Defining Relation in Generative Relational Being - A Position Paper
ENGLISH
Defining Relation in Generative Relational Being
A Position Paper
Wanhong Huang · huangwanhong@serendip.ngo
Abstract
Generative relational being places relation at its centre and has so far left the concept open. This paper supplies a working definition: a relation is the constraint through which generation unfolds in history. Existing understandings of relation, as interaction, as background structure, as difference, as tie, and as correlation, are each stated at an instant, where a framework concerned with historical generation requires a concept answerable to succession. The definition’s historical clause carries the weight, since the constraint is borne and revised by the very process it constrains, which separates the proposal from structuralism. The paper argues that unconstrained succession fails to be maximal generation, since where succession is free nothing accumulates, and it answers the objection that a relation is a coupling and not only a constraint. A taxonomy on two axes follows, the domain of the relata and the mode of bearing, with some forty instances assigned across four modes. Relations borne by a single party are the decisive case, since relations whose counterpart does not exist are relations in the full sense here, while the interaction and tie readings must deny them the name.
Keywords: relation; constraint; generativity; historical generation; relational ontology; conceptual definition; generative relational being.
A note on the standing of this paper. This is a position paper, and its ambition is bounded accordingly. It does not offer a universal philosophical definition of relation, and it does not claim that the philosophical and sociological traditions surveyed in §2 have misunderstood their subject. It proposes a working definition of relation for one framework, generative relational being, states the considerations that recommend that definition over the alternatives available, and tests it against cases from several domains. Whether the definition earns its place is settled by what it lets the framework say and by what it forbids the framework from saying, and both are exhibited here as plainly as the author can manage. The definition is offered as revisable, which is a commitment the framework itself requires and not a courtesy. Objection, correction, and counter-example are welcome at huangwanhong@serendip.ngo.
§1 The Problem of an Undefined Primitive
Generative relational being is a framework built on a word it has not defined. Its claims are stated in terms of relation: that subject, meaning, value and normativity co-emerge through generative relational processes; that asymmetry in a relation produces power which sufficient generation absorbs; that what degrades in social life is a relational grammar and not only a distribution of goods. Each of these is a claim about relations, and each has so far borrowed its central term from the reader.
Leaving a primitive open has its uses, and the framework has drawn on them. An undefined term accommodates cases the author has not yet examined, and it postpones commitments that would be premature. There is a point, however, at which the postponement begins to cost more than it saves, and the framework has reached it. Three costs can be named.
The first is that the framework’s distinctive claims become indistinguishable from claims already made elsewhere. If relation means a tie between individuals, then the thesis that relations generate value restates network sociology; if it means an interaction, the thesis restates exchange theory; if it means a differential position in a system of signs, the thesis restates structuralism. The framework has been arguing that it says something these do not, and it cannot show this while its central term is supplied by whichever of them the reader happens to have read.
The second is that an open primitive silently imports the commitments of whatever fills it. A reader trained in network analysis will hear relation as a state variable, an edge that is present or absent at a time. On that hearing, several of the framework’s propositions become false or trivial: the proposition that a relation is revised by what happens within it becomes a claim about edge updating, which is a modelling convenience with no ontological weight, and the proposition that a subject is constituted in relation becomes a claim about the effects of network position, which has been studied for decades and is not what the framework means.
The third cost is internal. A framework that intends to model constraint evolution, as the historical branch of this programme does, needs to say how the constraint at one scale stands to the relations at another. That statement cannot be made while relation is undefined, since the two terms would be free to collapse into one another whenever the argument required it.
1.1 The Task and the Scope
The task of this paper is therefore narrow and, within its narrowness, foundational. It proposes one definition, argues for it, unpacks its terms, and illustrates it across five domains. It introduces no other part of the framework beyond what the argument requires.
The scope of the claim must be stated at the outset, since almost every difficulty in defining relation comes from taking the task to be larger than it is.
Scope. This paper does not attempt to provide a universal philosophical definition of relation. It proposes a working definition for generative relational being, whose purpose is to analyse generative processes across physical, biological, social and symbolic domains.
The consequence of this scope is that the paper is not in competition with Aristotle’s treatment of the relative, with Leibniz on relational space, with Whitehead’s prehension, with Cassirer’s functional concepts, with Simmel, with Latour, or with the relational political philosophy of the last two decades (Aristotle 1984; Leibniz & Clarke 1717; Whitehead 1929; Cassirer 1910; Simmel 1908; Latour 2005; Ceva 2016). Each of those is an answer to a question about what relation is. The question asked here is what concept of relation a particular framework requires in order to do the work it has set itself. The two questions can be answered differently without either being wrong, and a framework that conflates them takes on a burden of proof it does not need and cannot discharge.
1.2 The Central Claim
Central claim. Generative relational being understands relation as the historical constraint through which generation unfolds, and not as a static connection between entities. Everything that follows supports this one sentence.
The sections proceed in the order of the argument. §2 surveys what is available and identifies what none of it supplies. §3 states the definition and unpacks its four terms. §4 argues the point on which the definition stands or falls, that constraint is the condition of generation and no obstacle to it, and answers the objection that constraint omits what a coupling adds. §5 develops a taxonomy on two axes and works the cases. §6 marks what the definition is not and what it leaves unsettled. §7 places the result within the wider programme.
§2 Existing Understandings of Relation
What follows is a classification and not a literature review. Five readings of relation are distinguished, each stated in its strongest form, each credited with what it achieves, and each examined for one question only: whether it makes relation answerable to the historical unfolding of generation.
2.1 Relation as Interaction
On the first reading a relation is what accumulates from repeated interaction. Two parties act upon one another; the encounters leave a residue of expectation, obligation and habit; the residue is the relation. The lineage runs from Simmel’s account of sociation through symbolic interactionism to exchange theory (Simmel 1908).
The reading achieves something the others struggle to: it makes relation dynamic without special machinery, since a relation on this account simply is a history of encounters. Its limit is that it requires the parties to be individuated in advance of the relation, as beings capable of interacting before any relation obtains between them. A framework holding that subjects are constituted in relation cannot take this reading as basic, since the reading presupposes what the framework proposes to explain. There is a further limit, less often noticed. Interaction is an event, and a relation composed of events is present only when the events occur. The reading has difficulty saying what a relation is during the long intervals in which nothing passes between the parties, and yet those intervals are where much of relational life is lived.
2.2 Relation as Background Structure
On the second reading relations precede interactions and configure them. Positions exist before the occupants of positions; what two people can do to one another is set by the structure within which they stand. Structuralism holds this, and so does the relational sociology that follows Emirbayer’s programmatic statement, on which the transaction and not the substance is the primitive of social analysis (Emirbayer 1997).
This reading corrects the first at exactly the right point: relata can now be constituted by relations, and the framework’s ontological commitments become sayable. Its limit lies in the standing of the structure. The structure conditions everything and is itself conditioned by nothing within the account; it enters the analysis as given, and its own transformation is either left to a separate theory or supplied by exogenous shocks. For a framework whose central question is how constraint evolves, a concept of relation that leaves the evolution of relations outside the concept is unusable.
2.3 Relation as Difference
On the third reading relation is difference: a term has its identity through what it is distinguished from, and the system of distinctions is prior to any positive content. Saussure’s value, in which a sign is constituted by its differences from other signs, and Bateson’s difference that makes a difference, are the canonical statements (Saussure 1916; Bateson 1972).
The achievement is considerable. This reading dispenses with substance altogether, which no other reading manages, and it explains how relation can be efficacious without being a thing. Its limit is temporal. Difference is a synchronic notion: it describes the state of a system of distinctions at a moment, and it says nothing about how one moment gives way to the next. Bateson’s formulation gestures at succession, since a difference that makes a difference is a difference with a consequence, and the gesture is exactly what the present paper takes up. As it stands in the tradition, however, the reading gives a theory of contrast and no theory of course.
2.4 Relation as Tie
On the fourth reading a relation is an edge: a link between nodes, present or absent, weighted or unweighted, directed or undirected. This is the working concept of network analysis, and its virtue is that it is measurable. Whole literatures have been built on it, and their findings are real.
Its limit for present purposes is that the tie is a state variable. It records that a connection obtains and says nothing about what governs the succession of states within it. When network models let ties change, the rule of change is supplied from outside the concept of the tie, as a dynamics imposed upon the graph. The concept therefore locates relation in the wrong layer for a framework whose interest is precisely the rule of change.
2.5 Relation as Correlation
On the fifth reading, common in the sciences and often tacit, a relation is a statistical or functional dependence between quantities. This is operational and it travels well between domains.
Its limit is that correlation is symmetric and timeless, and that it does not distinguish a relation from a coincidence. Two quantities may covary because one constrains the succession of the other, because both are constrained by a third, or because a finite sample was unlucky. A framework that must tell these apart cannot take the undifferentiated notion as its primitive.
2.6 The Common Limit of the Surveyed Readings
Each reading captures something, and the framework has been drawing on all five without acknowledging that it was doing so. The point to be extracted from the survey is that they share a feature. Each defines relation at an instant. Interaction is an event at a time; structure is a configuration at a time; difference is a contrast at a time; a tie is a state at a time; a correlation is a property of a distribution, which is timeless by construction. Where succession enters any of these accounts it enters as something applied to the relation from outside.
A framework concerned with historical generation needs the opposite arrangement. It needs relation to be the thing in virtue of which a system’s later states depend on its earlier ones. That is the requirement the definition below is built to meet.
§3 The Definition
Definition (Relation in GRB). A relation is the constraint through which generation unfolds in history.
The sentence is short, and its brevity is deliberate: a definition of a primitive should be quotable and should carry no argument inside itself. All the argument is in the surrounding text. Four terms do the work, and each is now taken in turn.
3.1 Constraint
Constraint here means a restriction on succession. It concerns how the states of what is related may follow one another, and it does not concern which states exist. This is a narrower reading of the word than ordinary usage supplies, and the narrowing is essential; §4 shows that most of the resistance the definition provokes comes from hearing constraint in the wider sense.
The distinction can be put plainly. A constraint on configurations says that certain states are unavailable. A constraint on succession says that certain states, being available, may be reached only from certain others. The first impoverishes a system. The second gives it a shape in time. It is the second that is meant.
3.2 Generation
Generation is the appearance, within a system, of what was not specifiable in the system’s own prior terms. The formulation is deliberately thin, and it is thin for a reason that must be stated openly. The framework treats generative tendency as a postulate: it holds that relations exhibit generation, and it declines to explain why. The refusal is principled. To answer the question why systems unfold their own dynamics is to name some more fundamental good that generation serves, and generation would then become the means to that good. Any such answer, whatever term filled it, would convert the framework into a variety of utilitarianism. Physics does not explain why the action is extremal, and mathematics does not explain why sets exist. The parallel is claimed here as licence for the same abstention.
One consequence of the abstention should be recorded, since it bears on the standing of the definition and is taken up again in §3.6. Because generation appears in the definition of relation, the sentence relations exhibit generative tendency cannot be read off the definition as a discovery. It is a postulate about the systems the framework studies, and it must be stated as one.
3.3 Unfolding
Generation has a course. To say that generation unfolds is to say that it takes time, that it passes through states, and that its passage is neither predetermined nor arbitrary. A predetermined course would make the constraint the whole story and generation an illusion. An arbitrary course would make the constraint idle. The term marks the middle case, which is the only case in which the definition has content: a course that is shaped without being fixed.
3.4 History
This is the clause that carries the most weight, and it is the clause a reader is likeliest to take as decoration. It is not decoration. To say that generation unfolds in history is to say that the constraint through which it unfolds is itself borne by the process it constrains.
Without this clause the definition would be a statement of structuralism, and a weak one. The constraint would condition generation and would itself be given from outside, and the framework would have arrived, by a longer route, at the position identified as insufficient in §2. With the clause, relation is at once condition and product: it constrains the succession of states, and it is revised by the succession it constrains.
This is what makes the definition historical in a sense stronger than the observation that relations have pasts. Relations are not merely dated. They are made of what has passed through them. The point has a familiar formulation in the historical-materialist tradition, that people make their own history and do not make it under circumstances of their own choosing, where the circumstances are themselves the sediment of earlier making (Marx 1852). The definition proposed here is an attempt to state the structure of that sentence at the level of the concept of relation itself.
3.5 The Propositions Unfolded from the Definition
The definition may be unfolded into four propositions, which together constitute the position this paper defends.
Proposition 1 (Historicity). Relation is a historical concept and admits no timeless specification. A relation is individuated by the constraint it imposes on succession, and that constraint has a date, a provenance and a career.
Proposition 2 (Dynamism). Relation is defined over succession, and it is itself subject to succession. The constraint governs how states may follow one another, and the sequence so governed revises the constraint. Relation is therefore dynamic in two senses, and the second is what distinguishes this account from the structural reading.
Proposition 3 (Constraint as Condition). Constraint stands in no opposition to generation. It is the condition under which generation unfolds. Where succession is unconstrained, nothing accumulates and no course is retained, and what results is noise and no generation at all.
Proposition 4 (Method). Generative relational being individuates and studies relations by the part they play in historical generation, and not by the metaphysical status of their relata. Whether the relata are physical, biological, social, symbolic or imagined is immaterial to whether a relation obtains.
Proposition 3 is the philosophical contribution and is argued in §4. Proposition 4 is the methodological payoff and is exhibited in §5, where it does the work that lets a single definition span five domains.
3.6 The Standing of the Definition
A definition of this kind is stipulative, and honesty about that is worth more than a show of discovery. The paper does not claim that this is what relation has always meant, nor that other definitions are mistaken. It claims that a framework with these purposes requires a concept with these properties, and that the sentence above states one.
Two consequences follow, and both are constraints on how the framework may argue in future.
The first has been anticipated in §3. Since generation appears in the definiens, no proposition of the form relations are generative may be presented as a result. The substantive claims in this vicinity are existential and empirical: that constraints of the defined kind exist in physical, biological, social and symbolic systems, and that in those systems the constraint is in fact borne and revised by the succession it governs. Those are claims about the world and can be false. The definition itself cannot be false; it can only be useless, and its use is what §5 is for.
The second concerns teleology. A definition that ties relation to generation invites the reading that relations exist for the sake of generation, and that reading would be a serious error. The definition says how relation and generation stand to one another, and it assigns no purpose to either. The framework has independent reasons for refusing to make generation a good, since a system that treats the free unfolding of its own dynamics as an end can justify the destruction of whatever impedes it, and that justification is available in the framework’s own vocabulary unless the vocabulary is guarded. The guard is stated here so that the definition does not quietly undo it: relation is defined through generation, and generation is thereby given no normative standing whatever.
§4 Constraint as the Condition of Generation
The definition asks a reader to accept a sentence that sounds false on first hearing. This section takes the appearance seriously, states it in its strongest form, and answers it.
4.1 The Received Intuition
The intuition runs as follows. A constraint removes options. Fewer options mean less freedom. Less freedom means less creation. Constraint therefore stands opposed to generation, and defining generation’s condition as constraint is a paradox at best and an equivocation at worst.
The intuition is not naive. It underwrites a great deal of moral and political reasoning, and in the cases it is drawn from it is correct: the prisoner has fewer options and generates less; the censored writer has fewer options and generates less. Any answer that dismisses the intuition will be dismissed in turn.
4.2 The Argument from Unconstrained Succession
The answer begins by asking what a system with no constraint on succession would look like. Its next state would be independent of its present one. Nothing that happened would bear on what happened next. Such a system passes through states without passing through a course: it has no trajectory in any sense that survives inspection, since a trajectory is a sequence whose parts are answerable to one another. Nothing accumulates in it, because accumulation requires that the past bear on the present. Nothing can be built in it, because building requires that a step taken remain taken.
This system is at the maximum of unconstrained succession and at the minimum of generation. It is noise. And noise is the limiting case that the received intuition never examines, because the intuition is drawn from cases in the middle of the range, where a constraint is removed from a system that has plenty of others left.
The general form of the point is that generation requires the retention of its own past, and constraint on succession is what retention consists in. A relation, on the definition offered, is exactly what makes a system’s later states answerable to its earlier ones. Where there is no such answerability there is no history, and where there is no history there is nothing for generation to unfold in.
Four familiar cases display the same structure, and they are offered as analogies and not as parts of the definition. Grammar constrains which strings count as sentences, and the constraint is the condition under which an unbounded set of new sentences becomes sayable and understandable. Counterpoint constrains which voices may move how against which, and composers have found in the constraint the condition of invention and not its enemy. A crystal lattice constrains which positions an atom may occupy, and the constraint is what allows structure to propagate over distances no unconstrained aggregate could span. An institution constrains what its members may do, and the constraint is what allows an action taken today to still mean something next year.
4.3 The Limit of the Argument
The argument establishes that constraint is necessary for generation. It does not establish that constraint is sufficient, and the definition should not be read as claiming this. Some constraints on succession close a system’s continuations down to one, and a system so constrained generates nothing further. The distinction between constraint that leaves continuations open and constraint that forecloses them is the substance of the framework’s account of relational degradation, and it is deliberately left outside this paper.
What the definition contributes at this point is the ability to state the question. On the readings surveyed in §2, the difference between a relation that sustains generation and one that ends it must be imported from a theory of something else, since none of those readings has succession inside the concept of relation. On the definition proposed here, the difference is a difference between two constraints on succession, and it can be posed as one question about one kind of object.
4.4 Constraint and Coupling
One objection deserves its own treatment, because it is the most serious available and because it was raised against this definition during its development. It runs as follows. A relation does more than restrict. In physics, the coupling between two spins is a constraint, and it is also a coupling: a channel along which influence passes. In institutions, a relation restricts what may be done, and it also establishes the routes through which coordination, influence and joint development occur. Constraint appears to name only half of what a relation is, and the missing half is precisely the productive half.
The objection is answered by attending to the level at which the constraint is predicated. Take a system of two spins with a coupling term in its Hamiltonian. The coupling forbids no configuration whatever: every joint state remains in the state space. What it does is make the transitions of one spin depend on the state of the other. That single fact admits two accurate descriptions. Described one way it is a restriction, since the first spin’s succession is no longer free of the second. Described the other way it is a channel, since influence now passes from the second to the first. There are not two structures here, one restrictive and one productive. There is one structure and two vocabularies for it.
Claim (Identity of restriction and channel). A restriction on joint succession and a channel of influence are one structure under two descriptions. Constraint on succession therefore already contains what the objection asks to be added, and no further term is required in the definition.
The objection has a source, and naming it disarms the residual discomfort. Constraint predicated of configurations does not contain coupling: a rule that forbids certain states says nothing about influence passing between anything. Since configurational constraint is what the word ordinarily suggests, a reader’s first hearing of the definition will be the hearing on which the objection is sound. This is why §3 narrowed the term at the outset. Constraint on succession is the whole of what is meant, and on that reading a relation is a channel in the same breath in which it is a restriction.
§5 The Classification of Relations
A definition of a primitive earns its place by classifying. If the definition proposed here is doing work, it should sort relations into kinds, the sorting should follow from the definition and not be imported alongside it, and the resulting classes should hold across domains ordinarily treated by separate theories. This section attempts that, and then works the cases.
5.1 The Principle of Classification
Two candidate taxonomies present themselves, and each fails alone in a way that shows what a successful one must do.
The first classifies by the domain of the relata: relations between bodies, between organisms, between persons, between signs, and between a party and a figure that does not exist. This is how the disciplines divide, it is immediately recognisable, and it has the merit of being exhaustive in a rough and useful way. It cannot be the framework’s principle of classification, since Proposition 4 holds that relations are individuated by the part they play in constraining succession and not by the metaphysical status of their relata. A taxonomy keyed to that status would contradict the proposition it is meant to illustrate. Nor is it a taxonomy in the strict sense: it is a list of regions with no principle generating them, and it has nothing to say about why a relation in one region should resemble a relation in another.
The second candidate is the triad of the real, the symbolic and the imaginary, which is available and which several of the framework’s neighbours use (Lacan 1977). It is set aside here for a specific reason, and the reason is worth stating because the triad is otherwise attractive. Those three are registers of a subject. They classify the modes in which a subject stands toward its world, and each of them presupposes a subject to stand in it: there is no imaginary without one who imagines, and no symbolic order for a lattice of spins. A framework proposing to treat physical coupling, synaptic efficacy, institutional role and inherited obligation as instances of one concept cannot take its top-level division from a theory of human subjectivity without narrowing its own claim at the first step.
The definition supplies a principle that neither candidate has. It has two clauses. The first, that a relation is a constraint on succession, is common to every relation and classifies nothing. The second, that the constraint is borne by the process it constrains, varies systematically. Relations differ in what carries the constraint and in the channel through which the carrier is revised, and that difference has consequences: it determines what a relation can survive, how it changes, and how it fails.
The classification adopted here is therefore two-dimensional. The domain of the relata is retained as the first axis, since it is what a reader recognises and since the coverage of the definition is best displayed against it. It carries no theoretical weight, and nothing in the framework is derived from it. The mode of bearing is the second axis, it is derived from the definition, and it does the work. The cross-tabulation of the two is where the taxonomy pays, and it is given in §5.9.
Modes of bearing and their order
Four modes are distinguished, ordered by a single criterion, namely what the constraint can survive the loss of.
A constraint is materially borne when it is carried by a physical configuration and revised by physical process. It survives the loss of all representation of it. Nothing need know of it, and it holds.
A constraint is inscribed when it is carried by a record and revised through a specified procedure operating on that record. It survives the loss of anyone’s memory of it and the lapse of its use, since a dormant statute remains law and an unread rule still executes. It does not survive the loss of the record, nor does it change except as the procedure allows.
A constraint is circulated when it is carried by a token maintained in use among more than one party and revised by that use. It survives the loss of any particular party and does not survive an interruption of the circulation. Nothing is written down, and revision requires no procedure and no decision.
A constraint is singularly borne when it is carried by one party’s figure of a counterpart and revised by that party’s own succession of states. It survives the loss of the counterpart and of the community alike, and it does not survive the loss of the party who bears it.
The series descends in independence, from a constraint independent of everyone, through one independent of use, through one independent of any individual, to one dependent on a single party. Each position carries its own characteristic failure, set out in §5.10.
The independence of the axes
The two axes coincide often enough that a reader may suspect the second of being the first renamed. They come apart in both directions, and the cases where they do are the proof that two axes are needed.
A relation whose counterpart does not exist may be borne in circulation and not in one party. A shared myth, a nation, a lineage venerating its founder: in each of these the figure is maintained by a whole community, and no member’s private representation carries it. Anderson’s central observation about national belonging is precisely this, that the unmet co-members are supplied to each member by an apparatus he did not build (Anderson 1983). The relatum is imagined and the bearing is circulated.
Conversely, a relation whose counterpart exists in full may be borne singularly. A junior scholar’s relation to a living authority he has never met, sustained entirely by his figure of what that authority would say, is a relation to an existing person borne in one party. The authority may be unaware of him. Should the two ever meet, the figure would be corrected by something outside the bearer, and the bearing would change mode while the relation persisted.
5.2 The Protocol of Examination
Each case below is put to the same three questions, and the discipline of answering all three is what distinguishes an illustration from an assertion.
The first question is what the constraint on succession consists in: concretely, what may follow what, and what could have followed what in its absence. An answer that cannot name the foreclosed successions has not identified a constraint.
The second question is that of jointness: whose states are made answerable to whose. This clause keeps the definition from making every regularity of succession a relation, since a law governing the states of one system relates nothing to anything. An answer must name two terms and say in which direction the answerability runs.
The third question is that of bearing: what carries the constraint, and through what channel the carrier is revised. This is the historical clause of the definition, and a case that cannot answer it exhibits a structure and no relation in the sense defined.
5.3 Relations of Material Bearing
Coupled spins
Consider a lattice of two-valued sites with couplings between neighbours, of the kind Ising introduced (Ising 1925). The constraint on succession is exact and is the whole of the model: which configurations may follow which is set by the couplings. In their absence each site would evolve without reference to any other, and every joint succession would be available. Jointness is likewise exact, since the transition of each site is answerable to the current values of its neighbours, symmetrically.
The third question exposes something the model is usually not asked. The couplings are fixed by hand and have no career, so such a system satisfies the first clause of the definition and not the second: it has dynamics, and it has no history. It becomes a full instance when the couplings are permitted to evolve on a slower timescale under the influence of the site statistics they govern, at which point two timescales appear, with states succeeding one another under fixed constraint on the fast one, and the constraint revised by the succession it has governed on the slow one.
The case is placed first because it exhibits Proposition 3 in its cleanest available form. Long-range order in such a system is produced by constraint and by nothing else, and it extends over distances vastly greater than the range of any individual coupling. Remove the couplings and the lattice becomes maximally free at every site, and it produces noise. The received intuition of §4 predicts the opposite, and here it is not a matter of interpretation which prediction is right.
The synapse
A synapse constrains succession in the same sense: it makes the firing of one cell answerable to the recent firing of another, and a pattern of such answerabilities is what allows an activity pattern to have a successor worth calling a computation. Jointness is directional and is stated by the anatomy.
Bearing here needs no artificial supplement, since the biology provides it. Synaptic efficacy is revised by the activity it conditions, along lines Hebb proposed and a large experimental literature has since refined (Hebb 1949). The relation between two cells is at once the constraint on what may follow what and the running product of what has followed what, on timescales separated by orders of magnitude. The separation is what makes such a system stable enough to act and plastic enough to learn.
The case matters because it removes the suspicion that the two-timescale structure is a figure imported from social theory into nature. It is a commonplace of the neuroscience, and the definition names a structure that discipline already studies.
Further instances, compressed
The chemical bond constrains which nuclear configurations may follow which and is revised by the reactions it makes possible. A resonance between orbiting bodies constrains which orbital phases may follow which and is revised, over long times, by the exchange of angular momentum it governs. A trophic coupling constrains which population states may follow which and is revised by the selection those successions impose on both populations. A symbiosis constrains the metabolic states available to each partner. A contact structure in an epidemic constrains which infection states may follow which and is revised by the immunity and behavioural change the transmissions produce. Built infrastructure belongs here as well: a rail gauge, a road network or a port constrains which movements may follow which, and is revised, slowly and expensively, by the traffic it has carried. Co-presence in a room is the humblest instance and among the most consequential, since it constrains which exchanges may follow which by the plain fact of who can hear whom.
The last two instances are worth a remark, since both are materially borne constraints produced by human action, which shows that this class is no class of the natural. What places a constraint here is that it holds whether or not anyone represents it. A bridge no one remembers building still constrains what may follow what.
The boundary of the class
Not every physical regularity is a relation, and the second question is what excludes the rest. A law of motion constrains the succession of a system’s states without making the states of two terms answerable to one another, and it is a constraint and no relation. This is the jointness clause doing the work assigned to it in §6, and the material class is where it can be seen doing so most plainly.
5.4 Relations of Inscribed Bearing
The statute
A statute constrains which acts of an official may follow which acts of a citizen, and which claims may follow which facts. Jointness runs between the parties it binds, and through the record that binds them. What distinguishes this class is the third question. The constraint is carried by a text, and it is revised through a procedure: amendment, repeal, judicial construction. It changes when the procedure is exercised and at no other time, which is exactly what gives written law its peculiar temporality. A statute may sit unused for a century and bind on the day it is invoked.
The scoring model
A model that assigns a person to a category constrains which offers, prices and refusals may follow which records of him. Jointness holds: what the model may output is answerable to his recorded states, and what he may do next is answerable to its output. Bearing is inscribed, since the constraint is carried by a fitted object and revised by an update rule operating on data.
This case was entered in an earlier draft of this paper as a candidate anomaly, on the ground that it fitted no mode then available. The four-mode account absorbs it without amendment, and the absorption is worth marking because it shows that the anomaly was an artefact of a taxonomy borrowed from elsewhere. What made the case look strange was that its revision channel is neither physical process nor communal use. Once inscription is admitted as a mode in its own right, the scoring model takes its place beside the statute, and the two share the properties that matter: revision only through a specified procedure, persistence through disuse, and indifference to whether anyone understands the record.
Further instances, compressed
A technical standard constrains which components may follow which in an assembly and is revised by a standards body. A protocol constrains which messages may follow which. A liturgy constrains which acts may follow which within a rite, and is revised by an authority and not by the congregation. An organisation chart constrains which instructions may follow which, and is revised by reorganisation. A contract is the inscribed form of a promise, and the difference from the circulated form is instructive: the promise between friends lapses with the practice that sustains it, while the contract survives the parties’ loss of interest and is revised only through its own machinery. An accounting standard constrains which representations of a firm’s condition may follow which transactions.
The genome sits at the edge of this class and is entered here with the qualification marked. It is a record, it is copied, and it is revised through channels that are specified and not arbitrary. Whether the description is more than a convenient one is a question this paper does not settle, and it is noted because the phrase genetic code may be less metaphorical than it is usually taken to be.
The characteristic vulnerability of the class
Two failures follow from inscription. The first is the dead letter: because the constraint survives disuse, a record may go on constraining succession long after the relation it once described has gone. The second is more consequential for the framework. Because revision requires a procedure, and because a procedure operates on what the record can express, an inscribed constraint tends to reshape the relation it governs into the form the record can hold. What cannot be entered into the record ceases to bear on what may follow what. This is the mechanism by which indices come to displace what they were introduced to measure, and it is the reason the framework treats inscription as the most powerful and the most dangerous of the four modes.
5.5 Relations of Circulated Bearing
A name held by a community
Consider the relation between a person and a name under which a community holds him. The constraint on succession falls on what may follow what in the community’s dealings with him: what may be said next about him, what may be proposed to him, what may be expected of him, what an ambiguous action of his may be taken to have been. In the absence of the name, successions are available that the name forecloses.
Jointness runs in both directions, and this is easily missed. The community’s states are answerable to the name, since what may be said next is constrained by it. The name’s own state is answerable to what the community keeps saying, since a name is nothing beyond its use.
Bearing is by circulation, and the consequence is the property that makes this class the seat of the framework’s account of degradation. Nobody holds the constraint. It is carried in use and revised in use, so it changes without anyone deciding that it should, and no event marks the moment at which a description hardens into a classification. This lets a distinction be drawn that the surveyed readings cannot draw: between a community that retains a distinction and fails to act on it, and a community for which the distinction has ceased to be available. The first is a failure of generation under an intact constraint. The second is a change in the constraint. The two are indistinguishable in the conduct they produce, and they are different relations.
The teacher and the student
Given that one party stands as teacher to the other, a correction may be followed by revision and not by insult, a question may be asked without loss of standing, an assertion may be answered in ways available in no other setting. Remove the relation and the successions change: the correction is followed by affront, the question by embarrassment.
The received intuition would read this as limitation, and would note further that the relation is asymmetric and that asymmetry is the seat of power. Both observations are correct, and the framework holds elsewhere that asymmetry in a relation always produces a power which sufficient generation absorbs. Neither observation touches the point at issue, which is that the constraint is the condition of the teaching. Without it the exchange is unavailable, and there is nothing left for power to be exercised over.
Bearing is circulated, since what carries the constraint is a pair of roles maintained in use well beyond these two people. This is why the relation can be entered by strangers on a first meeting, and why it is revised by what passes between them: by the student who comes to surpass the teacher, by the teacher who ceases to invest, by an accumulation of exchanges that leaves the parties differently placed than they began. No one need decide upon those revisions. Where the same relation is also inscribed, in an enrolment record and a set of regulations, the two modes coexist and may diverge, and the divergence between what the roles have become in use and what the regulations still say is a familiar institutional condition.
Further instances, compressed
A promise constrains which acts of the promiser may follow, and is revised by the keeping and breaking of promises within a community that maintains the practice. Money constrains which exchanges may follow which holdings and is revised by the exchanges it carries. A living language constrains which continuations of a string are available and is revised by the speaking. An academic attribution constrains what may follow from a work and to whom it accrues, and is revised by the citing practice of a field. A form of address constrains which openings may follow which encounters. A reputation constrains which dealings may follow which offers.
5.6 Relations of Singular Bearing
The class in which the constraint is carried by one party is the hardest and the most revealing. A person may stand in relation to the dead, to a god, to posterity, to a discipline, to a fictional figure, to an anticipated judge of his work, to his own future self, to a rival he has never met, or to an audience he believes to be evaluating him. The literature on being seen, from Otto’s account of the holy through Buber’s address and Levinas’s face, describes a constitution of the subject under a regard whose bearer is nowhere present (Otto 1917; Buber 1923; Levinas 1961).
The protocol in the hardest case
The first question is answerable, and concretely. The scholar who will not publish work he would be ashamed for a long-dead teacher to read has certain successions foreclosed to him, and one may say which. The believer whose conduct is ordered by the conviction that he is seen has others foreclosed. The constraint is observable exactly where the definition says to look, in what may follow what.
The second question is where this class threatens the definition, and the threat must be stated before it is answered. Jointness requires two terms with states. Where the counterpart does not exist it has no states, and the relation appears to collapse into a one-place property of the party: a disposition, misdescribed as a relation for rhetorical effect.
The answer is that the relatum is the figure, and the figure has states. The god need not exist for the figure of the god to have determinate content, a history and a career; what the anticipated judge would approve is a matter of fact about the figure at a time, and it changes.
This answer has an obvious cost, since the figure is carried by the very party whose states it constrains, and a relation whose two terms are both housed in one party invites the collapse just denied. The reply is that the collapse does not occur, and that whether it occurs is testable. The mark of a relation here is that the party does not control the figure’s succession. One cannot decide that the anticipated judge approves, and one cannot settle by resolution that the dead teacher would have been satisfied. The inability is no failure of will. Where a party can set the figure’s states at will, there is a disposition being described in relational language and no relation. Where he cannot, the two terms are distinct and jointness holds. The criterion is sharp enough to be applied to particular cases and to be argued about.
The third question is answered with unusual clarity here, since nothing enters from the counterpart. The figure is revised solely by the succession the constraint has been governing, which is precisely what the definition says a relation’s revision consists in. Singular bearing is thus the purest instance of the historical clause, and the fact that the purest instance is also the one the alternative readings must reject is the strongest evidence this paper has to offer.
The evidential force of the class
On the interaction reading many of these are not relations, since nothing passes between the parties. On the tie reading they are not relations, since one endpoint is missing or unreachable. On the correlation reading they are unavailable, since one of the two quantities has no values. Each reading must treat them as figurative uses of the word, or as psychological facts about one party dressed in relational language. On the definition proposed here they are relations in the full sense, and no amendment is required to make them so.
One instance deserves separate mention because of the work it does elsewhere in the framework. An audience whose evaluation is believed in need contain no one who evaluates. It suffices that a party takes himself to stand within an order in which he may be seen, placed and assessed. The constraint on succession is then fully operative with no bearer outside the party subject to it, which is why conduct organised around such an audience is so difficult to alter by showing that no one in particular is watching.
5.7 Composite Relations and the Standing of the Social
The social has not been given a class of its own on either axis, and the omission is deliberate.
A social relation is ordinarily a composite: several constraints on succession, borne in different modes, holding between the same parties at once. A family relation is borne materially in co-presence and in the dependencies of a household, circulated in kinship terms maintained well beyond the family, inscribed in registers and law, and singularly in obligations owed to the dead. A national relation is borne circulatedly in a common practice, inscribed in documents and statute, singularly in each member’s figure of the unmet others, and materially in territory and infrastructure. Money is inscribed in a settlement system, circulated in a unit of account, and borne singularly in each holder’s expectation of what others will accept. A workplace hierarchy is inscribed in an organisation chart, circulated in the practice of deference, and borne singularly in the figure of the one whose regard decides who counts.
Treating the social as a class would obscure all of this, and it would place a heterogeneous category beside homogeneous ones. Treating it as composite yields two returns. The first is that a composite fails component-wise, which is what partial degradation is: the circulated component of a relation may lapse while the inscribed persists, which is the exact condition of an institution that retains its rules and has lost its practice, and the reverse condition is that of a practice that has outgrown its rules. The second is that a number of long-running disputes in social theory can be read as disputes over which component of a composite carries the weight, which is a more tractable question than the one usually asked.
5.8 The Cross-Tabulation of Domain and Bearing
The two axes may now be crossed, and the table below does so. Its cells give a representative instance where one exists, and are left empty where the combination does not arise.
Table 1. Domain of the relata against mode of bearing.
| Domain | Material | Inscribed | Circulated | Singular |
|---|---|---|---|---|
| Physical | Coupled spins, chemical bond | |||
| Biological | Synapse, symbiosis | Genome (edge case) | ||
| Social | Co-presence, infrastructure | Statute, org chart | Role, custom, reputation | The believed audience |
| Symbolic | Standard, protocol, accounting rule | Living language, a name in use | A private idiom | |
| Imagined | Scripture, liturgy | Shared myth, nation | The dead teacher, a god |
The pattern of empty cells is itself a result and should not be read as a gap in the survey. Modes beyond the material become available only where at least one term is represented by some party, and the domains are ordered by how much representation their terms require. Physical relations admit material bearing alone. Imagined relations admit every mode except the material, since a figure cannot be carried by a configuration that no one represents. The two axes are therefore neither independent nor identical, and the shape of their dependence is a substantive claim of this section: representation is what opens the higher modes of bearing, and it opens them without regard to whether the relatum exists.
The cell crossing the imagined domain with circulated bearing carries the case that most needs it. A national relation is imagined in its relatum and circulated in its bearing, which is why it is neither a private fantasy nor an ordinary institution, and why it resists the treatments that suit either.
5.9 Summary of the Modes and the Coverage
The table below sets out the four modes with the properties that distinguish them, followed by two tables gathering the instances worked or named above, each stated in the form the first question of §5 requires.
Table 2. Modes of bearing and their properties.
| Mode | Bearer | Revision channel | Survivable loss | Characteristic failure |
|---|---|---|---|---|
| Material | Physical configuration | Physical process | All representation | Rupture or decay |
| Inscribed | A record | A specified procedure | Memory, and use | Dead letter; the record reshapes the relation |
| Circulated | A token in use | The use itself | Any particular party | Congealing; lapse through disuse |
| Singular | A party’s figure of a counterpart | That party’s own succession | The counterpart, and the community | Collapse of the figure; its capture |
Table 3. Instances of material and inscribed bearing.
| Instance | Constrained succession |
|---|---|
| Material bearing | |
| Coupled spins | Joint configurations reachable from a given one |
| Chemical bond | Nuclear configurations reachable from a given one |
| Orbital resonance | Orbital phases available to each body |
| Synapse | Firing states of one cell, given recent firing of another |
| Trophic coupling | Population states available to predator and prey |
| Symbiosis | Metabolic states available to each partner |
| Contact structure | Infection states reachable within a population |
| Built infrastructure | Movements available between places |
| Co-presence | Which exchanges may follow, by who can hear whom |
| Inscribed bearing | |
| Statute | Which official acts may follow which citizen acts |
| Contract | Which acts of the bound party may follow |
| Property title | Which uses of a thing may follow whose decision |
| Scoring model | Which offers and refusals may follow which records |
| Technical standard | Which components may follow which in an assembly |
| Protocol | Which messages may follow which |
| Liturgy | Which acts may follow which within a rite |
| Organisation chart | Which instructions may follow which, and from whom |
| Accounting standard | Which representations may follow which transactions |
| Genome (edge case) | Which cellular states may follow which, by a copied record |
Table 4. Instances of circulated, singular, and composite bearing.
| Instance | Constrained succession |
|---|---|
| Circulated bearing | |
| A name held of a person | What may be said, proposed and expected next |
| Teacher and student | Which responses may follow a correction or a question |
| Promise | Which acts of the promiser may follow |
| Money | Which exchanges may follow which holdings |
| Living language | Which continuations of a string are available |
| Academic attribution | What may follow from a work, and to whom it accrues |
| Reputation | Which dealings may follow which offers |
| Form of address | Which openings may follow which encounters |
| Singular bearing | |
| The dead teacher | Which works may be published, and in what condition |
| A god | Which acts may follow, in the absence of any witness |
| Posterity | Which present sacrifices may follow which prospects |
| One’s own future self | Which present acts may follow a commitment |
| A fictional figure | Which construals of one’s own situation may follow |
| An unmet authority | Which submissions may follow which drafts |
| A believed audience | Which conduct may follow, where none in fact evaluates |
| Composite bearing | |
| Family | Co-presence, kinship terms, registers, and the absent |
| Nation | Practice, statute, unmet co-members, and territory |
| Workplace hierarchy | Chart, deference, and the figure of the one who decides |
5.10 The Limit of the Taxonomy
Three limits are entered against what has been claimed.
The modes are modes of bearing and no kinds of thing. It is a mistake to ask whether a given relation is really inscribed or really circulated, and the right question is which of its constraints is borne in which mode. Most relations of any interest are composite, as §5.7 argued, and the modes earn their keep in the decomposition and not in the labelling.
The modes are argued from cases and not derived. The criterion ordering them, what a constraint survives the loss of, is drawn from the definition, and nothing here shows that it is the only principle the definition supplies. A different principle drawn from the same definition might cut differently and cut better.
The boundary between inscription and circulation will bear pressure. A record that no procedure governs, revised by whoever edits it and answerable to use, is inscribed in its bearer and circulated in its revision channel, and the fixed corpora of an oral tradition sit on the same line from the other side. The classification is by revision channel where the two diverge, since the revision channel is what the definition’s historical clause makes decisive, and the ruling is stipulated here and not argued.
§6 Delimitations
A definition is as much a set of refusals as a set of commitments, and the refusals are set out here.
6.1 Exclusions from the Definition
It is not an ontology. The definition says nothing about whether relations are more fundamental than their relata, whether relata exist independently of relations, or whether the world is at bottom relational. Positions on these questions are available, from Leibniz through Whitehead to the relational reading of quantum mechanics and to agential realism (Leibniz & Clarke 1717; Whitehead 1929; Rovelli 1996; Barad 2007), and the framework may eventually take one. The present definition is compatible with several and requires none.
It is not an epistemology. The definition does not say how relations are known, observed or measured. That relations of the defined kind are often invisible to the parties standing within them is an important claim, and it is a separate one.
It is not a theory of interaction. Interaction is one mode in which a constraint on succession is realised, and §5 exhibited modes in which no interaction occurs at all.
It is not a claim about the word. Physics, sociology and philosophy will go on using relation in their own senses, correctly. What is proposed is a term of art for one framework.
6.2 Scale and the Passage Between Levels
A question the definition raises and does not settle is that of scale. The same word is used in the framework at two levels: for the microscopic constraint that holds between particular terms, and for the macroscopic constraint that a historical situation imposes on everything within it. The definition above is stated at the first level.
The relation between the two levels is a substantive matter and is treated in the historical branch of the programme, where the constraint of a historical situation is proposed to be a macroscopic phase of the relational field and no container standing outside it. The point to be marked here is only that the two must be kept apart in the vocabulary, since a definition of relation as constraint, applied at both levels at once, would collapse a distinction the framework needs. Relation is constraint at the scale at which the constraint holds; what constrains at one scale is generated at another; and the passage between scales is a problem, and no matter of definition.
6.3 Open Problems in the Definition
Four questions are left open, and they are the natural next work.
The first is individuation. The definition says what a relation is and does not say how to count relations, nor how to tell one relation from two that co-occur. A criterion is wanted.
The second is the boundary of the concept. Not every constraint on succession is a relation, or the definition would make relation coextensive with law. The clause doing the excluding is jointness, that the constraint makes the states of two or more terms answerable to one another. §5 supplied a criterion for the hard case, that a term is distinct from the party who bears it when that party cannot set its states at will, and the criterion was argued from the imagined class. Whether it generalises, and whether it can be stated without appeal to the will of a party, is unsettled.
The third is the criterion of §4: what distinguishes constraint that leaves continuations open from constraint that forecloses them. The framework’s normative work rests on this distinction, and this paper has only made it statable.
The fourth is formalisation. A definition framed in terms of succession invites statement in the language of dynamical systems, where a relation would answer to a restriction on the transition structure of a joint state space, and its historical clause to a slow dynamics on the restriction itself. Whether such a statement adds anything beyond notation is a question this paper leaves open, and the abstention is the same one made in the companion work: a formal apparatus that derives nothing borrows a rigour the argument has not earned.
§7 Place Within the Programme
The framework of generative relational being concerns how subject, meaning, value and normativity co-emerge through generative relational processes (Huang n.d.). Around it a set of branches has grown: an epistemology, an economics of generated value, a governance theory, and a philosophy of history concerned with the evolution of historical constraint. All of them are stated in terms of relation, and until now none of them could say what the term meant.
What the definition supplies to each is the same thing. It puts succession inside the concept. The economics can then distinguish a relation that returns what it generates to its participants from one that directs it elsewhere, and can pose the difference as a difference between two constraints on succession. The governance theory can ask what a relation permits to follow what, and can treat institutional design as the design of such permissions. The historical branch, whose subject is the evolution of constraint, acquires a microscopic term to stand under its macroscopic one, with the relation between the scales named as an open problem in §6. The taxonomy of §5 bears on each branch in the same way, since a claim about relational change is a claim about a revision channel, and the four modes have four different ones: physical process, a specified procedure, use itself, and the succession of a single party. A proposal for institutional design that addresses itself to the wrong channel will fail for reasons that have nothing to do with its merits, and the inscribed mode is where such proposals most often address themselves, since it is the only one of the four that can be altered by decision.
The claim of this paper is modest in what it asserts and immodest in what it makes possible. It asserts one sentence: a relation is the constraint through which generation unfolds in history. Everything the framework says about degradation, absorption, recognition and historical change is a claim about such constraints, and each of those claims now has a subject.
A note on revisability. A framework holding that constraints are borne by the processes they constrain owes the same treatment to its own definitions. This one is offered as a working definition, revisable by the work it makes possible, and the phrasing is not a hedge. Three failure modes are visible from where the paper stands, and each is stated so that a reader may look for it. Should the cases of §5 be shown to require amendments that differ by domain, the claim to a single concept spanning them fails, and the definition should be withdrawn or split. Should the jointness clause prove unstatable in the general form §6 requires, the definition is too wide and admits every law of succession as a relation. Should the four modes of bearing prove not to be modes of one thing, or should the ordering criterion that generates them prove arbitrary, the taxonomy of §5 falls and the definition loses the principal evidence offered for it here.
References
Anderson, Benedict (1983). Imagined Communities: Reflections on the Origin and Spread of Nationalism. London: Verso.
Aristotle. Categories, ch. 7. In The Complete Works of Aristotle, ed. Jonathan Barnes. Princeton: Princeton University Press, 1984.
Barad, Karen (2007). Meeting the Universe Halfway: Quantum Physics and the Entanglement of Matter and Meaning. Durham: Duke University Press.
Bateson, Gregory (1972). Steps to an Ecology of Mind. New York: Ballantine Books.
Buber, Martin (1923). I and Thou. Trans. Walter Kaufmann. New York: Scribner, 1970.
Cassirer, Ernst (1910). Substance and Function. Trans. William Curtis Swabey and Marie Collins Swabey. Chicago: Open Court, 1923.
Ceva, Emanuela (2016). Interactive Justice: A Proceduralist Approach to Value Conflict in Politics. London: Routledge.
Emirbayer, Mustafa (1997). Manifesto for a Relational Sociology. American Journal of Sociology, 103(2), 281–317.
Hebb, Donald O. (1949). The Organization of Behavior: A Neuropsychological Theory. New York: Wiley.
Huang, Wanhong. Responding to the Crises of Symbol and Subject in Modernity. SSRN Working Paper. DOI: 10.2139/ssrn.5752104.
Ising, Ernst (1925). Beitrag zur Theorie des Ferromagnetismus. Zeitschrift für Physik, 31(1), 253–258.
Lacan, Jacques (1977). The Four Fundamental Concepts of Psycho-Analysis. Ed. Jacques-Alain Miller, trans. Alan Sheridan. London: Hogarth Press.
Latour, Bruno (2005). Reassembling the Social: An Introduction to Actor-Network-Theory. Oxford: Oxford University Press.
Leibniz, G. W., and Samuel Clarke (1717). The Leibniz–Clarke Correspondence. Ed. H. G. Alexander. Manchester: Manchester University Press, 1956.
Levinas, Emmanuel (1961). Totality and Infinity: An Essay on Exteriority. Trans. Alphonso Lingis. Pittsburgh: Duquesne University Press, 1969.
Marx, Karl (1852). The Eighteenth Brumaire of Louis Bonaparte. In Marx–Engels Collected Works, vol. 11. London: Lawrence & Wishart, 1979.
Otto, Rudolf (1917). The Idea of the Holy. Trans. John W. Harvey. Oxford: Oxford University Press, 1923.
Rovelli, Carlo (1996). Relational Quantum Mechanics. International Journal of Theoretical Physics, 35(8), 1637–1678.
Saussure, Ferdinand de (1916). Course in General Linguistics. Ed. Charles Bally and Albert Sechehaye, trans. Roy Harris. London: Duckworth, 1983.
Simmel, Georg (1908). Soziologie: Untersuchungen über die Formen der Vergesellschaftung. Leipzig: Duncker & Humblot.
Whitehead, Alfred North (1929). Process and Reality: An Essay in Cosmology. Corrected edition, ed. David Ray Griffin and Donald W. Sherburne. New York: Free Press, 1978.
中文
在生成性关系存在中定义关系
一篇立场论文
黄万宏 · huangwanhong@serendip.ngo
摘要
生成性关系存在把关系置于它的中心，而迄今把这个概念留作开放。本文供出一个工作定义：关系是历史过程中生成得以展开的约束。关于关系的诸现存理解，作为互动、作为背景结构、作为差异、作为纽带，以及作为相关，每一个都在一个瞬间被陈述，而一个关切历史性生成的框架要求一个对接续负责的概念。那个定义的历史子句承载分量，因为那个约束被它所约束的那个过程本身所承载并被修订，而这把这一提议同结构主义分开。本文论证不受约束的接续未能成为极大的生成，因为在接续自由之处什么也不累积，而它回答一个关系是一个耦合、而不仅是一个约束这个反对。一个在两个轴上的分类法随之而来，即关系项的域与承载的方式，而约四十个实例被跨四个方式指派。由单一一方承载的诸关系是那个决定性的情形，因为其对应方并不存在的诸关系在此处是完整意义上的关系，而互动读法与纽带读法却必须否认它们那个名字。
关键词： 关系；约束；生成性；历史性生成；关系本体论；概念定义；生成性关系存在。
关于本文定位的一则说明。 这是一篇立场论文，而它的抱负相应地被限定。它不提供一个普适的关系哲学定义，而它不主张§2中所概览的哲学与社会学诸传统误解了它们的主题。它为一个框架，即生成性关系存在，提议一个关系的工作定义，陈述那些推荐那个定义甚于诸可得替代方案的考虑，并对照来自数个域的案例检验它。那个定义是否挣得它的位置，由它让那个框架能说什么、以及由它禁止那个框架说什么来了结，而两者都在此处被尽作者所能清楚地展现。那个定义作为可修订的被提供，这是那个框架本身所要求的一个承诺、而非一份客套。反对、更正与反例欢迎寄至 huangwanhong@serendip.ngo。
§1 一个未被定义之原初对象的问题
生成性关系存在是一个建立在一个它未曾定义之词上的框架。它的诸主张以关系的术语被陈述：主体、意义、价值与规范性通过生成性关系过程共同涌现；一个关系中的不对称产生权力，而充分的生成吸收它；社会生活中所败坏的是一套关系语法、而不仅是诸好处的一个分配。这些中的每一个都是一个关于关系的主张，而每一个迄今都从读者那里借来它的中心术语。
把一个原初对象留作开放有它的用处，而那个框架已汲取它们。一个未被定义的术语容纳作者尚未考察的诸情形，而它推延会是过早的诸承诺。然而有一个点，在其上那推延开始耗费多于它所省下的，而那个框架已抵达它。三个代价可被命名。
第一个是那个框架的诸独特主张变得与别处已作出的诸主张不可区分。倘若关系意味诸个体之间的一个纽带，那么关系生成价值这个论题重述网络社会学；倘若它意味一个互动，那个论题重述交换理论；倘若它意味一个符号系统中的一个差异性位置，那个论题重述结构主义。那个框架一直在论证它说了这些所不说的某样东西，而它无法显示这一点，只要它的中心术语由读者恰好读过的那些之中的无论哪一个来供出。
第二个是一个开放的原初对象悄悄地导入无论什么填充它之物的诸承诺。一个受过网络分析训练的读者将把关系听作一个状态变量，一条在一个时间在场或不在场的边。在那个听法上，那个框架的若干命题变得虚假或平凡：一个关系被它之内所发生之事修订这个命题，成为一个关于边更新的主张，而那是一个没有本体论分量的建模便利，而一个主体被在关系中构成这个命题，成为一个关于网络位置之效果的主张，而那已被研究数十年、并不是那个框架所指的。
第三个代价是内部的。一个意图为约束演化建模的框架，一如这个纲领的历史分支所做，需要说出一个尺度上的约束如何相对于另一个尺度上的诸关系而立。那个陈述无法在关系未被定义时被作出，因为那两个术语会自由地在论证要求时坍缩进彼此。
1.1 任务与范围
因而本文的任务是狭窄的，而在它的狭窄之内是基础性的。它提议一个定义、为它论证、拆解它的诸术语，并跨五个域例示它。它不引入那个框架的任何其他部分，超出论证所要求者。
那个主张的范围必须在开篇被陈述，因为几乎每一个定义关系的困难都来自把那个任务当作比它所是的更大。
范围。 本文不试图提供一个普适的关系哲学定义。它为生成性关系存在提议一个工作定义，后者的目的是跨物理、生物、社会与象征诸域分析生成过程。
这个范围的后果是本文不与亚里士多德对相对者的处理、不与莱布尼茨论关系性空间、不与怀特海的摄受、不与卡西尔的函数性概念、不与齐美尔、不与拉图尔，或不与过去二十年的关系性政治哲学竞争（亚里士多德 1984；莱布尼茨与克拉克 1717；怀特海 1929；卡西尔 1910；齐美尔 1908；拉图尔 2005；切瓦 2016）。那些中的每一个都是对一个关于关系是什么的问题的回答。此处所问的问题是一个特定框架为做它给自己设定的工作而要求什么样的关系概念。那两个问题可被不同地回答而没有任一个是错的，而一个把它们混为一谈的框架承担了一份它不需要且无法履行的举证责任。
1.2 中心主张
中心主张。 生成性关系存在把关系理解为生成得以展开所经由的历史性约束，而非诸实体之间的一个静态连接。随之而来的一切都支持这一个句子。
诸节以论证的次序推进。§2 概览可得之物，并辨认它们无一供出之物。§3 陈述那个定义，并拆解它的四个术语。§4 论证那个定义立足或倒塌于其上的那一点，即约束是生成的条件、而非它的障碍，并回答约束略去一个耦合所添加之物这个反对。§5 发展一个在两个轴上的分类法并处理诸案例。§6 标记那个定义不是什么、以及它留作未决之物。§7 把这一结果置于那个更宽的纲领之内。
§2 关于关系的诸现存理解
随之而来的是一个分类、而非一篇文献综述。关系的五个读法被区分，每一个都以它最强的形式被陈述、每一个都被记以它所成就之物，而每一个都只为一个问题被考察：它是否使关系对生成的历史性展开负责。
2.1 关系作为互动
在第一个读法上，一个关系是从重复的互动中累积之物。两方彼此作用；那些遭遇留下一份期望、义务与习惯的残余；那份残余是那个关系。这一谱系从齐美尔对结社的说明，经由符号互动论，到交换理论（齐美尔 1908）。
这个读法成就某样其他读法挣扎着才能成就之物：它使关系动态而无需特殊机械，因为一个关系在这个说明上简单地就是一段遭遇的历史。它的界限是它要求诸方在那个关系之前便被个体化，作为在任何关系在它们之间成立之前便有能力互动的存在者。一个主张主体在关系中被构成的框架无法把这个读法当作基础，因为那个读法预设那个框架提议去解释之物。有一个进一步的界限，较少被注意。互动是一个事件，而一个由诸事件构成的关系只在那些事件发生时在场。这个读法难以说出一个关系在其中没有任何东西在诸方之间经过的那些漫长间隔中是什么，而然而那些间隔正是关系生活的许多被生活之处。
2.2 关系作为背景结构
在第二个读法上，诸关系先于诸互动并配置它们。诸位置在诸位置的占据者之前存在；两个人能对彼此做什么由他们立于其内的那个结构所设定。结构主义主张这一点，而追随埃米尔巴耶纲领性陈述的那种关系社会学也如此，在其上是那个交易、而非那个实体，是社会分析的原初对象（埃米尔巴耶 1997）。
这个读法恰恰在正确的点上更正第一个：诸关系项如今能被诸关系所构成，而那个框架的诸本体论承诺变得可说。它的界限在于那个结构的地位。那个结构条件化一切，而它自身在那个说明之内不被任何东西所条件化；它作为已给定的进入那个分析，而它自己的转变或被留给一个分开的理论、或由外生冲击所供出。对一个其中心问题是约束如何演化的框架，一个把诸关系的演化留在那个概念之外的关系概念是不可用的。
2.3 关系作为差异
在第三个读法上，关系是差异：一个术语通过它被区别于什么而有它的同一性，而那个区别的系统先于任何正面内容。索绪尔的价值，其中一个符号由它同其他符号的诸差异所构成，以及贝特森的造成一个差异的差异，是那些经典的陈述（索绪尔 1916；贝特森 1972）。
这一成就是可观的。这个读法完全免除实体，这是没有别的读法所能做到的，而它解释关系如何能在不是一个东西的情况下有效力。它的界限是时间性的。差异是一个共时的概念：它描述一个区别系统在一个瞬间的状态，而它对一个瞬间如何让位于下一个什么也没说。贝特森的表述向接续示意，因为一个造成一个差异的差异是一个带一个后果的差异，而那一示意恰恰是当下这篇论文所接手之物。然而如它在那个传统中所立，那个读法给出一个关于对比的理论、而没有关于进程的理论。
2.4 关系作为纽带
在第四个读法上，一个关系是一条边：诸节点之间的一个连结，在场或不在场、加权或不加权、有向或无向。这是网络分析的工作概念，而它的德性是它可度量。整个文献已建立在它之上，而它们的诸发现是真实的。
它就当下目的而言的界限是那条纽带是一个状态变量。它记录一个连接成立、而对什么支配它之内诸状态的接续什么也没说。当网络模型让诸纽带改变时，改变的规则从那条纽带的概念之外被供出，作为一个被强加于那个图之上的动力学。因而那个概念把关系定位在错误的层，对一个其旨趣恰恰是改变之规则的框架。
2.5 关系作为相关
在第五个读法上，在诸科学中常见、且常是默会的，一个关系是诸量之间的一个统计或函数依赖。这是可操作的，而它在诸域之间行进得好。
它的界限是相关是对称的且无时间的，而它不把一个关系同一个巧合区分开来。两个量可能协变，因为一个约束另一个的接续、因为两者都被一个第三者所约束，或因为一个有限样本运气不好。一个必须把这些区分开来的框架无法把那个未加区分的概念当作它的原初对象。
2.6 所概览诸读法的共同界限
每一个读法都捕捉某样东西，而那个框架一直在汲取所有五个、而不承认它在这样做。要从这个概览中提取的点是它们共享一个特征。每一个都在一个瞬间定义关系。互动是一个时间的一个事件；结构是一个时间的一个配置；差异是一个时间的一个对比；一条纽带是一个时间的一个状态；一个相关是一个分布的一个性质，而那按构造是无时间的。在接续进入这些说明中任何一个之处，它作为某样从外部被应用于那个关系之物而进入。
一个关切历史性生成的框架需要相反的安排。它需要关系成为凭之一个系统的较晚状态依赖于它较早状态的那个东西。那正是下面的定义被建来满足的要求。
§3 那个定义
定义（生成性关系存在中的关系）。 关系，是历史过程中生成得以展开的约束。
这个句子是短的，而它的简短是刻意的：一个原初对象的定义应可被引述、且不应在它自身内部携带任何论证。全部论证都在周围的文本中。四个术语做工，而每一个现在被依次取来。
3.1 约束
约束在此意味对接续的一个限制。它关乎所关联之物的诸状态可如何彼此接续，而它不关乎哪些状态存在。这是一个比寻常用法所供出的更狭窄的这个词的读法，而这一收窄是本质的；§4 显示这个定义所引起的大部分抗拒来自以那个更宽的意义听约束。
那个区分可被直白地放下。一个对诸构型的约束说某些状态不可得。一个对接续的约束说某些状态，作为可得的，可能只从某些其他状态被抵达。第一个使一个系统贫乏。第二个给它一个在时间中的形状。所指的是第二个。
3.2 生成
生成是，在一个系统之内，那不可在那个系统自己的先前术语中被界定之物的出现。这一表述是刻意地薄的，而它薄是出于一个必须被公开陈述的缘由。那个框架把生成性倾向当作一个公设：它主张诸关系展现生成，而它谢绝解释为什么。这一拒绝是有原则的。回答系统为什么展开它们自己的动态这个问题，是命名生成所服务的某种更根本的善，而生成于是会成为通往那个善的手段。任何这样的回答，无论什么术语填充它，都会把那个框架转成功利主义的一个变种。物理学不解释作用为什么是极值的，而数学不解释集合为什么存在。此处这一平行被主张为对同一个克制的许可。
这一克制的一个后果应被记录，因为它关乎那个定义的地位、并在§3.6中被再次接手。因为生成出现在关系的定义中，诸关系展现生成性倾向这个句子无法作为一个发现从那个定义读出。它是一个关于那个框架所研究之诸系统的公设，而它必须作为一个公设被陈述。
3.3 展开
生成有一个进程。说生成展开，是说它需要时间、说它经过诸状态，而说它的经过既非被预定的也非任意的。一个被预定的进程会使那个约束成为整个故事、而使生成成为一个幻象。一个任意的进程会使那个约束闲置。这个术语标记那个中间情形，而那是那个定义有内容的唯一情形：一个被塑造而不被固定的进程。
3.4 历史
这是承载最多分量的那个子句，而它是一个读者最可能当作装饰的那个子句。它不是装饰。说生成在历史中展开，是说它借之展开的那个约束本身被它所约束的那个过程所承载。
没有这个子句，那个定义会是结构主义的一个陈述，而且是一个弱的。那个约束会条件化生成、而它自身会从外部被给出，而那个框架会经由一条更长的路径抵达在§2中被辨认为不充分的那个立场。有了这个子句，关系同时是条件与产物：它约束诸状态的接续，而它被它所约束的那个接续所修订。
这正是使那个定义在一个强于诸关系有过去这个观察的意义上是历史的东西。诸关系不仅仅被标了日期。它们由经过它们之物构成。这一点在历史唯物主义传统中有一个熟悉的表述，即人们创造他们自己的历史、而不在他们自己选择的境况下创造它，其中那些境况本身是较早创造的沉积（马克思 1852）。此处所提议的定义是一个在关系概念本身的层次陈述那个句子之结构的尝试。
3.5 从那个定义展开出的诸命题
那个定义可被展开为四个命题，它们合起来构成本文所辩护的立场。
命题 1（历史性）。 关系是一个历史概念，且不容许任何无时间的界定。一个关系由它施于接续之上的那个约束所个体化，而那个约束有一个日期、一个来处与一段生涯。
命题 2（动态性）。 关系在接续之上被定义，而它本身受制于接续。那个约束支配诸状态可如何彼此接续，而如此被支配的那个序列修订那个约束。因而关系在两个意义上是动态的，而第二个正是把这个说明同结构读法区分开来之物。
命题 3（约束作为条件）。 约束同生成不处在任何对立之中。它是生成得以展开所处的条件。在接续不受约束之处，什么也不累积、而没有任何进程被保留，而所得的是噪声、而根本没有生成。
命题 4（方法）。 生成性关系存在由诸关系在历史性生成中所扮演的角色、而非由它们诸关系项的形而上学地位，来个体化并研究诸关系。诸关系项是物理的、生物的、社会的、象征的还是被想象的，对一个关系是否成立无关紧要。
命题 3 是那个哲学贡献，并在§4中被论证。命题 4 是那个方法论回报，并在§5中被展现，在那里它做那让一个单一定义横跨五个域的工作。
3.6 那个定义的地位
一个这种定义是约定性的，而对那一点的诚实比一场发现的表演更有价值。本文不主张这是关系一直所意味之物，也不主张其他定义是弄错的。它主张一个带这些目的的框架要求一个带这些性质的概念，而上面的那个句子陈述了一个。
两个后果随之而来，而两者都是关于那个框架未来可如何论证的约束。
第一个已在§3中被预示。既然生成出现在那个定义项中，没有任何形如诸关系是生成性的的命题可作为一个结果被呈现。这一临近处的诸实质主张是存在性的与经验的：这种被定义之约束存在于物理、生物、社会与象征诸系统中，而在那些系统中那个约束事实上被它所支配的那个接续所承载并被修订。那些是关于世界的主张、且能是假的。那个定义本身不能是假的；它只能是无用的，而它的用处正是§5所为之目的。
第二个关乎目的论。一个把关系系于生成的定义招致这个读法，即诸关系为生成之故而存在，而那个读法会是一个严重的错误。那个定义说关系与生成如何相对于彼此而立，而它不给任一者指派任何目的。那个框架有独立的理由拒绝使生成成为一个善，因为一个把它自己动态的自由展开当作一个目的的系统能为摧毁无论什么阻碍它之物辩护，而那个辩护在那个框架自己的语汇中可得，除非那个语汇被守卫。那道守卫在此被陈述，以使那个定义不悄悄地拆掉它：关系通过生成被定义，而生成由此不被给予任何规范地位。
§4 约束作为生成的条件
那个定义要求一个读者接受一个初次听来虚假的句子。本节认真对待那一表象、以它最强的形式陈述它，并回答它。
4.1 那个既得直觉
那个直觉如下运行。一个约束移除诸选项。更少的选项意味更少的自由。更少的自由意味更少的创造。因而约束同生成相对立，而把生成的条件定义为约束往好里说是一个悖论、往坏里说是一个含混。
那个直觉不是天真的。它支撑一大批道德与政治推理，而在它从中被抽取的那些情形中它是正确的：囚犯有更少的选项并生成得更少；被审查的作家有更少的选项并生成得更少。任何驳斥那个直觉的回答都将反过来被驳斥。
4.2 来自不受约束之接续的论证
那个回答从问一个对接续没有约束的系统会看起来像什么开始。它的下一个状态会独立于它当前的状态。所发生的任何东西都不会关涉接下来所发生之事。这样一个系统经过诸状态而不经过一个进程：它没有任何经受住考察之意义上的轨迹，因为一条轨迹是一个其诸部分彼此负责的序列。它其中什么也不累积，因为累积要求过去关涉当前。它其中什么也不能被建造，因为建造要求一个被采取的步骤保持被采取。
这个系统处在不受约束之接续的极大处、并处在生成的极小处。它是噪声。而噪声是那个既得直觉从不考察的极限情形，因为那个直觉是从那个范围中间的诸情形中被抽取的，在那里一个约束从一个尚有充足其他约束剩下的系统中被移除。
这一点的一般形式是生成要求对它自己过去的保留，而对接续的约束正是保留所在。一个关系，在所提供的定义上，恰恰是那使一个系统的较晚状态对它较早状态负责之物。在没有这样的负责之处便没有历史，而在没有历史之处便没有任何东西供生成在其中展开。
四个熟悉的情形展现同一个结构，而它们作为类比、而非作为那个定义的部分被提供。语法约束哪些字符串算作句子，而那个约束是一个无界的新句子集合变得可说与可理解所处的条件。对位约束哪些声部可如何相对于哪些声部而行进，而作曲家们已在那个约束中发现发明的条件、而非它的敌人。一个晶格约束一个原子可占据哪些位置，而那个约束是允许结构在没有不受约束的聚集体所能跨越之距离上传播的东西。一个制度约束它的成员可做什么，而那个约束是允许一个今天被采取的行动明年仍意味某样东西的东西。
4.3 那个论证的界限
那个论证确立约束对生成是必要的。它不确立约束是充分的，而那个定义不应被读作主张这一点。某些对接续的约束把一个系统的诸延续关闭到只剩一个，而一个如此被约束的系统不再生成任何东西。留下诸延续开放的约束与封闭它们的约束之间的区分，是那个框架关系败坏说明的实质，而它被刻意地留在本文之外。
那个定义在这一点上所贡献的，是陈述那个问题的能力。在§2中所概览的诸读法上，一个维系生成的关系与一个终结它的关系之间的差别必须从某样别的东西的理论中被导入，因为那些读法无一在关系概念之内有接续。在此处所提议的定义上，那个差别是两个对接续之约束之间的一个差别，而它可作为一个关于一种对象的问题被提出。
4.4 约束与耦合
一个反对配得上它自己的处理，因为它是可得的最严重的一个，且因为它在这个定义的发展过程中被提出以对抗它。它如下运行。一个关系做多于限制。在物理学中，两个自旋之间的耦合是一个约束，而它也是一个耦合：一条影响沿之传递的通道。在诸制度中，一个关系限制什么可被做，而它也确立协调、影响与联合发展经由之发生的诸路径。约束看来只命名一个关系所是之物的一半，而那缺失的一半恰恰是那个生产性的一半。
那个反对由留意那个约束被谓述所处的层次而被回答。取一个带一个耦合项在它哈密顿量中的两自旋系统。那个耦合根本不禁止任何构型：每一个联合状态都留在那个状态空间中。它所做的是使一个自旋的诸转变依赖于另一个的状态。那单一的事实容许两个准确的描述。以一种方式被描述它是一个限制，因为第一个自旋的接续不再自由于第二个。以另一种方式被描述它是一个通道，因为影响如今从第二个传到第一个。这里没有两个结构，一个限制性的与一个生产性的。有一个结构与两套关于它的语汇。
主张（限制与通道的同一）。 一个对联合接续的限制与一条影响的通道是一个结构在两个描述之下。因而对接续的约束已然含有那个反对要求被添加之物，而那个定义中不要求任何进一步的术语。
那个反对有一个来源，而命名它化解那残余的不适。谓述于诸构型的约束不含耦合：一个禁止某些状态的规则对影响在任何东西之间的传递什么也没说。既然构型约束是那个词通常所暗示之物，一个读者对那个定义的初次听法将是那个反对在其上有理的那个听法。这正是§3在开篇收窄那个术语的缘由。对接续的约束是所指之物的全部，而在那个读法上一个关系在它是一个限制的同一口气中是一条通道。
§5 关系的分类
一个原初对象的定义借分类而挣得它的位置。倘若此处所提议的定义在做工，它应把诸关系分入诸种类，那个分类应从那个定义随之而来、而非在它旁边被导入，而由此产生的诸类应跨通常被分开的诸理论所处理的诸域成立。本节尝试那一点，然后处理诸案例。
5.1 分类的原则
两个候选分类法呈现自身，而每一个单独都以一种显示一个成功的分类法必须做什么的方式失败。
第一个按关系项的域来分类：诸物体之间、诸有机体之间、诸人之间、诸符号之间，以及一方与一个并不存在之形象之间的诸关系。这是诸学科分划的方式，它立即可辨认，而它有以一种粗略且有用的方式是穷尽的这一可取之处。它不能是那个框架的分类原则，因为命题 4 主张诸关系由它们在约束接续中所扮演的角色、而非由它们诸关系项的形而上学地位所个体化。一个以那个地位为键的分类法会与它意在例示的那个命题相矛盾。它在严格意义上也不是一个分类法：它是一个诸区域的列表，没有生成它们的原则，而它对为什么一个区域中的一个关系应类似另一个区域中的一个关系无话可说。
第二个候选是实在、象征与想象的三元组，它可得、且那个框架的数个邻居使用它（拉康 1977）。它在此为一个特定的缘由被搁置，而那个缘由值得陈述，因为那个三元组否则是有吸引力的。那三者是一个主体的诸register。它们分类一个主体相对于它世界而立的诸方式，而它们中的每一个都预设一个主体立于其中：没有想象者便没有想象，而对一个自旋的点阵便没有象征秩序。一个提议把物理耦合、突触效能、制度角色与继承的义务当作一个概念之诸实例来处理的框架，无法在不于第一步便收窄它自己主张的情况下，从一个人类主体性的理论取来它的顶层分划。
那个定义供出一个两个候选都没有的原则。它有两个子句。第一个，即一个关系是对接续的一个约束，是每一个关系所共同的、而分类不出任何东西。第二个，即那个约束被它所约束的那个过程所承载，系统地变化。诸关系在什么承载那个约束、以及在那个承载者被修订所经由的通道上有别，而那个差别有诸后果：它决定一个关系能存活什么、它如何改变，以及它如何失败。
因而此处所采纳的分类是二维的。关系项的域作为第一个轴被保留，因为它是一个读者所辨认之物、且因为那个定义的覆盖最好被对照它显示。它不承载任何理论分量，而那个框架中没有任何东西从它被导出。承载的方式是第二个轴，它从那个定义被导出，而它做那工作。两者的交叉制表是那个分类法付回报之处，而它在§5.8中被给出。
承载的诸方式及其次序
四个方式被区分，由一个单一判据排序，即那个约束能存活什么的丧失。
一个约束是物质地承载的，当它被一个物理构型所承载、并被物理过程所修订。它存活对它的全部表示的丧失。无物需知道它，而它成立。
一个约束是被铭写的，当它被一个记录所承载、并通过一个在那个记录上运作的被界定程序被修订。它存活任何人对它记忆的丧失与它使用的失效，因为一个休眠的制定法仍是法律、而一个未被读的规则仍执行。它不存活那个记录的丧失，而它除了如那个程序所容许的之外不改变。
一个约束是被流通的，当它被一个在多于一方之间被维持在使用中的令牌所承载、并被那个使用所修订。它存活任何特定一方的丧失、而不存活那个流通的一次中断。没有任何东西被写下，而修订不要求任何程序、也不要求任何决定。
一个约束是被单方承载的，当它被一方对一个对应方的形象所承载、并被那一方自己的诸状态之接续所修订。它同样存活那个对应方与那个共同体的丧失，而它不存活承载它的那一方的丧失。
这个系列在独立性上递降，从一个独立于每个人的约束，经由一个独立于使用的，经由一个独立于任何个体的，到一个依赖于单一一方的。每一个位置都携带它自己的特征性失败，在§5.10中被铺陈。
那两个轴的独立性
那两个轴常常足够地重合，以致一个读者可能怀疑第二个是第一个被改名。它们在两个方向上分开，而它们分开的那些情形是两个轴被需要的证明。
一个其对应方并不存在的关系可能被在流通中、而非在一方中承载。一个共享的神话、一个民族、一个尊奉其奠基者的世系：在这些中的每一个中那个形象被一整个共同体所维持，而没有任何成员的私人表示承载它。安德森关于民族归属的中心观察恰恰是这一点，即那些未曾谋面的共同成员被一个他不曾建造的装置供给每一个成员（安德森 1983）。那个关系项是被想象的，而那个承载是被流通的。
反过来，一个其对应方完整地存在的关系可能被单方承载。一个初级学者对一个他从未谋面之在世权威的关系，完全由他对那个权威会说什么的形象所维系，是一个对一个存在的人的、被在一方中承载的关系。那个权威可能不知道他。倘若两者曾会面，那个形象会被承载者之外的某样东西所更正，而那个承载会改变方式而那个关系持续。
5.2 考察的协议
下面的每一个案例都被付予同样的三个问题，而回答所有三个的纪律正是把一个例示同一个断言区分开来之物。
第一个问题是那个对接续的约束由什么构成：具体地，什么可接续什么，以及在它缺席时什么本可接续什么。一个无法命名那些被封闭之接续的回答未曾辨认一个约束。
第二个问题是联合性的问题：谁的诸状态被弄得对谁的负责。这个子句使那个定义不把每一个接续的规律弄成一个关系，因为一个支配一个系统诸状态的定律不把任何东西关联于任何东西。一个回答必须命名两个术语并说那个负责在哪个方向上运行。
第三个问题是承载的问题：什么承载那个约束，以及那个承载者经由什么通道被修订。这是那个定义的历史子句，而一个无法回答它的案例展现一个结构、而没有在所定义之意义上的关系。
5.3 物质承载的诸关系
耦合的诸自旋
考虑一个带诸邻居之间之耦合的两值位点的点阵，属于伊辛所引入的那种（伊辛 1925）。那个对接续的约束是精确的、且是那个模型的全部：哪些构型可接续哪些由那些耦合所设定。在它们缺席时每一个位点会不参照任何其他位点而演化，而每一个联合接续都会是可得的。联合性同样是精确的，因为每一个位点的转变对称地对它诸邻居的当前值负责。
第三个问题暴露某样那个模型通常不被问之物。那些耦合被手动固定、且没有生涯，故这样一个系统满足那个定义的第一个子句、而不满足第二个：它有动态，而它没有历史。它成为一个完整的实例，当那些耦合被容许在一个更慢的时间尺度上、在它们所支配之位点统计的影响下演化，在那一点上两个时间尺度出现，诸状态在那个快的上在固定约束之下彼此接续，而那个约束在那个慢的上被它所支配的那个接续所修订。
这个案例被放在第一位，因为它以它可得的最干净形式展现命题 3。这样一个系统中的长程序由约束、且由无别之物所产生，而它在远大于任何单一耦合之程的距离上延伸。移除那些耦合，那个点阵在每一个位点变得极大地自由，而它产生噪声。§4的那个既得直觉预测相反，而在这里哪一个预测是对的不是一个诠释的事。
突触
一个突触在同样的意义上约束接续：它使一个细胞的放电对另一个的近期放电负责，而一个这样之诸负责的模式正是允许一个活动模式有一个值得称为一个计算的后继的东西。联合性是有向的、并由那个解剖学所陈述。
承载在此不需要任何人工的补充，因为那个生物学提供它。突触效能被它所条件化的那个活动所修订，沿赫布所提议、而一个大的实验文献自那以来已精炼的诸路线（赫布 1949）。两个细胞之间的关系同时是对什么可接续什么的约束与什么已接续什么的运行产物，在被数个数量级分开的诸时间尺度上。那个分开正是使这样一个系统稳定到足以行动、且可塑到足以学习之物。
这个案例要紧，因为它移除那个疑虑，即那个两时间尺度的结构是一个从社会理论被导入自然的比喻。它是那个神经科学的一个老生常谈，而那个定义命名一个那个学科已然研究的结构。
进一步的实例，压缩
化学键约束哪些核构型可接续哪些、并被它所使成为可能的那些反应所修订。绕行诸体之间的一个共振约束哪些轨道相位可接续哪些、并在长时间上被它所支配的角动量交换所修订。一个营养耦合约束哪些种群状态可接续哪些、并被那些接续施于两个种群之上的选择所修订。一个共生约束每一个伙伴可得的诸代谢状态。一个流行病中的接触结构约束哪些感染状态可接续哪些、并被那些传播所产生的免疫与行为改变所修订。建成的基础设施也属于这里：一个轨距、一个道路网络或一个港口约束哪些移动可接续哪些、并被它所承载的交通缓慢且昂贵地修订。一个房间中的共同在场是最卑微的实例、且在最有后果的实例之中，因为它凭谁能听到谁这个平实的事实约束哪些交换可接续哪些。
最后两个实例值得一句评说，因为两者都是由人类行动所产生的物质地承载之约束，这显示这一类不是一个自然之类。把一个约束置于这里之物，是它无论是否有任何人表示它都成立。一座无人记得建造的桥仍约束什么可接续什么。
那一类的边界
不是每一个物理规律都是一个关系，而第二个问题是什么排除其余。一个运动定律约束一个系统诸状态的接续、而不使两个术语的诸状态对彼此负责，而它是一个约束、而非一个关系。这是那个联合性子句在做§6中指派给它的工作，而物质类是它能最平实地被看到如此做之处。
5.4 铭写承载的诸关系
制定法
一个制定法约束一个官员的哪些行为可接续一个公民的哪些行为，以及哪些主张可接续哪些事实。联合性在它所约束的诸方之间、并经由约束它们的那个记录运行。把这一类区分开来之物是第三个问题。那个约束被一个文本所承载，而它通过一个程序被修订：修订、废止、司法解释。它在那个程序被行使时改变、而不在任何其他时候改变，而这恰恰是给予成文法它奇特的时间性之物。一个制定法可能未被使用地搁置一个世纪、而在它被援引的那天有约束力。
评分模型
一个把一个人指派到一个范畴的模型约束哪些要约、价格与拒绝可接续关于他的哪些记录。联合性成立：那个模型可输出什么对他被记录的诸状态负责，而他接下来可做什么对它的输出负责。承载是被铭写的，因为那个约束被一个被拟合的对象所承载、并被一个在数据上运作的更新规则所修订。
这个案例在本文一份较早的草稿中作为一个候选反常被引入，理由是它适合当时可得的任何方式都不。那个四方式的说明无需修正地吸收它，而那一吸收值得标记，因为它显示那个反常是一个从别处借来的分类法的人为产物。使那个案例看起来奇怪之物，是它的修订通道既非物理过程也非共同使用。一旦铭写作为一个自成其类的方式被接纳，那个评分模型就在那个制定法旁边就位，而两者共享那些要紧的性质：只通过一个被界定的程序修订、通过弃用而持续，以及对是否有任何人理解那个记录漠不关心。
进一步的实例，压缩
一个技术标准约束哪些组件可在一个装配中接续哪些、并被一个标准机构所修订。一个协议约束哪些消息可接续哪些。一个礼仪约束哪些行为可在一个仪式之内接续哪些、并被一个权威而非那个会众所修订。一个组织架构图约束哪些指令可接续哪些、并被重组所修订。一个合同是一个承诺的被铭写形式，而同那个被流通形式的差别是有教益的：朋友之间的承诺随维系它的那个实践而失效，而那个合同存活诸方对兴趣的丧失、且只通过它自己的机械被修订。一个会计标准约束一个公司状况的哪些表示可接续哪些交易。
基因组坐落于这一类的边缘、并带着被标记的限定被引入这里。它是一个记录、它被复制，而它通过被界定而非任意的诸通道被修订。那个描述是否多于一个便利的描述，是一个本文不了结的问题，而它被记下，因为遗传密码这个短语可能不如它通常被认为的那样是隐喻的。
那一类的特征性脆弱
两个失败从铭写随之而来。第一个是死条文：因为那个约束存活弃用，一个记录可能在它曾描述的那个关系已消失之后很久仍继续约束接续。第二个对那个框架更有后果。因为修订要求一个程序，且因为一个程序在那个记录能表达之物上运作，一个被铭写的约束倾向于把它所支配的那个关系重塑为那个记录能持有的形式。不能被录入那个记录之物停止关涉什么可接续什么。这是诸指标渐渐取代它们被引入去度量之物所经由的机制，而它是那个框架把铭写当作四个方式中最强大且最危险者的缘由。
5.5 流通承载的诸关系
一个被一个共同体持有的名字
考虑一个人与一个共同体在其之下持有他的名字之间的关系。那个对接续的约束落在什么可在那个共同体对他的交往中接续什么之上：接下来关于他可说什么、可对他提议什么、可对他期望什么、他一个含混的行动可被认为曾是什么。在那个名字缺席时，诸接续可得，而那个名字封闭它们。
联合性在两个方向上运行，而这易被漏看。那个共同体的诸状态对那个名字负责，因为接下来可说什么被它约束。那个名字自己的状态对那个共同体持续所说之物负责，因为一个名字不外乎它的使用。
承载是通过流通，而那个后果是使这一类成为那个框架败坏说明之所在的那个性质。无人持有那个约束。它被在使用中承载、并被在使用中修订，故它在没有任何人决定它应改变的情况下改变，而没有任何事件标记一个描述硬化为一个分类的那一刻。这让一个那些所概览之读法无法划出的区分被划出：一个保有一个区分而未能据之行动的共同体，与一个那个区分已停止可得的共同体之间。第一个是一个在一个完好约束之下的生成失败。第二个是那个约束中的一个改变。两者在它们所产生的行为中不可区分，而它们是不同的关系。
教师与学生
给定一方作为教师而立于另一方，一个更正可能被修订、而非被侮辱所接续，一个问题可能被问而不失去地位，一个断言可能以在没有别的情境中可得的诸方式被回答。移除那个关系，诸接续改变：那个更正被冒犯所接续，那个问题被尴尬所接续。
那个既得直觉会把这读作限制，并会进一步指出那个关系是不对称的、而不对称是权力之所在。两个观察都是正确的，而那个框架在别处主张一个关系中的不对称总产生一个充分的生成所吸收的权力。两个观察都不触及成问题的那一点，即那个约束是那个教学的条件。没有它那个交换不可得，而没有任何东西剩下供权力被行使于其上。
承载是被流通的，因为承载那个约束之物是一对被维持在使用中、远超这两个人的角色。这正是那个关系能被陌生人在一次初次会面时进入的缘由，也是它被在它们之间经过之物所修订的缘由：被那个渐渐超过教师的学生、被那个停止投入的教师、被一份留下诸方比它们开始时被不同地安置的诸交换的累积。无人需决定那些修订。在同一个关系也被铭写之处，在一份注册记录与一套规章中，那两个方式共存并可能分歧，而在那些角色在使用中已成为之物与那些规章仍所说之物之间的分歧，是一个熟悉的制度状况。
进一步的实例，压缩
一个承诺约束那个承诺者的哪些行为可接续、并被一个维持那个实践之共同体内诸承诺的守与破所修订。货币约束哪些交换可接续哪些持有、并被它所承载的那些交换所修订。一门活的语言约束一个字符串的哪些延续可得、并被那个说话所修订。一个学术归属约束什么可从一件作品接续、以及它归于谁，并被一个领域的引用实践所修订。一个称呼形式约束哪些开场可接续哪些遭遇。一个声誉约束哪些交往可接续哪些要约。
5.6 单方承载的诸关系
那个约束被一方所承载的那一类是最难的、且最富启示的。一个人可能立于对死者、对一个神、对后世、对一门学科、对一个虚构形象、对他作品一个被预期之判者、对他自己未来的自我、对一个他从未谋面的对手，或对一个他相信正在评价他的观众的关系中。关于被看见的文献，从奥托对神圣的说明，经由布伯的呼唤与列维纳斯的面容，描述一个主体在一个其承载者无处在场之注视之下的构成（奥托 1917；布伯 1923；列维纳斯 1961）。
那个协议在最难的情形中
第一个问题是可回答的、且具体地。那个不愿发表他会为一个久已去世的教师读到而羞愧之作品的学者，有某些接续对他被封闭，而人可说出是哪些。那个其行为被他被看见这个确信所安排的信徒，有另一些被封闭。那个约束恰恰在那个定义所说去看之处可观察，在什么可接续什么之中。
第二个问题是这一类威胁那个定义之处，而那个威胁必须在它被回答之前被陈述。联合性要求两个带诸状态的术语。在那个对应方并不存在之处它没有诸状态，而那个关系看来坍缩进那一方的一个一位属性：一个性情，为修辞效果被误描为一个关系。
那个回答是那个关系项是那个形象，而那个形象有诸状态。那个神无需存在，那个神的形象便可有确定的内容、一段历史与一段生涯；那个被预期的判者会赞许什么，是一个关于那个形象在一个时间的事实，而它改变。
这个回答有一个明显的代价，因为那个形象被它所约束诸状态的那一方本身所承载，而一个其两个术语都被安置于一方之中的关系招致方才被否认的那个坍缩。那个答复是那个坍缩不发生，而它是否发生是可检验的。一个关系在此的标志是那一方不控制那个形象的接续。人无法决定那个被预期的判者赞许，而人无法凭决心了结那个已故的教师本会满意。那个无能不是一个意志的失败。在一方能随意设定那个形象诸状态之处，有一个性情正被以关系语言描述、而没有关系。在他不能之处，那两个术语是有别的、而联合性成立。那个判据锐利到足以被应用于特定案例、并被争论。
第三个问题在此被以不寻常的清晰回答，因为没有任何东西从那个对应方进入。那个形象仅被那个约束一直在支配的那个接续所修订，而那恰恰是那个定义所说一个关系的修订所由构成之物。因而单方承载是那个历史子句最纯粹的实例，而那个最纯粹的实例也是那些替代读法必须拒绝的那一个这个事实，是本文所能提供的最强证据。
那一类的证据之力
在互动读法上这些中的许多不是关系，因为没有任何东西在诸方之间经过。在纽带读法上它们不是关系，因为一个端点缺失或不可达。在相关读法上它们不可得，因为那两个量之一没有值。每一个读法都必须把它们当作那个词的比喻用法，或当作关于一方、被以关系语言装扮的心理事实。在此处所提议的定义上它们是完整意义上的关系，而不要求任何修正使它们如此。
一个实例配得上单独的提及，因为它在那个框架别处所做的工作。一个其评价被相信的观众无需含有任何评价的人。它足以使一方把自己当作立于一个他可能被看见、被安置与被评估的秩序之内。那个对接续的约束于是完全运作，而在那个受制于它的一方之外没有任何承载者，这正是围绕这样一个观众组织的行为如此难以通过显示没有任何特定的人在观看来改变的缘由。
5.7 复合的诸关系与社会的地位
社会未曾在任一轴上被给予它自己的一类，而这一省略是刻意的。
一个社会关系通常是一个复合体：数个对接续的约束，被以不同方式承载，同时在同样的诸方之间成立。一个家庭关系被物质地在共同在场与一个家户的诸依赖中承载、被流通地在远超那个家庭而被维持的亲属称谓中承载、被铭写地在户籍与法律中承载，并被单方地在欠死者的诸义务中承载。一个民族关系被流通地在一个共同实践中承载、被铭写地在诸文件与制定法中承载、被单方地在每一个成员对那些未曾谋面之他人的形象中承载，并被物质地在领土与基础设施中承载。货币被铭写地在一个结算系统中承载、被流通地在一个记账单位中承载，并被单方地在每一个持有者对他人将接受什么的期望中承载。一个工作场所层级被铭写地在一个组织架构图中承载、被流通地在那个尊从的实践中承载，并被单方地在那个其注视决定谁算数者的形象中承载。
把社会当作一类会遮蔽所有这一切，而它会把一个异质的范畴放在诸同质的范畴旁边。把它当作复合体产出两个回报。第一个是一个复合体逐组分地失败，而那正是部分败坏所是之物：一个关系的那个被流通组分可能失效、而那个被铭写的持续，而那是一个保有它规则、而已丧失它实践之制度的精确状况，而那个相反的状况是一个已长出它规则之外的实践的状况。第二个是社会理论中若干长期运行的争论可被读作关于一个复合体的哪个组分承载分量的争论，而那是一个比通常被问的问题更易处理的问题。
5.8 域与承载的交叉制表
那两个轴现在可被交叉，而下表如此做。它的诸单元格在一个实例存在之处给出一个代表性的实例，而在那个组合不出现之处被留空。
表 1。关系项的域对照承载的方式。
| 域 | 物质 | 铭写 | 流通 | 单方 |
|---|---|---|---|---|
| 物理 | 耦合的诸自旋、化学键 | |||
| 生物 | 突触、共生 | 基因组（边缘情形） | ||
| 社会 | 共同在场、基础设施 | 制定法、组织架构图 | 角色、习俗、声誉 | 被相信的观众 |
| 象征 | 标准、协议、会计规则 | 活的语言、一个使用中的名字 | 一种私人习语 | |
| 想象 | 经文、礼仪 | 共享的神话、民族 | 已故的教师、一个神 |
那个空单元格的模式本身是一个结果、而不应被读作那个概览中的一个缺口。物质之外的诸方式只在至少一个术语被某方所表示之处变得可得，而诸域按它们诸术语要求多少表示被排序。物理关系只容许物质承载。想象关系容许除物质之外的每一个方式，因为一个形象无法被一个无人表示的构型所承载。因而那两个轴既非独立、也非同一，而它们依赖的形状是本节的一个实质主张：表示是那开启承载之诸更高方式之物，而它开启它们、不顾那个关系项是否存在。
那个把想象域同流通承载相交叉的单元格，携带那个最需要它的情形。一个民族关系在它的关系项上是被想象的、在它的承载上是被流通的，这正是它既非一个私人幻想、也非一个寻常制度的缘由，也是它抗拒适合任一者之处理的缘由。
5.9 诸方式与覆盖的概要
下表铺陈那四个方式，连同那些把它们区分开来的性质，其后是两个汇集上面所处理或所命名之诸实例的表，每一个都以§5第一个问题所要求的形式被陈述。
表 2。承载的诸方式及其性质。
| 方式 | 承载者 | 修订通道 | 可存活的丧失 | 特征性失败 |
|---|---|---|---|---|
| 物质 | 物理构型 | 物理过程 | 全部表示 | 断裂或衰变 |
| 铭写 | 一个记录 | 一个被界定的程序 | 记忆，以及使用 | 死条文；那个记录重塑那个关系 |
| 流通 | 一个使用中的令牌 | 那个使用本身 | 任何特定一方 | 凝结；通过弃用而失效 |
| 单方 | 一方对一个对应方的形象 | 那一方自己的接续 | 那个对应方，以及那个共同体 | 那个形象的坍缩；它的被捕获 |
表 3。物质与铭写承载的诸实例。
| 实例 | 被约束的接续 |
|---|---|
| 物质承载 | |
| 耦合的诸自旋 | 从一个给定构型可达的诸联合构型 |
| 化学键 | 从一个给定构型可达的诸核构型 |
| 轨道共振 | 每一个体可得的诸轨道相位 |
| 突触 | 一个细胞的诸放电状态，给定另一个的近期放电 |
| 营养耦合 | 捕食者与猎物可得的诸种群状态 |
| 共生 | 每一个伙伴可得的诸代谢状态 |
| 接触结构 | 一个种群之内可达的诸感染状态 |
| 建成的基础设施 | 诸地方之间可得的诸移动 |
| 共同在场 | 哪些交换可接续，凭谁能听到谁 |
| 铭写承载 | |
| 制定法 | 哪些官员行为可接续哪些公民行为 |
| 合同 | 那个被约束一方的哪些行为可接续 |
| 财产所有权 | 一个东西的哪些使用可接续谁的决定 |
| 评分模型 | 哪些要约与拒绝可接续哪些记录 |
| 技术标准 | 哪些组件可在一个装配中接续哪些 |
| 协议 | 哪些消息可接续哪些 |
| 礼仪 | 哪些行为可在一个仪式之内接续哪些 |
| 组织架构图 | 哪些指令可接续哪些，以及来自谁 |
| 会计标准 | 哪些表示可接续哪些交易 |
| 基因组（边缘情形） | 哪些细胞状态可接续哪些，凭一个被复制的记录 |
表 4。流通、单方与复合承载的诸实例。
| 实例 | 被约束的接续 |
|---|---|
| 流通承载 | |
| 一个被持有于一个人的名字 | 接下来什么可被说、被提议与被期望 |
| 教师与学生 | 哪些回应可接续一个更正或一个问题 |
| 承诺 | 那个承诺者的哪些行为可接续 |
| 货币 | 哪些交换可接续哪些持有 |
| 活的语言 | 一个字符串的哪些延续可得 |
| 学术归属 | 什么可从一件作品接续，以及它归于谁 |
| 声誉 | 哪些交往可接续哪些要约 |
| 称呼形式 | 哪些开场可接续哪些遭遇 |
| 单方承载 | |
| 已故的教师 | 哪些作品可被发表，以及在什么状况下 |
| 一个神 | 哪些行为可接续，在没有任何见证者的情况下 |
| 后世 | 哪些当前牺牲可接续哪些前景 |
| 一个人自己未来的自我 | 哪些当前行为可接续一个承诺 |
| 一个虚构形象 | 一个人对他自己处境的哪些构想可接续 |
| 一个未曾谋面的权威 | 哪些呈递可接续哪些草稿 |
| 一个被相信的观众 | 哪些行为可接续，在事实上无人评价之处 |
| 复合承载 | |
| 家庭 | 共同在场、亲属称谓、户籍，以及那些缺席者 |
| 民族 | 实践、制定法、未曾谋面的共同成员，以及领土 |
| 工作场所层级 | 架构图、尊从，以及那个决定者的形象 |
5.10 那个分类法的界限
三个界限被对照所主张之物提出。
诸方式是承载的诸方式、而非诸种类的东西。问一个给定的关系是真被铭写还是真被流通是一个错误，而那个正确的问题是它的哪一个约束以哪一个方式被承载。任何有旨趣的诸关系大多是复合的，一如§5.7所论证，而诸方式在那个分解中、而非在那个贴标签中挣得它们的价值。
诸方式从诸案例被论证、而非被导出。为它们排序的那个判据，即一个约束存活什么的丧失，从那个定义被抽取，而此处没有任何东西显示它是那个定义所供出的唯一原则。一个从同一个定义抽取的不同原则可能切得不同、并切得更好。
铭写与流通之间的边界将承受压力。一个没有任何程序支配、被无论谁编辑它者所修订、并对使用负责的记录，在它的承载者上是被铭写的、在它的修订通道上是被流通的，而一个口头传统的固定语料从另一侧坐落在同一条线上。那个分类在两者分歧之处按修订通道进行，因为修订通道是那个定义的历史子句所使成为决定性之物，而那个裁定在此被约定、而非被论证。
§6 界定
一个定义既是一套拒绝、也是一套承诺，而那些拒绝在此被铺陈。
6.1 从那个定义中的诸排除
它不是一个本体论。那个定义对诸关系是否比它们的诸关系项更根本、诸关系项是否独立于诸关系而存在，或世界是否在根底上是关系性的，什么也没说。关于这些问题的诸立场可得，从莱布尼茨经由怀特海，到量子力学的关系性读法与到能动实在论（莱布尼茨与克拉克 1717；怀特海 1929；罗韦利 1996；巴拉德 2007），而那个框架最终可能取一个。当下的定义与数个相容、且不要求任何一个。
它不是一个认识论。那个定义不说诸关系如何被知道、被观察或被度量。这种被定义之关系常对立于它们之内的诸方不可见，是一个重要的主张，而它是一个分开的主张。
它不是一个互动的理论。互动是一个对接续的约束被实现所处的一个方式，而§5展现了没有任何互动发生的诸方式。
它不是一个关于那个词的主张。物理学、社会学与哲学将继续在它们自己的诸意义上、正确地使用关系。所提议的是供一个框架的一个术语。
6.2 尺度与诸层次之间的过渡
一个那个定义引起而不了结的问题是尺度的问题。同一个词在那个框架中被在两个层次上使用：为那个在特定术语之间成立的微观约束，以及为一个历史情境施于它之内一切之上的那个宏观约束。上面的定义在第一个层次被陈述。
那两个层次之间的关系是一个实质的事项、并在这个纲领的历史分支中被处理，在那里一个历史情境的约束被提议为那个关系场的一个宏观相、而非一个立于它之外的容器。此处要标记的点只是那两者必须在语汇中被分开，因为一个把关系定义为约束、同时在两个层次上被应用的定义，会坍缩一个那个框架所需的区分。关系是约束，在那个约束成立所处的尺度上；在一个尺度上约束之物在另一个尺度上被生成；而诸尺度之间的过渡是一个问题、而非一个定义的事。
6.3 那个定义中开放的诸问题
四个问题被留作开放，而它们是那自然的下一份工作。
第一个是个体化。那个定义说一个关系是什么、而不说如何计数诸关系，也不说如何把一个关系同两个共同出现的关系区分开来。一个判据是被想要的。
第二个是那个概念的边界。不是每一个对接续的约束都是一个关系，否则那个定义会使关系与定律同延。做那排除的那个子句是联合性，即那个约束使两个或更多术语的诸状态对彼此负责。§5为那个难的情形供出一个判据，即一个术语区别于承载它的那一方，当那一方无法随意设定它的诸状态时，而那个判据从那个想象类被论证。它是否一般化，以及它是否能在不诉诸一方之意志的情况下被陈述，是未定的。
第三个是§4的判据：什么把留下诸延续开放的约束同封闭它们的约束区分开来。那个框架的规范工作依据这个区分，而本文只使它成为可陈述的。
第四个是形式化。一个以接续的术语被定框的定义招致在动力系统的语言中的陈述，在其中一个关系会答对一个对一个联合状态空间之转变结构的限制，而它的历史子句答对一个在那个限制本身上的慢动力学。这样一个陈述是否添加超出记号的任何东西，是一个本文留作开放的问题，而这一克制是那个在那件伴随工作中所作的同一个：一个推导无物的形式装置借来一份那个论证未曾挣得的严格。
§7 在纲领中的位置
生成性关系存在的框架关切主体、意义、价值与规范性如何通过生成性关系过程共同涌现（黄，无日期）。围绕它一套分支已生长：一门认识论、一门被生成价值的经济学、一门治理理论，以及一门关切历史约束之演化的历史哲学。它们全都以关系的术语被陈述，而直到现在它们无一能说出那个术语所意味之物。
那个定义供给每一个的是同样的东西。它把接续放进那个概念。那门经济学于是能把一个把它所生成之物返回给它参与者的关系，同一个把它导向别处的关系区分开来，并能把那个差别作为两个对接续之约束之间的一个差别提出。那门治理理论能问一个关系允许什么接续什么，并能把制度设计当作这样诸许可的设计。那个历史分支，它的主题是约束的演化，获得一个微观术语立于它宏观术语之下，而诸尺度之间的关系被作为一个开放问题在§6中命名。§5的分类法以同样的方式关乎每一个分支，因为一个关于关系改变的主张是一个关于一个修订通道的主张，而那四个方式有四个不同的修订通道：物理过程、一个被界定的程序、使用本身，以及单一一方的接续。一个把它自己针对错误通道的制度设计提议将因与它的优点毫无关系的诸缘由而失败，而那个铭写方式是这样的提议最常把它们自己针对之处，因为它是四个中唯一能被决定所改变的那一个。
本文的主张在它所断言之物上是谦逊的、而在它所使成为可能之物上是不谦逊的。它断言一个句子：关系是历史过程中生成得以展开的约束。那个框架关于败坏、吸收、承认与历史改变所说的一切都是一个关于这样诸约束的主张，而那些主张中的每一个现在都有一个主题。
关于可修订性的一则说明。 一个主张诸约束被它们所约束之过程所承载的框架，欠它自己的诸定义同样的处理。这一个作为一个工作定义被提供，可被它所使成为可能的那份工作所修订，而这一措辞不是一个含糊其辞。三个失败模式从本文所立之处可见，而每一个都被陈述以使一个读者可寻找它。倘若§5的诸案例被显示为要求逐域有别的诸修正，那个横跨它们的单一概念的主张便失败，而那个定义应被撤回或被拆分。倘若那个联合性子句被证明在§6所要求的一般形式中不可陈述，那个定义便太宽、并接纳每一个接续的定律作为一个关系。倘若那四个承载方式被证明不是一个东西的诸方式，或倘若那个生成它们的排序判据被证明是任意的，§5的分类法便倒下，而那个定义丧失此处为它所提供的主要证据。
参考文献
Anderson, Benedict (1983). Imagined Communities: Reflections on the Origin and Spread of Nationalism. London: Verso.
Aristotle. Categories, ch. 7. In The Complete Works of Aristotle, ed. Jonathan Barnes. Princeton: Princeton University Press, 1984.
Barad, Karen (2007). Meeting the Universe Halfway: Quantum Physics and the Entanglement of Matter and Meaning. Durham: Duke University Press.
Bateson, Gregory (1972). Steps to an Ecology of Mind. New York: Ballantine Books.
Buber, Martin (1923). I and Thou. Trans. Walter Kaufmann. New York: Scribner, 1970.
Cassirer, Ernst (1910). Substance and Function. Trans. William Curtis Swabey and Marie Collins Swabey. Chicago: Open Court, 1923.
Ceva, Emanuela (2016). Interactive Justice: A Proceduralist Approach to Value Conflict in Politics. London: Routledge.
Emirbayer, Mustafa (1997). Manifesto for a Relational Sociology. American Journal of Sociology, 103(2), 281–317.
Hebb, Donald O. (1949). The Organization of Behavior: A Neuropsychological Theory. New York: Wiley.
Huang, Wanhong. Responding to the Crises of Symbol and Subject in Modernity. SSRN Working Paper. DOI: 10.2139/ssrn.5752104.
Ising, Ernst (1925). Beitrag zur Theorie des Ferromagnetismus. Zeitschrift für Physik, 31(1), 253–258.
Lacan, Jacques (1977). The Four Fundamental Concepts of Psycho-Analysis. Ed. Jacques-Alain Miller, trans. Alan Sheridan. London: Hogarth Press.
Latour, Bruno (2005). Reassembling the Social: An Introduction to Actor-Network-Theory. Oxford: Oxford University Press.
Leibniz, G. W., and Samuel Clarke (1717). The Leibniz–Clarke Correspondence. Ed. H. G. Alexander. Manchester: Manchester University Press, 1956.
Levinas, Emmanuel (1961). Totality and Infinity: An Essay on Exteriority. Trans. Alphonso Lingis. Pittsburgh: Duquesne University Press, 1969.
Marx, Karl (1852). The Eighteenth Brumaire of Louis Bonaparte. In Marx–Engels Collected Works, vol. 11. London: Lawrence & Wishart, 1979.
Otto, Rudolf (1917). The Idea of the Holy. Trans. John W. Harvey. Oxford: Oxford University Press, 1923.
Rovelli, Carlo (1996). Relational Quantum Mechanics. International Journal of Theoretical Physics, 35(8), 1637–1678.
Saussure, Ferdinand de (1916). Course in General Linguistics. Ed. Charles Bally and Albert Sechehaye, trans. Roy Harris. London: Duckworth, 1983.
Simmel, Georg (1908). Soziologie: Untersuchungen über die Formen der Vergesellschaftung. Leipzig: Duncker & Humblot.
Whitehead, Alfred North (1929). Process and Reality: An Essay in Cosmology. Corrected edition, ed. David Ray Griffin and Donald W. Sherburne. New York: Free Press, 1978.