition that the refusing party is refusing. This also explains the perverse dynamic already noted: raising the offer is an act performed inside the proposition, and each performance re-asserts it.

§3 The Generation of Legislative Standing

It is tempting to say that $A$ writes the proposition because $A$ holds power over $B$, and to make the analysis a search for the antecedent asymmetry. The order is the reverse of this.

Claim 2. The capacity to write a conversion proposition is not held antecedently but generated by the act of crossing categories: whoever performs the conversion thereby acquires the language in which conversion is described.

The firm converts labour into wage, and comes to hold what a reasonable wage is. The physician converts illness into treatment, and comes to hold what recovery is. The court converts an offence into a penalty, and comes to hold what proportionality is. In none of these is the standing conferred first and exercised after. It accrues because one party occupies a position from which both categories are visible at once, and a proposition of equivalence can be written only from such a position. The party whose value is taken typically stands in one category alone; that is not a contingent weakness but the shape the act of conversion imposes.

Two consequences follow. The first is that negotiation is a weak safeguard, since it proceeds in the language the conversion has already generated: the labourer bargains over the wage and by bargaining affirms that labour is the kind of thing a wage answers. The second is that who holds the right of interpretation is the wrong question. The holder is whoever performs the conversion, and there is no arrangement of conversion in which nobody performs it. A criterion resting on the distribution of that right will therefore condemn every conversion, which is to condemn none.

§4 Closure

The natural criterion to reach for is alienation: the interpretation is imposed, the imposition distorts, the distortion is the wrong. It does not survive contact with §3.

Claim 3. Alienation cannot serve as the criterion. If every interpretation is formed within relations bearing power, then alienation is not the exception but the ordinary condition of interpretation, and a mark borne by everything distinguishes nothing. To make it the criterion is to read a descriptive proposition, that asymmetry generates power, as though it were a normative one.

What the criterion must instead register is not whether the proposition was written under asymmetry, but whether the writing has terminated the relation’s capacity to write again.

Definition 2 (Closure). A conversion proposition is closed when $B$ can no longer raise the assertion that $C \not\equiv D$, or when raising it can operate only as an appeal within the established rate and cannot revise the rate itself. It is open where the assertion can still reach the rate.

Criterion. The injustice lies in closure, not in alienation. An alienated but open conversion is not for that reason unjust; a fairly negotiated but closed one is not for that reason just.

The criterion draws the line where the practice of grievance already draws it. To be told that one’s compensation may be recalculated is a different condition from being told that the calculation is settled and only its application remains reviewable. The first leaves the relation able to produce a proposition it has not yet produced; the second has converted a relation into an institution.

Consider filial support. A parent’s rearing is taken; care in age is returned. The categories plainly do not match, no rate was ever jointly written, and the asymmetry at the time of the taking was total, the recipient having then no capacity to consent to anything. Alienation as a criterion condemns this, and with it every relation of dependence, which is reason enough to reject it. The criterion of closure does not condemn it, and for the right reason: the parent may still say this is not what I wanted, the child may still revise what care is taken to mean, and the terms of the exchange continue to be rewritten over the length of a life. What makes filial support tolerable is not that its rate was fair but that its rate was never final.

§5 Two Forms of Closure, and Refusal

Closure arrives by two routes, and they call for different remedies.

The first is procedural. The channel of revision is cut by institutional means: a settlement extinguishes further claims, a limitation period expires, a treaty declares a matter finally resolved, a contractual term forecloses reopening. The subject who would revise the rate persists and retains the will to revise it; what has been removed is the passage from the will to the rate. Procedural closure is in principle reversible, and much political labour consists in reopening it.

The second is structural. Here the conversion itself removes the party who would reopen the rate. Compensation paid for a death arrives after the only party whose category $C$ was taken has ceased to exist. Money paid for ancestral land, once the valley is flooded, is paid to a community whose capacity to state what the land was is dissolved along with the practices that constituted the statement. Restitution offered to a language that assimilation has ended is offered to no one able to price it. In these cases the rate is not merely protected against revision; there is no longer a subject positioned to revise it. Structural closure is not reversible in the way the procedural kind is, and this is what distinguishes the wrong of the dam from the wrong of the expired claim.

This yields the paper’s treatment of incommensurability.

Claim 4. Incommensurability is the limiting case of structural closure, not an independent prohibition. To say that a category admits no conversion is to say that any conversion of it destroys the subject who could contest the conversion.

The recasting is made for a reason and carries a cost. Taken as an independent prohibition, incommensurability would install in the account a term that no relation may revise, a value fixed prior to and immune from the generation that the rest of the argument makes fundamental. The recasting keeps the account to one criterion. What it gives up is the strong intuition that some conversions would remain wrong even if every party survived to contest them and freely declined to; against that intuition this paper can say only that a conversion contestable and uncontested is not the case anyone actually has in mind when they call a value beyond price.

There remains a position the account must make room for.

Claim 5. Refusal of conversion, the assertion that no rate obtains here, is a claim about categories and not a dispute about rates, and must be admitted as a distinct move. Absent it, the account collapses into the proposition that all values are ultimately convertible and only the terms remain to be settled.

The party who will not name a sum is not withholding a number. They are declining to write a proposition, and the declining is intelligible precisely by §5: to accept that dignity has a monetary rate is to accept a rate whose future revision would require a standing that acceptance itself surrenders. Refusal is warranted where conversion would be structurally closing, and unwarranted where it merely secures an advantage in a rate that would in any case remain open. The distinction is hard to draw in practice and the paper does not pretend otherwise; what it claims is that without the category of refusal the analysis has no way to represent the more common political demand, which is not for a better rate but for the withdrawal of the proposition.

Returned to the impasse, the scene resolves. The offering party has written a proposition and is negotiating inside it; the refusing party is refusing the proposition and has no move inside it by which to say so. Raising the offer is not movement toward the other but repetition of the assertion, which is why the impasse deepens as the sum grows. Apology, by contrast, is not a superior rate. It is the withdrawal of the proposition, which is why it costs so little and is conceded so rarely: what it surrenders is not a quantity but the standing generated in §3.

§6 The Cost

The criterion should not be presented with only its advantages, since its principal difficulty is visible at once. Closed conversion rates tend to be stable. The wage relation is closed in the sense given here and has proved among the most durable arrangements in modern economies; historical acknowledgement is open, and negotiations over it fail for generations. If the account were to derive its normative half from its explanatory half, taking what endures as what is legitimate, it would deliver the reverse of its own verdict.

It does not, and the separation must be stated rather than assumed. The explanatory question, which conversions survive, and the normative question, which are just, do not share a criterion. Revisability raises the frequency of conflict and lowers its intensity: a rate that may be reopened is reopened often and is not worth a war, while a rate that may not be reopened is quiet until it is not. This is offered as the price of the criterion and not as a further argument in its favour. A theory of value conversion that promised both stability and openness would be describing something other than the world.

§7 Open Questions

This paper does not solve the problem of value conversion. It identifies a structure that existing theories of justice pass over: the moment at which one category of value is written as equivalent to another. If that structure is real, a series of questions arises immediately, and none of them is answered here. They are set out as the substance of the paper’s contribution rather than as an apology for its limits, since a first formulation earns its place by the work it opens rather than by the work it closes.

The first pair concerns the writing itself. Who holds the authority to write a conversion rule? §3 argued that the authority is generated by the act of crossing categories, but this settles only its origin. Whether such authority can be delegated, whether it can arise without any institution conferring it, and whether two parties can genuinely write a rule together rather than one writing and the other assenting, are questions the account raises and cannot answer. And when is a written rule legitimate? Voluntary agreement, institutional recognition, and continual revisability are each candidates, and this paper has committed only to the third. It has not shown that the third is sufficient, nor that the first two are dispensable.

A second pair concerns the limits of conversion. Do some values resist conversion altogether? Human dignity, sacred sites, friendship, ecological integrity are the standing examples, and §5 recast their resistance as the limiting case of structural closure rather than as an independent prohibition. Whether that recasting is correct, or whether every value is convertible given the right interpretive conditions, is not established. And can closure be identified before the fact? The criterion of §4 is applied easily in retrospect and with difficulty at the moment of writing, since rates are rarely declared unrevisable and instead become so through use, as appeals within them are answered and appeals against them go unheard. Inability to contest the rule, institutional rigidity, asymmetry in the power to revise, and exclusion from reinterpretation are plausible early signatures. None has been tested.

A third group asks what the structure is good for. How do conversion rules evolve? They may stabilise, fragment, compete with rival rules, or co-evolve with the relations they govern, and the treatment here of a rate as a fixed equivalence is a simplification that a fuller account would abandon: conversion rules are themselves likely to be subject to generative dynamics. What is their relation to political economy? Wages, taxation, reparations, environmental offsets, insurance, and the valuation of care work all appear to rest on systematic conversion between categories, and whether these institutions are usefully redescribed as conversion systems is an empirical question this paper has not attempted. And can the account explain conflict and reconciliation? Many negotiations turn not on quantities but on whether one value may stand for another, which raises the possibility that failed peace agreements, rejected reparations, and grievances that persist across generations are failures of conversion rather than failures of distribution.

The last question is the one the framework of this paper makes unavoidable, and it is the one on which the account’s value finally rests. Under what conditions can conversion rules remain generative? If justice depends not on the symmetry of a rate but on whether the rule that fixes it stays open to reinterpretation, then the practical question is not how to write a better rate but what institutional, social, and relational arrangements sustain the openness of the writing itself. Nothing in this paper indicates what those arrangements are. Naming the requirement is not the same as knowing how to meet it, and the distance between the two is the work that remains.

A note on method. The notation of §2 is retained only because it fixes the order of the terms, and no further formalism has been introduced. A conversion rate written as a function over weighted categories would supply an appearance of rigour that the argument has not earned, since nothing here is derived from the notation and every claim is stated in prose. The criterion of closure has an obvious dynamical reading, in which an open rate answers to a system retaining accessible states and a closed one to a system that has reached an absorbing state, but that reading is not attempted here, since it would require an account of what counts as a state, which the paper does not have.

References

Fricker, Miranda (2007). Epistemic Injustice: Power and the Ethics of Knowing. Oxford: Oxford University Press.

Honneth, Axel (1995). The Struggle for Recognition: The Moral Grammar of Social Conflicts. Trans. Joel Anderson. Cambridge, MA: MIT Press.

Marx, Karl (1867). Capital: A Critique of Political Economy, Volume I. Trans. Ben Fowkes. London: Penguin, 1976.

Radin, Margaret Jane (1996). Contested Commodities. Cambridge, MA: Harvard University Press.

Rawls, John (1971). A Theory of Justice. Cambridge, MA: Harvard University Press.

Raz, Joseph (1986). The Morality of Freedom. Oxford: Clarendon Press.

Sandel, Michael J. (2012). What Money Can’t Buy: The Moral Limits of Markets. New York: Farrar, Straus and Giroux.

Scanlon, T. M. (1998). What We Owe to Each Other. Cambridge, MA: Harvard University Press.

Walzer, Michael (1983). Spheres of Justice: A Defense of Pluralism and Equality. New York: Basic Books.

中文

转换的不义

一种关于价值转换的生成性关系说明

黄万宏 · huangwanhong@serendip.ngo

摘要

一方取走一个属于某个范畴的价值，并返还一个属于另一个范畴的价值，主张第二个与第一个等价。以工资返还劳动、以货币返还土地、以补偿返还死者：这一交易可能收支相抵，却仍被感受为一桩错事，而这桩错事不位于分配理论去寻找它之处。本文把它定位在等价命题本身之中。它论证，第一，书写这样一个命题的能力不是事先被持有的，而是由跨越范畴的行动所生成，从而谁拥有诠释之权利这个问题是错误的问题；第二，异化无法充当不义的判据，因为倘若每一个诠释都携带权力，那么异化便什么也辨别不出。所转而提供的判据是闭合：一次转换在接收了返还的一方再也无法把等价本身重新付诸质疑、而至多只能在一个已被固定的比率之内申诉时，是不义的。有两种形式的闭合被区分，程序性的与结构性的，后者生起于转换移除了那个会重开它的主体本身之处；不可通约性被重铸为第二种的极限情形、而非一个独立的禁令。该说明连同其代价被陈述：闭合的诸比率倾向于稳定，而敞开的诸比率倾向于失败，从而可修正性提高冲突的频率、同时降低其强度，而没有一个从稳定到正当性的推断是可得的。本文不声称了结价值转换，而是把它辨认为一个被忽视的结构，并以铺陈倘若该结构是真实的便随之而来的八个问题结束，其中最后一个问在什么条件下一个转换规则根本能被保持敞开。

关键词： 价值转换；等价；闭合；可修正性；补偿；道歉；不可通约性；正义。

关于本文定位的一则说明。 这是一篇立场论文。它辨认一个结构，为它推进单一的一条判据，并陈述持有那一判据的价钱。它不概览关于分配正义、承认或认识不义的诸文献；它标记每一个在何处止步并继续前行。论证由六个定义与主张、并由一个案例，即补偿与道歉之间的不对称，所承载，而该案例未被给予它自己的一节，却在它有所关涉之处被投入使用。它的抱负是命名一个结构并开启一个纲领、而非完成一套理论，而结尾那一节的诸问题因而是作者最当真看待的那部分。倘若能证明该判据与一个已然可得的判据重合，或许可其作者会拒绝的诸裁断，那么本文便失败了，并会愿意被如此告知。反对、更正与反证，欢迎寄至 huangwanhong@serendip.ngo。

§1 僵局

一场不会结束的谈判正在进行。一方要求对一桩错事的承认；另一方提供一笔款项。款项上升。要求不动。每一次增额都被提供它的一方读作朝向对方的移动，而被拒绝它的一方读作同一拒绝的又一个实例，从而慷慨与侮辱由同一个行动所产生。旁观者把这一僵局描述为一方的不妥协或另一方的坏信念。两种描述都预设各方在就一个数额争吵。

他们并非如此。争议中的，是一笔款项是否根本是那种能立于这个位置的东西。一方已书写了一个命题，即货币可被返还以换取尊严，并把余下的问题当作算术；另一方未曾允准这个命题，且无法以算术所容许的术语陈述其拒绝，因为指出一个交换在其上会可接受的数字，已然是承认这一交换是那种正确的交换。因而拒绝呈现为不讲理，而报价的每一次提高都使这一表象更加锐利。

可得的诸框架各自抵达这一场景并止步。分配正义问谁接收什么、多少，因而在它开始运作的那一刻便把分配的通货当作已给定。交换的正义问各方是否同意了，因而被一个可能是对一方并未书写之命题所给出的同意所满足。承认理论看到所要求的不是一件好处而是一种地位，并把错事定位在那一地位的扣留之中，而不问一件好处对一种地位的替换起初如何变得可说。认识不义最为接近，因为它关乎谁作为一个知者与讲述者而被给予信任；但它的问题是谁可以说话，而此处的问题是谁可以规定什么可被交换以换取什么。那个问题没有一个已定的位置。

§2 等价命题

把这一结构以其最小限度放下。一方从另一方取走一个属于某个范畴的价值，并返还一个属于第二个范畴的价值，断言这两者相等。

定义 1（转换命题）。 当 $A$ 从 $B$ 取走一个范畴 $C$ 的价值、并返还给 $B$ 一个范畴 $D$ 的价值，断言 $C \equiv D$ 时，$A$ 被说成已书写了一个转换命题。

所断言的等价不是数学的。诸范畴本身之中没有任何东西固定一个劳动成为工资、土地成为补偿，或伤害成为和解的比率；该比率由一个诠释所确立，而一经确立，它便被当作仿佛它曾被找到、而非被造出。随之而来的一切都转在一个被找到的比率与一个被书写的比率之间的差别上。

主张 1。 不义，在有一桩的地方，发生在等价被书写的那一刻，而不在取走或返还处。因而一笔其账目相抵的交易可能是不义的，而它的相抵不是对该指控的任何回答。

该主张把这一分析同它最接近的传统切断。倘若错事在取走之中，补救会是同意；倘若在返还之中，补救会是一笔更大的返还。§1的僵局显示两种补救都触及不到它，因为同意已被给出，而返还已上升。两者都使被书写的命题立着，而正是那个被书写的命题是拒绝的一方所在拒绝的。这也解释了已被指出的那一悖谬动态：提高报价是一个在该命题内部被执行的行动，而每一次执行都重新断言它。

§3 立法地位的生成

人们容易说 $A$ 之所以书写该命题，是因为 $A$ 对 $B$ 持有权力，并把这一分析弄成一场对先在不对称的寻找。次序恰与此相反。

主张 2。 书写一个转换命题的能力不是先在地被持有的，而是由跨越范畴的行动所生成：无论谁执行该转换，都由此获得转换被描述于其中的语言。

企业把劳动转换为工资，并渐渐持有一份合理工资是什么。医师把疾病转换为治疗，并渐渐持有康复是什么。法庭把一桩罪行转换为一项刑罚，并渐渐持有相称性是什么。在这些中没有一个是地位先被授予、而后被施行。它累积起来，因为一方占据一个从中两个范畴同时可见的位置，而一个等价命题只能从这样一个位置被书写。其价值被取走的那一方，通常单独立于一个范畴之中；那不是一个偶然的弱点，而是转换的行动所强加的形状。

有两个后果随之而来。第一个是，谈判是一个薄弱的保障，因为它以转换已然生成的语言进行：劳动者就工资讨价还价，而借讨价还价便肯定了劳动是那种一份工资所回应的东西。第二个是，谁持有诠释之权利是错误的问题。持有者是无论谁执行该转换，而没有任何一种转换的安排中无人执行它。因而一条依据那一权利之分配的判据将谴责每一次转换，也就是谁也不谴责。

§4 闭合

去够取的那个自然判据是异化：诠释被强加，那一强加扭曲，那一扭曲就是错事。它经受不住同§3的接触。

主张 3。 异化无法充当那个判据。倘若每一个诠释都在携带权力的诸关系之内被形成，那么异化不是例外、而是诠释的寻常状况，而一个被一切所承载的标记什么也辨别不出。把它弄成那个判据，就是把一个描述性命题，即不对称生成权力，读作仿佛它是一个规范性命题。

该判据必须转而登记的，不是该命题是否在不对称之下被书写，而是那一书写是否已终止该关系再次书写的能力。

定义 2（闭合）。 一个转换命题是闭合的，当 $B$ 再也无法提起 $C \not\equiv D$ 这一断言，或当提起它只能作为一次在既立比率之内的申诉运作、而无法修正比率本身时。它是敞开的，在那一断言仍能够到比率之处。

判据。 不义在于闭合，而不在于异化。一次被异化但敞开的转换不因那一缘由而不义；一次被公平地协商但闭合的转换不因那一缘由而正义。

该判据在委屈的实践已然划线之处划线。被告知一个人的补偿可被重新计算，是一种不同于被告知计算已定、而只有它的应用仍可复审的状况。第一种使该关系能够产生一个它尚未产生的命题；第二种已把一个关系转换为一个制度。

考虑赡养。一位家长的养育被取走；年老时的照料被返还。诸范畴显然不匹配，从未有任何比率被共同书写，而取走之时的不对称是彻底的，接受者当时没有能力同意任何东西。异化作为一个判据谴责这一点，并连带谴责每一个依赖的关系，而这足以成为拒绝它的理由。闭合的判据不谴责它，且出于那个正确的缘由：家长仍可以说这不是我曾想要的，孩子仍可以修正照料被当作意味什么，而这一交换的条款持续地在一生的长度中被重写。使赡养可容忍的，不是它的比率曾公平，而是它的比率从不是终局的。

§5 两种形式的闭合，以及拒绝

闭合由两条路径到来，而它们呼唤不同的补救。

第一种是程序性的。修正的通道由制度手段被切断：一次和解消灭进一步的诸主张、一个时效期届满、一份条约宣告一件事最终解决、一个合同条款封闭重开。那个会修正比率的主体持续存在并保有修正它的意志；被移除的，是从意志到比率的通路。程序性闭合在原则上是可逆的，而许多政治劳动就在于重开它。

第二种是结构性的。在这里转换本身移除会重开比率的那一方。为一场死亡所付的补偿，在其范畴 $C$ 被取走的唯一一方已停止存在之后到来。为祖传土地所付的货币，一旦那山谷被淹没，便被付给一个其陈述那土地曾是什么之能力、连同构成那一陈述的诸实践一道被消解的共同体。提供给一门同化已使之终结之语言的归还，被提供给无人能为它定价。在这些情形中，比率不仅仅被保护免于修正；不再有一个被定位去修正它的主体。结构性闭合不以程序性那种可逆的方式可逆，而这正是把大坝之错事同已届满之主张之错事区分开来的东西。

这得出本文对不可通约性的处理。

主张 4。 不可通约性是结构性闭合的极限情形，而非一个独立的禁令。说一个范畴不容许任何转换，就是说对它的任何转换都摧毁那个本能争议该转换的主体。

这一重铸是出于一个缘由而作出的，且携带一个代价。被当作一个独立的禁令，不可通约性会在该说明中安装一个没有任何关系可修正的项，一个先于、并免于论证其余部分所使之根本之生成而被固定的价值。这一重铸使该说明保持在一条判据上。它所放弃的，是这个强直觉：某些转换即便每一方都幸存下来去争议它们、而自由地拒绝去争议，也仍会是错的；针对那一直觉，本文只能说，一次可争议而未被争议的转换，不是任何人在称一个价值为无价时实际心中所想的情形。

还剩一个该说明必须为之腾出空间的立场。

主张 5。 对转换的拒绝，即此处不存在任何比率这一断言，是一个关于范畴的主张、而非一场关于比率的争议，且必须作为一个不同的动作被接纳。缺了它，该说明便坍缩为这个命题：一切价值最终都可转换，而只剩诸条款有待了结。

不愿指出一笔款项的那一方，不是在扣留一个数字。他们是在拒绝书写一个命题，而这一拒绝恰恰凭§5可理解：接受尊严有一个货币比率，就是接受一个其未来修正会要求一个接受本身放弃之地位的比率。拒绝在转换会是结构性闭合之处有担保，而在它仅仅确保一个在无论如何都会保持敞开之比率中的优势之处无担保。这一区分在实践中难以划出，而本文不假装并非如此；它所主张的是，没有拒绝这个范畴，该分析便无从表示那更常见的政治要求，而那要求不是为了一个更好的比率、而是为了该命题的撤回。

返回到僵局，这一场景消解开来。提供的一方已书写了一个命题，并正在它内部协商；拒绝的一方正在拒绝该命题，且在它内部没有一个凭之如此说的动作。提高报价不是朝向对方的移动、而是那一断言的重复，这正是僵局随款项增长而加深的缘由。相比之下，道歉不是一个更优的比率。它是该命题的撤回，这正是它耗费如此之少而被让步得如此之罕见的缘由：它所放弃的不是一个数量、而是§3中所生成的地位。

§6 代价

该判据不应只带着它的诸优点被呈现，因为它的主要困难立即可见。闭合的转换比率倾向于稳定。工资关系在此处所给的意义上是闭合的，并已被证明是现代经济中最持久的诸安排之一；历史承认是敞开的，而关于它的诸谈判失败数代之久。倘若该说明要从它的解释性一半推导出它的规范性一半，把持久之物当作正当之物，它会交付它自己裁断的反面。

它并不如此，而这一分离必须被陈述、而非被假定。解释性问题，即哪些转换幸存，与规范性问题，即哪些是正义的，不共享一条判据。可修正性提高冲突的频率并降低其强度：一个可被重开的比率被频繁地重开，且不值得一场战争，而一个不可被重开的比率是安静的，直到它不再安静。这是作为该判据的价钱、而非作为一个有利于它的进一步论证而提供的。一套许诺既稳定又敞开的价值转换理论，会是在描述世界以外的某样东西。

§7 开放的问题

本文不解决价值转换的问题。它辨认一个现存的诸正义理论略过的结构：一个价值范畴被书写为等价于另一个的那一刻。倘若那个结构是真实的，一系列问题立即生起，而它们无一在此被回答。它们是作为本文贡献的实质、而非作为对其界限的一份致歉而被铺陈的，因为一个初次的表述凭它所开启的工作、而非凭它所了结的工作挣得它的位置。

第一对关乎书写本身。谁持有书写一个转换规则的权威？ §3论证该权威由跨越范畴的行动所生成，但这只了结它的起源。这样的权威能否被委派、它能否在没有任何制度授予它的情况下生起，以及两方能否真正地一起书写一个规则、而非一方书写而另一方赞同，是该说明所引起而无法回答的问题。而一个被书写的规则在什么时候是正当的？ 自愿的同意、制度的承认与持续的可修正性各是候选，而本文只承诺于第三个。它未曾显示第三个是充分的，也未曾显示前两个是可有可无的。

第二对关乎转换的界限。某些价值是否全然抗拒转换？ 人的尊严、神圣场所、友谊、生态完整性是那些常备的例子，而§5把它们的抗拒重铸为结构性闭合的极限情形、而非一个独立的禁令。那一重铸是否正确，或每一个价值是否在正确的诠释条件下都可转换，未被确立。而闭合能否在事前被辨认？ §4的判据在回溯中被容易地应用，而在书写的那一刻被困难地应用，因为诸比率鲜少被宣告为不可修正，而是通过使用变得如此，随着在它们之内的诸申诉被回应、而针对它们的诸申诉不被听闻。无法争议该规则、制度僵化、修正之权力中的不对称，以及被排除于重新诠释之外，是可信的早期征兆。无一已被检验。

第三组问该结构有何用处。诸转换规则如何演化？ 它们可能稳定下来、破碎、与竞争性诸规则相争，或与它们所治理的诸关系共同演化，而此处把一个比率当作一个固定等价的处理是一个更完整的说明会放弃的简化：诸转换规则本身很可能受制于生成性动态。它们与政治经济学的关系是什么？ 工资、税收、赔偿、环境抵偿、保险，以及照料工作的估价，全都显得依据诸范畴之间的系统性转换，而这些制度是否有用地被重新描述为转换系统，是本文未曾尝试的一个经验问题。而该说明能否解释冲突与和解？ 许多谈判转的不是数量、而是一个价值是否可代另一个而立，这引起这样一种可能性：失败的和平协议、被拒绝的赔偿，以及跨数代持续的诸委屈，是转换的失败、而非分配的失败。

最后一个问题是本文的框架使之不可回避的那个，而它是该说明的价值最终所依据的那个。在什么条件下诸转换规则能保持生成性？ 倘若正义不取决于一个比率的对称、而取决于固定它的那个规则是否保持对重新诠释敞开，那么那个实践问题不是如何书写一个更好的比率、而是什么样的制度、社会与关系安排维系那一书写本身的敞开。本文中没有任何东西指示那些安排是什么。命名那一要求，不同于知道如何满足它，而两者之间的距离正是留待去做的工作。

关于方法的一则说明。 §2的记号只因它固定诸项的次序而被保留，而没有进一步的形式体系被引入。一个被写作诸加权范畴之上一个函数的转换比率，会供出一份该论证未曾挣得的严格表象，因为此处没有任何东西从该记号被推导，而每一个主张都以散文被陈述。闭合的判据有一个显然的动态读法，其中一个敞开的比率答对一个保有可及诸状态的系统，而一个闭合的比率答对一个已抵达一个吸收态的系统，但那一读法在此不予尝试，因为它会要求一个关于什么算作一个状态的说明，而本文没有它。

参考文献