A Theory of Historical Generativity under Constraints - Towards Generative Relational History

ENGLISH

A Theory of Historical Generativity under Constraints

Towards Generative Relational History

Wanhong Huang · huangwanhong@serendip.ngo

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Abstract

We can create only what the historical framework permits. The claim is widely granted and seldom mechanized. Materialist, hermeneutic, and structure-agency readings each specify what constrains action, and each leaves in the dark the process by which the constraint itself is revised. This paper proposes, in preliminary form, Generative Relational History (GRH), the historical extension of the generative relational framework, and takes constraint evolution for its object. Its central proposal is that historical constraint may be understood as a macroscopic phase of the relational field itself, so that action and constraint compose one field observed at two scales. Three consequences are suggested. Goals become a dynamical category admitting three roles: structural goals optimize within existing constraints, generative goals inject perturbation, and non-structural norms hold open degrees of freedom that no goal can express. Agents’ blindness to slow variables is argued to follow from scale separation, a structural condition of the mean field. And the departure of a system from a stable historical stage is given a proposed mechanism in which perturbation functions as trigger, decisive where prior accumulation has already carried the system near a stability boundary. The paper is offered as a mechanism theory: it specifies how constraint may be updated, and declines to predict which constraints will be. Formal resources are borrowed from two physical settings under an explicit division of labour. Background-independent approaches supply the constitution of a stage that has no prior existence; the self-transport term of fluid dynamics supplies the co-evolution of a stage with what moves upon it. Both are taken as vocabulary and existence heuristic, and the paper marks the point at which each borrowing stops.

Keywords: historical constraint; constraint evolution; generative relational being; goal ontology; slow variables; criticality; intermittent generativity; philosophy of history.

A note on the standing of this paper. This is the first statement of Generative Relational History, and it has the standing of a proposal. It asks one question, how historical constraint is generated, maintained, and updated, and admits material insofar as that material discharges some part of the question. Where it borrows from physics it borrows a vocabulary and a demonstration that certain structures are coherently thinkable; the claim that societies are fluids, or that history carries a metric, lies outside it. Several of its load-bearing claims could be false, and the sections that state them say so. Objection, correction, and counter-evidence are welcome at huangwanhong@serendip.ngo.

§1 Introduction

We can create only what the historical framework permits. The claim is old, and in one form or another nearly every serious account of history has granted it. Human beings act within conditions they did not choose: what can be attempted, what can be organized, what can even be proposed as worth attempting, stands bounded in advance by a configuration that precedes the actors. The claim is also, in its ordinary form, nearly empty. It becomes substantive when one asks what the framework consists in, and it becomes difficult when one asks how the framework changes.

Three readings of the claim are standard, and each secures something the others leave aside. The materialist reading locates the constraint in the material conditions of production: what a society can create stands bounded by its productive forces and by the relations that organize them. The hermeneutic reading locates it in meaning: we act within a horizon of intelligibility we did not make, and what we can intend stands bounded by what our situation makes it possible to mean. The structure-agency reading holds that structure and action constitute one another, neither being prior. Each reading is a genuine achievement, and this paper takes all three as background. What they share, and what opens the space for the present argument, is that each specifies the constraint and leaves the updating of the constraint unmechanized. That constraints change is universally granted. How they change, by what process a configuration that bounds action comes to be a different configuration, is generally attributed to an accumulation whose discharge remains unexplained, or assigned to contingency, which names the gap while leaving it open.

This paper proposes, in preliminary form, that the question of constraint update is the proper object of a theory, and that the generative relational framework is positioned to supply one. The parent framework, generative relational being, holds that relation is prior to the entities it relates and that what exists is generated in and through relation; a governance extension, generative relational governance, treats how a generated relation is governed once it exists. What is proposed here is a third extension, generative relational history (GRH), which asks how relation generates the historical constraint under which further relation is generated. Where the parent framework treats relation as generating being, GRH treats relation as generating history: history taken as the constraint field that condenses out of relational generation and thereafter bounds it.

The object of the theory is narrower than its title suggests, and the narrowing is deliberate. GRH takes as its object constraint evolution, the process by which the bounding configuration is generated, maintained, and revised. Questions of periodization, of causation among events, and of the meaning of the historical process lie outside it. Most theories of history run from constraint to action, or from action to the historical record. Few ask why the constraint updates, and that question governs the organization of everything below.

The questions. The inquiry is governed by eight questions in two tiers. The first tier states what the historical phenomenon poses:

1. The emergence of individual and collective goals, and the manner of their coupling.
2. The constraint that history places upon goals, and the process by which goals in turn make historical constraint evolve.
3. The role of goals in driving the evolution of individual and collective dynamics.
4. The standing of what we decline to optimize. Following goals completely delivers utilitarianism, and normative practice declines to follow goals completely, structural ones especially. This tier asks how that refusal is to be understood, and how such non-structural commitments bear upon goals, dynamics, and constraint.

The second tier states what the framework must answer to be entitled to address the first:

5. The framework’s understanding of the dialectical movement of history and the individual.
6. The ontology of that movement.
7. Its formal modelling.
8. Its bearing on practice: on ethics, on normative conduct, on governance.

These are kept deliberately coarse. This is a first investigation, and finer questions would foreclose the space before it has been surveyed; the specific problems arising under each are treated where they arise.

The two tiers compose one architecture. Q1 through Q3 form a loop: constraint bounds the goals that can be formed, goals shape the dynamics that ensue, and the dynamics revise the constraint. Taken alone the loop is a fixed point, a system that would settle and remain settled, since each stage reproduces the conditions of the next. Q4 states the condition under which the loop fails to close. This is why a question that wears the appearance of normative philosophy is placed among the questions of historical dynamics: what escapes expression as a goal is, on the account developed below, what keeps the loop open.

The architecture also serves a disciplinary function worth naming at the outset. The material below touches philosophy of history, the historical-materialist tradition, dynamical systems, background independence, normative theory, governance, and methodology, and a project touching so many literatures risks becoming a survey of all of them. The eight questions supply the containment. Material earns its place in what follows by discharging some part of a named question; where it would be merely interesting, it is omitted or deferred to the research programme in §8. Each substantive part below discharges one question from each tier.

Premises taken from the parent framework. Three commitments are inherited and used without re-derivation. The first is the primacy of relation: relations are the condition under which relata are individuated at all. The second is the pairing of generativity with relationality as distinct dimensions, since a configuration may be relationally rich while generatively closed, and the two require separate assessment. The third is a criterion, the criterion of return: a value or norm is generative with respect to a system when the system’s own goals are unable to reach back and rewrite it, and has been captured once they can. These serve as premises here; the arguments for them belong to the parent framework.

What this theory delivers. The modelling commitments are worth stating before any apparatus appears, since several objections this paper would otherwise face are objections to claims it declines to make.

GRH is offered as a mechanism theory. It aims to specify how constraint update occurs: by what process, through what channels, under what conditions. Predicting which constraints a given society will come to have lies outside its scope, as does forecasting of any kind. It supplies no closed system of equations, and §5 argues that non-closure is generic to the class of systems at issue. It identifies no objective function that history maximizes, and §3 explains why introducing such a function would readmit teleology through a side door the framework is at some pains to close.

Formal resources are drawn from two physical settings under a division of labour that governs how the borrowings are to be read. Background-independent approaches to spacetime, general relativity and more sharply the group field theory and causal set programmes, are used for a constitutional question: whether a stage with no prior existence, generated together with what moves upon it, is a coherently thinkable structure. That question is answered once, in §3, and the borrowing stops there. The self-transport term of fluid dynamics is used for a distinct and diachronic question: the form taken by the mutual dragging of stage and performance, once their separation has been denied. The two address different questions and are under no obligation to converge. In neither case does the paper claim that society is the physical system in question. What is claimed is that certain structures, a background generated rather than presupposed, a field that transports itself, are coherent, have been rigorously developed elsewhere, and supply a vocabulary in which the social case can be stated without metaphor.

The role of this paper. This is the first proposal of GRH within the generative relational framework, and it carries the obligations of a first paper. It must state the questions the programme will pursue, commit to an ontology precise enough to be wrong, distinguish what has been established from what has merely been named, and leave a research programme that others can take up or refute. §8 accordingly forms a substantial part of the contribution: it sets out six research directions, a methodological position, the open problems visible from here, and the points of contact with contemporary work in the traditions surveyed in §2.

The remainder proceeds as follows. §2 surveys the existing frameworks and states what each achieves, organized throughout by its treatment of constraint update. §3 develops the ontology: the mutual determination of stage and performance, the spectrum of background independence, the commitment that constraint is a phase of the relational field, the limits of the programme, and the joint taxonomy of constraints and goals on which the later parts depend. §4 develops the epistemology, deriving agents’ blindness to slow variables and giving the mechanism by which a stable historical stage is departed. §5 sets out the formal modelling: self-transport, fast-slow structure, criticality, cascade, intermittency, and the division of labour between the two available descriptions. §6 treats the normative consequences, including the standing of what resists optimization. §7 turns to governance and practice. §8 states the research programme.

§2 Recognition of the Existing Frameworks

The question of how historical constraint is updated has been approached by a considerable body of work, and this section states what that work has secured. The intent is recognition. A framework arriving late to a well-tilled field owes its predecessors an account of what they achieved, and the account given here is meant to be accurate rather than convenient: the traditions surveyed have solved problems this paper takes over without re-solving, and several of them have posed the question of constraint update with a clarity GRH inherits. Each framework is presented in the same order: its central claim, the specific achievement it records on the question of constraint update, and the difficulty that the subsequent literature has raised on that point. A caution about the third element is required. Where a difficulty has been conceded within a tradition, or is common ground across its critics and defenders, it is reported as such. Where it remains contested, the contest is reported with it, and the reader should take the attribution to be to the critic named rather than to a consensus. No claim is made that any of these frameworks has been refuted, and the difficulties are selected for their bearing on constraint update rather than for their weight in the literature as a whole.

2.1 The Criterion of Selection

A survey of everything written on historical change would occupy more space than the argument it supports, and this section is confined by a single criterion: each framework is examined for its treatment of constraint update. Frameworks are admitted when they say something determinate about how a bounding configuration comes to be a different bounding configuration, and the discussion of each is limited to what it says on that point. Much else of value in these traditions goes unmentioned, and the omissions carry no verdict.

Three dimensions organize the examination and recur throughout. The first is the mode of existence the framework assigns to constraint: whether constraint is a container within which action occurs, a structure co-constituted with action, or something else. The second is the source of motion in the update: whether the drive toward change is located in accumulation, in contradiction, in agency, in contingency, or in an external parameter. The third is the epistemic standing of the agent: what the framework holds that historical actors can know about the constraints under which they act, and whether that knowledge is treated as attainable in principle. Table 1 summarizes the survey along these dimensions; the sections below supply the detail.

2.2 Dialectical Materialism and Its Schools

The Two Levels in Marx

Marx’s texts operate at two levels, and their relation has occupied the tradition since. At the first stands the account of productive forces and productive relations. The 1859 Preface gives it canonically: men enter into relations of production appropriate to a given stage in the development of their material productive forces; the totality of these relations constitutes the economic structure of society; and at a certain stage the material productive forces come into conflict with the existing relations of production, which turn from forms of development of the forces into their fetters, whereupon an epoch of social revolution begins [39]. At the second level stands the formulation of the Eighteenth Brumaire: men make their own history, and make it under circumstances existing already, given and transmitted from the past [38].

The achievement is twofold and considerable. The first level supplies a mechanism with definite content, and it remains the closest thing in the tradition to a theory of constraint update: it names a slow variable, identifies the condition under which the constraint becomes due for revision, and does so in terms that permit historical investigation. The second level states the general form of the problem this paper takes as its own, and states it with an economy never improved upon: action is conditioned by a configuration it did not choose, and alters that configuration nonetheless.

The limitation is the passage between the two levels. The first says that development in the forces eventually alters the relations; the second says that action under inherited circumstances alters them. Both assert that the constraint gives way. The process by which accumulated development converts into a changed configuration is described more often than specified: the language of fettering names the condition under which change becomes due, and leaves unstated what carries the system across. The point has been pressed from several directions. Analytical reconstruction found that the functional claim required an account of the feedback by which the forces select the relations [15, 17]; the tradition’s own political wing found the passage insufficient to guide action; and Althusser’s intervention was motivated in part by the observation that the transition demands conditions the general formula does not supply [1].

The Necessitarian Reading

The Second International inherited the first level and drew it tight. Kautsky’s widely circulated commentary on the Erfurt Program presented the development of the productive forces as the motor of a determinate succession of social formations, with the arrival of socialism following from the maturation of capitalism’s own conditions [28]; Plekhanov’s treatment of the role of the individual assigned to the great man the acceleration or retardation of an outcome fixed by the general course of development [44]. A qualification belongs here and is entered because the label is applied loosely in the secondary literature: Kautsky himself, in his exchange with Bax, explicitly denied that the materialist conception reduces thought to a reflex of economic conditions, and described it as a method for research into the driving forces of social development rather than a doctrine of determination [29]. What follows concerns the reading that predominated in the period and its consequences for the theory of constraint update, and not the whole of any individual author’s position.

The achievement is generally underrated in later criticism. The reading takes the question of mechanism seriously, and it answers with a slow variable whose accumulation is held to account for what appears at the surface as rupture. That structure, in which a slowly changing quantity governs the conditions under which fast events become consequential, is the structure GRH also adopts, and §4 states the debt.

Two limitations are widely accepted. The first is the evacuation of agency: where the succession is determined, the agent’s contribution reduces to acceleration or delay, and the political question of what is to be done loses its object. This was the animating objection of the Western Marxist response, and it was pressed from within the tradition well before it was pressed from outside [35, 24]. The second limitation is less often remarked and bears directly on the present argument: the slow variable is treated as exogenous and monotone. The forces develop; the development is not itself explained by the configuration it will overturn; and the arrow points one way. A framework in which the slow variable is generated by the very dynamics it later constrains cannot take this form, and §5 states the alternative.

Western Marxism

The Western Marxist tradition may be read, for present purposes, as three responses to the necessitarian reading’s evacuation of the agent, each of which enriches the account of constraint in a distinct way.

Lukács: reification and the standpoint of totality. The central claim is that the commodity form generalizes into a form of objectivity under which social relations present themselves as relations between things, and that this reification is a constraint on what can be apprehended rather than merely a distortion of what is believed. The constraint is transformed when a class comes to occupy the standpoint of totality from which the process appears as a process [35].

The achievement for constraint theory is substantial and is retained here: constraint operates through the forms in which a situation can be apprehended at all, and the epistemic position of the agent is internal to the historical process rather than external commentary upon it. This is a direct ancestor of what §3 treats as the constraint on expressibility.

The limitation most often pressed attaches to the vehicle rather than to the insight. The identification of the proletariat as the identical subject-object of history has been widely judged to import a Hegelian structure that the analysis of reification does not require, and the objection has become close to obligatory in discussions of the work. Lukács advanced a version of it himself in the 1967 preface, describing the identical subject-object as a metaphysical construct [36], though whether that preface states his original position accurately is itself disputed. The insight about apprehension stands independently of the vehicle, and it is the insight that is taken up here.

Gramsci: hegemony and the war of position. The central claim is that domination in developed civil societies operates through consent organized in a dense network of institutions, so that the constraint includes a settlement of common sense that must be contested on its own ground. The war of position names the corresponding form of struggle: protracted, distributed across the institutions of civil society, without a decisive moment [24].

The achievement is among the tradition’s most valuable for the present question. It describes constraint update as gradual, distributed, and cumulative, and it identifies the medium in which the accumulation occurs. It also supplies the notion of an organic crisis, in which the ruling settlement loses its capacity to organize consent while no successor has yet formed, which is the tradition’s most suggestive description of a system between configurations.

The accepted limitation concerns conversion. The war of position describes decades of accumulation and the crisis describes the interregnum, and the passage from the one to the other remains at the level of description. The concept has also been criticized for elasticity: hegemony has been applied to so wide a range of phenomena that its explanatory purchase in any given case requires separate argument, an objection registered from within the tradition as much as outside it [4].

Althusser: overdetermination and structural causality. The central claim is that a social formation is a complex whole with a structure in dominance, that contradictions are multiple and unevenly developed, and that a revolutionary rupture requires their fusion in a conjuncture rather than the maturation of a single contradiction. Structural causality names the mode in which a structure is present only in its effects [1, 2].

The achievement is a lasting gain and is taken over here. The rejection of a single expressive contradiction removes the last remnant of a Hegelian teleology from the materialist account, and structural causality is a near neighbour of what §3 argues for as constraint’s mode of existence: a constraint present in what it conditions rather than standing outside it.

The accepted limitations are two. The conjuncture in which fusion occurs is named with precision and specified only by the fusion that occurred, so that the concept identifies the moment after the fact. And the account was pressed hard on the question of agency: the treatment of the subject as an effect of interpellation, developed in the essay on ideological state apparatuses [3], raised the question of how a structure is transformed by those it constitutes. Thompson’s polemic put the objection at its sharpest [50]; the polemic was contested at the time and remains so, and what is reported here is the question it raised rather than the verdict it proposed.

Analytical Marxism

The central claim of the analytical current is methodological: the tradition’s theses should be stated with the clarity that permits assessment, and defended by the standards of argument prevailing elsewhere in philosophy and the social sciences. Cohen’s reconstruction gave the primacy of the productive forces its most rigorous form, arguing that relations of production obtain because they are functionally suited to develop the forces [15]. Elster pressed the demand for microfoundations: a macro-level claim is admissible only when underwritten by an account of the individual actions that realize it [17].

The achievements are two, and this paper accepts both. Functional explanation was given a defensible form, in which the explanation is licensed by a consequence law rather than by the mere identification of a benefit. And the demand for microfoundations remains binding on any successor: a mechanism theory that cannot say what agents are doing when the constraint changes has not yet supplied a mechanism.

The debate that followed is instructive, and its standing should be stated accurately, since it remains open rather than settled. Elster’s objection was that the conditions justifying functional explanation in evolutionary biology are absent in social theory, and that a functional explanation of a macro-phenomenon is admissible only where the mechanisms of individual behaviour producing the aggregate can be indicated at least schematically [17]. Cohen replied that the absence of such an elaboration weakens a functional explanation without invalidating it, offering the pre-genetic Darwinian explanation of hollow bones as a case of an explanation that was good before its mechanism was known [16]. The exchange leaves a requirement rather than a refutation, and this paper faces the requirement on its own account: §4 states the corresponding risk for the mechanism proposed here, together with the constraint that keeps it from arising. The current has also been criticized for the cost of its own method, in that the reduction to individual action set aside the relational and processual character of the original theory, which is precisely what the present framework takes as primitive.

World-Systems Analysis

The central claim is that the appropriate unit of analysis is the historical system rather than the national society, that the modern world-system is a capitalist world-economy with a core, semi-periphery, and periphery, and that this system has a developmental history with cycles and secular trends [51, 6].

The achievement, for the present question, is the treatment of scale and duration. Cycles of accumulation, hegemonic succession, and secular trends are described as processes whose periods exceed the horizon of any actor within them, and the analysis is conducted at a scale at which the constraint on any national society is visible as the product of a larger dynamic. This is a genuine theory of slow variables, and §5 takes up the same concern in a different vocabulary.

Two lines of criticism are worth reporting, the first as a position in a continuing debate and the second as a more general difficulty. Brenner argued that the account defines capitalism by exchange relations and the world division of labour rather than by production, and that this weakens its treatment of class dynamics [13]; the argument was contested by world-systems analysts and the debate has not closed. The second difficulty is less disputed: the number, dating, and boundaries of the long waves vary between analysts, and the mechanism generating the periodicity is specified less fully than the periodicity itself.

Post-Marxist Positions

The central claim of the post-Marxist current, in Laclau and Mouffe’s formulation, is that the social is discursively articulated, that no class occupies a privileged position given in advance by the relations of production, and that hegemonic settlements are contingent articulations of elements with no necessary belonging [32].

The achievement is the opening of the field of the possible. The pretension to have identified a historical law is set aside, the identification of the revolutionary subject ceases to be given by structural position, and the analysis of how political identities are constructed rather than expressed is substantially advanced.

The accepted limitation is the one that bears on this paper most directly. Contingency, having replaced necessity, is asked to perform the work of a mechanism. That a settlement might have been otherwise leaves unstated why this settlement gave way at this moment while others endured. An objection along these lines was pressed immediately by Geras, who argued that the position dissolves the object of analysis along with its determinism [22], and was answered by Laclau and Mouffe in the same venue; the exchange is a dispute rather than a settled finding. What is reported here is the narrower point that survives it and does not require Geras’s framing: a vocabulary describing the form of a settlement with great subtlety is not thereby equipped to say when one settlement passes into another.

2.3 Non-Marxist Frameworks

Weber and the Switchmen

The central claim relevant here is Weber’s image: not ideas, but material and ideal interests directly govern conduct, and yet the world images created by ideas have very often, as switchmen, determined the tracks along which action has been pushed by the dynamic of interest [53]. Ideas supply direction; interests supply motion.

The achievement is the distinction between two kinds of constraint that are often run together, and the demonstration that the ideational can be causally efficacious without constituting a separate motor. The analysis of the Protestant ethic supplied the worked case [52], and the account of rationalization supplied a slow variable of considerable power.

The accepted limitation is that the image describes the switch and leaves unspecified how a switch comes to be thrown. Weber’s own methodological commitments, and his suspicion of theories of historical development, made this a deliberate abstention rather than an oversight; it nonetheless leaves the question of constraint update open.

The Annales and the Long Duration

The central claim is a stratification of historical time: the almost motionless history of man in relation to his environment; the slowly rhythmic history of groups, economies, and states; and the history of events, which Braudel described as surface disturbances, crests of foam carried by the tides of history [11, 12].

The achievement is the clearest anticipation in historiography of what §5 treats as scale separation. Two consequences follow from taking it seriously, and both are retained here: historical constraint possesses more than one relaxation time, and an actor operating at the timescale of events has systematically restricted access to what operates below.

The accepted limitations are the coupling and the agent. The strata are distinguished with great power and their interaction is less specified: what conditions permit the deep stratum to become sensitive to the surface, and by what process the surface accumulates into the depth, are questions the framework poses more effectively than it answers. And the subordination of the event drew the standard objection that human agency is left with little to do, an objection sharpened by the tradition’s own later turn toward the history of mentalities and microhistory.

Historical Institutionalism

The central claims are that institutions constrain by making some paths more costly than others, that early choices are locked in through increasing returns, and that institutional development is punctuated by critical junctures during which the range of viable options widens [40, 43, 14]. A second generation added an account of gradual transformation, identifying displacement, layering, drift, conversion, and exhaustion as modes by which institutions change without rupture [49, 37].

The achievement is the most operational vocabulary available for constraint update. Path dependence with increasing returns supplies a mechanism for why constraints persist; the typology of gradual change supplies mechanisms by which a configuration becomes a different configuration in the absence of a rupture; and the emphasis on ambiguity in rules, and on the gap between rule and enforcement, identifies where the leverage for endogenous change is located [37].

The accepted limitation concerns the critical juncture, and it has been stated most clearly from within the tradition. Capoccia and Kelemen observe that despite the theoretical importance of critical junctures, analyses of path dependence have devoted little attention to them, and they undertake to reconstruct the concept, delimit its range, and supply methodological guidance for its use [14]. The reconstruction advances the matter considerably and identifies the juncture by a heightened probability that agents’ choices affect the outcome, relative to that probability before and after. The identification remains, in practice, retrospective: what marks a moment as a juncture is that the range of outcomes was wider then, which is established by the divergence that followed. What distinguishes a shock that opens the range from one the institution absorbs is where the present paper directs its contribution, and §4 states it.

Critical Realism

The central claims are a stratified ontology distinguishing the real, the actual, and the empirical; generative mechanisms possessed by structures and exercised whether or not their effects are actualized; emergence as the relation between strata; and, in Archer’s development, the morphogenetic cycle in which structural conditioning precedes social interaction, which in turn produces structural elaboration or reproduction [8, 9, 5].

The achievement is the ontological vocabulary closest to what this paper requires. Structures with generative powers are constraints present in their effects; emergence licenses talk of strata without reduction; and the morphogenetic cycle is a serious and explicitly temporal theory of how structures are reproduced and transformed. Archer’s analytical dualism, which holds structure and agency apart in time so that their interplay can be examined, is a considered solution to the problem §3 meets and answers differently.

The accepted limitations are two, and the second is a difference rather than a defect. The first is the objection, pressed from a broadly Popperian direction, that the generative mechanisms of the deep stratum are posited by retroduction from actualized effects, which places the ontology at some distance from independent test. The tradition’s response, that retroduction supports depth explanation beyond correlation and that scientific ontology is generally so posited, is a serious one, and the discussion is open. The second is the point on which GRH departs. Analytical dualism preserves the distinctness of structure and agency as a condition of the analysis, and this paper takes constraint and action to be one field observed at two scales, which forecloses the dualism. The departure creates an obligation, and §5 discharges it: scale separation supplies the analytical leverage that temporal separation was introduced to provide, while treating the strata as one thing at different resolutions.

Luhmann

The central claims are that social systems are operationally closed and autopoietic, reproducing themselves through their own operations; that a system’s environment perturbs rather than instructs it; that structural coupling names the arrangement by which a system is rendered sensitive to particular environments; and that evolution proceeds through variation, selection, and restabilization [33, 34].

Two achievements bear on this paper. Constraint is treated as a restriction on what can register as information within a system, which is close to what §3 calls the constraint on expressibility. And self-reference is placed at the centre of the theory rather than treated as an anomaly to be managed, which is the correct response to a situation in which the observer is inside what is observed.

Two difficulties are regularly raised. Individuals belong to the environment of social systems rather than to the systems themselves, which secures the theory’s consistency and leaves intentional action without an evident role in system transformation; Habermas pressed a version of this objection [25], and Luhmann’s defenders reply that the placement is a methodological decision rather than a denial of agency. And operational closure, having explained why systems are stable, makes the explanation of substantial structural change correspondingly demanding.

Framework	Mode of existence of constraint	Source of motion	Difficulty raised on update
Marx	Economic structure conditioning the whole	Development of forces against fettering relations	Passage from fettering to transformation described, unspecified
Second International	Container fixed by material development	Accumulation in an exogenous, monotone slow variable	Agency evacuated; slow variable unexplained by the system it governs
Lukács	Form of objectivity governing apprehension	Attainment of the standpoint of totality	Vehicle requires an identical subject-object widely judged unsupportable
Gramsci	Settlement of common sense in civil society	Protracted contest across civil institutions	Conversion of accumulation into crisis left at the level of description
Althusser	Structure present only in its effects	Fusion of multiple contradictions in a conjuncture	Conjuncture specified by the fusion that occurred; agency constrained
Analytical Marxism	Relations selected by their functional fit	Consequence law linking relations to development	Discrimination among candidate arrangements requires a feedback account
World-systems	Position within a single historical system	Cycles of accumulation and hegemonic succession	Periodization contested; generating mechanism less specified than the cycle
Post-Marxism	Hegemonic articulation without necessary belonging	Contingent rearticulation	Contingency asked to do the work of a mechanism
Weber	Tracks laid by world images	Interests, with ideas as switchmen	Throwing of the switch left unspecified by design
Annales	Stratified durations	Slow movement of the deep strata	Coupling between strata underspecified; event subordinated
Historical institutionalism	Differential cost of available paths	Increasing returns; ambiguity in rules	Juncture identified retrospectively by the divergence that followed
Critical realism	Generative powers of stratified structures	Morphogenetic cycle of conditioning and elaboration	Deep mechanisms posited by retroduction; dualism preserved by method
Luhmann	Restriction on what registers as information	Variation, selection, restabilization	Agency placed in the environment; closure makes deep change demanding

Table 1. The surveyed frameworks along the three dimensions of §2.1. The final column reports difficulties raised in the literature on the question of constraint update; where these remain contested, §2.2 and §2.3 report the contest.

2.4 The Common Position and the Point of Entry

The achievements gathered above admit a summary along the three dimensions. On the mode of existence of constraint, the tradition has moved steadily away from the container: structural causality, generative powers, and structural coupling all treat constraint as exercised through its effects. On the source of motion, several determinate answers are on offer, of which the development of the forces and the accumulation of increasing returns are the most fully specified. On the epistemic standing of the agent, it is established that agents’ access to their own conditions is systematically restricted, whether by reification, by ideology, by interpellation, or by the duration of the deep strata.

What the surveyed positions share is a common stopping point, and stating it precisely is the purpose of this section. In each case the fact of constraint update is registered, and the process of the update is described rather than mechanized. Accumulation is named without an account of why accumulation discharges at one moment while being absorbed at others, as in the fettering of the forces and in the approach to a critical juncture. Contingency is named as what makes the outcome open, which locates the gap and leaves it open. The conjuncture, the juncture, and the organic crisis are identified after the event by the divergence that followed them. Each of these occupies the position a mechanism would occupy.

Three requirements follow, and they organize the parts below. The first is an ontology of constraint precise enough that the question of how it changes has a determinate sense, which §3 supplies. The second is an account of what agents can and cannot know about the constraints under which they act, since a mechanism requiring agents to perceive what they are altering is a mechanism no historical actor could operate; §4 supplies it. The third is a dynamics in which accumulation and trigger are distinguished, so that the discharge of an accumulation has a stated condition, which §5 supplies. The remainder attempts these three in order.

§3 Ontology

§2 closed with three requirements, of which the first was an ontology of constraint precise enough that the question of how constraint changes has a determinate sense. This section supplies it. The order of exposition runs from the problem that forces the question, through the existing answers, to the commitment this paper makes, the limits under which that commitment is made, and the categorial apparatus the later parts depend upon.

3.1 The Mutual Determination of Stage and Performance

The problem may be stated with an image before it is stated with an argument. We act upon a stage: a configuration of possibilities, given in advance, within which what we do is done. The image is natural and nearly unavoidable, and it underwrites the container conception of constraint that §2 found the tradition steadily abandoning. What makes the image inadequate is a fact the tradition also registers: the performance reshapes the stage. What is done within the configuration alters the configuration, and it does so without any actor stepping outside to make the alteration.

The Absence of an External Vantage

Taken seriously, the mutual determination of stage and performance forecloses a position that most accounts quietly retain. If the stage is altered only from within, there is no vantage from which the alteration is surveyed. This has a consequence for theory and a consequence for the actor, and they should be kept apart. For theory, it means that any account positing an observer who tracks the configuration while standing outside it has helped itself to something the situation denies. For the actor, it means that the configuration under which one acts is altered by the acting, and that the alteration is not available to the actor as an object of view at the time it occurs. The second consequence is developed in §4; the first is what concerns the present section.

The Structure Underlying the Apparent Paradox

The mutual determination has the appearance of a paradox: the stage conditions the performance, the performance conditions the stage, and neither is prior. The appearance dissolves once the two are recognized as operating at different timescales. The stage conditions the performance at the timescale of action; the performance conditions the stage at a timescale much longer, over which the effects of many performances accumulate. Circular determination between quantities at a single timescale would indeed be vicious. Determination running in both directions between a fast quantity and a slow one is an ordinary structure, thoroughly studied, and the subject of §5.

What remains after the paradox dissolves is a question about the kind of thing the stage is. If the stage is altered by what occurs upon it, and if no actor stands outside to alter it, then the stage and what occurs upon it cannot be two independent kinds of thing related externally. The remainder of this section states what they are instead.

3.2 The Historical Ontologies of the Existing Frameworks

The Container Conception

The container conception treats historical constraint as a bounded region within which action occurs: the conditions are given, action takes place inside them, and the conditions are altered by forces of a different order from the action they contain. The conception is rarely defended in this form and frequently presupposed. Its attraction is that it makes the constraint determinate and the analysis tractable, since a container can be described independently of what it contains. Its defect is the one just stated: it requires that the alteration of the container be effected by something other than what the container holds, and in the historical case there is nothing else.

Co-Constitution and the Question It Leaves

The structure-agency literature abandoned the container and put co-constitution in its place: structure is the medium and outcome of the practices it recursively organizes, in Giddens’s formulation [23], and structure and agency are held apart analytically in Archer’s, precisely so that their mutual conditioning can be examined in sequence [5]. Both are advances on the container, and both leave a question standing that §2 identified as the tradition’s common stopping point.

The question is what co-constitution consists in. To say that structure and action constitute one another names a relation and specifies neither its mechanism nor the mode of existence of the terms. Giddens’s duality of structure locates structure in memory traces and in its instantiation in practice, which secures the mutuality at the cost of leaving structure without a mode of existence between instantiations. Archer’s analytical dualism secures the mode of existence by holding the terms apart in time, at the cost of preserving as an ontological result what was introduced as a methodological device. The present paper takes a third route: the terms are not two kinds of thing requiring a relation, and what appears as two is one field observed at two resolutions.

Stratified Ontologies

Critical realism’s stratification of the real, the actual, and the empirical, together with emergence as the relation between strata, supplies the most developed alternative [8, 9]. Its gain is that constraint acquires a mode of existence independent of its actualization: a structure possesses generative powers whether or not those powers are exercised. Its cost, for present purposes, is that the strata are distinguished as levels of reality, so that the relation between them requires an account of emergence that carries substantial metaphysical weight. What follows retains the insight that constraint exists in a manner distinct from its instances, and locates the distinction in scale rather than in level.

3.3 The Spectrum of Background Independence

Before the commitment of §3.4 can be stated without metaphor, one thing must be shown: that a structure of the required kind is coherently thinkable. The required kind is a background that is generated together with what it conditions, rather than presupposed by it. Physics supplies the demonstration, and the demonstration is all that is borrowed here. Whether societies resemble spacetimes is not at issue, and nothing below depends on their doing so.

The Treatment of the Metric in General Relativity

In Newtonian mechanics, space and time are the stage: fixed, given in advance, and unaffected by what occurs within them. General relativity removes the fixity. The metric that determines spatiotemporal relations is itself a dynamical variable, determined by the field equations from the distribution of matter and energy, while that same metric determines how matter and energy move. Neither term is prior; the geometry is a solution rather than a setting.

This is the first and weakest sense of background independence, and it already suffices to establish the point at issue in §3.1. The mutual determination of a configuration and what occurs within it is the ordinary structure of a theory that has been in successful use for a century.

The Residual Manifold in Canonical Approaches

Canonical quantizations of gravity carry background independence further while retaining a residue. Geometric operators acquire discrete spectra, and the theory is formulated so as to respect diffeomorphism invariance, yet a differentiable manifold remains as the arena on which the fields are defined [46]. The relevant point is that background independence admits degrees: a theory may dispense with a fixed metric while retaining a fixed manifold, and the question of how much background has been dispensed with is a substantive one.

The Treatment of Spacetime in Group Field Theory and Causal Sets

The strongest form dispenses with the manifold. In group field theory, the fundamental degrees of freedom are combinatorial and algebraic, defined on a group manifold with no spacetime interpretation, and continuum spacetime with its geometry is expected to emerge as a collective phase of a large number of these degrees of freedom, by a process of the condensate type [41, 42]. Causal set theory proceeds differently, taking a discrete partial order as fundamental and recovering continuum geometry as an approximation to it [48].

What these programmes establish, for the purposes of this paper, is a single point of principle: a background may be a phase of something more fundamental rather than a presupposition of it. The stage need not be a stage. It may be what a large number of relational degrees of freedom look like when they are in a particular collective state, and the question of what state they are in becomes a legitimate question with a determinate sense.

The Extent of the Borrowing

The borrowing stops here, and stating its limit is part of making it. Three things are taken. The first is the demonstration just given, that a generated background is a coherent construction rather than a figure of speech. The second is a vocabulary: phase, order parameter, condensate, collective state. The third is a warning, developed in §3.5, about what the social case lacks that these programmes possess.

Three things are not taken. No claim is made that social relations satisfy the equations of any of these theories, or any equations resembling them. No claim is made that the analogy licenses transfer of results: nothing established about spacetime emergence is thereby established about historical constraint. And no numerical or structural correspondence is asserted between the two domains. The borrowing is an existence demonstration and a vocabulary, and the sections that follow use it as such.

3.4 The Ontological Commitment

The Statement of the Phase Claim

The commitment may now be stated.

Claim 1 (the phase claim). Historical constraint is a macroscopic phase of the relational field. It is what a large number of relations look like when they stand in a particular collective state, and its properties are the properties of that state. It occupies the position that a container is imagined to occupy, and it occupies that position as a description of the relations themselves at a scale at which individual relations go unresolved.

Three terms in the claim require definition, and the definitions are given here rather than assumed.

The relational field is the totality of relations obtaining among the participants in a historical situation, taken together with the manner in which those relations condition one another. The parent framework’s primacy of relation is doing work here: the field is not built from prior individuals who then enter relations, since what individuates a participant is its position in the field. The field is the primitive.

A phase is a collective state of a large number of components, characterized by properties that belong to the aggregate and are undefined for any component taken singly. The term is used in its technical sense, and the claim is not a metaphor. Two features of phases matter here. A phase possesses order parameters, quantities defined on the aggregate that specify which collective state obtains. And a phase can change: the same components, under altered conditions, can settle into a collective state with different macroscopic properties.

Constraint is what the relational field makes impossible, unsayable, or unrankable for a participant in it, in virtue of the collective state the field is in. The three modes are distinguished in §3.6. The essential point is that constraint describes the relations themselves, at a scale at which individual relations go unresolved.

The Standing of Stage and Actor under the Claim

The phase claim dissolves the problem of §3.1 rather than solving it. If constraint is a macroscopic phase of the field and action is what occurs among the relations composing that field, then stage and actor are not two kinds of thing between which a relation must be found. They are one field described at two resolutions: constraint is the field coarse-grained, action is the field resolved. The mutual determination that appeared paradoxical is the ordinary relation between a coarse description and a fine one in a system where the coarse quantities are functions of the fine and the fine evolve under conditions the coarse specify.

This has an immediate consequence for the analytical dualism of §2.3. Holding structure and agency apart in time is unavailable to a framework that denies they are distinct kinds, and the leverage that the temporal separation was introduced to provide must be recovered by other means. The means is scale separation, and §5 supplies it. The obligation is recorded here so that its discharge can be checked.

The Constraint Field

The claim licenses a notation used throughout the rest of the paper. Let $\Gamma$ denote the constraint field: the coarse-grained state of the relational field, the macroscopic phase whose properties constitute what is possible, sayable, and rankable for participants. $\Gamma$ names the relational field under coarse-graining, and its dynamics, treated in §5, are the dynamics of the field at that resolution. Where the later sections write equations in $\Gamma$, the subject of those equations is what this section has defined.

What the Commitment Costs

The phase claim is the paper’s principal risk, and the risk should be stated rather than managed. If constraint is a phase in the technical sense, then order parameters exist for it, and the question of which phase a given historical situation occupies has a determinate answer. If no such order parameters exist, even in principle, then the term is doing metaphorical work and the sections that build on it lose their support. The paper does not exhibit an order parameter for any historical case, and §3.5 explains why it holds that none can be exhibited from within. That combination, a commitment to the existence of a quantity together with an argument that the quantity is not computable by participants, is a substantive position rather than an evasion, and §8 lists its identification as the first research direction.

3.5 The Limits of the Programme

Three limits bound what the ontology just stated can be developed into, and they have distinct sources. Naming the sources is more useful than listing the limits, since it shows which are inherited and which belong to the social case alone.

The Constitutional Limit: No Independently Motivated Symmetry

The first limit is inherited from the constitutional borrowing. In the physical programmes, the emergence of a background from more fundamental degrees of freedom is disciplined by symmetry: the group structure is independently motivated, and it constrains which collective states are admissible. The social case has no such group. What plays the corresponding role, if anything does, would be a set of invariants preserved under rewriting of the relational grammar, and no such set has been identified. The consequence is that the emergence claimed in §3.4 is claimed structurally and cannot be derived. §8 states the identification of invariants as an open problem.

The Dynamical Limit: No Closure

The second limit is inherited from the dynamical borrowing of §5. Systems whose evolution is governed by nonlinear self-transport do not admit closed descriptions at the coarse-grained level: averaging the equations of motion produces terms involving higher-order correlations, and the hierarchy does not terminate. The social case inherits this, and §5.10 argues that it inherits it as a generic feature rather than as a special defect. The consequence is that no closed system of equations for $\Gamma$ is available, and none is offered.

The Limit Peculiar to the Social Case: Self-Reference

The third limit belongs to the social case alone, and neither physical borrowing supplies a precedent. Participants in the relational field read the constraint under which they act, and their reading enters the field as a further relation. The metric, in the physical case, does not consult its own value. Moreover the reading is multivalued: two participants may read the same configuration differently, and both readings become part of what is to be described. This is Luhmann’s point about self-reference [33], entered here as a limit rather than as a resource. The consequence is that the coarse-graining relating $\Gamma$ to the underlying field is not a fixed map, since what participants take the constraint to be is among the things the constraint supervenes upon.

Taken together, the three limits state the difficulty of the social case with more precision than an undifferentiated list of caveats would allow: the social case carries the constitutional problem of a background with no prior existence, the dynamical problem of a system that transports itself, and a problem of self-reference that neither physical case faces.

The Exclusion of an Action Principle

One further exclusion follows from the limits and is stated separately because of what it protects. It would be natural, given the vocabulary borrowed in §3.3, to seek an action functional for the relational field, from whose stationarity the dynamics would follow. This paper declines to do so, and the reason is not technical difficulty. An action principle supplies a quantity that the system’s trajectories extremize, and a historical theory equipped with such a quantity has committed itself to a magnitude that history maximizes. That is teleology in the form that the framework is at pains to exclude: not the overt claim that history has a goal, but the formal apparatus from which such a claim can be recovered. §8 returns to the boundary against teleology; the exclusion is recorded here because it constrains what §5 may write down.

3.6 The Joint Categorization of Constraints and Goals

The apparatus of the remaining sections requires two categorizations, and they must be given together. A typology of constraints alone leaves unspecified how constraint enters the dynamics, since what converts a configuration into a course of action is the goals formed under it. A typology of goals alone leaves the distinction between kinds of goal without ontological grounding, since what distinguishes them is which constraints they operate upon. The two are given here, in the ontology, because goals determine how constraint enters dynamics and therefore belong to the ontology of the historical process rather than to its ethics.

Constraints Typed by Mode of Holding

Constraints are distinguished by the manner in which they hold, rather than by the substrate in which they are realized. A typology by substrate, distinguishing material from institutional from symbolic constraints, would contradict the phase claim, which holds that all of these are states of one field. Three modes are distinguished.

Constraints of possibility determine what cannot be done. Material and technical limits are the clearest instances. This mode is the slowest to change and the most nearly exogenous to the dynamics it constrains.

Constraints of expressibility determine what cannot be said, and in particular what cannot be formulated as a goal. A course of action that cannot be articulated within the available vocabulary is unavailable in a manner different from physical impossibility, and the difference matters: the boundary of the expressible moves, and its movement is the layer at which this paper locates the main work of constraint update.

Constraints of evaluability determine what counts as better. They comprise the standards by which courses of action are ranked, and they constitute the evaluation functional under which optimization proceeds. This mode changes fastest of the three and is the one that goal ontologization, treated in §6, rewrites.

The three have different relaxation times and couple to different segments of the loop set out in §1. That they are three modes of one field, rather than three kinds of thing, is what the phase claim secures. Table 2 sets them out.

Mode	What it holds	Relative relaxation time	Standing in this paper
Possibility	What cannot be done: material and technical limits	Slowest	Largely exogenous to the dynamics it constrains
Expressibility	What cannot be said, and in particular what cannot be formulated as a goal	Intermediate	The layer at which constraint update principally occurs
Evaluability	What counts as better: the standards by which courses of action are ranked	Fastest	The evaluation functional that goal ontologization rewrites

Table 2. Constraints typed by mode of holding. The typology cuts by manner of holding rather than by substrate, since a typology by substrate would contradict the phase claim.

Goals Typed by Expressive Standing

Goals are distinguished first by their standing with respect to expression.

Structural goals are expressible, rankable, and optimizable. Wealth, output, power, survival, efficiency, profit, and their institutional proxies are instances. They enter the evaluation functional directly, and they constitute the domain in which economics, control theory, and utilitarian normative theory operate with full legitimacy. This paper disputes none of that legitimacy, and §6 disputes only the extension of the domain to the whole.

Non-structural goals are normatively effective and cancel themselves when stated as goals. The classical instance is the injunction to dwell in the low places that others disdain, of which it is characteristic that no end is served by the dwelling; pressed for a justification, one can say only that it is fitting. Trust, humility, generosity, and sincerity share the structure, and share a diagnostic feature: the more thoroughly they are optimized, the more thoroughly they vanish. Trusting in order to be trusted, humility performed in order to appear humble, and art made to raise a score are each self-defeating in a manner that has nothing to do with the sincerity of the agent. What is defeated is the thing itself, by the form of the pursuit.

Generative goals are directed without being terminal. Their logic is the making of possibility rather than the reaching of a state: exploration, play, wandering, encounter, venture, creation. They inject into the field configurations that no evaluation functional has ranked, and, under conditions specified in §4, such configurations can be amplified into changes of the constraint field itself.

A note on the name is required, since an earlier formulation called these stochastic goals. The name misdescribes them. What is unpredictable is the historical effect, and the goal itself may be perfectly definite: one may set out to explore the unknown with complete clarity about what one is doing. Randomness, moreover, implies structurelessness, and the claim here is that these goals are directed, differing from structural goals in lacking a terminal state rather than in lacking direction. Exploration has a form. The name generative is continuous with the parent framework and records what the category does.

Goals Typed by Dynamical Role

The second axis assigns each goal a role in the dynamics of the constraint field, and it is the axis on which the categorization does its work.

Injection generates new relational configurations, adding to the field what was not there. Transport carries configurations across scales without generating or fixing them. Dissipation fixes configurations into rules, removing them from the dynamics by making them settled.

The two axes cross, and the crossing yields the result this section is for. Structural goals act predominantly as dissipation: to optimize is to fix, and what is optimized ceases to vary. Generative goals act as injection, and the absence of a terminal state is precisely what makes them a source rather than a sink. Non-structural goals act as transport: they hold open the range across which configurations can move, generating none and fixing none. This last assignment is derived here from the categorization, and §6 takes it as established rather than assuming it. Table 3 gives the crossing together with the interlocking treated below.

Type of goal	Expressive standing	Dynamical role	Mode of constraint engaged
Structural	Expressible, rankable, optimizable: wealth, output, power, survival, efficiency, profit	Dissipation	Evaluability: acts under a ranking and, in the limit, rewrites it
Non-structural	Normatively effective and self-cancelling when stated: trust, humility, generosity, sincerity	Transport	Expressibility: holds open what has yet to be formulated
Generative	Directed without being terminal: exploration, play, wandering, encounter, venture, creation	Injection	Below all three, since what is injected has yet to acquire standing

Table 3. Goals typed by expressive standing and by dynamical role, with the mode of constraint each engages. The three are distinguished by dynamical role rather than by content.

The Interlocking of the Two Categorizations

The two typologies engage at determinate points. Structural goals operate upon constraints of evaluability, since to optimize is to act under a ranking and, in the limit, to rewrite the ranking. Non-structural goals bear upon constraints of expressibility, holding open what has not yet been formulated and cannot be formulated without being destroyed. Generative goals operate below all three modes, since what they inject has not yet acquired the standing that would place it under any of them.

The interlocking is what supplies the ontological grounding required at the outset of §3.6. The distinction between kinds of goal is a distinction of dynamical role, and the roles are individuated by which mode of constraint each engages; content and the psychology of those who hold them leave the classification untouched. Goals, on this account, belong to the ontology of the historical process: they are the mechanism by which the coarse state of the field conditions the fine dynamics, and by which the fine dynamics alter the coarse state.

A Note on the Term Generative

The framework is named for generativity and one category of goal is named generative, and the two uses must be distinguished. Framework-level generativity is a property of a system: the capacity to continue producing relations and constraints not derivable from the present configuration. Generative goals name the class of goals whose dynamical function is injection. The relation between them is that generative goals are one contributor to system-level generativity, and §6 argues that they are insufficient for it on their own, since injection without transport is damped before it propagates. Both terms are retained, and the level at which each is used is marked wherever ambiguity could arise.

§4 Epistemology

The second requirement stated at the close of §2 was an account of what agents can and cannot know about the constraints under which they act. The requirement is not merely a matter of completeness. A mechanism of constraint update that requires agents to perceive the constraint they are altering is a mechanism no historical actor could operate, and the plausibility of the account given in §4.5 depends on the epistemology given first.

The tradition has an established position on this question, and §4.1 states it. The position taken here differs in its explanation rather than in its verdict: agents’ access to their own conditions is restricted, and the restriction follows from the structure of scales rather than from a failure of the agents.

4.1 The Historical Epistemology of the Existing Frameworks

Ideology and the Critique of Consciousness

The materialist tradition’s central epistemic thesis is that consciousness is conditioned by social position, and that the conditioning systematically distorts. In its early form the thesis concerns the inversion by which the products of human activity present themselves as independent powers; in Lukács it becomes the account of reification, under which the commodity form generalizes into a form of objectivity that makes the process appear as a collection of things [35]; in Althusser it becomes interpellation, by which individuals are constituted as subjects who recognize themselves in the positions the structure assigns [3].

The achievement is the recognition that epistemic access is internal to the historical process. What an agent can know about the conditions of action is itself conditioned, and the conditioning is structural rather than accidental. This paper retains that recognition without qualification.

The point of departure concerns the modality of the restriction. In each of these accounts the restriction carries a normative charge: it is a distortion, a false consciousness, an occlusion, and its removal is the goal of a critique. The restriction is, in principle, remediable, and the achievement of the standpoint from which the process appears as a process is the form the remedy takes. §4.2 argues that a substantial part of the restriction is remediable by no critique whatever, since it follows from scale rather than from position.

Effective-Historical Consciousness

The hermeneutic tradition arrives at a related restriction by a different route. Understanding occurs within a horizon that the understander did not construct, prejudices in the neutral sense are the condition of understanding rather than obstacles to it, and consciousness of being affected by history is at the same time an acknowledgement that the effects cannot be fully brought before consciousness [18].

The achievement here is the removal of the normative charge: the situatedness of the understander is a condition of understanding rather than a defect in it, and the demand for a view from nowhere is set aside as incoherent rather than as merely difficult. This paper follows the hermeneutic tradition on that point and departs on another. The hermeneutic restriction is a restriction on the understanding of meaning, and its source is finitude. The restriction argued for below is a restriction on the observability of a quantity, and its source is the relation between timescales. The two are compatible, and they are different.

The Shared Presupposition

Both traditions, for all their difference, presuppose that the epistemic difficulty is of a kind that better positioning would improve. Critique promises the standpoint of totality; hermeneutics promises a fusion of horizons that widens what can be understood. In each case the restriction is a function of where the agent stands, and movement is possible.

The following section argues that a component of the restriction is invariant under any movement available to a participant. It is a property of the observation relation itself, and it would persist for an agent free of ideology and possessed of every relevant fact about the present.

4.2 The Structural Derivation of Blindness

The Mean-Field Position of the Participant

Consider the epistemic position of a participant in the relational field as §3 defined it. The participant stands in a definite and small number of relations, and acts within them. What the participant encounters, in acting, is the local configuration: the specific relations obtaining here, and the aggregate effect of everything else, which arrives as a general condition rather than as a set of resolved relations.

This is the situation described in physics as a mean-field position. A component of a large system interacts with its immediate neighbours individually and with the remainder only through an averaged influence. The averaged influence is what the order parameter of the system is defined upon, and it is precisely what a component in this position cannot resolve. The component registers the mean field as a condition of its own dynamics; the value of the order parameter, which is a property of the aggregate, appears to it as the way things are.

The transfer of this description to the historical case requires the ontology of §3 and nothing further. Once constraint is a macroscopic phase of the relational field rather than an object external to it, the participant’s relation to constraint is the relation of a component to the collective state of which it is part. The participant acts under the constraint and contributes to it, and encounters it as the general condition within which the local relations obtain.

The Timescale of the Slow Variable

A second consideration compounds the first. The macroscopic state of a large system relaxes slowly, and the relaxation time grows with the extent of the correlated region. Where a state is coherent across a large domain, the time required for that state to respond to a local disturbance is long compared with the time in which the disturbance occurs.

Applied to the historical case, this gives the reason why constraint is slow. Constraints of possibility, of expressibility, and of evaluability are states coherent across large populations, and their response times are correspondingly long. What follows is a relation between two timescales, and the relation is what matters: the interval over which a participant acts, deliberates, and observes is short compared with the interval over which the constraint responds. Within the shorter interval, the constraint presents as fixed.

The Statement of the Result and Its Modality

The two considerations together yield a result.

Claim 2 (blindness to the slow variable). A participant in the relational field is unable to observe the state of the constraint field or its displacement, and the inability follows from the participant’s position with respect to scale. The displacement of a slow variable is unobservable on the timescale of the fast variables through which the participant acts, and the state of the aggregate is unresolvable from a position within it.

Three qualifications determine what the claim does and does not assert.

The claim concerns observation from within by a participant, and leaves untouched the position of a later observer. Historians reconstruct constraint displacements routinely and correctly, and they do so from a position after the relaxation has completed. The claim is that the displacement is unavailable at the time of acting, and it is consistent with the displacement’s being obvious afterward.

The claim concerns a quantity rather than a meaning, which distinguishes it from the hermeneutic restriction and makes it compatible with that restriction. An agent may understand the meaning of a situation very well and remain unable to observe the state of the aggregate of which the situation forms a part.

The claim is structural, which is what distinguishes it from the tradition’s account of ideology. Ideology critique proposes that a restriction on consciousness may be lifted by attaining a different standpoint. The restriction described here persists for any participant, at any standpoint, however free of distortion, because the restriction attaches to the relation between the scale at which the participant acts and the scale at which the constraint is defined. A participant who knew every relevant fact about the present configuration would still stand at a definite place in a large system, and would still act on a timescale short compared with the response of the aggregate.

4.3 The Transplanted Concepts and Their Content

Three concepts have now been used, and each carries a definite technical content that should be stated so that the extent of the transfer can be assessed. These are concepts of statistical physics rather than of the constitutional programmes of §3.3, and their use here is independent of that borrowing.

An order parameter is a quantity defined on an aggregate that specifies which collective state the aggregate occupies, and which is undefined or uninformative for any component taken singly. Its transfer to the present setting identifies constraint with the order parameter of the relational field: what mode of constraint holds, and how strongly, is a specification of the collective state.

A mean field is the averaged influence of an aggregate upon one of its components, standing in for the resolved influence of every other component. Its transfer identifies the participant’s epistemic position: what a participant encounters as the general condition of action is the mean field of the relational aggregate.

A phase transition is a change in the collective state of an aggregate, in which macroscopic properties change while the components remain what they were. Its transfer identifies constraint update: the participants and their capacities persist, and what they compose changes state.

The limits of the transfer are stated in §3.5 and hold here without modification. In particular, no order parameter is exhibited for any historical case, and §4.2 has just argued that none is available to a participant. What the transfer supplies is a specification of what would be required for the constraint field to have a determinate state, and an account of why that state is unavailable from within.

4.4 Three Consequences

The Retrospective Availability of Constraint Displacement

The first consequence follows immediately. Agents discover that the constraint has shifted after the shift has occurred, and the discovery takes the form of recognizing that what was formerly difficult has become ordinary, or that what was formerly sayable has ceased to be. The recognition is reliable and comes late by structural necessity rather than by inattention.

This has a corollary for the historiographical situation. The later observer’s advantage over the participant is a matter of position with respect to the relaxation rather than a matter of superior insight, and the temptation to read the participants’ failure to see what was happening as a failure of intelligence or nerve is, on this account, a misattribution.

The By-Product Principle

The second consequence bears directly on the question of constraint update. A course of action undertaken to achieve a goal generates relations beyond those the goal specifies. The generation is unavoidable: to organize people, materials, and procedures toward an end is to bring into being a configuration of relations, and no goal specifies the configuration completely. The relations so generated are, by construction, undescribed by the goal that occasioned them.

Claim 3 (the by-product principle). The realization of a goal generates relations the goal does not describe, and it is among these by-products, rather than among the described achievements, that displacements of the constraint field originate.

The principle answers a question the tradition leaves in an awkward position. If constraint update proceeded through the achievement of goals, then the constraint would be revised in the direction the goals specified, and history would be the record of intentions realized at the level of the framework. The historical record supports no such reading. The by-product principle locates the update elsewhere: in what the pursuit of goals brought into being without describing.

The principle as stated is incomplete, and the incompleteness is worth marking before §4.5 supplies the remedy. By-products are generated continuously and in enormous number, and almost all of them are absorbed without trace. A principle that identifies the site of constraint update leaves unanswered the question of which by-products, among the multitude, are the ones through which the update proceeds.

The Standing of the Remainder

The third consequence identifies a category the normative part will require. §3.6 introduced constraints of expressibility and non-structural goals, and §4.2 has now supplied what those categories rest upon. There exists, in any historical configuration, a dimension of the relational field that participants cannot represent: unresolvable from within by the argument of §4.2, and unavailable to formulation as a goal by the argument of §3.6. Call this dimension the remainder.

The remainder is not mysterious, and the epistemology just given is what removes the mystery. It is the aggregate state of the field, together with those of its degrees of freedom that the prevailing evaluation functional does not rank. Its inaccessibility is a consequence of the participant’s position rather than an obscurity in the thing. §6 argues that norms protect this dimension without representing it, and the argument requires exactly what has been established here: that the dimension is real, that it is consequential, and that it is unavailable to the participants whose norms protect it.

4.5 The Departure from a Stable Historical Stage

The Question

A question stands behind much of §2 and is rarely posed directly. A social formation that optimizes within its constraints becomes better adapted to those constraints over time: the structural goals of §3.6 are pursued, the evaluation functional is served, and the configuration is progressively tuned. Such a system should settle. Why, then, does any historical formation leave its settled state? Why did feudal Europe give way, why has capitalism failed to arrive at a configuration and remain there, and why do revolutions occur at all?

The tradition supplies three answers, and §2 recorded them: the accumulation of contradiction, the development of the productive forces, and contingency. Each identifies a real feature of the situation, and each stops short of a mechanism in a way that can now be stated precisely.

Accumulation of contradiction says that tension builds, and leaves unstated why the tension discharges at one moment while being absorbed at others. Development of the forces identifies a slow variable, and treats it as exogenous to the configuration it will overturn and as monotone in its direction. Contingency correctly locates the trigger in something particular and unforeseen, and supplies no account of why this trigger propagated when a thousand comparable ones were damped.

The Proposed Mechanism

The elements are now in place. The goal categorization of §3.6 supplies three dynamical roles; the epistemology of §4.2 supplies the participant’s position; and the by-product principle supplies the site at which update originates.

Claim 4 (the mechanism of departure). Generative goals inject into the relational field configurations that the prevailing evaluation functional does not rank. Non-structural norms maintain a range across which such configurations can propagate. Where the constraint field stands near a boundary of stability, a configuration so injected and so propagated can be amplified until the field passes into a different phase, and the system leaves the state it had occupied.

The mechanism has three components, and the division of labour among them is what distinguishes it from the answers just reviewed. Injection supplies the material: configurations that were not there before and that the ranking does not capture. Transport supplies the propagation: without a range across which an injected configuration can move, injection is damped locally and has no consequence at scale. Amplification supplies the passage: the nonlinear character of the field’s own dynamics, treated in §5, is what converts a small configuration into a change of phase.

Trigger and Cause

A condition on the mechanism must be stated at once, since without it the mechanism claims far too much.

Claim 5 (the criticality condition). A perturbation is amplified into a change of phase only where the constraint field already stands near a boundary of stability. Away from such a boundary, injected configurations are damped, and the formation is robust to perturbations of the same magnitude that would be decisive nearby.

The condition has an immediate consequence for how historical causation is to be described. The perturbation is the trigger of a transition, and what determines whether a transition occurs is the state the system had already reached. Two sources of historical change are thereby distinguished, and they operate on different timescales and through different agents.

Structural accumulation is the slow displacement of the constraint field toward a boundary of stability. It proceeds through the ordinary operation of the formation, it is unobservable to participants by Claim 2, and by itself it produces no visible change.

Generative triggering is the injection of a configuration that, given the state accumulation has reached, is amplified. The trigger need not be large, and need not be distinguished in any way from the many comparable events that were damped. What distinguishes it is the state of the field it entered.

History, on this account, is the joint product of the two, and neither necessity nor contingency describes it alone. The state reached by accumulation determines whether any trigger can succeed; the particular trigger determines the moment and the manner.

The Two Filters

The mechanism selects twice, and the two selections should be kept distinct, since they answer different questions and each is insufficient alone.

The first filter determines survival. A configuration that the prevailing evaluation functional ranks is acted upon: it is optimized, institutionalized, and thereby fixed, which is to say removed from the dynamics. A configuration the functional does not rank is left alone, and its being left alone is what permits it to persist in an unfixed state. What has no goal-form escapes the machinery that would settle it.

The second filter determines amplification. Survival delivers a configuration that remains available; whether it propagates depends on the state of the field, by Claim 5. The same configuration, identical in content and equally unranked, is inert in a formation far from its stability boundary and decisive in one near it.

Stating both is what distinguishes the mechanism from a restatement of the phenomenon. The first filter explains why the configurations that matter are drawn from what the indices do not measure. The second explains why the overwhelming majority of such configurations nonetheless come to nothing.

The Three-Stage Reading of Quantitative and Qualitative Change

The mechanism yields a reading of the relation between quantitative and qualitative change that answers a question the classical formulation leaves open: why quantitative change should produce a qualitative change at one point and fail to at every prior point.

In the first stage the formation occupies a stable state. Its recovery capacity is high, perturbations are absorbed, and the historical record shows continuity. In the second stage, long quantitative change displaces the constraint field toward a boundary. Recovery capacity declines while the macroscopic configuration continues to present as stable, and the decline is unobservable to participants. In the third stage, a perturbation of ordinary magnitude is amplified, the boundary is crossed, and a different phase is established.

Quantitative change acquires, on this reading, a specific referent. Its content is the displacement of the constraint field and the associated decline in recovery capacity, rather than an accumulation of more of something. And the final event is relieved of a burden it was never able to carry: the preparatory work belongs to the second stage, which may have occupied decades or centuries, and the trigger contributes the timing.

The reading is offered as an interpretation of a formulation that has been read in many ways, and its warrant is that it supplies the missing condition. It gives quantitative change a determinate dynamical content, and it states what must be true for the qualitative change to follow.

The Consequence for the Position of the Participant

Claim 2 and Claim 5 together produce a result sharper than either alone. The proximity of the constraint field to a boundary of stability is a property of the aggregate and of the slow variable, and it is therefore unobservable to participants for precisely the reasons given in §4.2. Participants are unable to determine whether they stand deep within a stable configuration or at the edge of a transition.

The consequence is that an identical action carries entirely different historical weight depending on a condition its author cannot assess. The same demonstration, the same publication, the same refusal is absorbed without trace in one decade and becomes the occasion of a transition in another, and the difference resides in the state of the field rather than in any property of the action.

This accounts for a pattern in the historical record that is otherwise puzzling. Events acquire their status as turning points retrospectively, and the participants’ failure to recognize the significance of what they were doing is the normal case rather than the exceptional one. It also accounts for the peculiar temporal signature of major transitions, which appear impossible until shortly before they appear to have been inevitable. Both descriptions are correct, and they are descriptions of different stages of the same process viewed from a position that cannot distinguish them in advance.

The Discriminating Power of the Mechanism

The mechanism must be tested against the objection that defeated functional explanation in the exchange recorded in §2.2. If injection followed by amplification accounts for departure from any stable formation, then it accounts for every transition equally, discriminates among none, and earns nothing.

The criticality condition supplies the first part of the answer, since it entails that most injections produce nothing, and that the mechanism predicts stability at least as often as it predicts change. The two-filter structure supplies the second, since it entails that the configurations through which transitions proceed are drawn from a specifiable region: the part of the field the prevailing indices do not measure.

Together these yield expectations that can be disappointed. Transitions should be preceded by a decline in recovery capacity rather than by an increase in the magnitude of perturbations. They should originate in domains that the prevailing evaluation functional does not rank, rather than in the domains that the formation measures and manages most closely. And formations whose institutionalization has consumed the range across which configurations propagate should exhibit greater stability together with a diminished capacity to generate new constraint, which is a conjunction that the account of §6 requires and that observation could contradict.

The Standing of the Mechanism

A boundary on the claim closes this section. That historical systems generally exhibit criticality in the sense the physical sciences give the term is unestablished, and this paper does not assert it. What is proposed is a mechanistic hypothesis: that major updates of historical constraint are more likely where the constraint field stands near a boundary of stability than where it stands far from one, and that the mechanism of Claims 3 through 5 describes how such updates proceed when they proceed at all.

The hypothesis is consistent with the standing declared in §1. GRH specifies a process and declines to predict outcomes, and the criticality condition is a statement about the conditions under which a process operates rather than a law governing the succession of historical formations. §5 gives the mechanism its formal setting and states, more precisely than has been possible here, what would have to hold for the hypothesis to be true.

§5 Multiscale Historical Dynamics

The third requirement stated at the close of §2 was a dynamics in which accumulation and trigger are distinguished, so that the discharge of an accumulation has a stated condition. §4 gave the mechanism in words. This section gives it a form.

Two obligations from earlier sections are also discharged here. §3.4 recorded that a framework denying the distinctness of structure and agency owes a replacement for the analytical leverage that holding them apart in time was introduced to provide; §5.3 supplies it. §3.5 recorded that the coarse-grained description admits no closure; §5.10 states what follows.

5.1 The Object and the Ambition of the Modelling

A Mechanism Theory

What follows specifies a class of structures and the behaviour available to systems having that structure. It does not specify a system, and it fits no parameters. The distinction matters for how the equations below are to be read: they state the form of a dynamics, and the claim attaching to them is that historical constraint evolves in a manner having this form, and that a good deal follows from the form alone.

The Range of the Borrowing

The borrowing from fluid dynamics is confined to structure. Three features are taken: a nonlinear term by which a field transports itself, a transfer of activity across scales with a range in which transfer occurs without generation or removal, and a concentration of that removal into sparse and intermittent structures. What is left behind is everything that makes the equations of fluid motion the equations of a fluid: conservation of mass and momentum, an equation of state, the constitutive relation for the stress, and the dimensional analysis that gives the theory its predictive power.

The distinction may be put as a rule for reading the sections below. Where a structural feature of the equations is used, the argument stands or falls on whether social systems possess that feature. Where a quantitative result of fluid mechanics might be invoked, it is not invoked, and §5.7 states the one case in which the temptation is strongest and the refusal most necessary.

Three Grades of Formal Commitment

Formal statements in this section carry one of three grades, and each is marked where it occurs.

A statement is schematic when it exhibits the form of a relation without licensing calculation: the equation displays which terms are present and how they enter, and no solution is claimed. A statement is structural when it asserts that a system possesses a property defined for a class of dynamical systems, such as multiple attractors or a spectral gap. A statement is analogical when it transfers a construct from the physical case whose social counterpart has yet to be constructed. Schematic and structural statements carry the argument. Analogical statements illustrate, and §5.7 is the only extended instance.

5.2 Nonlinear Self-Transport

The Structure of the Self-Transport Term

In the equations of fluid motion the acceleration of a fluid parcel includes a term in which the velocity field transports itself. Written schematically, the evolution of the velocity $\mathbf{v}$ contains

$$\partial_t \mathbf{v} + (\mathbf{v}\cdot\nabla)\mathbf{v} = \ldots$$

where the omitted terms carry pressure, viscosity, and any external forcing. The second term on the left is the one of interest. It is quadratic in the field, and it says that what carries the field from place to place is the field itself. No external agent moves the fluid; the motion redistributes itself.

Two consequences of the term are relevant here. It is the source of the nonlinearity from which the characteristic behaviour of these systems follows, including sensitivity to small disturbances under some conditions and complete insensitivity under others. And it makes the system’s evolution unavailable to decomposition into a background plus a disturbance upon it, since the disturbance participates in its own transport.

The Self-Transport of the Constraint Field

The social counterpart is written schematically:

$$\partial_t \Gamma + (\Gamma\cdot\nabla)\Gamma = \ldots$$

with $\Gamma$ the constraint field defined in §3.4. The statement is schematic in the sense of §5.1: it exhibits a form, and no solution is claimed for it. What the form asserts is that the configuration under which relations are formed is carried by the relations it configures, and that the carrying is quadratic in the field rather than linear in some external drive.

The reading of the omitted terms follows the categorization of §3.6. Injection enters as a source, supplied by generative goals. Dissipation enters as a sink, supplied by the institutionalization in which structural goals issue. The transport is the term written, and non-structural norms bear upon the range across which it operates, in a manner §5.5 makes precise.

The Displacement of the Control Form

The form of the self-transport equation may be contrasted with the form standard in control theory, in which a state $x$ evolves under

$$\dot{x} = F(x, u)$$

with $u$ a control input. The two forms differ in what they place outside the system. The control form requires a $u$ that is set rather than evolved, and therefore a controller occupying a position outside the state whose evolution is described. Applied to historical constraint, the control form would require an agent who alters the configuration while standing outside it, which §3.1 argued to be unavailable.

The self-transport form dispenses with the requirement. Every term is a function of the field, the sources and sinks included, since injection and dissipation are supplied by goals that are themselves configurations within the field. This is a commitment with consequences beyond the present paper, and it is stated as such: a framework built on relational primacy has no room for a controller, and the analytical habit of asking what the lever is, and who holds it, has no purchase on a system that transports itself. What replaces the question is treated in §7.

5.3 Fast and Slow Structure

The Separation of Variables

The loop of §1 may be written in the form standard for systems with two timescales:

$$\dot{x} = f(x, y)$$

$$\varepsilon, \dot{y} = g(x, y), \qquad 0 < \varepsilon \ll 1$$

in which $x$ collects the fast variables and $y$ the slow. The statement is structural: it asserts that historical systems, over the ranges in which the assertion holds, possess two well-separated timescales.

The assignment of variables follows the ontology. Fast variables comprise individual action, daily interaction, short-horizon goals and the structural goals prominent among them, transactions, and the movement of opinion: quantities that change on the timescale at which participants act. Slow variables comprise institutions, culture, structures of trust, the boundary of the expressible, and the constraint field itself: quantities whose relaxation times exceed the horizon of the participants, for the reason given in §4.2. What occurs daily is change in $x$. Change in $y$ requires the accumulated effect of many such changes.

Singular Perturbation and the Slow Manifold

Systems of this form have been studied under the theory of singular perturbations, and the results relevant here concern the behaviour in the limit of small $\varepsilon$ [20, 26, 31]. Setting $\varepsilon$ to zero yields an algebraic constraint $g(x,y) = 0$, whose solution set is the critical manifold; for small nonzero $\varepsilon$ and under a normal hyperbolicity condition, a nearby invariant slow manifold exists, and trajectories are rapidly attracted to it and thereafter move along it slowly.

The result licenses a description in which the fast variables are enslaved to the slow: given the slow state, the fast dynamics settle quickly into a configuration determined by it, and the interesting motion is the slow drift of that configuration. This is the formal content of the observation that a stable historical period exhibits a great deal of activity and very little change.

The Description Available Far from Criticality

The reduction supplies what a stable era looks like from within. The fast variables move continuously, the slow manifold determines where they settle, and disturbances to the fast variables decay at a rate set by the attraction to the manifold. An observer at the timescale of the fast variables sees activity that leaves the configuration unaltered, and the observation is correct rather than illusory: over the observation window the configuration is, to good approximation, fixed.

Normal hyperbolicity is a condition rather than a guarantee, and the conditions under which it fails are the subject of §5.4.

The Order of Priority Between the Two Forms

The two forms so far written stand in a definite relation, and stating it prevents a misreading. The self-transport equation is the general form, and the fast-slow system is a reduced description available under a condition. The condition is the separation of timescales, and where it holds, the field admits decomposition into a slowly drifting component and a rapidly equilibrating one.

The order matters because the fast-slow form reintroduces, in appearance, what §5.2 expelled: a state vector evolving under a given vector field, with the field’s dependence on the state suppressed. The appearance is a consequence of the reduction. The vector fields $f$ and $g$ are themselves functionals of the field, and their apparent fixity is an artefact of describing the system over an interval in which the slow state changes little. Self-transport is the ontology; fast-slow structure is a regime-specific approximation to it.

The Determination of an Event’s Significance

A consequence follows immediately and states, in dynamical terms, the thesis with which the paper began. Consider an identical disturbance to the fast variables, applied at two moments. In the first, the system sits well inside the domain of attraction of the slow manifold, and the disturbance decays. In the second, the slow variable has drifted to a position at which attraction has weakened, and the same disturbance carries the system elsewhere. The disturbances are identical; the outcomes differ; and what differs is the slow state.

The significance of an event is therefore a property of the configuration in which it occurs rather than a property of the event. This is the formal counterpart of the observation in §4.5 that key events acquire their standing retrospectively.

5.4 Criticality and the Boundary of Stability

Recovery Capacity and Susceptibility

Two quantities characterize a system’s response to disturbance. Recovery capacity measures the disturbance a system absorbs while returning to its prior configuration. Susceptibility measures the response of the system’s state to a small change in conditions. The two vary inversely, and both are properties of the slow state rather than of the disturbance.

Far from a boundary of stability, recovery capacity is high and susceptibility low: disturbances are absorbed, and a system may absorb them for a very long time. As the slow state approaches a boundary, recovery capacity declines and susceptibility grows, and disturbances of unchanged magnitude produce responses of growing magnitude. At the boundary, susceptibility diverges in the idealized case, and arbitrarily small disturbances suffice to carry the system across.

The Derivation of Criticality from Fast and Slow Structure

The criticality condition of §4.5 requires no separate postulate. It follows from the structure already written. The slow variable drifts; the drift carries the system toward a configuration at which normal hyperbolicity fails; at such a configuration the fast dynamics cease to be enslaved, and a disturbance that would elsewhere decay instead grows.

This is the section’s most useful result for the argument as a whole. The mechanism of §4 joins accumulation to trigger by an assertion; the fast-slow structure derives the joining. Accumulation is the drift of the slow variable, the trigger is a disturbance to the fast variables, and the condition under which the trigger is consequential is the condition under which the reduction of §5.3 fails.

The Closing of the Spectral Gap

The failure has a characterization worth stating separately, since it governs §5.6. The reduction of §5.3 requires a gap between the rate at which fast variables relax and the rate at which slow variables drift. Approach to a boundary of stability narrows the gap: the relaxation of the fast variables slows as attraction weakens, and at the boundary the timescales become comparable. The separation on which the two-timescale description rests thereby fails precisely where the interesting transitions occur.

The Refusal to Construct a Control Parameter

In the physical cases, the approach to a boundary is parameterized: a quantity is identified whose variation carries the system toward the transition, and the distance to the boundary is computed from it. This paper constructs no such quantity for the historical case, and the refusal is a position rather than an omission.

Two reasons support it. The first is §3.5: the identification of a control parameter requires an independently motivated structure on the space of configurations, and none is available. The second is §4.2: were a control parameter constructible from quantities available to participants, the distance to a boundary would be measurable from within, and the epistemic result of §4 would be false. The refusal is therefore required by the rest of the account, and §8 states the identification of such a quantity, should one exist, as an open problem whose resolution would revise §4.2 rather than merely supplement it.

Critical Slowing and the Question of Observability

One qualification is required, and it bears on the strength of the epistemic claim. Systems approaching a boundary of stability exhibit critical slowing: recovery from small disturbances takes longer, and the resulting changes in variance and autocorrelation have been proposed as generic early warning signals [47]. The signal has the useful property of requiring no knowledge of the control parameter, since it is read from the response to disturbance rather than from the position in configuration space.

Whether the corresponding measurement can be made in historical systems is an open question, and §8 lists it. The qualification is entered here because it identifies the point at which the epistemic result of §4.2 could be weakened: that result concerns the unavailability of the slow variable itself, and it leaves open whether some functional of the fast variables carries information about the slow state. Should such a functional prove measurable, the blindness would admit degrees, and §4.2 would require the corresponding amendment.

5.5 Cascade and the Coupling of Scales

The Correction of the Two-Timescale Picture

The fast-slow description partitions activity into two bands. The turbulent case suggests a different picture, in which activity is distributed across a continuum of scales and the transfer between them is the object of interest. The two pictures are reconciled in §5.6; the present section states the second.

The Inertial Range

In a turbulent flow, energy enters at large scales, leaves at small ones, and passes between them across a range in which it is neither supplied nor removed. This intermediate band is the inertial range, and its defining property is that activity within it is transferred rather than generated or dissipated [21].

The social reading follows the categorization of §3.6. Injection occurs where generative goals produce configurations that no ranking has evaluated. Dissipation occurs where institutionalization fixes configurations into rules and removes them from the dynamics. Between them lies a range across which configurations are carried without being either produced or fixed, and the function assigned to non-structural norms in §3.6 is the maintenance of this range. The claim of §6, that what resists optimization protects the system’s capacity for constraint update, is in these terms the claim that dissipation consuming the inertial range severs the transfer on which update depends.

Transfer Toward Larger Scales

Transfer toward smaller scales is the ordinary case in three dimensions. Two-dimensional flows exhibit the opposite: energy is transferred toward larger scales, accumulating at scales greater than those at which it entered [30, 10]. The inverse cascade supplies the image required by the argument of §4: local activity, individually inconsequential, accumulating into a change at a scale far above the scale of its production.

The Question of an Inverse Cascade in Social Systems

Whether social systems exhibit a transfer of this kind is a substantive question and is left open. What would be required is evidence that activity at the scale of individual relations accumulates preferentially toward larger scales rather than being dissipated at the scale of its production, and that the accumulation exhibits the statistical regularity that would distinguish transfer from coincidence. The question is stated as a research direction in §8, and the argument of this paper is constructed so as to require the possibility of upward accumulation rather than the existence of a cascade in the technical sense.

5.6 The Division of Labour Between the Two Descriptions

A Presupposed Gap and a Denied One

The two descriptions stand in apparent conflict. The fast-slow reduction requires a gap between timescales, and its results follow from the gap. The cascade picture describes a continuum with no gap, and its results follow from the absence of one. A framework using both owes an account of when each applies.

The Applicability of Each Description

The account follows from §5.4. Far from a boundary of stability, the gap exists: fast variables relax quickly, the slow manifold is normally hyperbolic, and the two-timescale description is accurate. This is the regime of the stable historical era, and the epistemic results of §4 are results about this regime. As the slow state approaches a boundary, the gap narrows; at the boundary the timescales merge, the reduction fails, and the description in which activity is coupled across a continuum of scales becomes the appropriate one. This is the regime of transition.

The conflict is thereby resolved into a partition. The fast-slow description governs the long intervals in which little changes; the cascade description governs the intervals in which the system reorganizes. Neither is general, and the transition between regimes is the closing of the gap.

The Index That Selects Between the Descriptions

The partition is indexed by a single quantity, the distance of the slow state from a boundary of stability, and the account inherits the standing of that quantity. §5.4 declined to construct it, and the consequence is that the index is well defined and unavailable for computation from within. This is the same combination noted at §3.4, and the same qualification applies: a commitment to the existence of a quantity, together with an argument that participants cannot compute it, is a substantive position whose vindication would require the work listed in §8.

5.7 The Balance of Injection and Dissipation

The Social Reading of the Source Term

Injection is the production of relational configurations that no ranking has evaluated. Its sources are the generative goals of §3.6, and its rate is a property of a society’s arrangements: the room available for exploration, the tolerance of activity without a stated end, and the extent to which such activity escapes evaluation.

The Social Reading of the Sink Term

Dissipation is the fixing of configurations into rules. Institutionalization is its principal form, and the mechanism is the one treated in §6: a configuration that becomes a rule ceases to vary, and a variable that ceases to vary leaves the dynamics.

The Standing of the Dimensionless Ratio

In fluid mechanics the ratio of the nonlinear transport to the dissipative term is the Reynolds number, and its value determines the character of the flow. The temptation to construct a social counterpart is considerable, and this paper declines it.

The refusal is stated in the strong form. No social Reynolds number is proposed here, and the balance of injection against dissipation is offered as a qualitative consideration: a society in which fixing outpaces production of the unevaluated will exhibit a narrowing inertial range, and one in which production outpaces fixing will exhibit a widening one. This is the whole of the claim, and it is an analogical statement in the sense of §5.1.

What the Dimensionless Group Would Require

The reasons for the refusal indicate what a successful construction would demand. A dimensionless group requires dimensioned quantities, a characteristic scale, and a characteristic velocity, none of which the social case supplies. It requires, further, that the group be predictive across systems: the utility of the Reynolds number is that flows at equal values behave alike regardless of the fluid, and a social counterpart lacking this property would be a ratio rather than a dimensionless group. The cascade structure of §5.5 carries the argument, and the ratio contributes an illustration.

5.8 Intermittent Generativity

The Concentration of Dissipation

In turbulent flows, dissipation is distributed with great unevenness: it concentrates in sparse structures occupying a small fraction of the volume, and the statistics of the small scales depart from those a uniform distribution would produce [21]. Intermittency names the phenomenon, and it is a robust feature rather than a correction to a smoother picture.

The Temporal Pattern of Constraint Update

The social counterpart is the temporal pattern the argument has been assembling. Constraint update occurs in a manner distributed with corresponding unevenness: long intervals in which the slow state drifts and little at the surface changes, punctuated by brief intervals in which the configuration reorganizes. The pattern follows from §5.4 and §5.6: the drift is slow because the slow manifold is attracting, the reorganization is brief because it occurs where attraction has failed, and the alternation is the alternation of the two regimes.

The Locality of Grammar Rewriting

Intermittency has a spatial aspect as well as a temporal one. Reorganization of the constraint field is expected to concentrate in regions of the field rather than proceeding uniformly across it: particular domains of practice, particular institutions, particular relations. The expectation supplies a target for empirical work, and §8 states it.

The Observable Signature of the Mechanism

The three preceding sections yield a claim about the shape of historical change.

Claim 6 (intermittent generativity). Historical constraint is updated intermittently. Long intervals of drift, during which the configuration is stable and activity leaves it unaltered, alternate with brief intervals of reorganization concentrated in limited regions of the field. The alternation follows from the structure of the dynamics rather than from the distribution of events, and it is the observable signature by which the proposed mechanism may be recognized.

The claim states what distinguishes this account from a continuous conception of historical development on one side and from a conception of history as a sequence of ruptures on the other. Continuity holds within a regime, discontinuity marks the passage between regimes, and the alternation is a property of a system possessing the structure set out above.

5.9 The Non-Evaluative Character of Stability

Recovery Capacity and Optimality

A distinction is required at this point, since the vocabulary of stability invites a reading the account must exclude. An attractor is stable in virtue of recovery capacity, which measures response to disturbance. Optimality is a ranking of configurations by a criterion. The two are independent: recovery capacity is a dynamical property, and rankings are supplied from outside the dynamics.

The Neutrality of Stability with Respect to Value

It follows that a configuration may be stable and just, stable and unjust, stable and efficient, stable and inefficient. Stability reports the response to disturbance and reports nothing about the arrangement’s merits. A long and stable historical period may be read as a period in which nothing needed changing, or as a period in which what needed changing was suppressed, and the dynamics adjudicates between the readings in neither direction.

The Compatibility of Degradation with Stability

The distinction cuts against the present framework as much as against others, and the case should be stated plainly. A system whose inertial range has been consumed by dissipation, in the sense of §5.5, has fewer live disturbances to absorb, and it may on that account be more stable than a system retaining its capacity for update. Degradation of the capacity for constraint update and stability of the current configuration are therefore compatible, and may be positively associated.

The Discipline Imposed on the Later Sections

The consequence for §6 is a discipline. The claim developed there, concerning what the projection of all goals into a single optimizable space costs a system, is a claim about a capacity rather than about the merits of the configurations produced. Reading stability as health, or as concealment, would import into the dynamics a judgment the dynamics does not supply, and the sections that follow are written so as to avoid it.

5.10 The Closure Problem

The Moment Hierarchy

A system governed by a quadratic self-transport term resists description in terms of its averages. Averaging the equation produces a term involving the average of a product, which is not the product of the averages; describing that term requires an equation for the second-order correlation, whose average involves the third; and the hierarchy continues without terminating. This is the closure problem, and it is a consequence of the quadratic nonlinearity rather than a limitation of technique [21, 45].

The Position of the Social Case

The social case inherits the problem in the same form. A description of the constraint field in terms of aggregate quantities requires the correlations among relations, and those require correlations of higher order. The point worth making is one of standing: non-closure here is an instance of a general feature of systems with self-transport, and its presence in the social case reflects the structure of such systems rather than any special deficiency of social inquiry.

The Standing of Non-Closure Across the Class

The observation has a use beyond consolation. Approximations to closure in the physical case are made by supplying a relation between the unclosed term and the resolved quantities, and the relation is justified by physical argument rather than derived. Any corresponding move in the social case will require an analogous justification, and the demand supplies a criterion by which such moves may be assessed. §8 states the construction of social closure approximations as a research direction.

5.11 The Connection to the Study of Complex Systems

The Range of Systems Sharing the Structure

The structure set out in this section is exhibited by a range of systems that have been studied independently and in detail. Seismicity displays long accumulation of stress punctuated by rupture. Neural systems display slow modulation of excitability with rapid transitions to seizure. Climate systems display slow forcing with transitions between states [47, 7]. Evolutionary systems display long intervals of relative stasis with intervals of rapid change [19]. In each case the analytical content is a slow variable whose drift alters the conditions under which fast dynamics operate, and in each case the study of the system has produced results about the approach to transitions.

The Place of Turbulence in the Multiscale Class

The relation of the turbulent case to the others is worth stating, since §5.2 and §5.5 draw on it heavily. Turbulence is the case in which self-transport and scale coupling are exhibited with the greatest clarity, and it is for those two features that it is used here. The multiscale structure is the genus; turbulence is one species of it, distinguished by the particular form its nonlinearity takes.

The Available Exchange

Placing the account within this literature identifies what could be gained from it and what would have to be established first. The methods of geometric singular perturbation theory, of averaging, and of coarse-graining across scales are available in developed form, and §8 lists their application as a direction. What would have to be established first is that the historical case admits the structures those methods require, and §5.6 has stated the principal obstacle: the index by which the applicable description is selected is a quantity the account holds to be unavailable from within the system it indexes.

§6 Normative Consequences

The preceding sections were descriptive. This one asks what follows for the assessment of goals and norms, and the placement is deliberate: the normative consequences developed here are read off the dynamics of §5 rather than argued independently and then illustrated by it.

The order of exposition runs from the reconstruction of goals in relational terms, through their coupling and the process by which they harden into standards, to the standing of what resists such hardening, and closes with the relocation of utilitarianism this account implies. Q4 of §1 is discharged here.

6.1 The Relational Reconstruction of Goals

Goals and the Ordering of Preferences

A goal, on the account taken here, is the condensation of relational tension at the level of the expressible. Where the standard treatment begins with an agent possessing an ordering over outcomes and derives action from the ordering, this account begins with a configuration of relations in which some tension obtains, and treats the goal as what that tension becomes when it is put into words.

The difference is consequential in three ways. Preference orderings are attributes of individuals, and tensions are attributes of configurations, so that the account locates the origin of goals in the field rather than in those who hold them. Preference orderings are complete by construction, and tensions admit no such assumption: a tension may obtain without any available formulation, which is the condition §3.6 called the constraint of expressibility. And preference orderings are given prior to the dynamics, while tensions are generated by it, so that the formation of goals falls within what the theory must explain.

The Source of Individual Tension

Individual tension arises from the incompatibility of relational positions. A participant stands in many relations at once, and the positions these confer make demands that cannot always be jointly satisfied. What is required of one as a colleague, as a member of a family, as a participant in a professional community, and as a citizen may be jointly unsatisfiable in a particular situation, and the residue of that incompatibility is the material from which goals are formed.

The account has the consequence that the richer a participant’s relational position, the more tension is available for condensation, and that a participant occupying a single position has correspondingly little. Both are stated as consequences rather than as observations, and §8 lists their examination.

The Source of Collective Tension

Collective tension arises from asymmetries in the relational field that admit no local resolution. An asymmetry between two participants may be resolved between them. An asymmetry that reproduces itself across the field, so that resolving any instance leaves the pattern intact, is a tension of the collective, and it is from such tensions that collective goals are formed.

The distinction between the local and the non-local instance is what the analysis turns on. A grievance settled by the parties to it produces no collective goal. A grievance whose settlement in one instance is followed by its recurrence in another indicates that the tension is a property of the configuration, and the goal that condenses from it is a goal of the collective in the sense that matters here: its content refers to the configuration rather than to any of the instances.

6.2 The Three Couplings

Individual and collective goals are coupled, and the coupling takes three forms with different consequences. Q1 of §1 is discharged by their statement.

Expressive Coupling

The collective supplies the vocabulary in which individual tension can be formulated. A participant with a tension and no words for it has, in the strict sense of §3.6, no goal; acquiring the vocabulary converts the tension into something that can be pursued, communicated, and evaluated.

The coupling operates in both directions, and the second direction is the one worth marking. In acquiring the vocabulary, the individual goal is rewritten into a form the collective can recognize. What is gained is the possibility of pursuit; what is exacted is that the tension be expressed in terms the collective already possesses, and whatever exceeded those terms is left behind. The mechanism is the one treated at greater length elsewhere in this framework, by which a system produces the participants its own dynamics require.

Resource Coupling

The collective determines which individual goals obtain the conditions of their realization. This is the coupling most visible and most studied, and it requires little comment here beyond the observation that it operates upon goals already formed. Resource coupling allocates; it does not constitute.

Reverse Coupling

The third coupling runs from the individual to the collective, and it is the one on which constraint update depends. A tension for which the available vocabulary has no formulation does not thereby disappear. It persists as something registered without being stated: as difficulty, as a pattern of conduct that fits no available description, as an unease that resists formulation. Such a residue is the sole entry point by which the constraint on expressibility is revised, for the reason that a vocabulary is extended only under pressure from what it fails to accommodate.

The connection to §4 should be made explicit. The by-product principle held that the pursuit of goals generates relations the goals did not describe. The present section identifies where such by-products register: in the residue of tensions the vocabulary cannot state. And §5 supplies the condition under which the register becomes consequential, since a residue in a system far from a boundary of stability is absorbed, and the same residue near a boundary is amplified.

6.3 The Ontologization of Goals

From Direction to Standard

A goal begins as a direction: a formulation of a tension, indicating what would relieve it. Under conditions that obtain widely, it becomes something else. The formulation acquires a measure; the measure acquires an institutional home; and what began as an indication of where to go becomes a standard by which conduct is assessed. The goal has become a criterion.

The transformation is ordinary and, within limits, benign. A measure permits coordination, comparison, and accountability, and a collective goal without a measure is difficult to pursue collectively at all. What follows concerns the consequences of the transformation for the dynamics, and leaves its local usefulness undisputed.

From Tension-Driven to Index-Driven Dynamics

The consequence is a change in what drives the system. A tension-driven dynamics is one in which conduct responds to relational configurations, and such systems characteristically possess multiple stable configurations and exhibit dependence on the path by which a configuration was reached. An index-driven dynamics is one in which conduct responds to a measure, and such systems characteristically possess a single optimum toward which conduct converges.

The change is a change in the type of the dynamics rather than in its parameters. What was a field with several stable configurations becomes a landscape with a peak, and the difference is visible in the behaviour: exploration of alternative configurations, which in the first case is how the system finds its way, becomes in the second case error to be corrected.

The Statement of the Projection Claim

The claim toward which this subsection has been building may now be stated, and it is stated in a form more careful than the slogan that summarizes it.

Claim 7 (the cost of totalized projection). On the problem of the continued generation of historical constraint, projecting all goals into a single optimizable space reduces a system’s capacity to retain relational degrees of freedom that resist expression.

Each qualification in the claim is load-bearing, and the argument requires all four.

The claim is restricted to a problem: the continued generation of historical constraint. Optimization of logistics, of clinical protocol, of the allocation of a fixed budget falls outside the restriction, and such cases are neither counterexamples to the claim nor applications of it.

The claim concerns projection into a single space rather than optimization. Optimizing structural goals within their own domain remains legitimate and rational, as §3.6 granted. What the claim concerns is the treatment of the entire goal system as one optimization problem, in which every goal is rendered commensurable with every other by reduction to a common measure.

The claim asserts a reduction in capacity rather than an elimination. A system so projected retains some capacity to hold relational degrees of freedom, and projection may generate new constraints of its own. The claim is comparative and admits of degree.

And what is reduced is the capacity to retain degrees of freedom that resist expression, which is a specific quantity rather than a general good. The claim says nothing about welfare, justice, or the quality of the configurations a projected system produces.

The Argument for the Claim

The argument for Claim 7 runs through the dynamics and requires no evaluative premise.

Optimization damps disturbance. This is what optimization is, considered dimensionally: a procedure that moves a system toward an extremum of a criterion returns the system to that extremum when displaced, and the return is the damping of the displacement. A system under thoroughgoing optimization is a system in which departures from the optimum are corrected.

Disturbances are the material of constraint update. §4 argued that the configurations capable of altering the constraint field are those the evaluation functional fails to capture, and §5 argued that their amplification requires them to survive long enough to be transported. A procedure that corrects departures removes precisely the configurations on which update depends, since a departure from the optimum is what an unranked configuration looks like from within an index-driven dynamics.

The conclusion follows. Totalized projection damps the disturbances that constitute the material of constraint update, and thereby reduces the system’s capacity for such update. The argument concerns a rate rather than a valuation, and it would go through unchanged for an observer indifferent to whether historical constraint is ever updated.

The Relation to the Mechanisms of Degradation

The transformation described here is the specific mechanism by which the evaluative layer of the constraint field is rewritten. §3.6 distinguished the constraint of evaluability as the fastest of the three modes, and goal ontologization is what rewrites it: the standards by which courses of action are ranked are replaced by the measure that the ontologized goal supplies. The account thereby locates within the dynamics a process treated elsewhere in this framework as the rewriting of a relational grammar.

6.4 The Remainder and Non-Structural Norms

The Self-Cancellation of the Stated Norm

A norm of the kind §3.6 called non-structural exhibits a feature that distinguishes it sharply from a goal: stating it as a goal destroys it.

The classical instance is the injunction to occupy the low places that others disdain. Asked what end the occupation serves, one finds no answer of the ordinary kind, and pressed further one can say only that it is fitting. Suppose the injunction were reformulated as a goal, with a measure attached and performance assessed against it. What would then be pursued is a rank on that measure, and the pursuit of a rank on a measure of humility is not humility. The same holds throughout the class. Trust extended in order to be trusted is calculation; sincerity performed for its effect is performance; and a work made to raise a score on a scale of beauty stands in a different relation to beauty than a work made otherwise.

The self-cancellation has nothing to do with the sincerity of the agent, and the point is worth insisting on. What is destroyed is the thing itself, by the form of the pursuit, and an agent of perfect sincerity who adopts the goal-form destroys it as thoroughly as a cynic.

The Classification of Non-Structural Norms

The natural response to the foregoing is to classify such norms as goals of an unusual kind, and the response should be resisted. A goal is a formulation of a tension, indicating what would relieve it, and a norm that cancels itself when so formulated is not a formulation of that kind.

The alternative classification follows from §3.6. Non-structural norms hold open the range across which relational configurations may move, and their function in the dynamics is transport. They are, in the vocabulary of §3.6, boundary conditions on the goal system: conditions that determine the space within which goals are formed and pursued, standing to that space as a condition rather than as an element of it.

The Source of Normative Force

A consequence follows for the standing of such norms, and it inverts the ordinary expectation. That a norm resists formulation as a goal is generally treated as a defect: a norm that cannot be stated as an objective is thought to be vague, unenforceable, or ill-defined.

On the present account the resistance is the source of the norm’s function. What such norms protect is a set of relational degrees of freedom that no ranking has evaluated, and a norm capable of being stated as a rankable objective would, by §6.3, be a procedure for damping departures rather than for preserving them. The resistance to formulation and the capacity to protect are the same property described in two ways.

Purposiveness Without a Purpose

The structure has an ancestor in the philosophical tradition, and the connection strengthens the account rather than decorating it. Kant’s analysis of aesthetic judgment identifies a class of judgments that are purposive without any representable purpose: what pleases in the beautiful pleases without a concept and without the object’s being brought under an end [27]. The judgment has a lawfulness, and it is a lawfulness that supplying a determinate concept would destroy.

The parallel holds at the point that matters. The reason the injunction of §6.4 can be defended only as fitting, and the reason a norm so defended loses its character when a purpose is supplied, are one structure appearing in two settings. What the present account adds is the dynamical function: the tradition establishes that judgments of this form are coherent and possess their own lawfulness, and §3.6 assigns them a role in the transport of relational configurations across scales.

6.5 Protection under Conditions of Blindness

The Standing of Intentional Protection

The main claim of this section may now be stated.

Claim 8 (protection under blindness). In a system whose participants have no access to the slow variable, mechanisms of protection adopted with the intention of protecting the system’s capacity for constraint update fail, since the intention places the mechanism within the fast-variable optimization it was adopted to counteract. Norms held without such an intention retain the capacity that intentional mechanisms lose.

The argument proceeds in three steps. §4 established that participants have no access to the slow variable. It follows that a mechanism adopted in order to protect the slow variable is adopted under a description of its purpose that participants cannot verify against the state of the thing protected. Assessment of the mechanism must therefore proceed by proxy, and the proxy is a measure. But a mechanism assessed against a measure is a structural goal in the sense of §3.6, whose dynamical role is dissipation. The mechanism has become an instance of the process it was adopted to counteract.

The Standing of Norms Held on Other Grounds

The corresponding positive claim follows from §6.4. A norm held for its own sake, and defended when challenged by an appeal to its fittingness rather than to its consequences, resists conversion into a measure for the reason given in §6.4, and it retains the transport function assigned in §3.6.

The formulation requires care. The claim is not that ignorance is preferable to knowledge, nor that agents should refrain from reflecting on what their norms accomplish. It is that a norm’s protective function survives reflection on that function only where the norm continues to be held on other grounds. An agent may know perfectly well what a norm accomplishes; what the agent cannot do, without cost, is hold the norm because of that accomplishment.

The Descriptive Standing of the Claim

Claim 8 is descriptive. It states what happens to a mechanism of protection under specified conditions, and it recommends nothing.

The distinction is easily lost, since the claim has an obvious use in argument, and the use should be declined here. Nothing in the dynamics establishes that the capacity for constraint update is worth protecting; §5.9 held that stability is not an evaluative notion, and the same holds of generativity. A society that has lost the capacity for constraint update has lost a capacity, and whether the loss is to be regretted is a question the dynamics leaves open. What the account supplies is the price of the loss, stated in terms of what the system can thereafter do.

The Relation of the Claim to the Transition Mechanism

An objection arises at this point, and the account is stronger for meeting it directly than for leaving it to be discovered.

Claim 8 holds that intentional protection fails. §4 and §3.6 hold that non-structural norms do protect the degrees of freedom on which constraint update depends. If such norms protect effectively, then maintaining them appears to be an intentional strategy of protection, and Claim 8 appears to rule out what the rest of the account requires.

The resolution lies in the distinction between a function and a reason. Non-structural norms protect as a consequence of being held for their own sake, and the protection is a by-product of the holding rather than its object. An agent who maintains such a norm because it protects has supplied the norm with a purpose, and by §6.4 the norm so supplied is no longer of the kind that protects. The self-cancellation that made the class difficult to state is precisely what does the work here: it is the reason the protective function survives only where it is not the reason for the holding.

The consequence for practice is severe, and §7 takes it up rather than softening it. An institution that maintains a space of non-optimization because such spaces are valuable has already converted the space into an instrument, and the conversion is not undone by the sincerity of those who perform it.

6.6 The Dynamical Statement of the Remainder

Dissipation and the Inertial Range

The claims of this section admit restatement in the vocabulary of §5, and the restatement is where the two lines of the paper meet.

§5.5 identified a range of scales across which relational configurations are transported without being generated or fixed, and §5.7 identified institutionalization as the process by which configurations are fixed. If fixing extends across the whole range, transport ceases: configurations are removed at the scale of their production, and nothing survives to accumulate. The system retains injection and dissipation and loses the transfer between them.

The Function of Non-Structural Norms in These Terms

The function assigned to non-structural norms in §3.6 is, in this vocabulary, the maintenance of the range. They neither produce configurations nor fix them, and what they contribute is the interval across which configurations produced at one scale can persist long enough to accumulate at another.

The claim of §6.3 and the claim of §6.5 may thereby be read as one claim stated at two levels. Totalized projection extends fixing across the range; the range is what transport requires; and a system whose range has been consumed retains its capacity to optimize and loses its capacity to be revised.

The Convergence of the Vocabularies

Three descriptions have been used in this paper for what is here claimed to be one structure, and their convergence is the appropriate place to check whether the paper’s borrowings have earned their place. The relational vocabulary speaks of degrees of freedom that no ranking has evaluated. The dynamical vocabulary speaks of an inertial range across which transport occurs. The normative vocabulary speaks of what cannot be pursued as a goal without being destroyed. The proposal here is that these pick out one thing under three descriptions, and the identification is the substantive content of this subsection rather than a summary of it.

6.7 The Criterion and the Forms of Its Failure

The Criterion of Return

§1 took from the parent framework a criterion, and it can now be applied. A norm retains its non-structural character just in case the goals it serves cannot reach back and rewrite it. Where the goals of a system can modify a norm to suit them, the norm has become an instrument of those goals, whatever its content.

The criterion has the merit of being applicable without an account of the norm’s content, and the corresponding limitation that it requires a judgment about a counterfactual: whether the norm would be revised under pressure, rather than whether it has been.

The Co-opted Norm

Failure of the criterion has a characteristic form, and instances are readily supplied. A commitment to fairness that becomes a measured target, reported and optimized, has been rewritten by the goals it was to constrain. A commitment to sustainability that becomes an index has undergone the same conversion. In each case the content of the norm survives in the vocabulary, and its dynamical role has changed from transport to dissipation.

What makes such cases instructive is that they proceed without bad faith. The conversion is generally performed by those most committed to the norm, and for the best of reasons: a norm that is measured can be defended, budgeted for, and enforced. The account developed here explains why the improvement carries the cost it does, and §7 considers what, if anything, can be done about it.

The Limitations of the Criterion

Three limitations should be entered. The criterion is counterfactual, and its application requires a judgment about how a norm would fare under pressure it has not experienced. It is binary, where the phenomenon admits degrees, since a norm may be partially co-opted. And it is retrospective in practice: the clearest evidence that a norm could be rewritten is that it has been. §8 lists the construction of a criterion that is positive rather than counterfactual as an open problem.

6.8 The Relocation of Utilitarianism

The Domain of Adequacy

The account developed here bears on utilitarianism, and the bearing is a relocation rather than a refutation.

Utilitarianism is a correct theory of one region of the goal table of §3.6. Where goals are structural in the sense of §3.6, the aggregation of consequences under a common measure is the appropriate form of assessment, and the tradition’s development of that form is a genuine achievement. The relocation concerns the extension of the treatment to the whole table: to goals whose formulation as rankable objectives destroys them, and to the generative goals whose function is the production of configurations that no ranking has yet evaluated.

The parallel with Claim 7 is close, and the two may be read as one structure appearing at different levels. Claim 7 concerns the projection of a goal system into a single optimizable space. The relocation of utilitarianism concerns the extension of a theory adequate to one class of goals across the class of all goals. The second is the first as it appears in normative theory.

The Dynamics of a System with No Remainder

The relocation admits a second and equivalent statement. A utilitarian treatment of the whole goal system is adequate to a system in which the remainder is zero: a system in which every consideration bearing on conduct can be expressed, ranked, and aggregated, with nothing left over.

Such a system is consistent, and §5 states what its dynamics would be. With no unranked configurations, injection ceases; with nothing to transport, the inertial range is idle; and the constraint field settles into a configuration from which its own dynamics cannot displace it. The loop of §1 closes and becomes a fixed point. This is the sense in which Q4 is the condition under which the loop fails to close, and it is why the question was placed among the questions of historical dynamics rather than among the questions of ethics.

The Form of the Argument

The form of the argument deserves comment, since the standard case against utilitarianism takes a different form. That case proceeds by counterexample: a scenario is constructed in which the utilitarian verdict conflicts with a confident judgment, and the conflict is offered as evidence against the theory. The exchange that follows concerns whether the intuition or the theory should yield.

The present argument makes no appeal of this kind. It observes that a system organized as utilitarian theory recommends has a determinate dynamical consequence, and it states the consequence. An interlocutor who accepts the consequence has understood the argument, and the disagreement that remains concerns whether the capacity for constraint update is worth retaining, which is a question the dynamics leaves open by §6.5.

The Standing of the Result for Moral Theory

A last misreading should be excluded. The account might be taken to hold that a utilitarian framework requires supplementation by non-consequentialist commitments in order to be morally adequate, and this is not the claim.

The claim concerns a dynamical condition. Non-structural norms occupy a position in the dynamics of the constraint field, and their function is the maintenance of an interval on which the field’s capacity for update depends. Whether the norms are also morally required is a separate question on which the present account is silent. What has been shown is that a system lacking them has a determinate structure, and that the structure is one in which historical constraint ceases to be revised by the dynamics it constrains.

§7 Application and Practice

Q8 of §1 asked how the account bears on practice. This section answers, and the answer is constrained by what the preceding sections established. Three results in particular narrow what may be said here, and they are stated at the outset so that the modesty of what follows is understood as a consequence rather than as a reticence.

§4 established that participants have no access to the slow variable. §5.4 declined to construct a quantity measuring the distance to a boundary of stability, and gave reasons that would apply to any such construction attempted from within. §6.5 argued that a space of non-optimization maintained because such spaces are valuable has thereby been converted into an instrument. Taken together, these hold that the practitioner cannot see the variable that matters, cannot measure the proximity of the transition that matters, and cannot protect what matters by intending to protect it.

A section on practice written under these constraints has two honest forms. It may state what the constraints rule out, which is considerable and worth stating precisely. And it may identify the residual space in which action remains possible, which is narrower than a reader arriving at this section would expect. Both are attempted below. What is declined is the third form, in which the constraints are acknowledged in an opening paragraph and then set aside.

7.1 The Design Paradox

The Statement of the Paradox

The central difficulty may be stated in three steps.

A system’s capacity for constraint update depends on maintaining relational degrees of freedom that no ranking has evaluated, by §6.6. Such degrees of freedom are maintained by norms that resist formulation as goals, by §6.4. And a norm adopted in order to maintain them has been supplied with a purpose, which by §6.4 destroys the property that made it capable of maintaining anything.

The consequence is that deliberate institutional design of the required kind is self-defeating in a specific and structural way. The designer who understands the account thereby loses the capacity to act on it, since the understanding supplies exactly the purpose that converts the norm into an instrument. This is the design paradox, and the sections that follow neither dissolve it nor treat it as a reason to abandon the question.

The Standing of Sincerity

One response is available and should be closed immediately. It may be suggested that the paradox is a matter of motive, and that a designer who genuinely values the norm, rather than valuing it for its effects, escapes the difficulty.

The suggestion fails for the reason given in §6.4. What converts a norm into an instrument is the form of the pursuit rather than the state of mind of the pursuer. An institution that establishes a protected space, documents the reasons for the protection, and reviews the space against those reasons has instituted a measure, and it has done so whatever the sincerity of those who established it. The paradox is structural, and structural difficulties are not addressed by good faith.

The Limits of the Paradox

The paradox has a definite scope, and stating it prevents an overextension that would make the section pointless.

What the paradox rules out is the deliberate maintenance of non-structural norms for the sake of their dynamical function. It does not rule out the maintenance of such norms for other reasons, including the reasons internal to them: an institution may hold to a practice because the practice is fitting, and the dynamical function follows without being the reason. Nor does the paradox extend to the constraint of possibility or to the constraint of evaluability, which are open to deliberate alteration in the ordinary way. And it does not rule out the removal of impediments, which §7.3 treats as the principal form of available action.

7.2 Governance under the Account

The Position of Governance in the Framework

Governance, in the framework to which this paper belongs, concerns how a generated relation is governed once it exists. The present section supplies what the historical extension adds: the object of governance is a relational field whose constraint structure is itself in motion, and the motion is not available to those who govern.

The Unavailability of the Governing Target

The most consequential result for governance is negative and follows from §5.4. A governance programme framed as keeping a system away from a boundary of stability requires knowing where the boundary lies. The account holds that this distance is unavailable to participants, and that its unavailability is structural rather than a deficiency of current measurement.

The result rules out a class of proposals that would otherwise be natural. Early warning systems for institutional crisis, resilience indices, and dashboards reporting a society’s distance from a transition are, on this account, proposals to measure a quantity whose measurement from within is what the framework denies. §5.4 entered the one qualification: statistical signatures of critical slowing may be readable from the response to disturbance without knowledge of the underlying parameter, and whether historical systems admit such measurement is an open question rather than a settled impossibility.

The Hazard of Index-Based Governance

A second result is the specification of a hazard that governance by measure carries, and it follows from §6.3 rather than from the epistemic results.

Governing by index is a special case of the projection treated in Claim 7. A governing body that adopts a measure, reports against it, and adjusts conduct to improve it has instituted an index-driven dynamics in the domain it governs, and by §6.3 has thereby begun damping the disturbances on which that domain’s capacity for constraint update depends. The claim is comparative and admits of degree, as Claim 7 requires: an index applied to a bounded domain, alongside domains left unmeasured, differs from an index applied across a society’s whole range of activity.

The practical content of the result is a question to be asked of any proposed measure. It is not whether the measure captures what matters, which is the usual question and a reasonable one. It is what proportion of the governed domain the measure leaves unmeasured, and whether that remainder is large enough to carry the disturbances the domain requires. A governance regime may be assessed on this dimension without any judgment about the merits of the measures it employs.

The Standing of the Inertial Range in Governance

The corresponding positive statement is weaker than one would wish, and is entered at the strength the account supports. A governance regime that leaves substantial domains of activity unmeasured retains, in those domains, the transfer treated in §5.5. Whether the retention can be pursued as a policy is precisely what §7.1 places in question, since a domain left unmeasured in order to preserve transfer has been assigned a function and thereby measured in the relevant sense.

What survives the paradox is a distinction between omission and provision. A governance regime that has not extended measurement into a domain differs from one that has designated the domain as a protected reserve, and the difference is the one §6.4 identifies. The first leaves a space; the second has instituted one. Only the first supports the dynamical function, and no programme can produce the first, since a programme of leaving-alone is a form of attention.

7.3 Institutional Practice under Non-Optimizability

The Removal of Impediments

The paradox constrains provision and leaves removal open, and this asymmetry is where the practical content of the account is concentrated.

Consider two institutional acts. The first establishes a protected space for unmeasured activity, with a rationale and a review. The second discontinues a measurement that had been extended over a domain previously unmeasured. The first supplies a purpose and, by §6.4, converts the space. The second removes an instrument and supplies nothing in its place. The domain that results is unmeasured in the manner of §7.2’s first case, since nothing has been designated and no function assigned.

The asymmetry gives the account’s principal practical recommendation, and it is a recommendation about what to stop rather than what to do: the extension of measurement into domains that had done without it is the mechanism by which the inertial range is consumed, and the extension is generally reversible in a way that provision is not.

Redundancy, Dissent, and Unabsorbed Activity

Three institutional features are commonly defended on grounds independent of this account, and the account supplies an additional consideration bearing on each. The independence matters: since each is already held for its own reasons, the additional consideration does not supply the purpose that §7.1 warns against.

Redundancy is ordinarily defended as insurance against failure. On the present account it also preserves configurations that a fully optimized arrangement would eliminate, and its elimination narrows the range across which transfer occurs.

Dissent is ordinarily defended by appeal to the interests of dissenters or to the epistemic value of criticism. On the present account it also supplies configurations that the prevailing evaluation functional does not rank, which is the condition §4 identified for a disturbance to survive selection.

Activity that no institution has absorbed is ordinarily left undefended, being visible chiefly as waste. On the present account it is the domain in which generative goals operate, and its elimination removes the injection term of §5.7.

In each case the account supplies a consideration to be weighed by those already disposed to preserve these features on other grounds. Whether a consideration so supplied can be acted upon without converting the feature is the question §7.1 leaves open, and §7.4 returns to it.

Institutional Forms That Resist Conversion

A narrower question is available and admits of a more definite answer: which institutional forms resist conversion into measures, whatever the intentions of those who operate them.

Three properties bear on this. A practice whose value is realized in its performance rather than in an outcome resists measurement, since the measure would have to be taken of the performance itself. A practice whose participants are not selected for their performance of it resists optimization, since selection pressure is the mechanism by which practices are tuned to measures. And a practice whose discontinuation carries no visible cost resists the accountability that generates measurement, at the price of being easy to discontinue.

The third property is worth marking as a hazard rather than a recommendation. The features that make a practice resistant to conversion into a measure are the same features that make it indefensible when its budget is questioned, and the account offers no way around this: a practice that could be defended by demonstrating its contribution would be a practice whose contribution had been measured.

The Assessment of a Regime

The foregoing supports assessment more readily than design, and the distinction is where the account’s practical usefulness lies.

Three questions may be put to an existing arrangement, and each is answerable from features that are visible. What proportion of activity within the arrangement is subject to measurement, and what proportion has never been measured? Has the proportion measured been increasing, and over what period? Do the practices held for their own sake within the arrangement retain that character, or have they acquired rationales, reviews, and reported measures?

The third question is the criterion of return of §6.7 in a form that can be applied to institutions. Its answer is retrospective, as §6.7 conceded, and retrospective assessment is nonetheless assessment: an institution can determine whether its practices have been converted, even where it cannot determine whether they are about to be.

7.4 Ethics and Normative Conduct

The Position of the Individual

The account bears on individual conduct, and the bearing is limited in a manner that follows from Claim 8. An individual who understands the account and adopts non-structural commitments for the reasons the account supplies has, by §6.4, adopted them in the goal-form and destroyed what was to be adopted.

What remains available is a distinction that the account clarifies rather than creates. A person may hold a commitment because it is fitting, and may separately understand what such commitments contribute. The two stand in a relation that requires care: the understanding must not become the reason, and there is no procedure that guarantees this. The account’s contribution to individual conduct is therefore diagnostic rather than directive. It supplies a way of recognizing when a commitment has been converted, which is when its defense begins to proceed by demonstrating its contribution.

The Standing of the Ethical Vocabulary

A consequence follows for how ethical claims are to be read within this framework. §6.5 held that the dynamics establishes nothing about whether the capacity for constraint update is worth having, and the same restriction applies here. The account establishes what a system loses when its non-structural commitments are converted, and it leaves the evaluation of that loss to whatever normative theory the reader brings.

The restriction is worth observing carefully, because the temptation to overstate is considerable at this point. An account that explains the function of humility, trust, and sincerity in the dynamics of historical constraint might readily be presented as a vindication of those virtues. It is not one. It is a description of what a system containing them can do and what a system without them cannot, and the step from that description to a recommendation requires a premise the account does not supply.

The Ethics of the Practitioner

One case deserves separate treatment, since the paper’s own position falls within it. A person who studies these dynamics professionally, and who advises institutions on the basis of that study, occupies the position the design paradox most directly concerns.

The account offers such a person little of the ordinary kind. It supplies no programme to recommend, and its principal practical content is a recommendation to discontinue certain extensions of measurement rather than to institute anything. It suggests that the advisory relation itself carries the hazard treated in §7.2, since advice given and adopted becomes a rationale, and a rationale is the beginning of a measure. What it supplies instead is a description precise enough that a practitioner can recognize the conversion of a practice when it occurs, and the discipline to decline the proposals that would accelerate it.

7.5 The Standing of This Section

The recommendations assembled here are thin, and their thinness is a result rather than an omission. An account holding that the relevant variable is unobservable, that the relevant distance is unmeasurable, and that the relevant protection is destroyed by being intended will not yield a programme, and a section that produced one would have contradicted the sections preceding it.

Two things have been established. The account rules out a class of proposals with some precision: governance targeting proximity to a transition, protected reserves designated as such, and the defense of practices by demonstration of their contribution are each shown to be self-defeating, and shown to be so for stated reasons rather than by general skepticism. And a narrower space of action has been identified, consisting in the removal of impediments rather than the provision of protections, and in the assessment of arrangements rather than their design.

Whether the space so identified is wide enough to be useful is a question this paper leaves to those who work in it. §8 lists the search for institutional forms that survive the design paradox as a research direction, and records that the difficulty is, at present, unresolved.

§8 The Research Programme

A first paper in a programme owes its readers an account of what has been done, what has merely been named, and what would have to be established for the whole to stand. This section supplies that account. It states the place of the framework within the larger effort to which it belongs, sets out the directions in which the work continues, states the methodological position under which it is conducted, lists the problems that remain open, marks the boundary that separates the account from a form of explanation it declines, and identifies the points of contact with work currently under way in the traditions surveyed in §2.

8.1 The Place of the Framework and the Contribution of This Paper

Position Within the Larger Effort

The framework to which this paper belongs treats relation as prior to what it relates and as the medium in which what exists is generated. Its first development concerns how relation generates being; a second concerns how a generated relation is governed once it exists; and the present extension concerns how relation generates the historical constraint under which further relation is generated.

The three stand in a definite order. The first supplies the primitive, the second treats a relation already in existence, and the third treats the condition under which relations of any kind are formed. Read in this order, the historical extension supplies what the other two presuppose: both operate within a constraint structure whose generation neither was designed to explain.

What This Paper Establishes

Four things have been argued rather than asserted, and they are what the paper offers for assessment. Each is offered as a proposal that the work listed below would be required to secure.

An ontology has been committed to and its terms defined: constraint as a macroscopic phase of the relational field, with the definitions of §3.4 and the risk stated at §3.4. A result has been derived rather than assumed: participants’ blindness to the slow variable follows from their mean-field position, by the argument of §4.2. A mechanism has been given for the departure of a system from a stable configuration, in which accumulation and trigger are distinguished and the condition for a trigger to be consequential is stated, by §4 and §5.4. And a normative consequence has been derived from the dynamics rather than argued independently, in Claim 7 and its argument at §6.3.

What This Paper Leaves Unestablished

Three things have been named without being established, and the distinction should be recorded plainly.

No order parameter has been exhibited for any historical case, and §3.4 conceded that the phase claim requires one to exist. No solution or approximation has been offered for the self-transport equation, which remains schematic in the sense of §5.1. And the mechanism of §4 has been given no empirical test, its discriminating power having been argued at §4.5 rather than demonstrated.

The Question of Generality

An observation is worth recording without being acted upon. The apparatus assembled here, in which a constraint structure conditions the goals formed under it while being revised by their pursuit, is not obviously restricted to the historical case. Organizations, disciplines, professional communities, and other configurations in which participants act under conditions they collectively revise exhibit the same structure at smaller scale.

The observation is recorded as a direction rather than a claim. A first paper that asserted the generality would have weakened the focus by which §1 justified its inclusions, and the assessment of whether the account extends is a matter for work that has established it in one case first.

8.2 Directions of Research

Six directions follow, one for each part of the account from §3 onward, so that no part is implied to be finished.

Ontological Directions

The identification of invariants is the first problem, and it is the problem on which the ontology’s standing rests. §3.5 argued that the social case lacks an independently motivated symmetry group, and what would replace it is a set of quantities preserved under rewriting of the relational grammar. Their identification would supply what the phase claim requires and §3.4 conceded to be missing.

Two further questions belong here. Whether the three modes of constraint distinguished in §3.6 are exhaustive, and whether they are the right cut, is open: the typology was justified by its fit with the goal categorization rather than derived. And the extent to which container ontology can be dispensed with in practice, as against in principle, is worth examining, since the analytical convenience of treating constraint as a container is considerable and the account forgoes it entirely.

Epistemological Directions

Whether blindness admits degrees is the principal question. §4.2 stated the result in a modality that §5.4 then qualified: if statistical signatures of critical slowing are readable from the response to disturbance, some information about the slow state is available without knowledge of the slow variable itself, and the result requires amendment. Establishing whether such signatures are measurable in historical systems would settle a question on which §7 also turns.

A second question concerns collective epistemic apparatus. Institutions of record, measurement, and analysis extend what participants can know, and whether they extend it to the slow variable is not settled by the argument of §4.2, which concerned the position of a participant rather than the capabilities of an apparatus. The question carries a tension worth stating: an apparatus that made the slow variable visible would weaken Claim 8, since intentional protection would then have a target, and the account would require revision at a load-bearing point.

Formal Directions

The self-transport equation of §5.2 admits development in three directions. Its solution or numerical treatment under simplifying assumptions would establish whether the form supports the behaviour attributed to it. The construction of closure approximations, in the manner of §5.10, requires a justification of the same kind that physical closures receive, and supplying one would convert the analogy into a model. And the multiscale apparatus named in §5.11, comprising geometric singular perturbation theory, averaging, and coarse-graining across the constraint hierarchy, is available in developed form and awaits the demonstration that the historical case admits the structures it requires.

Normative Directions

A positive criterion for the remainder is the outstanding problem. §6.7 conceded that the criterion of return is counterfactual, binary, and retrospective in application, and a criterion identifying non-structural norms by what they are rather than by how they would fare under pressure would strengthen §6 considerably.

A typology of such norms would serve the same end. The class was introduced by instances and by a diagnostic feature, and whether it admits internal structure, and whether the instances share more than the diagnostic, is unexamined.

The systematic comparison with other normative traditions is a third direction. This paper treated utilitarianism structurally, in §6.8, because the structure of aggregation under a common measure is what Claim 7 concerns. Deontological, virtue-theoretic, and contractualist positions stand in relations to the account that have not been examined, and the treatment of virtue ethics in particular is likely to be substantive rather than incidental, given the affinity between non-structural norms and the virtues.

Practical and Governance Directions

The design paradox of §7.1 is the central problem, and §7.5 recorded it as unresolved. What is sought is an institutional form whose maintenance does not supply the purpose that converts it: a form that persists for reasons internal to it while contributing the dynamical function, without the contribution becoming the reason. Whether such forms exist is open, and §7.3 identified three properties that would characterize them.

Two further directions belong here. The interface with the governance extension of the framework requires specification: what a governance account gains from being given a constraint structure in motion, and what it must give up. And the study of index-based governance as a case of Claim 7 offers the most accessible empirical target the account supplies, since the extension of measurement into previously unmeasured domains is documented, datable, and comparable across settings.

Empirical Directions

Three empirical questions follow from the mechanism.

The characterization of intermittency is the first. Claim 6 holds that constraint update is distributed unevenly in time and concentrated in limited regions of the field, and the claim has observable content: the temporal distribution of institutional reorganizations, and their concentration in domains rather than their diffusion across them, are measurable in principle.

Evidence for upward accumulation is the second. §5.5 left open whether social systems exhibit transfer toward larger scales, and stated what would be required to establish it.

The mechanism’s own prediction is the third and the most direct. §4.5 held that transitions should originate in domains that the prevailing indices do not measure, which is a claim about where to look rather than about what will happen. Its examination requires historical cases in which the prevailing indices are documented, and the origin of the transition can be located relative to them.

8.3 Methodology

Two Methods and Their Defects

The account recommends a dialectic of two methods, and it is stated with the defect of each rather than with the strengths.

The traditional method, proceeding by textual study and philosophical argument, is difficult to verify or falsify. A claim developed by argument from a tradition’s texts can be defended against evidence indefinitely, and the discipline that would terminate the defense is supplied from outside.

The empirical method carries two defects. It cannot defeat the problem of induction, and it cannot cross from what is the case to what ought to be, so that no accumulation of evidence adjudicates a normative claim. And it estranges its object: a method that proceeds by measurement studies what has been measured, and the human matter of its inquiry is reached only through the proxies measurement supplies.

The Asymmetry of the Defects

The two defects are asymmetric, and neither method repairs the other. Empirical work cannot cure unfalsifiability in the domain where the gap between is and ought obtains, since the data that would adjudicate a normative claim are not the kind of thing data are. Traditional work cannot defeat induction, having no independent access to the regularities in question.

What the pairing accomplishes is the constraint of each method’s overreach. Empirical work holds speculation to the phenomena; traditional work prevents the identification of a measurable proxy with the thing it proxies for. The dialectic is therefore a discipline rather than a synthesis, and its two halves do not combine into a method without defects.

The Application of the Account to Inquiry

The second half of that discipline is Claim 7 applied to inquiry. A research programme that projects its object into the space of what it can measure has performed, at the level of method, the operation §6.3 described at the level of goals: what resists measurement is left out, and what is left out is the material on which the programme’s own revision would depend.

The estrangement named in §8.3 is therefore not an incidental cost of empirical method but the specific form the projection takes in inquiry. The account thereby applies to itself, and the application is a constraint on how this programme is to be conducted rather than an observation about others.

Discipline in Borrowing

The paper’s borrowings from physics were made under a discipline that later work should retain, and it is stated here as a rule rather than as a description of what was done.

A borrowing supplies vocabulary and demonstrates that a structure is coherently thinkable. It does not transfer results: what holds of a physical system is established for that system by argument the social case does not inherit. Where a borrowing might be extended into a quantitative correspondence, the extension requires independent justification, and §5.7 declined one such extension for reasons that generalize. And each borrowing should be given a stated point at which it stops, as §3.3 and §5.1 did, so that its reach can be assessed rather than inferred.

8.4 Open Problems

Five problems are open in the strong sense that the account does not indicate how they would be resolved.

The Existence of an Order Parameter

The phase claim requires that order parameters exist for historical constraint, and §3.4 conceded that none has been exhibited. The problem has an unusual structure, since §5.4 and §4 together hold that such a quantity is unavailable to participants. What is sought is therefore a quantity whose existence is compatible with its unavailability from within, and whether the two conditions are jointly satisfiable is itself unsettled.

A Positive Criterion for the Remainder

§8.2 stated this as a direction; it is entered here as a problem because the counterfactual character of the present criterion may be ineliminable. A norm’s resistance to conversion is a disposition, and dispositions are identified by what would happen rather than by what has. If no positive criterion exists, the account’s central normative distinction is permanently retrospective, and §7 inherits the consequence.

The Formal Treatment of Self-Reference

§3.5 identified self-reference as the limit belonging to the social case alone. Participants read the constraint under which they act; the readings enter the field; and the readings differ between participants, so that the coarse-graining relating the field to its description is neither fixed nor single-valued. No formal apparatus for this situation has been offered here, and the physical borrowings supply no precedent, the metric having no opinion about its own value.

The Conditions for a Slow Manifold

§5.6 partitioned the applicability of the two descriptions by distance to a boundary of stability, and the partition rests on the existence of a spectral gap in the regime far from the boundary. Whether historical systems exhibit such a gap, or whether activity is coupled across scales at all times, is unsettled. If the latter, the fast-slow description of §5.3 loses its warrant and the epistemic results derived from it require reconstruction on the cascade description alone.

The Character of the Approach to Criticality

The last problem is the most consequential and the one where premature resolution would do most damage.

The account holds that the slow variable drifts toward a boundary of stability, and it does not explain why the drift occurs. Two possibilities are available. The drift may be driven, so that the slow variable is carried by influences that could equally have carried it elsewhere. Or the system may organize itself toward the boundary, so that the approach is a consequence of the dynamics rather than of what acts upon it.

The second possibility has an attraction that should be regarded with suspicion. If the institutionalization that consumes the inertial range is itself the drift toward criticality, then Claim 7 and the criticality condition describe one process from two sides, and optimization is self-undermining in a strong and elegant sense: it would not merely damp the disturbances on which update depends but carry the system toward the state in which the remaining disturbances become decisive. The elegance is exactly why the possibility is entered as a problem. Establishing it would require an argument this paper has not made, and adopting it without one would supply history with a tendency, which is the boundary treated next.

8.5 The Boundary Against Teleology

The Form of the Distinction

The account is dialectical and declines to be teleological, and the distinction requires statement, since the vocabulary of transitions between configurations can be read either way.

A teleological account holds that the movement of history is directed toward a terminus, whether by the self-development of an idea, by the realization of a potential, or by convergence upon an end. The present account holds that a configuration gives way when the relational conditions sustaining it cease to sustain it. The negation is supplied by the conditions rather than by what the configuration is developing toward, and the successor configuration is whatever the dynamics produces rather than what the process was for.

The Observation Point That Teleology Requires

The account excludes teleology by a route more specific than a declaration of preference, and the route is worth stating because it connects the exclusion to the epistemic results.

A teleological reading of history requires a position from which the direction of the process is visible. Hegel’s philosophy of history supplies such a position, and the supply is not incidental: an account in which the process is directed requires that the direction be legible from somewhere, and the philosopher who reads it occupies the required place. §4 denies that any such position exists within the system, and §3.1 denies that one exists outside it. Teleology thereby loses its footing in this framework for the same reason that the cybernetic form was displaced in §5.2: both require an observer the ontology does not admit.

The Points of Exposure

Three points in the account are where teleology could re-enter, and each was closed by a specific measure.

An action principle would supply a quantity that history extremizes, and §3.5 declined to seek one. A control parameter would supply a direction of drift and, with it, a temptation to read the drift as tendency; §5.4 declined to construct one. And a self-organizing approach to criticality would supply history with a state it seeks; §8.4 entered the possibility as an open problem rather than a result, for precisely this reason.

The three exclusions have a common form, and stating it makes the boundary a policy rather than a series of decisions. Each declines a formal construction that would license reading a tendency into the dynamics, and each is declined on the grounds that the construction is unavailable rather than that its consequences are unwelcome.

8.6 Contact with Contemporary Work

§2 was retrospective, treating what the surveyed traditions achieved. This subsection is prospective: it identifies what those traditions are presently working on, where the account developed here bears on that work, and under what discipline the contact should be made.

Questions Currently Under Discussion

Several lines of contemporary work bear on the question of constraint update, and the following are the most direct.

The value-form tradition and the readings associated with it treat value as a social form rather than as a substance, and analyse the abstraction that makes commensuration possible. The associated notion of real abstraction holds that the abstraction occurs in practice rather than in thought: exchange abstracts from the particularity of what is exchanged, and the abstraction is performed by the transaction rather than by the observer.

Work on platform economies and on data as a condition of production examines an extension of measurement into domains that had not been measured, together with the forms of rent and control that follow.

Social reproduction theory examines the domain of activity on which production depends and which the analysis of production had excluded, and asks how the exclusion is maintained.

Ecological work in the tradition analyses the rift between social metabolism and the natural conditions it depends upon, and treats the rift as a consequence of the specific form the social process takes.

Post-Marxist work continues to develop the analysis of hegemony and contingency, and work associated with accelerationist positions asks what technical conditions make which political forms available.

World-systems analysis continues its examination of long waves and hegemonic succession, and the debate over microfoundations that followed the analytical current remains live.

The Common Limitation and the Rereading It Permits

The diagnosis of §2.4 extends to this body of work, and the extension is the ground on which contact is proposed. In each case the fact of constraint update is registered and its mechanism is left unspecified. Value-form analysis explains how the abstraction holds without treating how the boundary of the expressible moves. Post-Marxist work replaces necessity with contingency, and contingency states the openness of the outcome rather than the process producing it. Ecological work describes the rift as consequence without treating the scale structure of its occurrence. Social reproduction theory identifies the excluded domain without treating how the exclusion is maintained by the grammar that excludes it.

One rereading is worth stating in more detail, since it is an act of recognition rather than a correction. The tradition’s accumulated contradiction has been treated as the cause of rupture. On the present account it is the drift of the slow variable toward a boundary of stability, with the trigger supplied separately and selected by the criterion of §4.4. The rereading gives the tradition’s term a precise dynamical content and assigns the causal work to two factors rather than one, which is a division of labour neither account had alone.

Points of Contact

Five pairings follow, and each is a hypothesis of translation rather than an identification.

Real abstraction may correspond to the constraint on expressibility of §3.6, both concerning what a practice makes sayable. Metabolic rift may correspond to the consumption of the inertial range by dissipation, both concerning a transfer that has been severed. Hegemony may correspond to the expressive coupling of §6.2, both concerning the supply of the vocabulary in which a subject’s situation can be formulated. The measurement of previously unmeasured domains in platform economies may be an instance of Claim 7, and §8.2 recorded it as the most accessible empirical target. And long waves may correspond to the relaxation times of the slow variables of §5.3.

The Discipline of the Contact

Each pairing requires the qualification that a translation is proposed rather than established, and the first is the case in which the qualification carries most weight. Real abstraction and the constraint on expressibility arise in incompatible settings: the former presupposes an analysis of value in which the present account takes no position, and the resemblance between the two concepts is a resemblance of role rather than of content. Writing the pairing as an equivalence would import commitments this paper has declined to make.

The discipline applies to all five. What is proposed is a point at which two vocabularies may be brought into contact, and what would establish the contact is work in which a phenomenon is described in both and the descriptions are compared. Until that work is done, the pairings indicate where to look.

The relation the account seeks with these programmes should be stated in closing, since a first paper proposing a framework is easily read as claiming to supersede what it surveys. The claim made here is narrower. Each of these programmes has an account of what constrains action and a description of how constraint gives way; what the present framework offers is a mechanism for the second, stated in terms general enough to be attached to more than one account of the first. What it receives in return is the substantive content those programmes supply, without which a mechanism theory describes a form and never a history.

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A note on method. The formal statements in this paper carry the three grades distinguished in §5.1, and no statement has been given a grade higher than the argument supports. The self-transport equation and those following it exhibit forms; they are not solved, and nothing is derived from them that the prose does not derive independently. Where a quantitative construction was available and would have lent the account an appearance of rigour it has not earned, the construction was declined and the refusal recorded: §3.5 for an action principle, §5.4 for a control parameter, §5.7 for a dimensionless group. The account would be strengthened by any of the three, supplied with its own justification. It would be weakened by their assumption.

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中文

约束之下的历史生成性理论

迈向生成性关系历史

黄万宏 · huangwanhong@serendip.ngo

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摘要

我们只能创造历史框架所允许之物。这一主张被广泛承认而鲜少被机制化。唯物主义的、诠释学的以及结构-能动的诸读法各自规定什么约束着行动，而各自把那个约束本身据以被修订的过程留在暗处。本文以初步的形式提出生成性关系历史（GRH），即生成性关系框架的历史性扩展，并取约束演化为它的对象。它的核心提议是：历史约束可以被理解为关系场本身的一个宏观相，以致行动与约束构成在两个尺度上被观察的同一个场。三个后果被提示。目标成为一个容许三种角色的动力学范畴：结构性目标在既有约束之内优化，生成性目标注入扰动，而非结构性规范持守任何目标都无法表达的自由度。能动者对慢变量的盲目，被论证为出自尺度分离，即平均场的一个结构性条件。而一个系统对一个稳定历史舞台的离开，被给予一个所提议的机制，在其中扰动充任触发因素，在先前的累积已把系统携带到一个稳定性边界附近之处具有决定性。本文是作为一个机制理论被提出的：它规定约束可以如何被更新，而拒绝预测哪些约束将会被更新。形式资源在一个明确的分工之下从两个物理设置中被借来。背景独立的诸进路提供一个没有先在存在的舞台的构成；流体动力学的自输运项提供一个舞台与运动于其上之物的共同演化。二者都被取为词汇与存在启示，而本文标出每一个借用停止之点。

关键词： 历史约束；约束演化；生成性关系存在；目标本体论；慢变量；临界性；间歇性生成性；历史哲学。

关于本文分量的一则说明。这是生成性关系历史的第一次陈述，而它具有一个提议的分量。它问一个问题，即历史约束如何被生成、被维持、被更新，并在某一材料卸除那个问题的某一部分的限度内接纳该材料。凡它从物理学借用之处，它借用一个词汇以及一个”某些结构是可融贯地被思考的”这一证明；”社会是流体”、或”历史携带一个度规”这一主张，躺在它之外。它的若干承重的主张可能为假，而陈述它们的诸节这样说了。反对、纠正与反证，欢迎寄至 huangwanhong@serendip.ngo。

§1 引论

我们只能创造历史框架所允许之物。这一主张是古老的，而以某种形式或另一种，几乎每一个严肃的历史说明都承认它。人类在他们所未选择的诸条件之内行动：什么可被尝试、什么可被组织、什么甚至可被提议为值得尝试，都被一个先于诸行动者的格局预先界定。这一主张以它的寻常形式而言也几乎是空的。当人们问那个框架由什么构成时，它变得有实质；而当人们问那个框架如何改变时，它变得困难。

这一主张有三种标准的读法，而每一个都保得别的所搁置的某种东西。唯物主义的读法把那个约束定位于生产的物质条件：一个社会所能创造之物，被它的生产力以及组织它们的诸关系所界定。诠释学的读法把它定位于意义：我们在一个我们所未造的可理解性视域之内行动，而我们所能意图之物，被我们的处境所使之可意谓之物所界定。结构-能动的读法主张结构与行动相互构成，两者都不在先。每一个读法都是一个真正的成就，而本文取全部三者为背景。它们所共有的、并且为当前论证打开空间的，是每一个都规定那个约束、而把那个约束的更新留作未机制化。约束会改变，这被普遍承认。它们如何改变，即一个界定行动的格局经由何种过程成为一个不同的格局，一般而言被归于一个其释放仍未被解释的累积，或被指派给偶然性，而后者命名那个缺口、同时把它留作敞开。

本文以初步的形式提议：约束更新的问题是一个理论的恰当对象，而生成性关系框架被置于一个能够提供一个这样理论的地位。母框架，即生成性关系存在，主张关系先于它所关联的诸实体，而所存在之物在关系之中并通过关系被生成；一个治理性扩展，即生成性关系治理，处理一个被生成的关系一旦存在之后如何被治理。此处所提议的是一个第三扩展，即生成性关系历史（GRH），它问关系如何生成那个进一步的关系据以被生成的历史约束。凡母框架把关系当作生成存在之处，GRH 把关系当作生成历史：历史被取为那个从关系性生成中凝结出来、并此后界定它的约束场。

那个理论的对象比它的标题所提示的更窄，而那个收窄是刻意的。GRH 取约束演化为它的对象，即那个界定性的格局据以被生成、被维持、被修订的过程。分期的诸问题、诸事件之间因果的诸问题、以及历史过程之意义的诸问题，都躺在它之外。大多数历史理论从约束运行到行动、或从行动运行到历史记录。很少有理论问那个约束为何更新，而那个问题治理以下一切的组织。

那些问题。 这一探究由两层中的八个问题所治理。第一层陈述那个历史现象所提出者：

1. 个体目标与集体目标的涌现，以及它们耦合的方式。
2. 历史加于诸目标之上的约束，以及诸目标转而使历史约束演化的过程。
3. 诸目标在驱动个体动力学与集体动力学之演化中的角色。
4. 我们所拒绝优化之物的分量。完全地追随诸目标交付功利主义，而规范性的实践拒绝完全地追随诸目标，尤其是结构性的那些。这一层问那个拒绝应当如何被理解，以及此类非结构性的承诺如何关涉诸目标、动力学与约束。

第二层陈述那个框架为有资格处理第一层而必须回答者：

5. 那个框架对历史与个体之辩证运动的理解。
6. 那个运动的本体论。
7. 它的形式建模。
8. 它对实践的关涉：对伦理、对规范性行为、对治理。

这些被刻意地保持粗略。这是一个初次的探究，而更精细的问题会在那个空间被概览之前就封闭它；在每一个之下生起的具体问题在它们生起之处被处理。

这两层构成一个架构。Q1 至 Q3 构成一个回路：约束界定可被形成的诸目标，诸目标塑造随之而来的动力学，而动力学修订那个约束。单独来看，那个回路是一个不动点，一个会安顿并保持安顿的系统，因为每一个阶段都再生产下一个的诸条件。Q4 陈述那个回路未能闭合的条件。这正是为何一个佩带规范性哲学之外表的问题被置于历史动力学的诸问题之间：逃脱作为一个目标之表达之物，依以下所发展的说明，是那个使回路保持敞开之物。

那个架构也服务于一个值得在开端命名的学科性功能。以下的材料触及历史哲学、历史唯物主义传统、动力系统、背景独立、规范理论、治理与方法论，而一个触及如此多文献的工程有成为它们全部之概览的风险。那八个问题提供那个容纳。材料在以下所述中通过卸除一个被命名问题的某一部分而赢得它的位置；凡它会仅仅是有趣之处，它被略去、或被推迟到 §8 的研究纲领。以下每一个实质性部分都卸除每一层中的一个问题。

取自母框架的诸前提。 三个承诺被承袭并被不加重新推导地使用。第一个是关系的首要性：诸关系是被关联者竟能被个别化的条件。第二个是生成性与关系性作为彼此有别的诸维度的配对，因为一个格局可能在关系上丰富、同时在生成上封闭，而这两者要求分开的评估。第三个是一个判准，即归还判准：一个价值或规范相对于一个系统是生成性的，当那个系统自己的诸目标无法反回来改写它，而一旦它们能够，它便已被俘获。这些在此充任诸前提；为它们的论证属于母框架。

这个理论所交付之物。 那些建模承诺值得在任何装置出现之前被陈述，因为本文否则会面对的若干反对，是对它所拒绝作出的诸主张的反对。

GRH 是作为一个机制理论被提出的。它旨在规定约束更新如何发生：经由何种过程、通过何种通道、在何种条件之下。预测一个给定社会将会有哪些约束躺在它的范围之外，任何种类的预报也是。它不提供任何闭合的方程系统，而 §5 论证非闭合对所论那一类系统是普适的。它不指认任何历史所最大化的目标函数，而 §3 解释为何引入这样一个函数会经由框架颇费力气去关闭的一扇侧门重新接纳目的论。

形式资源在一个治理那些借用应当如何被读的分工之下，从两个物理设置中被抽取。对时空的背景独立诸进路，即广义相对论、以及更尖锐地群场论与因果集诸纲领，被用于一个构成性问题：一个没有先在存在、与运动于其上之物一同被生成的舞台，是否是一个可融贯地被思考的结构。那个问题被回答一次，在 §3 中，而那个借用在那里停止。流体动力学的自输运项被用于一个彼此有别的、历时性的问题：一旦舞台与表演的分离被否认，它们相互拖曳所采取的形式。这两者处理不同的问题，并且没有义务收敛。在任何一种情形中，本文都不主张社会就是所论的那个物理系统。所主张的是：某些结构，即一个被生成而非被预设的背景、一个输运它自身的场，是融贯的、已在别处被严格地发展、并提供一个社会案例可以在其中被不带隐喻地陈述的词汇。

本文的角色。 这是 GRH 在生成性关系框架之内的第一次提议，而它承载一篇第一论文的诸义务。它必须陈述那个纲领将追求的诸问题，承诺于一个精确到足以为错的本体论，把已被确立之物与仅仅被命名之物区别开来，并留下一个别人能够接过或反驳的研究纲领。因此，§8 构成那个贡献的一个实质部分：它列出六个研究方向、一个方法论立场、从此处可见的诸开放问题，以及与 §2 所概览的诸传统中当代工作的诸接触点。

其余部分如下推进。§2 概览现有诸框架并陈述每一个所成就之物，全篇由它对约束更新的处理所组织。§3 发展那个本体论：舞台与表演的相互决定、背景独立的谱、”约束是关系场的一个相”这一承诺、那个纲领的诸界限，以及较后诸部分所依赖的约束与目标的联合分类。§4 发展那个认识论，导出能动者对慢变量的盲目，并给出一个稳定历史舞台据以被离开的机制。§5 列出那个形式建模：自输运、快-慢结构、临界性、级联、间歇性，以及那两个可用描述之间的分工。§6 处理那些规范性后果，包括抗拒优化之物的分量。§7 转向治理与实践。§8 陈述那个研究纲领。

§2 对现有诸框架的认可

历史约束如何被更新这一问题，已被相当一批工作所趋近，而本节陈述那批工作所保得之物。其意图是认可。一个迟到于一片被耕耘良好之田地的框架，欠它的前辈一个关于它们所成就之物的说明，而此处所给出的说明意在准确、而不是便利：所概览的诸传统已解决了本文不加重新解决就接过的诸问题，而它们中的数个已以一种 GRH 所承袭的清晰性提出约束更新的问题。每一个框架都以同样的次序被呈现：它的核心主张、它在约束更新问题上所记录的具体成就，以及随后的文献在那一点上所提出的困难。关于那第三个要素需要一个审慎。凡一个困难已在一个传统之内被承认、或是跨其批评者与辩护者的共识之处，它被如此报告。凡它仍被争议之处，那个争议与它一同被报告，而读者应当把那个归属取为归于所命名的批评者、而不是归于一个共识。没有主张说这些框架中的任何一个已被反驳，而那些困难是因其对约束更新的关涉、而不是因其在整个文献中的分量而被选取的。

2.1 选取的判准

一个关于历史变化所写一切的概览会占据比它所支持的论证更多的篇幅，而本节被单一一个判准所限定：每一个框架都因其对约束更新的处理而被考察。诸框架在它们就”一个界定性格局如何成为一个不同的界定性格局”说出某种确定之物时被接纳，而对每一个的讨论都限于它在那一点上所说之物。这些传统中许多别的有价值之物未被提及，而那些省略不携带任何裁决。

三个维度组织那个考察并贯穿复现。第一个是那个框架指派给约束的存在方式：约束是一个行动发生于其内的容器、一个与行动共同构成的结构、还是别的什么。第二个是那个更新中的运动之源：那个朝向改变的驱动被定位于累积、于矛盾、于能动、于偶然、还是于一个外部参数。第三个是能动者的认识地位：那个框架主张历史行动者能够知道关于他们据以行动的诸约束之什么，以及那个知识是否被当作在原则上可达成的。表 1 沿这些维度概括那个概览；以下诸节提供细节。

2.2 辩证唯物主义及其诸学派

马克思中的两个层级

马克思的诸文本在两个层级上运作，而它们的关系自那以来占据了那个传统。在第一个层级立着关于生产力与生产关系的说明。1859 年《序言》以正典的方式给出它：人们进入与他们物质生产力发展的一个给定阶段相适应的生产关系；这些关系的总和构成社会的经济结构；而在某一阶段，物质生产力与既有的生产关系发生冲突，后者从诸力量的发展形式转为它们的桎梏，于是一个社会革命的时代开始 [39]。在第二个层级立着《雾月十八日》的表述：人们创造他们自己的历史，而在已然存在的、被给定并从过去传下的诸境况之下创造它 [38]。

那个成就是双重的、并且相当可观。第一个层级提供一个带确定内容的机制，而它仍然是那个传统中最接近于一个约束更新理论之物：它命名一个慢变量，指认那个约束成为可修订之条件，而以允许历史研究的术语这样做。第二个层级陈述本文取为它自己的那个问题的一般形式，并以一种从未被改进的经济性陈述它：行动被一个它所未选择的格局所条件化，而仍然改变那个格局。

那个局限是这两个层级之间的过渡。第一个说诸力量的发展最终改变诸关系；第二个说在被承袭境况之下的行动改变它们。二者都断言那个约束让位。被累积的发展经由何种过程转换为一个被改变的格局，被描述得多于被规定：桎梏的语言命名那个改变成为可期之条件，而把什么携带系统穿过留作未陈述。这一点已从数个方向被施压。分析性的重构发现那个功能性的主张要求一个关于诸力量据以选择诸关系的反馈的说明 [15, 17]；那个传统自己的政治一翼发现那个过渡不足以指导行动；而阿尔都塞的介入部分地是由”那个转变要求那个一般公式所不提供的诸条件”这一观察所促动的 [1]。

必然论的读法

第二国际承袭了第一个层级并把它拉紧。考茨基广为流传的对《爱尔福特纲领》的评注，把生产力的发展呈现为一个确定的社会形态更替序列的动力，而社会主义的到来从资本主义自己诸条件的成熟随之而来 [28]；普列汉诺夫对个人角色的处理，把一个由发展的一般进程所固定的结局的加速或延缓指派给伟人 [44]。一个限定属于此处，并被录入，因为那个标签在次级文献中被松散地应用：考茨基本人，在他与巴克斯的交流中，明确地否认唯物主义构想把思想化约为经济条件的一个反射，并把它描述为一个对社会发展之驱动力的研究方法、而不是一个决定的学说 [29]。以下所述关乎那个在那个时期占主导的读法及其对约束更新理论的后果，而不关乎任何个别作者立场的全部。

那个成就在较后的批评中一般被低估。那个读法认真对待机制的问题，而它以一个慢变量来回答，该慢变量的累积被认为解释在表面上显现为断裂之物。那个结构，即一个缓慢改变的量治理快事件成为有后果之条件，正是 GRH 也采纳的结构，而 §4 陈述那笔亏欠。

两个局限被广泛接受。第一个是能动的抽空：凡那个更替被决定之处，能动者的贡献化约为加速或延迟，而”什么是要做的”这一政治问题失去它的对象。这是西方马克思主义回应的激发性反对，而它在从外部被施压之前很久就已从那个传统之内被施压 [35, 24]。第二个局限较少被评说，并直接关涉当前的论证：那个慢变量被当作外生且单调的。诸力量发展；那个发展本身不由它将推翻的那个格局所解释；而那个箭头指向一个方向。一个其中那个慢变量由它后来所约束的那个动力学本身所生成的框架，不能采取这个形式，而 §5 陈述那个替代方案。

西方马克思主义

就当前目的而言，西方马克思主义传统可以被读作对必然论读法之能动者抽空的三个回应，其中每一个都以一种彼此有别的方式丰富了约束的说明。

卢卡奇：物化与总体性的立场。 那个核心主张是商品形式一般化为一个客观性形式，在其之下社会关系把自身呈现为诸物之间的关系，而这一物化是一个对”什么竟能被领会”的约束、而不仅仅是对”什么被相信”的一个扭曲。那个约束在一个阶级来占据那个过程显现为一个过程的总体性立场时被变换 [35]。

对约束理论的成就是实质性的，并在此被保留：约束通过一个处境竟能被领会的诸形式而运作，而能动者的认识位置是内在于那个历史过程的、而不是对它的外部评论。这是 §3 所处理为可表达性约束之物的一个直系祖先。

最经常被施压的局限附着于那个载体、而不是那个洞见。把无产阶级指认为历史的同一主体-客体，已被广泛判定为引入了一个物化分析所不要求的黑格尔式结构，而那个反对在关于该著作的诸讨论中已成为近乎义务性的。卢卡奇本人在 1967 年序言中推进了它的一个版本，把那个同一主体-客体描述为一个形而上学建构 [36]，尽管那个序言是否准确地陈述了他的原初立场本身有争议。关于领会的那个洞见独立于那个载体而立，而正是那个洞见在此被接过。

葛兰西：霸权与阵地战。 那个核心主张是发达公民社会中的支配通过在一个稠密的制度网络中被组织起来的同意而运作，以致那个约束包括一个必须在它自己的地面上被争夺的常识安顿。阵地战命名相应的斗争形式：持久的、分布于公民社会诸制度的、没有一个决定性时刻的 [24]。

那个成就属于那个传统中对当前问题最有价值的之列。它把约束更新描述为渐进的、分布的、累积的，而它指认那个累积于其中发生的媒介。它也提供有机危机的概念，在其中那个统治性的安顿失去它组织同意的能力、同时还没有一个后继者已然形成，而这是那个传统对一个处于诸格局之间的系统最富暗示性的描述。

那个被接受的局限关乎转换。阵地战描述数十年的累积，而那个危机描述那个空位期，而从一者到另一者的过渡仍停留在描述的层面。那个概念也因弹性而被批评：霸权已被应用于如此宽广一范围的现象，以致它在任何给定案例中的解释着力都要求分开的论证，一个从那个传统之内一如从外部被登记的反对 [4]。

阿尔都塞：多元决定与结构因果性。 那个核心主张是一个社会形态是一个带一个支配结构的复杂整体，诸矛盾是多重的且不平衡地发展的，而一个革命性的断裂要求它们在一个情势中的融合、而不是一个单一矛盾的成熟。结构因果性命名一个结构只在它的诸效果中在场的那个方式 [1, 2]。

那个成就是一个持久的收获，并在此被接过。对一个单一表达性矛盾的拒绝，从唯物主义的说明中移除了一个黑格尔式目的论的最后残余，而结构因果性是 §3 所论证为约束之存在方式之物的一个近邻：一个在它所条件化之物中在场、而不立于它之外的约束。

那些被接受的局限有两个。融合于其中发生的那个情势被精确地命名、而只由那个所发生的融合所规定，以致那个概念在事后指认那个时刻。而那个说明在能动问题上被强烈施压：把主体当作一个询唤之效果的处理，在关于意识形态国家机器的文章中被发展 [3]，提出了一个结构如何被它所构成者所变换的问题。汤普森的论战把那个反对置于它最尖锐处 [50]；那个论战在当时被争议、并仍然如此，而此处所报告的是它所提出的问题、而不是它所提议的裁决。

分析马克思主义

那个分析性潮流的核心主张是方法论性的：那个传统的诸论题应当以允许评估的清晰性被陈述，并以在哲学与社会科学别处盛行的论证标准被辩护。科恩的重构给予生产力的首要性它最严格的形式，论证生产关系之成立是因为它们功能上适于发展诸力量 [15]。埃尔斯特施压于对微观基础的要求：一个宏观层级的主张只在被一个关于实现它的诸个体行动的说明所担保时才可容许 [17]。

那些成就有两个，而本文接受二者。功能性解释被给予一个可辩护的形式，在其中那个解释由一个后果律、而不是由对一个益处的单纯指认所许可。而对微观基础的要求仍然约束着任何后继者：一个无法说出当那个约束改变时诸能动者在做什么的机制理论，尚未提供一个机制。

随之而来的争论是有教益的，而它的分量应当被准确地陈述，因为它仍然开放、而不是被了结。埃尔斯特的反对是：在进化生物学中为功能性解释作辩护的诸条件，在社会理论中缺席，而一个宏观现象的功能性解释只在产生那个聚合的诸个体行为机制至少能被示意性地指出之处才可容许 [17]。科恩回应说：这样一个阐发的缺席削弱一个功能性解释而不使它无效，并提供空心骨的前遗传学达尔文式解释作为一个”在它的机制被知道之前就是好的”的解释的案例 [16]。那个交流留下一个要求、而不是一个反驳，而本文以它自己的账目面对那个要求：§4 陈述对此处所提议机制的相应风险，连同那个使它不致生起的约束。那个潮流也因它自己方法的代价而被批评，即向个体行动的化约搁置了原初理论的关系性与过程性性质，而这恰恰是当前框架取为原始之物。

世界体系分析

那个核心主张是恰当的分析单位是历史体系、而不是民族社会，现代世界体系是一个带一个核心、半边缘与边缘的资本主义世界经济，而这个体系有一个带诸周期与诸长期趋势的发展史 [51, 6]。

那个成就，就当前问题而言，是对尺度与持续时间的处理。累积的诸周期、霸权的更替与诸长期趋势，被描述为其周期超过其内任何行动者之视域的诸过程，而那个分析在一个尺度上被进行，在其上对任何民族社会的约束都作为一个更大动力学的产物而可见。这是一个真正的慢变量理论，而 §5 以一个不同的词汇接过同一个关切。

两条批评线值得被报告，第一条作为一个持续争论中的立场，第二条作为一个更一般的困难。布伦纳论证那个说明以交换关系与世界分工、而不是以生产来定义资本主义，而这削弱它对阶级动力学的处理 [13]；那个论证被世界体系分析者所争议，而那个争论尚未关闭。第二个困难较少被争议：那些长波的数目、断代与边界在诸分析者之间变化，而生成那个周期性的机制被规定得不如那个周期性本身充分。

后马克思主义诸立场

后马克思主义潮流的核心主张，在拉克劳与墨菲的表述中，是社会是话语性地被链接的，没有任何阶级占据一个由生产关系预先给定的特权位置，而霸权的诸安顿是没有必然归属的诸元素的偶然链接 [32]。

那个成就是可能之场域的打开。那个”已指认一个历史律”的自负被搁置，对革命主体的指认停止由结构位置所给定，而对”诸政治身份如何被建构、而不是被表达”的分析被实质性地推进。

那个被接受的局限是最直接关涉本文的那一个。偶然性，在已取代必然性之后，被要求执行一个机制的工作。一个安顿本可以是别样的，这把”为何这个安顿在这个时刻让位、而别的持续”留作未陈述。一个沿这些路线的反对立刻被格拉斯所施压，他论证那个立场把分析的对象连同它的决定论一起消解 [22]，而被拉克劳与墨菲在同一场地所回答；那个交流是一个争论、而不是一个被了结的发现。此处所报告的是在它之后存活、并且不要求格拉斯之框定的那个更窄之点：一个以极大微妙描述一个安顿之形式的词汇，并不因此就被装备来说出一个安顿何时过渡为另一个。

2.3 非马克思主义诸框架

韦伯与扳道工

此处相关的核心主张是韦伯的意象：不是观念、而是物质的与理想的利益直接治理行为，然而由观念所创造的世界图像非常经常地、作为扳道工、决定了行动被利益的动力学所推动所沿的轨道 [53]。观念提供方向；利益提供运动。

那个成就是把两种经常被混作一谈的约束区别开来，以及”观念性的能够在因果上有效、而不构成一个分开的动力”这一证明。对新教伦理的分析提供了那个做过的案例 [52]，而对理性化的说明提供了一个相当有力的慢变量。

那个被接受的局限是那个意象描述那个扳道、而把一个扳道如何来被扳动留作未规定。韦伯自己的方法论承诺、以及他对历史发展诸理论的怀疑，使这成为一个刻意的克制、而不是一个疏忽；它仍然把约束更新的问题留作敞开。

年鉴学派与长时段

那个核心主张是历史时间的一个分层：人与其环境之关系的几乎静止的历史；诸群体、诸经济与诸国家的缓慢有节奏的历史；以及事件的历史，布罗代尔把它描述为表面的扰动，由历史的潮汐所携带的泡沫之峰 [11, 12]。

那个成就是史学中对 §5 所处理为尺度分离之物的最清晰的预见。认真对待它随之而来两个后果，而二者都在此被保留：历史约束拥有不止一个弛豫时间，而一个在事件的时间尺度上运作的行动者，对运作于其下之物有着系统地受限的通达。

那些被接受的局限是那个耦合与那个能动者。诸层被以极大的力量区别开来，而它们的相互作用被规定得较少：什么条件允许那个深层成为对表面敏感的、以及表面经由何种过程累积进那个深处，是那个框架提出得比它回答得更有效的诸问题。而对事件的从属招致了那个标准的反对，即人类能动被留下很少可做之事，一个被那个传统自己后来向心态史与微观史的转向所锐化的反对。

历史制度主义

那些核心主张是：诸制度通过使某些路径比别的更昂贵而约束，早期选择通过递增回报而被锁定，而制度发展被诸关键节点所标点，在其间可行诸选项的范围加宽 [40, 43, 14]。第二代添加了一个关于渐进变换的说明，指认置换、层叠、漂移、转化与耗竭为诸制度不经断裂而改变所经的诸模式 [49, 37]。

那个成就是约束更新可用的最可运作的词汇。带递增回报的路径依赖为”约束为何持续”提供一个机制；渐进变化的类型学提供诸机制，凭它们一个格局在一个断裂缺席时成为一个不同的格局；而对规则中歧义的、以及对规则与执行之间缺口的强调，指认内生变化的杠杆所在 [37]。

那个被接受的局限关乎那个关键节点，而它已从那个传统之内被最清晰地陈述。卡波恰与凯莱曼观察到，尽管关键节点在理论上重要，对路径依赖的诸分析对它们投入了很少注意，而他们着手去重构那个概念、界定它的范围，并为它的使用提供方法论指导 [14]。那个重构相当地推进了此事，并以”能动者的选择影响那个结局的概率相对于其前后的那个概率被抬高”来指认那个节点。那个指认在实践中仍然是回溯性的：把一个时刻标记为一个节点之物，是诸结局的范围当时更宽，而这由随之而来的分岔所确立。什么把一个打开那个范围的冲击与一个那个制度所吸收的冲击区别开来，是当前论文导向它贡献之处，而 §4 陈述它。

批判实在论

那些核心主张是一个区别实在的、现实的与经验的的分层本体论；由诸结构所拥有、并无论其效果是否被现实化都被行使的生成性机制；作为诸层之间关系的涌现；以及，在阿彻的发展中，那个形态生成循环，在其中结构性的条件化先于社会互动，后者转而产生结构性的阐发或再生产 [8, 9, 5]。

那个成就是最接近本文所要求之物的本体论词汇。带生成性力量的诸结构是在它们效果中在场的约束；涌现许可关于诸层而不化约的谈论；而那个形态生成循环是一个关于诸结构如何被再生产与被变换的、严肃而明确地时间性的理论。阿彻的分析性二元论，它把结构与能动在时间中持在分开，以便它们的相互作用能被考察，是对 §3 所遇到并以不同方式回答的那个问题的一个深思熟虑的解决方案。

那些被接受的局限有两个，而第二个是一个区别、而不是一个缺陷。第一个是那个从一个大体波普尔式方向被施压的反对，即那个深层的诸生成性机制是由从被现实化效果的溯因所设定的，而这把那个本体论置于与独立检验的某种距离。那个传统的回应，即溯因支持超出关联的深度解释、并且科学本体论一般而言是如此被设定的，是一个严肃的回应，而那个讨论是开放的。第二个是 GRH 所背离之点。分析性二元论把结构与能动的彼此有别保全为分析的一个条件，而本文取约束与行动为在两个尺度上被观察的同一个场，这封闭那个二元论。那个背离创造一个义务，而 §5 卸除它：尺度分离提供那个时间分离被引入来提供的分析杠杆，同时把诸层当作在不同分辨率上的同一个东西。

卢曼

那些核心主张是：社会系统是运作上封闭的且自创生的，通过它们自己的诸运作再生产它们自身；一个系统的环境扰动它而不指示它；结构耦合命名一个系统据以被弄得对特定诸环境敏感的那个安排；而演化经由变异、选择与再稳定化而进行 [33, 34]。

两个成就关涉本文。约束被当作一个对”什么能在一个系统之内登记为信息”的限制，而这接近 §3 所称的可表达性约束。而自我指涉被置于那个理论的中心、而不是被当作一个有待被管理的异常，而这是对一个”观察者在被观察之物之内”这一情形的正确回应。

两个困难被定期地提出。诸个体属于社会系统的环境、而不属于诸系统本身，这保得那个理论的一致性、并把有意的行动留下没有一个明显的系统变换角色；哈贝马斯施压了这个反对的一个版本 [25]，而卢曼的辩护者回应说那个安置是一个方法论决定、而不是对能动的一个否认。而运作上的封闭，在已解释诸系统为何稳定之后，使对实质性结构变化的解释相应地苛刻。

框架	约束的存在方式	运动之源	就更新所提的困难
马克思	条件化整体的经济结构	诸力量对桎梏诸关系的发展	从桎梏到变换的过渡被描述、未被规定
第二国际	由物质发展所固定的容器	一个外生的、单调的慢变量中的累积	能动被抽空；慢变量不由它所治理的系统所解释
卢卡奇	治理领会的客观性形式	总体性立场的达成	载体要求一个被广泛判定不可支持的同一主体-客体
葛兰西	公民社会中的常识安顿	跨公民诸制度的持久争夺	累积到危机的转换被留在描述的层面
阿尔都塞	只在其效果中在场的结构	一个情势中多重矛盾的融合	情势由那个所发生的融合所规定；能动被约束
分析马克思主义	由其功能契合所选择的诸关系	联系诸关系与发展的后果律	候选诸安排之间的区分要求一个反馈说明
世界体系	一个单一历史体系之内的位置	累积与霸权更替的诸周期	分期被争议；生成机制被规定得不如那个周期充分
后马克思主义	没有必然归属的霸权链接	偶然的重新链接	偶然性被要求去做一个机制的工作
韦伯	由世界图像所铺设的轨道	利益，以观念为扳道工	那个扳道的扳动被设计地留作未规定
年鉴学派	分层的诸持续时间	那些深层的缓慢运动	诸层之间的耦合被规定不足；事件被从属
历史制度主义	可用路径的差异成本	递增回报；规则中的歧义	节点由随之而来的分岔回溯性地被指认
批判实在论	分层诸结构的生成性力量	条件化与阐发的形态生成循环	深层机制由溯因所设定；二元论由方法所保全
卢曼	对”什么登记为信息”的限制	变异、选择、再稳定化	能动被置于环境；封闭使深层变化苛刻

表 1。所概览的诸框架沿 §2.1 的三个维度。最后一列报告文献中就约束更新问题所提的诸困难；凡这些仍被争议之处，§2.2 与 §2.3 报告那个争议。

2.4 那个共同立场与那个入口

上面所汇集的诸成就容许一个沿这三个维度的概括。在约束的存在方式上，那个传统已稳步地从容器移开：结构因果性、生成性力量与结构耦合，全都把约束当作通过它的效果被行使。在运动之源上，若干确定的答案在供，其中诸力量的发展与递增回报的累积是被规定得最充分的。在能动者的认识地位上，已确立的是能动者对他们自己诸条件的通达是系统地受限的，无论是被物化、被意识形态、被询唤、还是被那些深层的持续时间所限。

所概览的诸立场所共有的，是一个共同的停止点，而精确地陈述它是本节的目的。在每一种情形中，约束更新的事实被登记，而那个更新的过程被描述、而不是被机制化。累积被命名而无一个关于”为何累积在一个时刻释放、而在别的时刻被吸收”的说明，如在诸力量的桎梏中、以及在向一个关键节点的趋近中。偶然性被命名为使那个结局敞开之物，而这定位那个缺口、并把它留作敞开。那个情势、那个节点与那个有机危机，在事件之后由随之而来的分岔所指认。这些中的每一个都占据一个机制会占据的位置。

三个要求随之而来，而它们组织以下诸部分。第一个是一个约束的本体论，精确到”它如何改变”这一问题有一个确定的意义，而 §3 提供它。第二个是一个关于”能动者能够与不能够知道关于他们据以行动的诸约束之什么”的说明，因为一个要求能动者去感知他们所正在改变之物的机制，是一个没有历史行动者能够运作的机制；§4 提供它。第三个是一个其中累积与触发被区别开来的动力学，以致一个累积的释放有一个被陈述的条件，而 §5 提供它。其余部分依次尝试这三者。

§3 本体论

§2 以三个要求作结，其中第一个是一个约束的本体论，精确到”约束如何改变”这一问题有一个确定的意义。本节提供它。论述的次序从那个迫出问题的问题，经过现有的诸答案，到本文所作的承诺、那个承诺据以被作出的诸界限，以及较后诸部分所依赖的范畴装置。

3.1 舞台与表演的相互决定

那个问题可以先用一个意象、然后用一个论证被陈述。我们在一个舞台之上行动：一个预先给定的诸可能性格局，在其内我们所做之事被做。那个意象是自然的且几乎不可避免的，而它担保 §2 发现那个传统稳步放弃的那个约束的容器构想。使那个意象不适足之物，是那个传统也登记的一个事实：那个表演重塑那个舞台。在那个格局之内被做之物改变那个格局，而它这样做无需任何行动者跨出去来作出那个改变。

一个外部观察点的缺席

被认真对待，舞台与表演的相互决定封闭一个大多数说明悄然保留的位置。如果那个舞台只从内部被改变，那么就没有一个从其上那个改变被审视的观察点。这对理论有一个后果、对行动者有一个后果，而它们应当被持在分开。对理论而言，它意味着任何设定一个”追踪那个格局、同时立于它之外”的观察者的说明，都已擅取了那个情形所否认之物。对行动者而言，它意味着一个人据以行动的那个格局被那个行动所改变，而那个改变在它发生之时不作为一个观察的对象对那个行动者可用。第二个后果在 §4 中被发展；第一个是当前这一节所关切的。

那个表面悖论底下的结构

那个相互决定有一个悖论的外表：那个舞台条件化那个表演，那个表演条件化那个舞台，而两者都不在先。那个外表一旦这两者被认作在不同的时间尺度上运作便消散。那个舞台在行动的时间尺度上条件化那个表演；那个表演在一个长得多的时间尺度上条件化那个舞台，在其上许多表演的诸效果累积。在一个单一时间尺度上诸量之间的循环决定确实会是恶性的。在一个快量与一个慢量之间双向运行的决定是一个寻常的结构，被彻底研究过，并且是 §5 的主题。

那个悖论消散后所余下的，是一个关于那个舞台是何种东西的问题。如果那个舞台被发生于其上之物所改变，而如果没有行动者立于外部来改变它，那么那个舞台与发生于其上之物就不能是两个外在地被关联的独立种类的东西。这一节的其余部分陈述它们反而是什么。

3.2 现有诸框架的历史本体论

容器构想

容器构想把历史约束当作一个行动发生于其内的有界区域：诸条件被给定，行动在它们之内发生，而诸条件被一个与它们所含行动不同秩序的诸力量所改变。那个构想以这个形式很少被辩护、而频繁地被预设。它的吸引力是它使那个约束确定、使那个分析可处理，因为一个容器能够独立于它所含之物被描述。它的缺陷是刚被陈述的那一个：它要求那个容器的改变由那个容器所持之物以外的某种东西来施行，而在那个历史案例中没有别的东西。

共同构成及其所留下的问题

结构-能动文献放弃了那个容器并把共同构成置于它的位置：结构是它递归地组织的诸实践的媒介与结果，在吉登斯的表述中 [23]，而结构与能动在阿彻的表述中被分析地持在分开，恰恰为了它们的相互条件化能被依序考察 [5]。二者都是相对于那个容器的推进，而二者都留下一个 §2 指认为那个传统之共同停止点的问题。

那个问题是共同构成由什么构成。说结构与行动相互构成，命名一个关系、而既不规定它的机制、也不规定那些项的存在方式。吉登斯的结构之二重性把结构定位于记忆痕迹以及它在实践中的例示，这以”把结构留下在诸例示之间没有一个存在方式”为代价保得那个相互性。阿彻的分析性二元论以”把那些项在时间中持在分开”来保得那个存在方式，以”把作为一个方法论装置被引入之物保全为一个本体论结果”为代价。当前论文取一条第三路线：那些项不是要求一个关系的两个种类的东西，而显现为两个之物是在两个分辨率上被观察的同一个场。

分层的诸本体论

批判实在论对实在的、现实的与经验的的分层，连同作为诸层之间关系的涌现，提供了最被发展的替代方案 [8, 9]。它的收获是约束获得一个独立于它的现实化的存在方式：一个结构拥有生成性力量，无论那些力量是否被行使。它的代价，就当前目的而言，是那些层被区别为实在的诸层级，以致它们之间的关系要求一个携带实质形而上学分量的涌现说明。以下所述保留”约束以一种不同于它的诸实例的方式存在”这一洞见，而把那个区别定位于尺度、而不是层级。

3.3 背景独立的谱

在 §3.4 的承诺能被不带隐喻地陈述之前，一件事必须被表明：一个所要求那种的结构是可融贯地被思考的。所要求的那种是一个与它所条件化之物一同被生成、而不是被它所预设的背景。物理学提供那个证明，而那个证明是此处所借用的全部。社会是否类似于时空不在争议之中，而以下所述没有任何东西依赖于它们如此。

广义相对论中对度规的处理

在牛顿力学中，空间与时间是那个舞台：固定的、预先给定的、并不受发生于它们之内之物影响的。广义相对论移除那个固定性。决定时空诸关系的那个度规本身是一个动力学变量，由场方程从物质与能量的分布所决定，同时那同一个度规决定物质与能量如何运动。两者都不在先；那个几何是一个解、而不是一个设定。

这是背景独立的第一个、并且最弱的意义，而它已足以确立 §3.1 中所争之点。一个格局与发生于其内之物的相互决定，是一个已被成功使用一个世纪的理论的寻常结构。

正则诸进路中的残留流形

引力的诸正则量子化把背景独立推得更远、同时保留一个残余。几何算子获得离散谱，而那个理论被表述得尊重微分同胚不变性，然而一个可微流形作为诸场被定义于其上的竞技场而保留 [46]。相关之点是背景独立容许程度：一个理论可以免除一个固定的度规、同时保留一个固定的流形，而”多少背景已被免除”这一问题是一个实质性的问题。

群场论与因果集中对时空的处理

最强的形式免除那个流形。在群场论中，那些基本自由度是组合的与代数的，被定义于一个没有时空解释的群流形之上，而带其几何的连续时空被期望作为大量这些自由度的一个集体相、经由一个凝聚型的过程而涌现 [41, 42]。因果集理论以不同方式进行，取一个离散偏序为基本，并把连续几何复得为对它的一个近似 [48]。

这些纲领所确立的，就本文的目的而言，是一个单一的原则之点：一个背景可以是某种更基本之物的一个相、而不是它的一个预设。那个舞台无需是一个舞台。它可以是大量关系性自由度在它们处于一个特定集体态时所看上去的样子，而”它们处于何种态”这一问题成为一个带一个确定意义的合法问题。

那个借用的范围

那个借用在此停止，而陈述它的界限是作出它的一部分。三样东西被取。第一个是刚给出的那个证明，即一个被生成的背景是一个融贯的建构、而不是一个修辞。第二个是一个词汇：相、序参量、凝聚、集体态。第三个是一个警告，在 §3.5 中被发展，关于那个社会案例所缺、而这些纲领所拥有之物。

三样东西不被取。没有主张说社会关系满足这些理论中任何一个的方程、或任何类似它们的方程。没有主张说那个类比许可结果的转移：关于时空涌现所确立的没有任何东西因此就关于历史约束被确立。而没有数值的或结构的对应被断言于这两个领域之间。那个借用是一个存在证明与一个词汇，而随之而来的诸节如此使用它。

3.4 那个本体论承诺

那个相主张的陈述

那个承诺现在可以被陈述。

主张 1（那个相主张）。 历史约束是关系场的一个宏观相。它是大量关系在它们处于一个特定集体态时所看上去的样子，而它的诸属性是那个态的诸属性。它占据一个容器被想象为占据的位置，而它作为对那些关系本身、在一个个别关系不被分辨的尺度上的一个描述来占据那个位置。

那个主张中有三个术语要求定义，而那些定义在此被给出、而不是被假定。

那个关系场是在一个历史处境中的诸参与者之间成立的诸关系的总和，连同那些关系相互条件化的方式一起取来。母框架的关系首要性在此做工作：那个场不是从随后进入诸关系的先在诸个体建立起来的，因为个别化一个参与者之物是它在那个场中的位置。那个场是那个原始。

一个相是大量组成部分的一个集体态，由属于那个聚合、而对任何单独取来的组成部分无定义的诸属性所刻画。那个术语被以它的技术意义使用，而那个主张不是一个隐喻。相的两个特征在此要紧。一个相拥有序参量，即被定义于那个聚合之上、规定哪一个集体态成立的诸量。而一个相能够改变：同样的诸组成部分，在被改变的诸条件之下，能够安顿进一个带不同宏观属性的集体态。

约束是那个关系场凭借它所处于的那个集体态、为它之中的一个参与者所使成为不可能、不可说、或不可排名之物。三种模式在 §3.6 中被区别开来。要害之点是约束描述那些关系本身，在一个个别关系不被分辨的尺度上。

舞台与行动者在那个主张之下的分量

那个相主张消散 §3.1 的问题、而不是解决它。如果约束是那个场的一个宏观相，而行动是发生于构成那个场的诸关系之间之物，那么舞台与行动者就不是两个必须在其间找到一个关系的种类的东西。它们是在两个分辨率上被描述的同一个场：约束是被粗粒化的那个场，行动是被分辨的那个场。那个显得悖论性的相互决定，是一个系统中一个粗略描述与一个精细描述之间的寻常关系，在其中粗略诸量是精细诸量的函数，而精细诸量在粗略诸量所规定的诸条件之下演化。

这对 §2.3 的分析性二元论有一个即刻的后果。把结构与能动在时间中持在分开，对一个否认它们是彼此有别种类的框架不可用，而那个时间分离被引入来提供的杠杆必须由别的手段被复得。那个手段是尺度分离，而 §5 提供它。那个义务在此被记录，以便它的卸除能被查验。

那个约束场

那个主张许可一个贯穿本文其余部分被使用的记法。设 $\Gamma$ 记那个约束场：那个关系场的被粗粒化的态，那个其诸属性构成对诸参与者而言什么是可能、可说、可排名之物的宏观相。$\Gamma$ 命名在粗粒化之下的那个关系场，而它的动力学，在 §5 中被处理，是那个场在那个分辨率上的动力学。凡较后诸节以 $\Gamma$ 写方程之处，那些方程的主题是这一节所定义之物。

那个承诺所耗费之物

那个相主张是本文的主要风险，而那个风险应当被陈述、而不是被管理。如果约束是技术意义上的一个相，那么序参量为它而存在，而”一个给定历史处境占据哪一个相”这一问题有一个确定的答案。如果没有任何这样的序参量存在，甚至在原则上，那么那个术语是在做隐喻的工作，而建基于它的诸节失去它们的支持。本文不为任何历史案例展示一个序参量，而 §3.5 解释为何它主张没有任何一个能从内部被展示。那个组合，即一个对某个量之存在的承诺连同一个”那个量不可由诸参与者计算”的论证，是一个实质性的立场、而不是一个回避，而 §8 把它的指认列为第一个研究方向。

3.5 那个纲领的诸界限

三个界限界定刚被陈述的那个本体论能被发展成什么，而它们有彼此有别的来源。命名那些来源比列出那些界限更有用，因为它表明哪些是被承袭的、哪些独属于那个社会案例。

那个构成性界限：没有独立地被促动的对称性

第一个界限是从那个构成性借用被承袭的。在那些物理纲领中，一个背景从更基本的诸自由度中的涌现被对称性所约束：那个群结构被独立地促动，而它约束哪些集体态是可容许的。那个社会案例没有这样一个群。扮演相应角色之物，如果有任何东西扮演，会是一组在关系性语法的改写之下被保全的不变量，而没有任何这样一组被指认。其后果是 §3.4 中所主张的那个涌现是被结构地主张的、而不能被推导。§8 把不变量的指认陈述为一个开放问题。

那个动力学界限：没有闭合

第二个界限是从 §5 的那个动力学借用被承袭的。其演化由非线性自输运所治理的诸系统，不容许在粗粒化层级上的闭合描述：对运动方程取平均产生涉及更高阶关联的诸项，而那个谱系不终止。那个社会案例承袭这，而 §5.10 论证它作为一个普适特征、而不是作为一个特殊缺陷来承袭它。其后果是没有任何 $\Gamma$ 的闭合方程系统可用，而没有一个被提供。

独属于社会案例的那个界限：自我指涉

第三个界限独属于那个社会案例，而两个物理借用都不提供一个先例。那个关系场中的诸参与者读他们据以行动的那个约束，而他们的读法作为一个进一步的关系进入那个场。那个度规，在那个物理案例中，不咨询它自己的值。此外那个读法是多值的：两个参与者可能不同地读同一个格局，而两个读法都成为有待被描述之物的一部分。这是卢曼关于自我指涉之点 [33]，在此作为一个界限、而不是作为一个资源被录入。其后果是那个把 $\Gamma$ 关联到底层场的粗粒化不是一个固定的映射，因为诸参与者取那个约束为什么，是那个约束所依附于其上之物之列。

这三个界限合在一起，以一种比一份无差别的诸警告清单所会允许的更大的精确性陈述那个社会案例的困难：那个社会案例携带一个没有先在存在的背景的构成性问题、一个输运它自身的系统的动力学问题，以及一个两个物理案例都不面对的自我指涉问题。

一个作用量原理的排除

一个进一步的排除从那些界限随之而来，并被分开地陈述，因为它所保护之物。给定 §3.3 中所借用的那个词汇，去为那个关系场寻求一个作用量泛函，从它的驻定性动力学会随之而来，会是自然的。本文拒绝这样做，而那个理由不是技术困难。一个作用量原理提供一个那个系统的诸轨迹极值化之量，而一个被这样一个量所装备的历史理论已承诺于一个历史所最大化的量值。那就是框架颇费力气去排除的那个形式的目的论：不是”历史有一个目标”这一公开的主张，而是那个从其中这样一个主张能被复得的形式装置。§8 返回到那个针对目的论的边界；那个排除在此被记录，因为它约束 §5 可以写下之物。

3.6 约束与目标的联合分类

其余诸节的装置要求两个分类，而它们必须被一同给出。一个单独的约束类型学把”约束如何进入动力学”留作未规定，因为把一个格局转换为一个行动进程之物，是在它之下被形成的诸目标。一个单独的目标类型学把诸种类目标之间的区别留下没有本体论根基，因为把它们区别开来之物，是它们操作于其上的诸约束。这两者在此、在那个本体论中、被给出，因为诸目标决定约束如何进入动力学，因此属于那个历史过程的本体论、而不是它的伦理学。

按持守方式分类的诸约束

诸约束由它们所持守的方式、而不是由它们被实现于其中的基底所区别。一个按基底的类型学，把物质的与制度的与象征的诸约束区别开来，会与那个相主张相矛盾，后者主张所有这些都是同一个场的诸态。三种模式被区别开来。

可能性约束决定什么不能被做。物质的与技术的诸界限是最清晰的实例。这个模式是三者中改变最慢的、并且是对它所约束的动力学最近乎外生的。

可表达性约束决定什么不能被说，特别是什么不能被表述为一个目标。一个不能在可用词汇之内被清楚陈述的行动进程，以一种不同于物理不可能的方式不可用，而那个区别要紧：那个可表达者的边界移动，而它的移动是本文把约束更新的主要工作定位于其上的那一层。

可评价性约束决定什么算作更好。它们包括诸行动进程据以被排名的诸标准，而它们构成优化据以进行的那个评价泛函。这个模式在三者中改变最快，并且是那个目标本体论化、在 §6 中被处理、所改写的那一个。

这三者有不同的弛豫时间，并耦合于 §1 中所列出的那个回路的不同段。它们是一个场的三种模式、而不是三个种类的东西，正是那个相主张所保得的。表 2 列出它们。

模式	它所持守之物	相对弛豫时间	在本文中的分量
可能性	什么不能被做：物质的与技术的诸界限	最慢	对它所约束的动力学大体外生
可表达性	什么不能被说，特别是什么不能被表述为一个目标	中间	约束更新主要发生于其上的那一层
可评价性	什么算作更好：诸行动进程据以被排名的诸标准	最快	目标本体论化所改写的那个评价泛函

表 2。按持守方式分类的诸约束。那个类型学按持守方式、而不是按基底切分，因为一个按基底的类型学会与那个相主张相矛盾。

按表达地位分类的诸目标

诸目标首先由它们相对于表达的地位所区别。

结构性目标是可表达的、可排名的、可优化的。财富、产出、权力、生存、效率、利润及其制度性代理是实例。它们直接进入那个评价泛函，而它们构成经济学、控制理论与功利主义规范理论以完全的合法性运作于其中的领域。本文不争议那份合法性中的任何一部分，而 §6 只争议那个领域向整体的扩展。

非结构性目标是规范上有效的、并在被陈述为目标时取消它们自身。经典的实例是”居于别人所鄙夷的低处”这一告诫，其特征是没有任何目的被那种居所所服务；被追问一个证成，人们只能说它是合宜的。信任、谦逊、慷慨与真诚共享那个结构，并共享一个诊断特征：它们越被彻底地优化，它们越被彻底地消失。为了被信任而信任、为了显得谦逊而表演的谦逊、以及为了抬高一个分数而做的艺术，各自都以一种与那个能动者的真诚毫无关系的方式自我挫败。所被挫败的是那个东西本身，被那个追求的形式所挫败。

生成性目标是有方向而不是有终点的。它们的逻辑是可能性的制造、而不是一个态的抵达：探索、游戏、漫游、遭遇、冒险、创造。它们向那个场注入没有任何评价泛函排名过的诸格局，而在 §4 中所规定的诸条件之下，此类格局能够被放大为那个约束场本身的诸改变。

关于那个名称需要一则说明，因为一个较早的表述称这些为随机目标。那个名称误描述它们。不可预测的是那个历史效果，而那个目标本身可能是完全确定的：人们可以带着关于自己在做什么的完全清晰去着手探索未知。此外，随机性蕴涵无结构性，而此处的主张是这些目标是有方向的，它们在缺乏一个终点态、而不是在缺乏方向上不同于结构性目标。探索有一个形式。名称生成性与母框架相连续，并记录那个范畴所做之事。

按动力学角色分类的诸目标

第二个轴把一个角色指派给每一个目标在那个约束场的动力学中，而它是那个分类做它工作所在的轴。

注入生成新的关系性格局，向那个场添加原本不在那里之物。输运跨尺度携带诸格局而不生成或固定它们。耗散把诸格局固定成规则，通过使它们被安顿而把它们从动力学中移除。

这两个轴相交，而那个相交产出这一节所为的那个结果。结构性目标主要作为耗散而作用：优化就是固定，而被优化之物停止变化。生成性目标作为注入而作用，而一个终点态的缺席恰恰是那个使它们成为一个源、而不是一个汇之物。非结构性目标作为输运而作用：它们持守诸格局能移动所跨的那个范围，既不生成也不固定。这最后一个指派在此从那个分类被导出，而 §6 把它取为被确立、而不是假定它。表 3 给出那个相交连同下文所处理的那个互锁。

目标的类型	表达地位	动力学角色	所涉及的约束模式
结构性	可表达、可排名、可优化：财富、产出、权力、生存、效率、利润	耗散	可评价性：在一个排名之下作用，并在极限处改写它
非结构性	规范上有效、并在被陈述时自我取消：信任、谦逊、慷慨、真诚	输运	可表达性：持守尚未被表述之物
生成性	有方向而不是有终点：探索、游戏、漫游、遭遇、冒险、创造	注入	在全部三者之下，因为所注入之物尚未获得地位

表 3。按表达地位与按动力学角色分类的诸目标，连同每一个所涉及的约束模式。这三者由动力学角色、而不是由内容所区别。

那两个分类的互锁

这两个类型学在确定的诸点上啮合。结构性目标操作于可评价性约束之上，因为优化就是在一个排名之下作用、并在极限处改写那个排名。非结构性目标关涉可表达性约束，持守尚未被表述、并且不能不被摧毁就被表述之物。生成性目标操作于全部三种模式之下，因为它们所注入之物尚未获得那个会把它置于它们中任何一个之下的地位。

那个互锁正是那个提供 §3.6 开端所要求的本体论根基之物。诸种类目标之间的区别是一个动力学角色的区别，而那些角色由每一个所涉及的约束模式所个别化；内容以及持有它们者的心理学把那个分类留如不动。诸目标，依此说明，属于那个历史过程的本体论：它们是那个场的粗略态据以条件化那个精细动力学、以及那个精细动力学据以改变那个粗略态的机制。

关于”生成性”一词的一则说明

那个框架以生成性命名，而一个目标范畴被命名为生成性，而这两种用法必须被区别开来。框架层级的生成性是一个系统的一个属性：继续产生不可从当前格局导出的诸关系与诸约束的能力。生成性目标命名那一类其动力学功能是注入的目标。它们之间的关系是生成性目标是系统层级生成性的一个贡献者，而 §6 论证它们单靠自己对它是不充分的，因为没有输运的注入在它传播之前就被阻尼。两个术语都被保留，而每一个被使用于其上的层级在凡歧义可能生起之处被标出。

§4 认识论

在 §2 结尾所陈述的第二个要求，是一个关于”能动者能够与不能够知道关于他们据以行动的诸约束之什么”的说明。那个要求不仅仅是一件完备性之事。一个要求能动者去感知他们所正在改变的那个约束的约束更新机制，是一个没有历史行动者能够运作的机制，而 §4.5 中所给出说明的可信性依赖于首先被给出的那个认识论。

那个传统在这个问题上有一个已确立的立场，而 §4.1 陈述它。此处所取的立场在它的解释、而不是在它的裁决上有别：能动者对他们自己诸条件的通达是受限的，而那个限制出自诸尺度的结构、而不是出自能动者的一个失败。

4.1 现有诸框架的历史认识论

意识形态与意识批判

唯物主义传统的核心认识论论题是：意识被社会位置所条件化，而那个条件化系统地扭曲。在它的早期形式中那个论题关乎那个倒置，凭它人类活动的诸产物把自身呈现为独立的诸力量；在卢卡奇中它成为那个物化说明，在其之下商品形式一般化为一个使那个过程显现为一堆物的客观性形式 [35]；在阿尔都塞中它成为询唤，凭它诸个体被构成为在那个结构所指派的诸位置中认出自身的诸主体 [3]。

那个成就是”认识通达是内在于那个历史过程的”这一认识。一个能动者能够知道关于行动之诸条件之物，本身是被条件化的，而那个条件化是结构性的、而不是偶然的。本文不加限定地保留那个认识。

那个背离之点关乎那个限制的模态。在这些说明中的每一个中，那个限制携带一个规范性的电荷：它是一个扭曲、一个虚假意识、一个遮蔽，而它的移除是一个批判的目标。那个限制在原则上是可补救的，而那个过程显现为一个过程所从其上的那个立场的达成，是那个补救所采取的形式。§4.2 论证那个限制的一个实质部分不可由任何批判所补救，因为它出自尺度、而不是出自位置。

效果历史意识

诠释学传统经由一条不同的路线抵达一个相关的限制。理解发生于一个理解者所未建构的视域之内，中性意义上的诸偏见是理解的条件、而不是对它的障碍，而对被历史所影响的意识同时是一个”那些效果不能被完全地带到意识面前”的承认 [18]。

此处的成就是那个规范性电荷的移除：那个理解者的处境性是理解的一个条件、而不是它之中的一个缺陷，而对一个”来自无处的看法”的要求，作为不融贯的、而不是作为仅仅困难的被搁置。本文在那一点上追随诠释学传统，并在另一点上背离。那个诠释学的限制是对意义之理解的一个限制，而它的来源是有限性。以下所论证的限制是对一个量之可观测性的一个限制，而它的来源是诸时间尺度之间的关系。这两者是相容的，而它们是不同的。

那个被共享的预设

两个传统，尽管有它们的一切区别，都预设那个认识困难是一个更好的定位会改善的种类。批判允诺那个总体性立场；诠释学允诺一个加宽可被理解者的视域融合。在每一种情形中，那个限制是那个能动者所立于何处的一个函数，而移动是可能的。

以下这一节论证那个限制的一个组成部分在任何一个参与者可用的移动之下都是不变的。它是那个观察关系本身的一个属性，而它会为一个免于意识形态、并拥有关于当前的每一个相关事实的能动者持续。

4.2 盲目的结构性推导

那个参与者的平均场位置

考虑一个参与者在 §3 所定义的那个关系场中的认识位置。那个参与者立于一个确定而少数的诸关系之中，并在它们之内行动。那个参与者在行动中所遭遇之物，是那个局部格局：在此处成立的那些具体关系，以及其他一切之物的聚合效果，后者作为一个一般条件、而不是作为一组被分辨的关系而到来。

这是物理学中被描述为一个平均场位置的情形。一个大系统的一个组成部分与它的直接邻居各别地互动、而与其余部分只通过一个被平均的影响互动。那个被平均的影响是那个系统的序参量被定义于其上之物，而它恰恰是一个处于这个位置的组成部分所不能分辨之物。那个组成部分把那个平均场登记为它自己动力学的一个条件；那个序参量的值，它是那个聚合的一个属性，向它显现为事情所是的样子。

这个描述向那个历史案例的转移要求 §3 的本体论、而不要求更进一步之物。一旦约束是那个关系场的一个宏观相、而不是一个外在于它的对象，那个参与者对约束的关系就是一个组成部分对它所是其一部分的那个集体态的关系。那个参与者在那个约束之下行动并向它贡献，并把它遭遇为那些局部关系成立于其内的那个一般条件。

那个慢变量的时间尺度

一个第二考虑复合第一个。一个大系统的宏观态缓慢地弛豫，而那个弛豫时间随那个被关联区域的广度而增长。凡一个态跨一个大领域是相干的之处，那个态响应一个局部扰动所要求的时间，相比于那个扰动发生所在的时间是长的。

被应用于那个历史案例，这给出约束为何慢的理由。可能性约束、可表达性约束与可评价性约束是跨大人口相干的诸态，而它们的响应时间相应地长。随之而来的是两个时间尺度之间的一个关系，而那个关系是那个要紧之物：一个参与者据以行动、审议与观察的那个区间，相比于那个约束据以响应的那个区间是短的。在那个更短的区间之内，那个约束呈现为固定的。

那个结果的陈述及其模态

这两个考虑合在一起产出一个结果。

主张 2（对慢变量的盲目）。 那个关系场中的一个参与者无法观察那个约束场的态或它的位移，而那个无法出自那个参与者相对于尺度的位置。一个慢变量的位移在那个参与者据以行动的诸快变量的时间尺度上是不可观测的，而那个聚合的态从一个它之内的位置是不可分辨的。

三个限定决定那个主张所断言与所不断言之物。

那个主张关乎一个参与者从内部的观察，而把一个较后的观察者的位置留如不动。历史学家例行地并正确地重构约束位移，而他们从一个在那个弛豫已完成之后的位置这样做。那个主张是那个位移在行动之时不可用，而它与那个位移在事后是显然的相一致。

那个主张关乎一个量、而不是一个意义，这把它与那个诠释学限制区别开来、并使它与那个限制相容。一个能动者可以很好地理解一个处境的意义，而仍然无法观察那个处境构成其一部分的那个聚合的态。

那个主张是结构性的，这是那个把它与那个传统对意识形态的说明区别开来之物。意识形态批判提议一个对意识的限制可以通过达成一个不同的立场而被解除。此处所描述的限制为任何参与者、在任何立场、无论多么免于扭曲而持续，因为那个限制附着于那个参与者据以行动的尺度与那个约束被定义所在的尺度之间的关系。一个知道关于当前格局的每一个相关事实的参与者，仍然会立于一个大系统中的一个确定之处，并仍然会在一个相比于那个聚合的响应是短的时间尺度上行动。

4.3 那些被移植的概念及其内容

三个概念现在已被使用，而每一个都携带一个确定的技术内容，该内容应当被陈述，以便那个转移的范围能被评估。这些是统计物理、而不是 §3.3 的诸构成性纲领的概念，而它们在此的使用独立于那个借用。

一个序参量是一个被定义于一个聚合之上、规定那个聚合占据哪一个集体态、并对任何单独取来的组成部分无定义或无信息的量。它向当前设置的转移把约束与那个关系场的序参量相认同：什么约束模式成立、以及有多强，是那个集体态的一个规定。

一个平均场是一个聚合对它的组成部分之一的被平均的影响，代表每一个别的组成部分的被分辨的影响。它的转移认同那个参与者的认识位置：一个参与者遭遇为行动之一般条件之物，是那个关系性聚合的平均场。

一个相变是一个聚合的集体态的一个改变，在其中宏观属性改变、同时诸组成部分保持它们所是。它的转移认同约束更新：诸参与者及其诸能力持续，而它们所构成之物改变态。

那个转移的诸界限在 §3.5 中被陈述，并在此不加修改地成立。特别地，没有任何序参量为任何历史案例被展示，而 §4.2 刚论证没有任何一个对一个参与者可用。那个转移所提供的，是一个”那个约束场为拥有一个确定的态所会被要求之物”的规定，以及一个关于”那个态为何从内部不可用”的说明。

4.4 三个后果

约束位移的回溯性可用

第一个后果立刻随之而来。能动者在那个移动已发生之后发现那个约束已移动，而那个发现采取”认出先前困难之物已成为寻常、或先前可说之物已停止如此”的形式。那个认出是可靠的，并且由结构必然性、而不是由不留意而来得晚。

这对那个史学处境有一个推论。那个较后观察者相对于那个参与者的优势是一件相对于那个弛豫的位置之事、而不是一件更优洞见之事，而把诸参与者”未能看见正在发生什么”读作一个智力或胆识的失败的诱惑，依此说明，是一个错误归属。

副产品原理

第二个后果直接关涉约束更新的问题。一个为达成一个目标而被着手的行动进程，生成超出那个目标所规定者的诸关系。那个生成是不可避免的：把人、材料与程序朝一个目的组织起来，就是把一个关系的格局带入存在，而没有任何目标完全地规定那个格局。如此被生成的诸关系，按构造，不被那个引起它们的目标所描述。

主张 3（副产品原理）。 一个目标的实现生成那个目标所不描述的诸关系，而正是在这些副产品之中、而不是在那些被描述的成就之中，那个约束场的诸位移起源。

那个原理回答一个那个传统留在一个尴尬位置的问题。如果约束更新经由诸目标的达成而进行，那么那个约束会在诸目标所规定的方向上被修订，而历史会是在那个框架层级上被实现的诸意图的记录。历史记录不支持任何这样的读法。那个副产品原理把那个更新定位于别处：在追求诸目标所带入存在、而不加描述之物中。

那个原理如所陈述是不完备的，而那个不完备值得在 §4.5 提供那个补救之前被标出。副产品被持续地并以巨大的数目生成，而它们中的几乎全部都无踪迹地被吸收。一个指认约束更新之场址的原理，把”在那多数之中，哪些副产品是那个更新所经由的”这一问题留作未回答。

那个余项的分量

第三个后果指认一个那个规范性部分将要求的范畴。§3.6 引入了可表达性约束与非结构性目标，而 §4.2 现在已提供那些范畴所依赖之物。在任何历史格局中，存在那个关系场的一个维度，即诸参与者所不能表示的：由 §4.2 的论证从内部不可分辨，并由 §3.6 的论证不可用于作为一个目标的表述。称这个维度为余项。

那个余项不是神秘的，而刚给出的那个认识论正是那个移除那个神秘之物。它是那个场的聚合态，连同它的诸自由度中那个盛行的评价泛函所不排名的那些。它的不可通达是那个参与者位置的一个后果、而不是那个东西中的一个晦涩。§6 论证诸规范保护这个维度而不表示它，而那个论证恰恰要求此处所已确立之物：那个维度是真实的、它是有后果的、而它对那些其诸规范保护它的诸参与者不可用。

4.5 从一个稳定历史舞台的离开

那个问题

一个问题立于 §2 之大部分背后，而很少被直接提出。一个在它诸约束之内优化的社会形态随时间成为更好地适应那些约束的：§3.6 的诸结构性目标被追求，那个评价泛函被服务，而那个格局被渐进地调谐。这样一个系统应当安顿。那么，为何任何历史形态离开它的被安顿态？为何封建欧洲让位，为何资本主义未能抵达一个格局并停留于其中，而为何革命竟发生？

那个传统提供三个答案，而 §2 记录了它们：矛盾的累积、生产力的发展与偶然性。每一个都指认那个处境的一个真实特征，而每一个都以一种现在能被精确地陈述的方式止步于一个机制之前。

矛盾的累积说张力累积，而把”为何那个张力在一个时刻释放、而在别的时刻被吸收”留作未陈述。诸力量的发展指认一个慢变量，而把它当作对它将推翻的那个格局外生的、并在它的方向上单调的。偶然性正确地把那个触发因素定位于某个特定而未被预见之物，而不提供一个关于”为何这个触发因素传播了、而一千个可比的被阻尼了”的说明。

那个所提议的机制

那些元素现在就位。§3.6 的目标分类提供三个动力学角色；§4.2 的认识论提供那个参与者的位置；而那个副产品原理提供那个更新起源所在的场址。

主张 4（离开的机制）。 生成性目标向那个关系场注入那个盛行的评价泛函所不排名的诸格局。非结构性规范维持一个此类格局能传播所跨的范围。凡那个约束场立于一个稳定性边界附近之处，一个如此被注入并如此被传播的格局能够被放大，直到那个场过渡进一个不同的相，而那个系统离开它曾占据的态。

那个机制有三个组成部分，而它们之间的分工正是那个把它与刚被评述的诸答案区别开来之物。注入提供那个材料：原本不在那里、并且那个排名所不捕获的诸格局。输运提供那个传播：没有一个被注入的格局能移动所跨的范围，注入被局部地阻尼、并在尺度上没有后果。放大提供那个过渡：那个场自己动力学的非线性性质，在 §5 中被处理，正是那个把一个小格局转换为一个相之改变之物。

触发因素与原因

一个对那个机制的条件必须立即被陈述，因为没有它那个机制主张得过多。

主张 5（临界性条件）。 一个扰动只在那个约束场已经立于一个稳定性边界附近之处才被放大为一个相之改变。远离这样一个边界，被注入的诸格局被阻尼，而那个形态对同样量级的、在附近会具有决定性的诸扰动是稳健的。

那个条件对历史因果应当如何被描述有一个即刻的后果。那个扰动是一个转变的触发因素，而决定一个转变是否发生之物，是那个系统已经抵达的态。两个历史变化之源因此被区别开来，而它们在不同的时间尺度上、并通过不同的能动者运作。

结构性累积是那个约束场朝一个稳定性边界的缓慢位移。它经由那个形态的寻常运作而进行，它由主张 2 对诸参与者是不可观测的，而它本身产生不了可见的变化。

生成性触发是一个格局的注入，该格局，给定累积所已抵达的态，被放大。那个触发因素无需是大的，也无需以任何方式与那许多被阻尼的可比事件区别开来。把它区别开来之物，是它所进入的那个场的态。

历史，依此说明，是这两者的联合产物，而必然性与偶然性都不单独描述它。累积所抵达的态决定任何触发因素能否成功；那个特定的触发因素决定那个时刻与那个方式。

那两个过滤器

那个机制选取两次，而那两个选取应当被持在彼此有别，因为它们回答不同的问题，而每一个单独都是不充分的。

第一个过滤器决定存活。一个那个盛行的评价泛函排名的格局被作用于：它被优化、被制度化、并因此被固定，也就是说从动力学中被移除。一个那个泛函所不排名的格局被留如不动，而它之被留如不动正是那个允许它以一个未被固定的态持续之物。没有目标形式之物逃脱那个会安顿它的机制。

第二个过滤器决定放大。存活交付一个仍然可用的格局；它是否传播依赖于那个场的态，由主张 5。同一个格局，在内容上相同、并同样不被排名，在一个远离它稳定性边界的形态中是惰性的，而在一个它附近的形态中是决定性的。

陈述二者正是那个把那个机制与那个现象的一个重述区别开来之物。第一个过滤器解释为何那些要紧的格局是从那些指标所不度量之物中被抽取的。第二个解释为何此类格局的绝大多数仍然一无所成。

量变与质变的三阶段读法

那个机制产出一个对量变与质变之关系的读法，它回答一个那个经典表述留作敞开的问题：为何量变应当在一个点产生一个质变、而在每一个在先的点都未能。

在第一个阶段那个形态占据一个稳定态。它的恢复能力高，扰动被吸收，而历史记录显示连续性。在第二个阶段，长期的量变把那个约束场朝一个边界位移。恢复能力下降、同时那个宏观格局继续呈现为稳定，而那个下降对诸参与者不可观测。在第三个阶段，一个寻常量级的扰动被放大，那个边界被越过，而一个不同的相被确立。

量变，依这个读法，获得一个具体的指称对象。它的内容是那个约束场的位移以及相关联的恢复能力的下降，而不是更多某种东西的一个累积。而那个最终事件被卸下一个它从未能够承载的负担：那个准备性的工作属于那个第二阶段，它可能已占据数十年或数世纪，而那个触发因素贡献那个时机。

那个读法是作为对一个已被以许多方式读过的表述的一个解释被提出的，而它的凭据是它提供那个缺失的条件。它给量变一个确定的动力学内容，而它陈述为使那个质变随之而来什么必须为真。

对那个参与者位置的后果

主张 2 与主张 5 合在一起产生一个比任一个单独都更尖锐的结果。那个约束场对一个稳定性边界的邻近，是那个聚合与那个慢变量的一个属性，而它因此恰恰因 §4.2 中所给出的诸理由对诸参与者不可观测。诸参与者无法确定他们是立于一个稳定格局的深处、还是在一个转变的边缘。

其后果是一个相同的行动携带全然不同的历史分量，取决于一个它的作者所不能评估的条件。同一个示威、同一个出版、同一个拒绝，在一个十年中无踪迹地被吸收，而在另一个十年中成为一个转变的契机，而那个区别驻于那个场的态、而不是驻于那个行动的任何属性。

这解释了历史记录中一个否则令人费解的模式。诸事件回溯性地获得它们作为转折点的地位，而诸参与者未能认出他们所正在做之事的重要性，是那个正常的情形、而不是那个例外的情形。它也解释了大转变的那个特有的时间签名，它们显得不可能直到它们显得曾是不可避免的之前不久。两个描述都正确，而它们是同一个过程的不同阶段、从一个不能预先把它们区别开来的位置被观看的描述。

那个机制的区分能力

那个机制必须被对照那个在 §2.2 所记录的交流中击败了功能性解释的反对而被检验。如果注入后跟放大解释从任何稳定形态的离开，那么它平等地解释每一个转变，在没有一个之间区分，并赢得不了什么。

那个临界性条件提供那个答案的第一部分，因为它蕴涵大多数注入产生不了什么，而那个机制至少与它预测变化一样经常地预测稳定。那个两过滤器结构提供第二部分，因为它蕴涵那些转变所经由的格局是从一个可规定的区域被抽取的：那个场的、那些盛行指标所不度量的部分。

这两者合在一起产出能被辜负的诸期望。转变应当被一个恢复能力的下降、而不是被扰动量级的一个增加所先行。它们应当起源于那些盛行的评价泛函所不排名的领域、而不是起源于那个形态最贴近地度量与管理的诸领域。而那些其制度化已消耗了诸格局传播所跨的范围的诸形态，应当展现更大的稳定性连同一个被减损的生成新约束的能力，而这是一个 §6 的说明所要求、并且观察能够反驳的合取。

那个机制的分量

一个对那个主张的边界关闭这一节。历史系统一般而言在物理科学给予那个术语的意义上展现临界性，这是未被确立的，而本文不断言它。所提议的是一个机制性的假说：历史约束的大更新，在那个约束场立于一个稳定性边界附近之处，比在它远离一个之处更可能，而主张 3 至 5 的机制描述此类更新在它们竟进行之时如何进行。

那个假说与 §1 中所声明的分量相一致。GRH 规定一个过程而拒绝预测诸结局，而那个临界性条件是一个关于”一个过程运作于其下之诸条件”的陈述、而不是一个治理历史诸形态之更替的律。§5 给那个机制它的形式设置，并比在此处曾可能的更精确地陈述为使那个假说为真什么必须成立。

§5 多尺度历史动力学

在 §2 结尾所陈述的第三个要求，是一个其中累积与触发被区别开来的动力学，以致一个累积的释放有一个被陈述的条件。§4 以言辞给出了那个机制。本节给它一个形式。

来自较早诸节的两个义务也在此被卸除。§3.4 记录了一个否认结构与能动之彼此有别的框架，欠一个对”把它们在时间中持在分开被引入来提供的那个分析杠杆”的替代；§5.3 提供它。§3.5 记录了那个粗粒化描述不容许闭合；§5.10 陈述随之而来者。

5.1 那个建模的对象与抱负

一个机制理论

以下所述规定一类结构、以及对拥有那个结构的诸系统可用的行为。它不规定一个系统，而它不拟合任何参数。那个区别对以下诸方程应当如何被读要紧：它们陈述一个动力学的形式，而附着于它们的主张是历史约束以一种有这个形式的方式演化，而不少东西单从那个形式随之而来。

那个借用的范围

来自流体动力学的借用被限于结构。三个特征被取：一个凭它一个场输运它自身的非线性项、一个跨尺度的活动转移连同一个转移在其中不经生成或移除而发生的范围，以及那个移除进稀疏而间歇的诸结构的一个集中。所被留下之物是一切使流体运动方程成为一个流体的方程之物：质量与动量的守恒、一个态方程、应力的本构关系，以及给那个理论它的预测能力的量纲分析。

那个区别可以被表述为一个读以下诸节的规则。凡那些方程的一个结构性特征被使用之处，那个论证系于社会系统是否拥有那个特征而成败。凡流体力学的一个定量结果可能被援引之处，它不被援引，而 §5.7 陈述那个诱惑最强、而那个拒绝最必要的那一个情形。

三个形式承诺等级

本节中的形式陈述携带三个等级之一，而每一个在它出现之处被标出。

一个陈述是示意性的，当它展示一个关系的形式而不许可计算：那个方程展示哪些项在场以及它们如何进入，而没有解被主张。一个陈述是结构性的，当它断言一个系统拥有一个为一类动力系统所定义的属性，如多个吸引子或一个谱隙。一个陈述是类比性的，当它转移一个来自那个物理案例的、其社会对应物尚未被建构的建构。示意性的与结构性的陈述承载那个论证。类比性的陈述例示，而 §5.7 是唯一的延伸实例。

5.2 非线性自输运

那个自输运项的结构

在流体运动方程中，一个流体微团的加速度包括一个凭它那个速度场输运它自身的项。示意性地写出，那个速度 $\mathbf{v}$ 的演化含有

$$\partial_t \mathbf{v} + (\mathbf{v}\cdot\nabla)\mathbf{v} = \ldots$$

其中被略去的诸项携带压强、黏性与任何外部强迫。左边的第二项是那个所关切的。它在那个场中是二次的，而它说那个把那个场从一处携带到另一处之物是那个场本身。没有外部能动者移动那个流体；那个运动重新分配它自身。

那个项的两个后果在此相关。它是那个非线性之源，从它这些系统的特有行为随之而来，包括在某些条件之下对小扰动的敏感、以及在别的条件之下的完全不敏感。而它使那个系统的演化不可用于分解为一个背景加上一个对它的扰动，因为那个扰动参与它自己的输运。

那个约束场的自输运

那个社会对应物被示意性地写出：

$$\partial_t \Gamma + (\Gamma\cdot\nabla)\Gamma = \ldots$$

以 $\Gamma$ 为 §3.4 中所定义的那个约束场。那个陈述在 §5.1 的意义上是示意性的：它展示一个形式，而没有解为它被主张。那个形式所断言的，是诸关系据以被形成的那个格局，被它所配置的那些关系所携带，而那个携带在那个场中是二次的、而不是在某个外部驱动中是线性的。

被略去诸项的读法追随 §3.6 的分类。注入作为一个源进入，由生成性目标所提供。耗散作为一个汇进入，由结构性目标所发为的那个制度化所提供。那个输运是那个被写出的项，而非结构性规范关涉它运作所跨的那个范围，以一种 §5.5 弄精确的方式。

那个控制形式的移置

那个自输运方程的形式可以被与控制理论中标准的形式对比，在其中一个态 $x$ 在

$$\dot{x} = F(x, u)$$

之下演化，以 $u$ 为一个控制输入。这两个形式在它们置于系统之外之物上有别。那个控制形式要求一个被设定、而不是被演化的 $u$，因此要求一个占据一个外在于其演化被描述的那个态的位置的控制者。被应用于历史约束，那个控制形式会要求一个”改变那个格局、同时立于它之外”的能动者，而 §3.1 论证了这是不可用的。

那个自输运形式免除那个要求。每一个项都是那个场的一个函数，包括那些源与汇，因为注入与耗散由那些本身就是那个场之内诸格局的目标所提供。这是一个带超出当前论文之后果的承诺，而它被作为如此陈述：一个建于关系首要性之上的框架没有一个控制者的余地，而”那个杠杆是什么、谁持有它”这一分析习惯，对一个输运它自身的系统没有着力。什么取代那个问题在 §7 中被处理。

5.3 快与慢结构

变量的分离

§1 的那个回路可以被以对带两个时间尺度之系统标准的形式写出：

$$\dot{x} = f(x, y)$$

$$\varepsilon, \dot{y} = g(x, y), \qquad 0 < \varepsilon \ll 1$$

在其中 $x$ 汇集那些快变量、而 $y$ 汇集那些慢的。那个陈述是结构性的：它断言历史系统，在那个断言成立的诸范围之上，拥有两个良好分离的时间尺度。

变量的指派追随那个本体论。快变量包括个体行动、日常互动、短视域目标以及其中显要的诸结构性目标、诸交易，以及意见的移动：在诸参与者据以行动的时间尺度上改变的诸量。慢变量包括诸制度、文化、信任的诸结构、那个可表达者的边界，以及那个约束场本身：其弛豫时间超过诸参与者视域的诸量，因 §4.2 中所给出的理由。日常发生之物是 $x$ 中的变化。$y$ 中的变化要求许多这样变化的累积效果。

奇异摄动与那个慢流形

这个形式的诸系统已在奇异摄动理论之下被研究，而此处相关的诸结果关乎在小 $\varepsilon$ 的极限中的行为 [20, 26, 31]。把 $\varepsilon$ 设为零产出一个代数约束 $g(x,y) = 0$，其解集是那个临界流形；对于小的非零 $\varepsilon$、并在一个正规双曲性条件之下，一个邻近的不变慢流形存在，而诸轨迹被迅速地吸引到它、并此后沿它缓慢移动。

那个结果许可一个其中那些快变量被奴役于那些慢变量的描述：给定那个慢态，那个快动力学迅速安顿进一个由它所决定的格局，而那个有趣的运动是那个格局的缓慢漂移。这是”一个稳定历史时期展现大量的活动与极少的变化”这一观察的形式内容。

远离临界性所可用的描述

那个约化提供一个稳定时代从内部看上去的样子。那些快变量连续地移动，那个慢流形决定它们安顿于何处，而对那些快变量的扰动以一个由对那个流形的吸引所设定的速率衰减。一个在那些快变量之时间尺度上的观察者看到把那个格局留如不改变的活动，而那个观察是正确的、而不是虚幻的：在那个观察窗口之上那个格局，以良好的近似，是固定的。

正规双曲性是一个条件、而不是一个保证，而它失败于其下的诸条件是 §5.4 的主题。

那两个形式之间的优先次序

到目前为止所写的这两个形式立于一个确定的关系之中，而陈述它防止一个误读。那个自输运方程是那个一般形式，而那个快-慢系统是一个在一个条件之下可用的约化描述。那个条件是那些时间尺度的分离，而凡它成立之处，那个场容许分解为一个缓慢漂移的组成部分与一个迅速平衡的组成部分。

那个次序要紧，因为那个快-慢形式在外表上重新引入 §5.2 所驱逐之物：一个在一个给定向量场之下演化的态矢量，而那个场对那个态的依赖被压制。那个外表是那个约化的一个后果。那些向量场 $f$ 与 $g$ 本身是那个场的泛函，而它们的表面固定性是”在一个其中那个慢态改变很少的区间之上描述那个系统”的一个赝象。自输运是那个本体论；快-慢结构是对它的一个特定于区制的近似。

一个事件之重要性的决定

一个后果立刻随之而来，并以动力学的术语陈述本文由之开始的那个论题。考虑对那些快变量的一个相同的扰动，被应用于两个时刻。在第一个中，那个系统坐在那个慢流形的吸引域深处，而那个扰动衰减。在第二个中，那个慢变量已漂移到一个吸引已减弱的位置，而同一个扰动把那个系统携带到别处。那些扰动是相同的；那些结局有别；而有别之物是那个慢态。

因此，一个事件的重要性是它发生于其内的那个格局的一个属性、而不是那个事件的一个属性。这是 §4.5 中”关键事件回溯性地获得它们的地位”这一观察的形式对应。

5.4 临界性与稳定性边界

恢复能力与感受性

两个量刻画一个系统对扰动的响应。恢复能力度量一个系统在返回它先前格局时所吸收的扰动。感受性度量那个系统的态对诸条件一个小改变的响应。这两者反向变化，而二者都是那个慢态、而不是那个扰动的属性。

远离一个稳定性边界，恢复能力高而感受性低：扰动被吸收，而一个系统可以吸收它们很长时间。随着那个慢态趋近一个边界，恢复能力下降而感受性增长，而未改变量级的扰动产生增长量级的响应。在那个边界处，感受性在那个理想化情形中发散，而任意小的扰动足以把那个系统携带越过。

从快与慢结构对临界性的推导

§4.5 的那个临界性条件不要求一个分开的公设。它从已被写出的那个结构随之而来。那个慢变量漂移；那个漂移把那个系统携带向一个正规双曲性失败的格局；在这样一个格局处那个快动力学停止被奴役，而一个在别处会衰减的扰动反而增长。

这是本节对整个论证最有用的结果。§4 的机制以一个断言把累积联结到触发因素；那个快-慢结构推导那个联结。累积是那个慢变量的漂移，那个触发因素是对那些快变量的一个扰动，而那个触发因素有后果所在的条件是 §5.3 的约化失败所在的条件。

那个谱隙的关闭

那个失败有一个值得分开陈述的刻画，因为它治理 §5.6。§5.3 的约化要求那些快变量弛豫的速率与那些慢变量漂移的速率之间的一个隙。对一个稳定性边界的趋近收窄那个隙：那些快变量的弛豫随着吸引减弱而变慢，而在那个边界处那些时间尺度成为可比的。那个两时间尺度描述所搁于其上的那个分离因此恰恰在那些有趣的转变发生之处失败。

拒绝建构一个控制参数

在那些物理案例中，对一个边界的趋近被参数化：一个量被指认，其变化把那个系统携带向那个转变，而到那个边界的距离从它被计算。本文不为那个历史案例建构任何这样的量，而那个拒绝是一个立场、而不是一个省略。

两个理由支持它。第一个是 §3.5：一个控制参数的指认要求诸格局的空间上一个独立地被促动的结构，而没有一个可用。第二个是 §4.2：设若一个控制参数可从对诸参与者可用的诸量被建构，那么到一个边界的距离会从内部可测，而 §4 的认识论结果会为假。因此那个拒绝被那个说明的其余部分所要求，而 §8 把这样一个量、若一个存在、的指认陈述为一个开放问题，其解决会修订 §4.2、而不仅仅补充它。

临界减缓与可观测性问题

一个限定被要求，而它关涉那个认识论主张的强度。趋近一个稳定性边界的诸系统展现临界减缓：从小扰动的恢复花更长时间，而所得的方差与自关联的诸变化已被提议为普适的早期预警信号 [47]。那个信号有那个”不要求关于那个控制参数的知识”这一有用属性，因为它是从对扰动的响应、而不是从在格局空间中的位置被读出的。

那个相应的测量能否在历史系统中被作出是一个开放问题，而 §8 列出它。那个限定在此被录入，因为它指认 §4.2 的认识论结果能被削弱之点：那个结果关乎那个慢变量本身的不可用，而它把”那些快变量的某个泛函是否携带关于那个慢态的信息”留作敞开。倘若这样一个泛函被证明可测，那个盲目会容许程度，而 §4.2 会要求相应的修正。

5.5 级联与诸尺度的耦合

对那个两时间尺度图景的纠正

那个快-慢描述把活动划分为两个带。那个湍流案例提示一个不同的图景，在其中活动被分布于一个诸尺度的连续统之上，而它们之间的转移是那个所关切的对象。这两个图景在 §5.6 中被调和；当前这一节陈述第二个。

那个惯性区

在一个湍流中，能量在大尺度进入、在小尺度离开，并在它们之间跨一个它既不被供给也不被移除的范围传递。这个中间带是那个惯性区，而它的定义性属性是它之内的活动被转移、而不是被生成或被耗散 [21]。

那个社会读法追随 §3.6 的分类。注入发生于生成性目标产生没有任何排名评价过的诸格局之处。耗散发生于制度化把诸格局固定成规则并把它们从动力学中移除之处。在它们之间躺着一个诸格局被携带而不被或产生或固定所跨的范围，而 §3.6 中指派给非结构性规范的功能是这个范围的维持。§6 的主张，即抗拒优化之物保护那个系统的约束更新能力，以这些术语言之是”耗散消耗那个惯性区就切断更新所依赖的那个转移”这一主张。

朝更大尺度的转移

朝更小尺度的转移在三维中是那个寻常的情形。二维流展现相反者：能量被朝更大尺度转移，在比它进入所在的尺度更大的尺度累积 [30, 10]。那个逆级联提供 §4 的论证所要求的那个意象：局部的、各别地无后果的活动，累积进一个远高于它生产之尺度的尺度上的一个变化。

社会系统中一个逆级联的问题

社会系统是否展现这一种转移是一个实质性的问题，并被留作敞开。所会被要求的，是”个体关系尺度上的活动优先地朝更大尺度累积、而不是在它生产的尺度被耗散、并且那个累积展现会把转移与巧合区别开来的统计规律性”的证据。那个问题在 §8 中作为一个研究方向被陈述，而本文的论证被建构得要求向上累积的可能性、而不是技术意义上一个级联的存在。

5.6 那两个描述之间的分工

一个被预设的隙与一个被否认的隙

这两个描述立于表面的冲突之中。那个快-慢约化要求诸时间尺度之间的一个隙，而它的诸结果从那个隙随之而来。那个级联图景描述一个没有隙的连续统，而它的诸结果从一个隙的缺席随之而来。一个使用二者的框架欠一个关于每一个何时适用的说明。

每一个描述的适用性

那个说明从 §5.4 随之而来。远离一个稳定性边界，那个隙存在：快变量迅速弛豫，那个慢流形是正规双曲的，而那个两时间尺度描述是准确的。这是那个稳定历史时代的区制，而 §4 的认识论结果是关于这个区制的结果。随着那个慢态趋近一个边界，那个隙收窄；在那个边界处那些时间尺度合并，那个约化失败，而那个其中活动跨一个诸尺度的连续统被耦合的描述成为那个恰当的。这是那个转变的区制。

那个冲突因此被解决进一个划分。那个快-慢描述治理那些其中少有改变的长区间；那个级联描述治理那些其中那个系统重新组织的区间。两者都不是一般的，而诸区制之间的那个转变是那个隙的关闭。

那个在诸描述之间选取的指标

那个划分由一个单一的量所指标化，即那个慢态离一个稳定性边界的距离，而那个说明承袭那个量的分量。§5.4 拒绝建构它，而其后果是那个指标是良定义的、而不可用于从内部计算。这是在 §3.4 所指出的同一个组合，而同一个限定适用：一个对某个量之存在的承诺连同一个”诸参与者不能计算它”的论证，是一个实质性的立场，其证成会要求 §8 中所列出的那个工作。

5.7 注入与耗散的平衡

那个源项的社会读法

注入是没有任何排名评价过的诸关系性格局的生产。它的诸源是 §3.6 的诸生成性目标，而它的速率是一个社会诸安排的一个属性：可供探索的余地、对没有一个被陈述目的之活动的容忍，以及此类活动逃脱评价的程度。

那个汇项的社会读法

耗散是诸格局固定成规则。制度化是它的主要形式，而那个机制是 §6 中所处理的那一个：一个成为一个规则的格局停止变化，而一个停止变化的变量离开动力学。

那个无量纲比的分量

在流体力学中那个非线性输运与那个耗散项之比是雷诺数，而它的值决定那个流的性质。建构一个社会对应物的诱惑是相当大的，而本文拒绝它。

那个拒绝以那个强的形式被陈述。没有社会雷诺数在此被提议，而注入对耗散的平衡是作为一个定性的考虑被提出的：一个其中固定超过对未被评价者之生产的社会，将展现一个收窄的惯性区，而一个其中生产超过固定的社会，将展现一个加宽的。这是那个主张的全部，而它在 §5.1 的意义上是一个类比性的陈述。

那个无量纲群会要求之物

那个拒绝的诸理由指出一个成功的建构会要求什么。一个无量纲群要求带量纲的诸量、一个特征尺度与一个特征速度，而那个社会案例中没有一个提供。它进一步要求那个群跨诸系统是预测性的：雷诺数的效用是在相等值处的诸流一样地表现、无论那个流体为何，而一个缺乏这个属性的社会对应物会是一个比、而不是一个无量纲群。§5.5 的那个级联结构承载那个论证，而那个比贡献一个例示。

5.8 间歇性生成性

耗散的集中

在湍流中，耗散被以极大的不均匀性分布：它集中于占据体积一小部分的稀疏诸结构，而那些小尺度的统计量偏离一个均匀分布会产生的那些 [21]。间歇性命名那个现象，而它是一个稳健的特征、而不是对一个更平滑图景的一个修正。

约束更新的时间模式

那个社会对应物是那个论证一直在组装的那个时间模式。约束更新以一种带相应不均匀性分布的方式发生：那些其中那个慢态漂移、而表面少有改变的长区间，被那些其中那个格局重新组织的短区间所标点。那个模式从 §5.4 与 §5.6 随之而来：那个漂移慢是因为那个慢流形是吸引的，那个重新组织短是因为它发生于吸引已失败之处，而那个交替是那两个区制的交替。

语法改写的局部性

间歇性有一个空间方面、一如一个时间方面。那个约束场的重新组织被期望集中于那个场的诸区域、而不是均匀地跨它进行：特定的实践领域、特定的诸制度、特定的诸关系。那个期望提供一个经验工作的靶，而 §8 陈述它。

那个机制的可观测签名

前面三节产出一个关于历史变化之形状的主张。

主张 6（间歇性生成性）。 历史约束被间歇地更新。漂移的长区间，在其间那个格局是稳定的而活动把它留如不改变，与重新组织的短区间交替，后者集中于那个场的有限诸区域。那个交替从那个动力学的结构、而不是从诸事件的分布随之而来，而它是那个所提议机制可据以被认出的可观测签名。

那个主张陈述那个把这个说明与一侧的历史发展的一个连续构想、以及另一侧的历史作为一个断裂序列的构想区别开来之物。连续性在一个区制之内成立，不连续性标记诸区制之间的过渡，而那个交替是一个拥有上面所列出结构的系统的一个属性。

5.9 稳定性的非评价性质

恢复能力与最优性

一个区别在此被要求，因为稳定性的词汇招致一个那个说明必须排除的读法。一个吸引子凭借恢复能力而稳定，后者度量对扰动的响应。最优性是诸格局按一个判准的一个排名。这两者是独立的：恢复能力是一个动力学属性，而诸排名从动力学之外被提供。

稳定性相对于价值的中立

由此可得一个格局可以是稳定而正义的、稳定而不义的、稳定而高效的、稳定而低效的。稳定性报告对扰动的响应，而关于那个安排的诸优点什么也不报告。一个长期而稳定的历史时期可以被读作一个其中没有什么需要改变的时期、或一个其中需要改变之物被压制的时期，而那个动力学在两个方向上都不在这些读法之间裁决。

退化与稳定性的相容

那个区别既针对当前框架、也针对别的框架而切，而那个情形应当被明白地陈述。一个其惯性区已被耗散所消耗的系统，在 §5.5 的意义上，有更少的活扰动可吸收，而它可以据此比一个保留它更新能力的系统更稳定。约束更新能力的退化与当前格局的稳定性因此是相容的，并可能被正向地关联。

加于较后诸节之上的纪律

对 §6 的后果是一个纪律。那里所发展的主张，关乎把所有目标投影进一个单一可优化空间对一个系统所耗费之物，是一个关于一个能力、而不是关于所产生诸格局之优点的主张。把稳定性读作健康、或读作隐瞒，会向那个动力学引入一个那个动力学所不提供的判断，而随之而来的诸节被写得避免它。

5.10 那个闭合问题

那个矩谱系

一个由一个二次自输运项所治理的系统，抗拒以它的诸平均来描述。对那个方程取平均产生一个涉及一个乘积之平均的项，它不是那些平均之乘积；描述那个项要求一个关于那个二阶关联的方程，其平均涉及那个三阶；而那个谱系继续而不终止。这是那个闭合问题，而它是那个二次非线性的一个后果、而不是技术的一个局限 [21, 45]。

那个社会案例的位置

那个社会案例以同样的形式承袭那个问题。一个以聚合诸量描述那个约束场，要求诸关系之间的诸关联，而那些要求更高阶的诸关联。值得作的点是一个分量之点：此处的非闭合是带自输运之系统一个一般特征的一个实例，而它在那个社会案例中的在场反映此类系统的结构、而不是社会探究的任何特殊缺陷。

非闭合跨那一类的分量

那个观察有一个超出安慰的用处。在那个物理案例中对闭合的诸近似，是通过提供那个未闭合项与那些被分辨诸量之间的一个关系而作出的，而那个关系由物理论证所证成、而不是被推导。任何在那个社会案例中的相应举动，将要求一个类似的证成，而那个要求提供一个此类举动可据以被评估的判准。§8 把社会闭合近似的建构陈述为一个研究方向。

5.11 与复杂系统研究的连接

共享那个结构的诸系统的范围

本节所列出的那个结构被一系列已被独立地并详细地研究的系统所展现。地震活动展现应力的长期累积被破裂所标点。神经系统展现兴奋性的缓慢调制连同向癫痫发作的快速转变。气候系统展现缓慢的强迫连同诸态之间的转变 [47, 7]。进化系统展现相对停滞的长区间连同快速变化的诸区间 [19]。在每一种情形中那个分析内容是一个其漂移改变快动力学运作于其下之诸条件的慢变量，而在每一种情形中那个系统的研究已产生关于向诸转变之趋近的诸结果。

湍流在那个多尺度类中的位置

那个湍流案例对其余者的关系值得被陈述，因为 §5.2 与 §5.5 大量地取用它。湍流是那个其中自输运与尺度耦合以最大清晰性被展现的情形，而正是为那两个特征它在此被使用。那个多尺度结构是那个属；湍流是它的一个种，由它的非线性所采取的特定形式所区别。

那个可用的交换

把那个说明置于这个文献之内，指认什么能从它被获得、以及什么会不得不首先被确立。几何奇异摄动理论、平均法、以及跨尺度粗粒化的诸方法，以被发展的形式可用，而 §8 把它们的应用列为一个方向。所会不得不首先被确立之物，是那个历史案例容许那些方法所要求的诸结构，而 §5.6 已陈述那个主要障碍：那个借以选取可适用描述的指标，是那个说明主张对它所指标化的那个系统从内部不可用的一个量。

§6 规范性后果

前面诸节是描述性的。这一节问什么为诸目标与诸规范的评估随之而来，而那个安置是刻意的：此处所发展的诸规范性后果是从 §5 的动力学中读出的、而不是被独立地论证然后被它例示。

论述的次序从诸目标以关系性术语的重构，经过它们的耦合以及它们据以硬化成诸标准的过程，到抗拒此类硬化之物的分量，而以这个说明所蕴涵的对功利主义的重新定位作结。§1 的 Q4 在此被卸除。

6.1 诸目标的关系性重构

诸目标与诸偏好的排序

一个目标，依此处所取的说明，是关系性张力在可表达者层级上的凝结。凡那个标准处理从一个拥有一个对诸结局之排序的能动者开始、并从那个排序导出行动之处，这个说明从一个其中某种张力成立的诸关系的格局开始，并把那个目标当作那个张力在被诉诸言辞时所成为之物。

那个区别以三种方式有后果。偏好排序是诸个体的属性，而张力是诸格局的属性，以致那个说明把诸目标的起源定位于那个场、而不是定位于持有它们者。偏好排序按构造是完全的，而张力不容许任何这样的假定：一个张力可以成立而无任何可用的表述，而这是 §3.6 所称的可表达性约束的那个条件。而偏好排序先于动力学被给定，而张力被它所生成，以致诸目标的形成落在那个理论必须解释之物之内。

个体张力之源

个体张力从诸关系性位置的不相容中生起。一个参与者同时立于许多关系之中，而这些所授予的诸位置作出不能总是被联合地满足的诸要求。作为一个同事、作为一个家庭成员、作为一个专业共同体的一个参与者、以及作为一个公民所被要求于一个人之物，在一个特定处境中可能是联合地不可满足的，而那个不相容的余项是诸目标从其中被形成的材料。

那个说明有那个后果，即一个参与者的关系性位置越丰富，可供凝结的张力越多，而一个占据一个单一位置的参与者相应地有很少。二者都作为诸后果、而不是作为诸观察被陈述，而 §8 列出它们的考察。

集体张力之源

集体张力从那个关系场中不容许任何局部解决的诸不对称中生起。两个参与者之间的一个不对称可以在它们之间被解决。一个跨那个场再生产它自身、以致解决任何实例把那个模式留如完好的不对称，是一个集体的张力，而正是从此类张力中集体目标被形成。

那个局部实例与那个非局部实例之间的区别，是那个分析所转于其上之物。一个被它的诸方所解决的委屈产生不了集体目标。一个其在一个实例中的解决被它在另一个实例中的复发所跟随的委屈，指示那个张力是那个格局的一个属性，而从它凝结的那个目标是一个集体的目标，在此处所要紧的意义上：它的内容指涉那个格局、而不是诸实例中的任何一个。

6.2 那三个耦合

个体目标与集体目标被耦合，而那个耦合采取三个带不同后果的形式。§1 的 Q1 由它们的陈述所卸除。

表达性耦合

那个集体提供个体张力能在其中被表述的那个词汇。一个带一个张力而无关于它之言辞的参与者，在 §3.6 的严格意义上，没有目标；获得那个词汇把那个张力转换为某种能被追求、被传达、被评价之物。

那个耦合在两个方向上运作，而第二个方向是那个值得标出的。在获得那个词汇之中，那个个体目标被改写进一个那个集体能认出的形式。所被获得之物是追求的可能性；所被索取之物是那个张力被以那个集体已然拥有的术语来表达，而无论什么超过那些术语之物被留在后面。那个机制是那个在这个框架别处被更详加处理的机制，凭它一个系统产生它自己动力学所要求的诸参与者。

资源耦合

那个集体决定哪些个体目标获得它们实现的诸条件。这是那个最可见、最被研究的耦合，而它在此除了”它操作于已被形成的诸目标之上”这一观察之外，要求很少评论。资源耦合分配；它不构成。

逆向耦合

第三个耦合从个体运行到集体，而它是那个约束更新所依赖的。一个可用词汇没有为之表述的张力不因此就消失。它作为某种被登记而不被陈述之物持续：作为困难、作为一个契合于没有可用描述的行为模式、作为一个抗拒表述的不安。这样一个余项是那个可表达性约束据以被修订的唯一入口，理由是一个词汇只在来自它未能容纳之物的压力之下才被扩展。

到 §4 的连接应当被显明地作出。那个副产品原理主张对诸目标的追求生成那些目标所不描述的诸关系。当前这一节指认此类副产品登记于何处：在那个词汇所不能陈述的诸张力的余项中。而 §5 提供那个登记成为有后果之条件，因为一个在一个远离一个稳定性边界之系统中的余项被吸收，而同一个余项在一个边界附近被放大。

6.3 诸目标的本体论化

从方向到标准

一个目标开始为一个方向：一个张力的一个表述，指示什么会缓解它。在广泛成立的诸条件之下，它成为别的东西。那个表述获得一个度量；那个度量获得一个制度性归宿；而开始为一个”去往何处”之指示之物，成为一个行为据以被评估的标准。那个目标已成为一个判准。

那个变换是寻常的，并且，在限度之内，是良性的。一个度量允许协调、比较与问责，而一个没有一个度量的集体目标根本很难被集体地追求。以下所述关乎那个变换对那个动力学的诸后果，而把它的局部有用留作不争议。

从张力驱动到指标驱动的动力学

那个后果是那个驱动那个系统之物的一个改变。一个张力驱动的动力学是一个其中行为响应关系性诸格局的动力学，而此类系统特有地拥有多个稳定格局并展现对一个格局据以被抵达之路径的依赖。一个指标驱动的动力学是一个其中行为响应一个度量的动力学，而此类系统特有地拥有一个行为向之收敛的单一最优。

那个改变是那个动力学之类型、而不是它诸参数的一个改变。曾是一个带若干稳定格局的场之物，成为一个带一个峰的地景，而那个区别在那个行为中可见：对替代诸格局的探索，它在第一种情形中是那个系统找到它道路的方式，在第二种情形中成为有待被纠正的错误。

那个投影主张的陈述

这个小节一直在建立的那个主张现在可以被陈述，而它以一个比那个概括它的口号更审慎的形式被陈述。

主张 7（总体化投影的代价）。 在历史约束之持续生成的问题上，把所有目标投影进一个单一可优化空间，减少一个系统保留抗拒表达的关系性自由度的能力。

那个主张中的每一个限定都是承重的，而那个论证要求全部四个。

那个主张被限于一个问题：历史约束的持续生成。对后勤、对临床协议、对一个固定预算之分配的优化落在那个限制之外，而此类案例既不是对那个主张的反例、也不是对它的应用。

那个主张关乎投影进一个单一空间、而不是优化。在结构性目标自己的领域之内优化它们仍然是合法且理性的，如 §3.6 所承认。那个主张所关乎的，是把整个目标系统当作一个优化问题的处理，在其中每一个目标通过化约为一个共同度量而被弄得与每一个别的目标可通约。

那个主张断言一个能力的减少、而不是一个消除。一个如此被投影的系统保留某种持有关系性自由度的能力，而投影可能生成它自己的新约束。那个主张是比较性的、并容许程度。

而所被减少的是保留抗拒表达的自由度的能力，它是一个具体的量、而不是一个一般的善。那个主张关于福利、正义、或一个被投影系统所产生诸格局的质量什么也不说。

为那个主张的论证

为主张 7 的论证贯穿那个动力学并不要求任何评价前提。

优化阻尼扰动。这是优化之所是，从量纲上考虑：一个把一个系统朝一个判准的一个极值移动的程序，在那个系统被位移时把它归还到那个极值，而那个归还是那个位移的阻尼。一个在彻底优化之下的系统，是一个其中对那个最优的偏离被纠正的系统。

扰动是约束更新的材料。§4 论证那些能够改变那个约束场的格局是那些那个评价泛函未能捕获的，而 §5 论证它们的放大要求它们存活足够长以被输运。一个纠正偏离的程序恰恰移除那个更新所依赖的诸格局，因为一个对那个最优的偏离正是一个未被排名的格局从一个指标驱动动力学之内看上去的样子。

那个结论随之而来。总体化投影阻尼那些构成约束更新之材料的扰动，并因此减少那个系统对此类更新的能力。那个论证关乎一个速率、而不是一个估值，而它会为一个对”历史约束是否曾被更新”漠不关心的观察者不加改变地通过。

与退化诸机制的关系

此处所描述的那个变换是那个约束场的评价层据以被改写的具体机制。§3.6 把可评价性约束区别为三种模式中最快的，而目标本体论化正是那个改写它之物：诸行动进程据以被排名的诸标准被那个被本体论化的目标所提供的度量所取代。那个说明因此把一个在这个框架别处被处理为一个关系性语法之改写的过程，定位于那个动力学之内。

6.4 那个余项与非结构性规范

那个被陈述规范的自我取消

一个 §3.6 所称为非结构性的种类的规范，展现一个把它与一个目标尖锐地区别开来的特征：把它陈述为一个目标摧毁它。

那个经典的实例是”占据别人所鄙夷的低处”这一告诫。被问那个占据服务什么目的，人们找不到寻常种类的答案，而被进一步追问人们只能说它是合宜的。假设那个告诫被重新表述为一个目标，带一个被附加的度量、并对照它评估表现。所会被追求之物于是是那个度量上的一个排名，而对一个谦逊度量上一个排名的追求不是谦逊。同样在整个那一类中成立。为了被信任而被给予的信任是计算；为了它的效果而被表演的真诚是表演；而一个为在一个美之标度上抬高一个分数而被做的作品，立于一个不同于一个别样被做之作品对美的关系。

那个自我取消与那个能动者的真诚毫无关系，而那一点值得被坚持。所被摧毁之物是那个东西本身，被那个追求的形式所摧毁，而一个采纳那个目标形式的完全真诚的能动者，如一个愤世者一样彻底地摧毁它。

非结构性规范的分类

对前述的那个自然回应是把此类规范分类为一个不寻常种类的目标，而那个回应应当被抵制。一个目标是一个张力的一个表述，指示什么会缓解它，而一个在被如此表述时取消它自身的规范不是那个种类的一个表述。

那个替代分类从 §3.6 随之而来。非结构性规范持守关系性诸格局可移动所跨的那个范围，而它们在那个动力学中的功能是输运。它们是，在 §3.6 的词汇中，对那个目标系统的边界条件：决定诸目标被形成与被追求于其内之空间的诸条件，作为一个条件、而不是作为它的一个元素而立于那个空间。

规范性力量之源

一个后果为此类规范的分量随之而来，而它倒置那个寻常的期望。一个规范抗拒作为一个目标的表述，一般被当作一个缺陷：一个不能被陈述为一个目标之规范被认为是含混的、不可执行的、或界定不良的。

依当前的说明，那个抗拒是那个规范之功能的来源。此类规范所保护之物是一组没有任何排名评价过的关系性自由度，而一个能够被陈述为一个可排名目标的规范会，由 §6.3，是一个阻尼偏离、而不是保全它们的程序。对表述的抗拒与保护的能力，是被以两种方式描述的同一个属性。

无一个目的的合目的性

那个结构在哲学传统中有一个祖先，而那个连接加强那个说明、而不是装饰它。康德对审美判断的分析指认一类判断，它们是合目的的而无任何可表示的目的：美中所悦人之物无一个概念、无那个对象被置于一个目的之下地悦人 [27]。那个判断有一个合律性，而它是一个提供一个确定概念会摧毁的合律性。

那个平行在那个要紧之点成立。§6.4 的那个告诫只能作为合宜的被辩护的理由，以及一个如此被辩护的规范在一个目的被提供时失去它性质的理由，是一个在两个设置中出现的结构。当前说明所添加之物是那个动力学功能：那个传统确立这个形式的诸判断是融贯的并拥有它们自己的合律性，而 §3.6 把一个”跨尺度输运关系性诸格局”的角色指派给它们。

6.5 盲目条件之下的保护

有意保护的分量

这一节的主要主张现在可以被陈述。

主张 8（盲目之下的保护）。 在一个其诸参与者对那个慢变量没有通达的系统中，为保护那个系统的约束更新能力之意图而被采纳的诸保护机制失败，因为那个意图把那个机制置于它被采纳来对抗的那个快变量优化之内。不带这样一个意图而被持有的诸规范保留那些有意机制所失去的能力。

那个论证以三步进行。§4 确立诸参与者对那个慢变量没有通达。由此可得一个为保护那个慢变量而被采纳的机制，是在一个诸参与者不能对照那个被保护之物的态来核实的目的描述之下被采纳的。因此对那个机制的评估必须经由代理进行，而那个代理是一个度量。但一个对照一个度量被评估的机制，是 §3.6 意义上的一个结构性目标，其动力学角色是耗散。那个机制已成为它被采纳来对抗的那个过程的一个实例。

基于别的根据被持有之诸规范的分量

那个相应的肯定性主张从 §6.4 随之而来。一个为它自己之故被持有、并在被挑战时以对它合宜性、而不是对它后果的一个诉诸被辩护的规范，因 §6.4 中所给出的理由抗拒转换为一个度量，而它保留 §3.6 中所指派的那个输运功能。

那个表述要求审慎。那个主张不是无知比知识更可取，也不是能动者应当避免反思他们的诸规范所成就之物。它是一个规范的保护功能只在那个规范继续基于别的根据被持有之处才在对那个功能的反思中存活。一个能动者可以很好地知道一个规范成就什么；那个能动者所不能做、不带代价地做之物，是因为那个成就而持有那个规范。

那个主张的描述性分量

主张 8 是描述性的。它陈述在被规定的诸条件之下一个保护机制发生什么，而它不推荐任何东西。

那个区别容易被丢失，因为那个主张在论证中有一个明显的用处，而那个用处应当在此被谢绝。那个动力学中没有任何东西确立那个约束更新能力值得被保护；§5.9 主张稳定性不是一个评价概念，而同样在生成性上成立。一个已失去约束更新能力的社会已失去一个能力，而那个丧失是否应被惋惜，是一个那个动力学留作敞开的问题。那个说明所提供之物是那个丧失的代价，以那个系统此后所能做之物的术语被陈述。

那个主张对那个转变机制的关系

一个反对在此生起，而那个说明因直接迎接它、而不是把它留待被发现，而更强。

主张 8 主张有意保护失败。§4 与 §3.6 主张非结构性规范确实保护那个约束更新所依赖的诸自由度。如果此类规范有效地保护，那么维持它们显得是一个有意的保护策略，而主张 8 显得排除那个说明其余部分所要求之物。

那个解决在于一个功能与一个理由之间的区别。非结构性规范作为为它们自己之故被持有的一个后果而保护，而那个保护是那个持有的一个副产品、而不是它的对象。一个因为一个规范保护而维持它的能动者，已给那个规范提供一个目的，而由 §6.4，如此被提供的那个规范不再是那个保护的种类。那个使那一类难以陈述的自我取消，恰恰是那个在此做工作之物：它是那个保护功能只在它不是那个持有之理由之处才存活的理由。

对实践的后果是严峻的，而 §7 接过它、而不是软化它。一个因为不优化的诸空间是有价值的而维持一个不优化空间的制度，已把那个空间转换为一个工具，而那个转换不被那些执行它者的真诚所撤销。

6.6 那个余项的动力学陈述

耗散与那个惯性区

这一节的诸主张容许以 §5 的词汇的重述，而那个重述是本文的两条线相会之处。

§5.5 指认一个关系性诸格局跨它被输运而不被生成或固定的尺度范围，而 §5.7 指认制度化为诸格局据以被固定的过程。如果固定跨整个范围延伸，输运停止：诸格局在它们生产的尺度被移除，而没有什么存活以累积。那个系统保留注入与耗散，而失去它们之间的转移。

非结构性规范在这些术语中的功能

§3.6 中指派给非结构性规范的功能，在这个词汇中，是那个范围的维持。它们既不产生诸格局也不固定它们，而它们所贡献之物是那个在一个尺度被生产的诸格局能持续足够长以在另一个尺度累积所跨的区间。

§6.3 的主张与 §6.5 的主张因此可以被读作在两个层级被陈述的一个主张。总体化投影把固定跨那个范围延伸；那个范围是输运所要求之物；而一个其范围已被消耗的系统保留它优化的能力、而失去它被修订的能力。

诸词汇的收敛

三个描述在本文中已为此处被主张为一个结构之物被使用，而它们的收敛是查验本文的诸借用是否赢得它们位置的恰当之处。那个关系性词汇谈论没有任何排名评价过的诸自由度。那个动力学词汇谈论一个输运跨它发生的惯性区。那个规范性词汇谈论不能不被摧毁就作为一个目标被追求之物。此处的提议是这些在三个描述之下挑出一个东西，而那个认同是这个小节的实质内容、而不是它的一个概括。

6.7 那个判准及其失败的诸形式

归还判准

§1 从母框架取了一个判准，而它现在能被应用。一个规范保留它的非结构性性质，恰当它所服务的诸目标不能反回来并改写它。凡一个系统的诸目标能够修改一个规范以适合它们之处，那个规范已成为那些目标的一个工具，无论它的内容为何。

那个判准有那个”无需一个关于那个规范之内容的说明就可应用”的优点，以及那个相应的局限，即它要求一个关于一个反事实的判断：那个规范是否会在压力之下被修订，而不是它是否已被。

那个被收编的规范

那个判准的失败有一个特有的形式，而实例被现成地提供。一个成为一个被度量的靶、被报告并被优化的对公平的承诺，已被它本要约束的诸目标所改写。一个成为一个指标的对可持续性的承诺，已经历同样的转换。在每一种情形中那个规范的内容在那个词汇中存活，而它的动力学角色已从输运改变为耗散。

使此类案例有教益之物是它们不带恶意地进行。那个转换一般由那些最委身于那个规范者、并为最好的诸理由而被执行：一个被度量的规范能被辩护、被列入预算、被执行。此处所发展的说明解释为何那个改善携带它所携带的代价，而 §7 考虑关于它，如果有什么，能被做什么。

那个判准的诸局限

三个局限应当被录入。那个判准是反事实的，而它的应用要求一个关于”一个规范会在它未曾经验的压力之下如何”的判断。它是二元的，而那个现象容许程度，因为一个规范可能被部分地收编。而它在实践中是回溯性的：一个规范能被改写的最清晰证据是它已被。§8 把一个肯定性、而不是反事实的判准的建构列为一个开放问题。

6.8 功利主义的重新定位

适足的领域

此处所发展的说明关涉功利主义，而那个关涉是一个重新定位、而不是一个反驳。

功利主义是 §3.6 那个目标表格之一个区域的一个正确理论。凡诸目标在 §3.6 的意义上是结构性的之处，诸后果在一个共同度量之下的聚合是那个恰当的评估形式，而那个传统对那个形式的发展是一个真正的成就。那个重新定位关乎那个处理向整个表格的扩展：向那些其作为可排名目标的表述摧毁它们的目标，以及向那些其功能是没有任何排名尚且评价过的诸格局之生产的生成性目标。

与主张 7 的平行是贴近的，而这两者可以被读作一个在不同层级出现的结构。主张 7 关乎一个目标系统进一个单一可优化空间的投影。功利主义的重新定位关乎一个适足于一类目标的理论跨所有目标那一类的扩展。第二个是第一个如它在规范理论中出现的样子。

一个没有余项之系统的动力学

那个重新定位容许一个第二而等价的陈述。一个对整个目标系统的功利主义处理，适足于一个其中那个余项为零的系统：一个其中每一个关涉行为的考虑都能被表达、被排名、被聚合、而没有什么剩下的系统。

这样一个系统是一致的，而 §5 陈述它的动力学会是什么。没有未被排名的格局，注入停止；没有什么可输运，那个惯性区闲置；而那个约束场安顿进一个它自己的动力学不能把它从其中位移的格局。§1 的那个回路闭合并成为一个不动点。这是 Q4 是那个回路未能闭合之条件的意义，而它是为何那个问题被置于历史动力学的诸问题、而不是伦理学的诸问题之间。

那个论证的形式

那个论证的形式值得评论，因为那个反对功利主义的标准案例采取一个不同的形式。那个案例以反例进行：一个情景被建构，在其中那个功利主义裁决与一个自信的判断相冲突，而那个冲突被作为反对那个理论的证据提出。随之而来的交流关乎那个直觉还是那个理论应当让步。

当前的论证不作这一种诉诸。它观察到一个如功利主义理论所推荐那样被组织的系统有一个确定的动力学后果，而它陈述那个后果。一个接受那个后果的对话者已理解那个论证，而所余下的分歧关乎那个约束更新能力是否值得被保留，而这是一个那个动力学由 §6.5 留作敞开的问题。

那个结果对道德理论的分量

一个最后的误读应当被排除。那个说明可能被取为主张一个功利主义框架要求由非后果主义的诸承诺来补充以便在道德上适足，而这不是那个主张。

那个主张关乎一个动力学条件。非结构性规范占据那个约束场之动力学中的一个位置，而它们的功能是一个那个场的更新能力所依赖之区间的维持。那些规范是否也在道德上被要求，是一个当前说明对之沉默的分开问题。所被表明之物是一个缺乏它们的系统有一个确定的结构，而那个结构是一个其中历史约束停止被它所约束的那个动力学所修订的结构。

§7 应用与实践

§1 的 Q8 问那个说明如何关涉实践。本节回答，而那个回答被前面诸节所确立之物所约束。三个结果尤其收窄此处可被说之物，而它们在开端被陈述，以便以下所述的谦抑被理解为一个后果、而不是一个缄默。

§4 确立诸参与者对那个慢变量没有通达。§5.4 拒绝建构一个度量到一个稳定性边界之距离的量，并给出会适用于任何从内部所尝试的这样建构的诸理由。§6.5 论证一个因为不优化的诸空间是有价值的而被维持的不优化空间，已因此被转换为一个工具。合在一起，这些主张那个从业者不能看见那个要紧的变量、不能度量那个要紧的转变的邻近、并不能通过意图去保护那个要紧之物来保护它。

一个在这些约束之下被写的实践之节有两个诚实的形式。它可以陈述那些约束所排除之物，那是相当可观的、并值得被精确地陈述。而它可以指认行动仍然可能所在的那个残余空间，它比一个抵达这一节的读者会期望的更窄。二者都在下面被尝试。所被谢绝的是第三个形式，在其中那些约束在一个开场段落中被承认、然后被搁置。

7.1 那个设计悖论

那个悖论的陈述

那个核心困难可以被以三步陈述。

一个系统的约束更新能力依赖于维持没有任何排名评价过的关系性自由度，由 §6.6。此类自由度被抗拒作为目标之表述的诸规范所维持，由 §6.4。而一个为维持它们而被采纳的规范已被提供一个目的，而这由 §6.4 摧毁那个使它能够维持任何东西的属性。

其后果是所要求那种的有意制度设计以一种具体而结构性的方式自我挫败。那个理解那个说明的设计者因此失去对它行动的能力，因为那个理解恰恰提供那个把那个规范转换为一个工具的目的。这是那个设计悖论，而随之而来的诸节既不消散它、也不把它当作一个放弃那个问题的理由。

真诚的分量

一个回应可用，并应当立即被关闭。可能被提议那个悖论是一件动机之事，而一个真正地珍视那个规范、而不是为它的效果而珍视它的设计者逃脱那个困难。

那个提议因 §6.4 中所给出的理由失败。把一个规范转换为一个工具之物是那个追求的形式、而不是那个追求者的心态。一个确立一个被保护空间、记录那个保护的诸理由、并对照那些理由审查那个空间的制度，已设立一个度量，而它已如此做，无论那些确立它者的真诚。那个悖论是结构性的，而结构性的困难不被善意所处理。

那个悖论的诸界限

那个悖论有一个确定的范围，而陈述它防止一个会使这一节无意义的过度扩展。

那个悖论所排除之物是为它们的动力学功能之故对非结构性规范的有意维持。它不排除为别的理由、包括它们所内在的诸理由对此类规范的维持：一个制度可以因为一个实践是合宜的而持守它，而那个动力学功能随之而来而不是那个理由。那个悖论也不延伸到可能性约束或到可评价性约束，它们以寻常的方式开放于有意的改变。而它不排除障碍的移除，而 §7.3 把这处理为可用行动的主要形式。

7.2 那个说明之下的治理

治理在那个框架中的位置

治理，在本文所属的那个框架中，关乎一个被生成的关系一旦存在之后如何被治理。当前这一节提供那个历史性扩展所添加之物：那个治理的对象是一个其约束结构本身在运动的关系场，而那个运动对那些治理者不可用。

那个治理靶的不可用

对治理最有后果的结果是否定性的，并从 §5.4 随之而来。一个被框定为”使一个系统远离一个稳定性边界”的治理纲领，要求知道那个边界躺在何处。那个说明主张这个距离对诸参与者不可用，而它的不可用是结构性的、而不是当前测量的一个缺陷。

那个结果排除一类否则会是自然的提议。对制度性危机的早期预警系统、韧性指标，以及报告一个社会离一个转变之距离的仪表盘，依此说明，是去度量一个其从内部的测量正是那个框架所否认之物的量的诸提议。§5.4 录入了那一个限定：临界减缓的统计签名可能从对扰动的响应、而不带关于那个底层参数的知识可读，而历史系统是否容许这样的测量是一个开放问题、而不是一个被了结的不可能。

基于指标之治理的危险

一个第二结果是对一个按度量之治理所携带的危险的规定，而它从 §6.3、而不是从那些认识论结果随之而来。

按指标治理是主张 7 中所处理的那个投影的一个特例。一个采纳一个度量、对照它报告、并调整行为以改善它的治理机构，已在它所治理的领域中设立一个指标驱动的动力学，而由 §6.3 已因此开始阻尼那个领域的约束更新能力所依赖的诸扰动。那个主张是比较性的、并容许程度，如主张 7 所要求：一个被应用于一个有界领域、连同被留下未度量之诸领域的指标，不同于一个被应用于一个社会整个活动范围的指标。

那个结果的实践内容是一个应向任何被提议度量所问的问题。它不是那个度量是否捕获那个要紧之物，那是那个寻常的问题、并且是一个合理的。它是那个度量把那个被治理领域的多少比例留下未度量，以及那个余项是否大到足以承载那个领域所要求的诸扰动。一个治理机制可以在这个维度上被评估、而不带任何关于它所采用之诸度量之优点的判断。

那个惯性区在治理中的分量

那个相应的肯定性陈述比人们会愿望的更弱，并被以那个说明所支持的强度录入。一个把活动的实质诸领域留下未度量的治理机制，在那些领域中保留 §5.5 中所处理的那个转移。那个保留能否作为一个政策被追求，恰恰是 §7.1 所置于问题之中的，因为一个为保全转移而被留下未度量的领域，已被指派一个功能、并因此在相关的意义上被度量。

在那个悖论中存活之物，是一个省略与提供之间的区别。一个尚未把测量延伸进一个领域的治理机制，不同于一个已把那个领域指定为一个被保护保留地的机制，而那个区别是 §6.4 所指认的那一个。第一个留下一个空间；第二个已设立一个。只有第一个支持那个动力学功能，而没有纲领能产生第一个，因为一个”留如不动”的纲领是一个注意的形式。

7.3 不可优化性之下的制度实践

障碍的移除

那个悖论约束提供、而把移除留作敞开，而这个不对称是那个说明的实践内容所集中之处。

考虑两个制度性行动。第一个为未被度量的活动确立一个被保护空间，带一个理由与一个审查。第二个停止一个曾被延伸于一个先前未被度量之领域的测量。第一个提供一个目的、并由 §6.4 转换那个空间。第二个移除一个工具、并在它的位置提供什么也没有。所得的那个领域以 §7.2 第一个情形的方式是未被度量的，因为没有什么被指定、也没有功能被指派。

那个不对称给出那个说明的主要实践建议，而它是一个关于”停止什么”、而不是”做什么”的建议：测量向那些曾不带它而运作之领域的延伸，是那个惯性区据以被消耗的机制，而那个延伸一般是以一种提供所不是的方式可逆的。

冗余、异议与未被吸收的活动

三个制度性特征通常基于独立于这个说明的诸根据被辩护，而那个说明提供一个关涉每一个的额外考虑。那个独立性要紧：因为每一个已为它自己的诸理由被持有，那个额外考虑不提供 §7.1 所警告的那个目的。

冗余通常作为对失败的保险被辩护。依当前的说明它也保全一个完全被优化的安排会消除的诸格局，而它的消除收窄转移跨它发生的范围。

异议通常以诉诸异议者的诸利益、或诉诸批评的认识价值被辩护。依当前的说明它也提供那个盛行的评价泛函所不排名的诸格局，而这是 §4 为一个扰动存活选取所指认的条件。

没有任何制度所吸收的活动通常被留下不被辩护，主要作为浪费而可见。依当前的说明它是那个生成性目标运作于其中的领域，而它的消除移除 §5.7 的那个注入项。

在每一种情形中那个说明提供一个供那些已倾向于基于别的根据保全这些特征者去掂量的考虑。一个如此被提供的考虑能否被作用于而不转换那个特征，是 §7.1 留作敞开的问题，而 §7.4 返回到它。

抗拒转换的诸制度形式

一个更窄的问题可用，并容许一个更确定的答案：哪些制度形式抗拒转换为诸度量，无论操作它们者的诸意图。

三个属性关涉这。一个其价值在它的表演、而不是在一个结局中被实现的实践，抗拒测量，因为那个度量会不得不被取于那个表演本身。一个其参与者不因他们对它的表演而被选取的实践，抗拒优化，因为选取压力是诸实践据以被调谐到诸度量的机制。而一个其停止携带不了可见代价的实践，抗拒那个生成测量的问责，以易于被停止为代价。

第三个属性值得被标为一个危险、而不是一个建议。使一个实践抗拒转换为一个度量的诸特征，是同样的使它在它的预算被质疑时不可辩护的诸特征，而那个说明不提供绕过这的办法：一个能通过证明它的贡献被辩护的实践，会是一个其贡献已被度量的实践。

一个机制的评估

前述支持评估比支持设计更现成，而那个区别是那个说明的实践有用所在。

三个问题可被向一个既有的安排提出，而每一个都可从那些可见的诸特征被回答。那个安排之内活动的多少比例受制于测量，而多少比例从未被度量过？那个被度量的比例一直在增加吗，而在什么时期之上？那个安排之内为它们自己之故被持有的诸实践保留那个性质吗，还是它们已获得诸理由、诸审查与诸被报告度量？

第三个问题是 §6.7 的归还判准以一个能被应用于诸制度的形式。它的答案是回溯性的，如 §6.7 所承认，而回溯性的评估仍然是评估：一个制度能够确定它的诸实践是否已被转换，即便在它不能确定它们是否即将被转换之处。

7.4 伦理与规范性行为

那个个体的位置

那个说明关涉个体行为，而那个关涉以一种从主张 8 随之而来的方式受限。一个理解那个说明、并为那个说明所提供的诸理由采纳非结构性诸承诺的个体，已由 §6.4 以目标形式采纳它们并摧毁了本要被采纳之物。

仍然可用之物是一个那个说明澄清、而不是创造的区别。一个人可以因为一个承诺是合宜的而持有它，而可以分开地理解此类承诺贡献什么。这两者立于一个要求审慎的关系之中：那个理解必须不成为那个理由，而没有程序保证这。因此那个说明对个体行为的贡献是诊断性的、而不是指示性的。它提供一个认出一个承诺何时已被转换的方式，即当它的辩护开始通过证明它的贡献而进行之时。

那个伦理词汇的分量

一个后果为伦理主张应当如何在这个框架之内被读随之而来。§6.5 主张那个动力学确立不了任何关于那个约束更新能力是否值得拥有之物，而同样的限制在此适用。那个说明确立一个系统在它的非结构性诸承诺被转换时所失去之物，而它把那个丧失的评价留给读者所带来的无论什么规范理论。

那个限制值得被审慎地遵守，因为夸大的诱惑在这一点上是相当大的。一个解释谦逊、信任与真诚在历史约束之动力学中之功能的说明，可能现成地被呈现为对那些德性的一个证成。它不是一个。它是对一个含有它们的系统所能做、以及一个没有它们的系统所不能做之物的一个描述，而从那个描述到一个建议的步骤要求一个那个说明所不提供的前提。

那个从业者的伦理

一个案例值得分开的处理，因为本文自己的立场落在它之内。一个专业地研究这些动力学、并在那个研究的基础上向诸制度建言的人，占据那个设计悖论最直接关切的位置。

那个说明对这样一个人提供很少寻常种类之物。它不提供任何可推荐的纲领，而它的主要实践内容是一个停止测量之某些延伸、而不是设立任何东西的建议。它提示那个建言关系本身携带 §7.2 中所处理的那个危险，因为被给出并被采纳的建言成为一个理由，而一个理由是一个度量的开端。它反而所提供之物，是一个精确到足以让一个从业者能在一个实践之转换发生时认出它的描述，以及去谢绝那些会加速它的诸提议的纪律。

7.5 这一节的分量

此处所组装的诸建议是单薄的，而它们的单薄是一个结果、而不是一个省略。一个主张”那个相关变量是不可观测的、那个相关距离是不可测的、而那个相关保护被它之被意图所摧毁”的说明，不会产出一个纲领，而一个产出了一个的节会已与它前面的诸节相矛盾。

两样东西已被确立。那个说明以某种精确性排除一类提议：以对一个转变之邻近为靶的治理、被指定为如此的被保护保留地，以及以证明它们的贡献对诸实践的辩护，各自都被表明是自我挫败的，并被表明为如此是为被陈述的诸理由、而不是靠一般的怀疑。而一个更窄的行动空间已被指认，在于障碍的移除、而不是保护的提供，以及在于诸安排的评估、而不是它们的设计。

如此被指认的那个空间是否宽到足以有用，是一个本文留给那些在其中工作者的问题。§8 把对存活那个设计悖论之诸制度形式的搜寻列为一个研究方向，并记录那个困难，目前，是未被解决的。

§8 那个研究纲领

一个纲领中的第一论文欠它的读者一个关于”什么已被做、什么仅仅被命名、以及为使整体站立什么会不得不被确立”的说明。本节提供那个说明。它陈述那个框架在它所属的那个更大努力之内的位置，列出那个工作继续所沿的诸方向，陈述它据以被进行的方法论立场，列出保持开放的诸问题，标出那个把那个说明与一个它所谢绝的解释形式分开的边界，并指认与 §2 所概览诸传统中当前正在进行之工作的诸接触点。

8.1 那个框架的位置与本文的贡献

在那个更大努力之内的位置

本文所属的那个框架把关系当作先于它所关联之物、并当作所存在之物于其中被生成的媒介。它的第一个发展关乎关系如何生成存在；一个第二个关乎一个被生成的关系一旦存在之后如何被治理；而当前的扩展关乎关系如何生成那个进一步的关系据以被生成的历史约束。

这三者立于一个确定的次序。第一个提供那个原始，第二个处理一个已然存在的关系，而第三个处理任何种类的诸关系被形成于其下的那个条件。以这个次序被读，那个历史性扩展提供另外两者所预设之物：二者都在一个其生成都不被设计来解释的约束结构之内运作。

本文所确立之物

四样东西已被论证、而不是被断言，而它们是本文所提供供评估之物。每一个都作为一个下面所列出的工作会被要求去保得的提议被提出。

一个本体论已被承诺、而它的诸术语被定义：约束作为那个关系场的一个宏观相，带 §3.4 的诸定义以及在 §3.4 所陈述的那个风险。一个结果已被推导、而不是被假定：诸参与者对那个慢变量的盲目从他们的平均场位置随之而来，由 §4.2 的论证。一个机制已被给出，为一个系统从一个稳定格局的离开，在其中累积与触发被区别开来、而一个触发因素有后果的条件被陈述，由 §4 与 §5.4。而一个规范性后果已从那个动力学被推导、而不是被独立地论证，在主张 7 及它在 §6.3 的论证中。

本文所留下未确立之物

三样东西已被命名而不被确立，而那个区别应当被明白地记录。

没有序参量为任何历史案例被展示，而 §3.4 承认那个相主张要求一个存在。没有解或近似为那个自输运方程被提供，它在 §5.1 的意义上仍然是示意性的。而 §4 的机制没有被给予经验检验，它的区分能力已在 §4.5 被论证、而不是被证明。

一般性的问题

一个观察值得被记录而不被作用于。此处所组装的装置，在其中一个约束结构条件化在它之下被形成的诸目标、同时被它们的追求所修订，不明显被限于那个历史案例。诸组织、诸学科、诸专业共同体，以及别的其中诸参与者在他们集体地修订的诸条件之下行动的诸格局，在更小的尺度展现同一个结构。

那个观察被作为一个方向、而不是一个主张被记录。一个断言那个一般性的第一论文会已削弱 §1 据以为它的诸接纳作辩护的那个聚焦，而”那个说明是否延伸”的评估是一件为已首先在一个案例中确立它的工作之事。

8.2 研究的诸方向

六个方向随之而来，一个为那个说明从 §3 起的每一个部分，以便没有部分被暗示为已完成。

本体论的诸方向

不变量的指认是第一个问题，而它是那个本体论之分量所搁于其上的问题。§3.5 论证那个社会案例缺乏一个独立地被促动的对称群，而所会取代它之物是一组在关系性语法之改写之下被保全的量。它们的指认会提供那个相主张所要求、而 §3.4 承认为缺失之物。

两个进一步的问题属于此处。§3.6 中所区别的那三种约束模式是否是穷尽的、以及它们是否是那个正确的切分，是开放的：那个类型学由它与那个目标分类的契合、而不是被推导所证成。而容器本体论在实践中、相对于在原则上、能被免除的程度值得被考察，因为把约束当作一个容器的分析便利是相当大的，而那个说明完全地放弃它。

认识论的诸方向

盲目是否容许程度是那个主要的问题。§4.2 以一个 §5.4 随后限定的模态陈述那个结果：如果临界减缓的统计签名从对扰动的响应可读，那么某种关于那个慢态的信息在不带关于那个慢变量本身的知识的情况下可用，而那个结果要求修正。确立此类签名是否在历史系统中可测，会了结一个 §7 也转于其上的问题。

一个第二问题关乎集体的认识装置。记录、测量与分析的诸制度扩展诸参与者所能知之物，而它们是否把它扩展到那个慢变量，不被 §4.2 的论证所了结，后者关乎一个参与者的位置、而不是一个装置的诸能力。那个问题携带一个值得陈述的张力：一个使那个慢变量可见的装置会削弱主张 8，因为有意保护于是会有一个靶，而那个说明会在一个承重点要求修订。

形式的诸方向

§5.2 的那个自输运方程容许三个方向上的发展。它在简化假定之下的解或数值处理会确立那个形式是否支持归于它的行为。闭合近似的建构，以 §5.10 的方式，要求物理闭合所接收的同一种证成，而提供一个会把那个类比转换为一个模型。而 §5.11 中所命名的那个多尺度装置，包括几何奇异摄动理论、平均法、以及跨那个约束谱系的粗粒化，以被发展的形式可用，并等待那个”历史案例容许它所要求诸结构”的证明。

规范性的诸方向

一个对那个余项的肯定性判准是那个突出的问题。§6.7 承认那个归还判准在应用中是反事实的、二元的、回溯性的，而一个由非结构性规范之所是、而不是由它们会在压力之下如何来指认它们的判准，会相当地加强 §6。

一个此类规范的类型学会服务于同一个目的。那一类由诸实例并由一个诊断特征被引入，而它是否容许内部结构、以及那些实例是否共享多于那个诊断之物，是未被考察的。

与别的规范传统的系统比较是一个第三方向。本文结构性地处理功利主义，在 §6.8 中，因为一个共同度量之下聚合的结构是主张 7 所关乎的。道义论的、德性理论的与契约论的诸立场立于对那个说明的、尚未被考察的诸关系，而对德性伦理的处理尤其可能是实质性的、而不是附带的，给定非结构性规范与那些德性之间的亲缘。

实践与治理的诸方向

§7.1 的那个设计悖论是那个核心问题，而 §7.5 记录它为未被解决。所被寻求的是一个其维持不提供那个转换它之目的的制度形式：一个为它所内在的诸理由持续、同时贡献那个动力学功能、而不使那个贡献成为那个理由的形式。此类形式是否存在是开放的，而 §7.3 指认了会刻画它们的三个属性。

两个进一步的方向属于此处。与那个框架的治理性扩展的接口要求规定：一个治理说明从被给予一个在运动的约束结构中获得什么、以及它必须放弃什么。而对基于指标之治理作为主张 7 一个案例的研究，提供那个说明所提供的最可通达的经验靶，因为测量向先前未被度量之领域的延伸是被记录的、可断代的、并跨诸设置可比的。

经验的诸方向

三个经验问题从那个机制随之而来。

间歇性的刻画是第一个。主张 6 主张约束更新在时间中被不均匀地分布、并集中于那个场的有限诸区域，而那个主张有可观测的内容：制度重新组织的时间分布，以及它们在诸领域中的集中、而不是它们跨诸领域的扩散，在原则上是可测的。

向上累积的证据是第二个。§5.5 把社会系统是否展现向更大尺度的转移留作敞开，并陈述了会被要求去确立它之物。

那个机制自己的预言是第三个、并且是最直接的。§4.5 主张转变应当起源于那些盛行指标所不度量的领域，而这是一个关于往何处看、而不是关于将发生什么的主张。它的考察要求那些其中盛行指标被记录、而那个转变的起源能相对于它们被定位的历史案例。

8.3 方法论

两个方法及其诸缺陷

那个说明推荐一个两个方法的辩证，而它是带每一个的缺陷、而不是带诸强处被陈述的。

那个传统方法，以文本研究与哲学论证进行，很难被验证或证伪。一个由从一个传统的诸文本的论证所发展的主张，能被对照证据无限地辩护，而那个会终结那个辩护的纪律从外部被提供。

那个经验方法携带两个缺陷。它不能击败归纳问题，而它不能从”是”跨到”应当”，以致没有证据的累积裁决一个规范性主张。而它疏离它的对象：一个以测量进行的方法研究已被度量之物，而它探究的人类事务只通过测量所提供的诸代理被抵达。

那些缺陷的不对称

这两个缺陷是不对称的，而两个方法都不修复另一个。经验工作不能在”是”与”应当”之间缺口成立的领域治愈不可证伪性，因为会裁决一个规范性主张的数据不是数据所是的种类。传统工作不能击败归纳，它对所论的诸规律性没有独立的通达。

那个配对所成就之物是每一个方法之过度伸展的约束。经验工作把思辨持于诸现象；传统工作防止一个可测代理与它所代理之物的认同。因此那个辩证是一个纪律、而不是一个综合，而它的两半不组合成一个没有缺陷的方法。

那个说明对探究的应用

那个纪律的第二半是主张 7 被应用于探究。一个把它的对象投影进它所能度量之空间的研究纲领，已在方法的层级执行 §6.3 在诸目标的层级所描述的那个操作：抗拒测量之物被留出，而所被留出之物是那个纲领自己的修订会依赖的材料。

§8.3 中所命名的那个疏离因此不是经验方法的一个附带代价、而是那个投影在探究中所采取的具体形式。那个说明因此应用于它自己，而那个应用是一个关于这个纲领应当如何被进行的约束、而不是一个关于别人的观察。

借用中的纪律

本文从物理学的诸借用是在一个较后工作应当保留的纪律之下被作出的，而它在此作为一个规则、而不是作为一个对所做之事的描述被陈述。

一个借用提供词汇并证明一个结构是可融贯地被思考的。它不转移结果：关于一个物理系统所成立之物由那个社会案例所不承袭的论证为那个系统被确立。凡一个借用可能被扩展进一个定量对应之处，那个扩展要求独立的证成，而 §5.7 因概括的诸理由谢绝了一个这样的扩展。而每一个借用都应当被给予一个它停止之被陈述之点，如 §3.3 与 §5.1 所做，以便它的所及能被评估、而不是被推断。

8.4 开放问题

五个问题在那个强意义上是开放的，即那个说明不指示它们会如何被解决。

一个序参量的存在

那个相主张要求序参量为历史约束而存在，而 §3.4 承认没有一个被展示。那个问题有一个不寻常的结构，因为 §5.4 与 §4 合在一起主张这样一个量对诸参与者不可用。因此所被寻求的是一个其存在与它从内部的不可用相容的量，而这两个条件是否联合地可满足，本身是未被了结的。

一个对那个余项的肯定性判准

§8.2 把这陈述为一个方向；它在此作为一个问题被录入，因为当前判准的反事实性质可能是不可消除的。一个规范对转换的抗拒是一个倾向，而诸倾向由会发生什么、而不是由已发生什么被指认。如果没有肯定性判准存在，那么那个说明的核心规范性区别是永久回溯性的，而 §7 承袭那个后果。

自我指涉的形式处理

§3.5 指认自我指涉为独属于那个社会案例的界限。诸参与者读他们据以行动的那个约束；那些读法进入那个场；而那些读法在诸参与者之间有别，以致那个把那个场关联到它描述的粗粒化既不是固定的、也不是单值的。没有为这个情形的形式装置在此被提供，而那些物理借用不提供先例，那个度规对它自己的值没有意见。

一个慢流形的诸条件

§5.6 由到一个稳定性边界之距离划分那两个描述的适用性，而那个划分搁于那个远离那个边界之区制中一个谱隙的存在。历史系统是否展现这样一个隙、还是活动在所有时刻都跨诸尺度被耦合，是未被了结的。如果是后者，§5.3 的那个快-慢描述失去它的凭据，而从它推导的诸认识论结果要求单独在那个级联描述上被重构。

向临界性之趋近的性质

最后一个问题是最有后果的、并且是那个其中过早的解决会造成最大损害的。

那个说明主张那个慢变量朝一个稳定性边界漂移，而它不解释那个漂移为何发生。两个可能性可用。那个漂移可能是被驱动的，以致那个慢变量被同样本可把它携带到别处的诸影响所携带。或那个系统可能朝那个边界组织它自身，以致那个趋近是那个动力学、而不是作用于它之物的一个后果。

第二个可能性有一个应当被以怀疑看待的吸引力。如果那个消耗那个惯性区的制度化本身就是那个朝临界性的漂移，那么主张 7 与那个临界性条件从两侧描述一个过程，而优化在一个强而优雅的意义上是自我拆台的：它会不仅仅阻尼那个更新所依赖的诸扰动、而是把那个系统携带向那个其中所余诸扰动成为决定性的态。那个优雅恰恰是为何那个可能性作为一个问题被录入。确立它会要求一个本文所未作的论证，而不带一个就采纳它会给历史提供一个倾向，而这是下面所处理的那个边界。

8.5 那个针对目的论的边界

那个区别的形式

那个说明是辩证的、而拒绝是目的论的，而那个区别要求陈述，因为诸格局之间转变的词汇能被任一方式读。

一个目的论说明主张历史的运动被朝一个终点导向，无论是被一个观念的自我发展、被一个潜能的实现、还是被向一个目的的收敛。当前的说明主张一个格局在那些维持它的关系性诸条件停止维持它时让位。那个否定由那些条件、而不是由那个格局正朝之发展之物所提供，而那个后继格局是那个动力学所产生之物、而不是那个过程所为之物。

目的论所要求的那个观察点

那个说明以一条比一个偏好之声明更具体的路线排除目的论，而那条路线值得被陈述，因为它把那个排除连接到那些认识论结果。

一个历史的目的论读法要求一个从其上那个过程的方向可见的位置。黑格尔的历史哲学提供这样一个位置，而那个提供不是附带的：一个其中那个过程被导向的说明要求那个方向从某处可读，而那个读它的哲学家占据那个被要求的位置。§4 否认任何这样的位置在那个系统之内存在，而 §3.1 否认一个在它之外存在。目的论因此在这个框架中失去它的立足，为与那个控制论形式在 §5.2 中被移置同样的理由：二者都要求一个那个本体论所不容许的观察者。

那些暴露之点

那个说明中的三个点是目的论能重新进入之处，而每一个被一个具体的措施所关闭。

一个作用量原理会提供一个历史极值化之量，而 §3.5 拒绝寻求一个。一个控制参数会提供一个漂移的方向、并随之一个把那个漂移读作倾向的诱惑；§5.4 拒绝建构一个。而一个自组织的向临界性之趋近会给历史提供一个它寻求之态；§8.4 把那个可能性作为一个开放问题、而不是一个结果录入，恰为这个理由。

这三个排除有一个共同的形式，而陈述它使那个边界成为一个政策、而不是一系列决定。每一个都谢绝一个会许可把一个倾向读进那个动力学的形式建构，而每一个都基于”那个建构是不可用的、而不是它的诸后果不受欢迎”这一根据被谢绝。

8.6 与当代工作的接触

§2 是回溯性的，处理所概览的诸传统所成就之物。这个小节是前瞻性的：它指认那些传统当前正在做什么、此处所发展的说明在何处关涉那个工作、以及那个接触应当在何种纪律之下被作出。

当前正在讨论的诸问题

若干当代工作线关涉约束更新的问题，而以下是最直接的。

价值形式传统以及与它相关联的诸读法，把价值当作一个社会形式、而不是当作一个实体，并分析那个使通约成为可能的抽象。相关联的实在抽象概念主张那个抽象在实践中、而不是在思想中发生：交换从被交换之物的特殊性中抽象，而那个抽象由那个交易、而不是由那个观察者所执行。

关于平台经济、以及关于数据作为一个生产条件的工作，考察测量向先前未被度量之领域的一个延伸，连同随之而来的诸种租金与控制形式。

社会再生产理论考察生产所依赖、而生产的分析所曾排除的那个活动领域，并问那个排除如何被维持。

那个传统中的生态工作分析社会新陈代谢与它所依赖的自然诸条件之间的裂缝，并把那个裂缝当作那个社会过程所采取之具体形式的一个后果。

后马克思主义工作继续发展对霸权与偶然性的分析，而与加速主义诸立场相关联的工作问什么技术条件使哪些政治形式可用。

世界体系分析继续它对长波与霸权更替的考察，而随那个分析性潮流而来的关于微观基础的争论仍然活跃。

那个共同局限与它所允许的重读

§2.4 的诊断延伸到这批工作，而那个延伸是接触被提议所在的根据。在每一种情形中约束更新的事实被登记而它的机制被留作未规定。价值形式分析解释那个抽象如何成立而不处理那个可表达者的边界如何移动。后马克思主义工作以偶然性取代必然性，而偶然性陈述那个结局的敞开、而不是产生它的那个过程。生态工作把那个裂缝描述为后果而不处理它发生的尺度结构。社会再生产理论指认那个被排除领域而不处理那个排除如何被那个排除它的语法所维持。

一个重读值得被更详细地陈述，因为它是一个认可的行动、而不是一个纠正。那个传统的被累积矛盾已被当作断裂的原因。依当前的说明它是那个慢变量朝一个稳定性边界的漂移，带那个触发因素被分开地提供并由 §4.4 的判准所选取。那个重读给那个传统的术语一个精确的动力学内容，并把那个因果工作指派给两个因素、而不是一个，而这是一个任一说明单独都没有的分工。

诸接触点

五个配对随之而来，而每一个都是一个翻译的假说、而不是一个认同。

实在抽象可能对应于 §3.6 的可表达性约束，二者都关乎一个实践使什么可说。新陈代谢裂缝可能对应于那个惯性区被耗散的消耗，二者都关乎一个已被切断的转移。霸权可能对应于 §6.2 的表达性耦合，二者都关乎一个主体的处境能在其中被表述的那个词汇的供给。平台经济中先前未被度量领域的测量可能是主张 7 的一个实例，而 §8.2 记录它为最可通达的经验靶。而长波可能对应于 §5.3 的诸慢变量的诸弛豫时间。

那个接触的纪律

每一个配对都要求一个翻译是被提议、而不是被确立的限定，而第一个是那个限定携带最多分量的情形。实在抽象与可表达性约束在不相容的诸设置中生起：前者预设一个价值的分析，在其中当前说明不取任何立场，而这两个概念之间的相似是一个角色的相似、而不是一个内容的相似。把那个配对写作一个等价会引入本文所已谢绝作出的诸承诺。

那个纪律适用于全部五个。所被提议的是一个两个词汇可被带入接触之点，而所会确立那个接触之物是”一个现象在二者中被描述、而那些描述被比较”的工作。直到那个工作被做，那些配对指示往何处看。

那个说明所寻求与这些纲领的关系应当在结尾被陈述，因为一个提议一个框架的第一论文容易被读作声称取代它所概览之物。此处所作的主张更窄。这些纲领中的每一个都有一个关于”什么约束行动”的说明以及一个”约束如何让位”的描述；当前框架所提供之物是一个为第二者的机制，以一般到足以被附加于对第一者不止一个说明的术语被陈述。它反过来所接收之物是那些纲领所提供的实质内容，没有它一个机制理论描述一个形式、而从不描述一段历史。

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关于方法的一则说明。本文中的诸形式陈述携带 §5.1 中所区别的那三个等级，而没有陈述被给予一个高于那个论证所支持的等级。那个自输运方程以及跟随它的诸方程展示诸形式；它们不被求解，而从它们不推导那个散文不独立地推导之物。凡一个定量建构可用、并会借给那个说明一个它未曾挣得的严格外表之处，那个建构被谢绝、而那个拒绝被记录：§3.5 为一个作用量原理，§5.4 为一个控制参数，§5.7 为一个无量纲群。那个说明会因这三者中的任何一个、被提供以它自己的证成、而被加强。它会因它们的假定而被削弱。

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