Abstract

Field Structuralism presents a scale-relative conceptual framework linking the formation of effective objects with a bounded account of conation and action. A field is defined as an organized distribution of content and coupling relations over a specified domain, while a distinct law structure specifies admissible transformations. As a field evolves, stable differences may be represented as nodes and persistent dependencies as edges. A network warrants treatment as an effective higher-scale field only when scientifically motivated coarse-graining identifies robust macroscopic variables, approximate dynamical closure within a declared regime, and organizational constraints on lower-level possibilities. The sequence from field to structure to new field may recur across scales without requiring identical content or an infinite hierarchy.

The practical extension introduces conative organization as a higher-scale organization capable of forming or maintaining goals, evaluating relevant conditions, and producing directed action. Relative to a selected focal-system boundary, the law, state, and conative fields are analytical roles rather than separate substances. Laws specify transformations; the state field represents the task-relevant external configuration; and the conative field represents the internal organization from which goals, capacities, and cognitive models are extracted. The ontology alone neither derives conation nor entails rational choice. Given conative organization, the practical framework represents valuation, bounded modeling, policy selection, law-constrained execution, feedback, and replanning.

The contribution is integrative. The framework distinguishes real structures from models, actual internal capacities from their estimates, context-relative implementability from either, and realized trajectories from policies. Its equations are formal schemas, not established empirical laws. Domain-specific applications require explicit variables, transition operators, coarse-graining maps, error tolerances, probability models, and empirical tests.

Keywords: field structuralism; emergence; scale-relative ontology; structural realism; conation; bounded rationality; three-field framework; receding-horizon planning

Part I: Fields, Structure, and Scale

1. From Asking What Things Are Made Of to Asking How They Are Generated

We commonly understand the world as a collection of objects: objects exist first, and only afterward enter into relations with one another. Tables, atoms, organisms, persons, and organizations appear to be already completed units.

This picture naturally leads to the question:

What indivisible entities ultimately constitute the world?

Field Structuralism changes the direction of inquiry. Rather than beginning with a search for ultimate material units, it asks:

How does an object arise from more basic processes of change, and how does it acquire a relatively stable identity?

Modern quantum field theory provides an important inspiration for this shift. In its usual formulation, an elementary-particle species is represented through excitations of quantum fields rather than through tiny solid objects that exist prior to those fields (Lancaster & Blundell, 2014). This does not establish that life, consciousness, institutions, or societies are physical fields of the same type. It serves here only as a well-established example of a more limited explanatory possibility:

Objects need not be the absolute starting points of change; they may instead be stable patterns formed by fields under particular conditions.

Taking this possibility as an ontological starting point rather than as a conclusion derived from quantum field theory, the framework adopts the following basic proposition:

At a selected scale, field descriptions are explanatorily prior to the objects stabilized within them; those objects are structured results of field evolution at that scale.

“Prior” refers not to temporal sequence but to explanatory order. To understand why an object is the object it is, one must examine the differences, relations, and constraints through which it is formed and maintained.

1.1. Contribution, Relation to Prior Work, and Structure

The proposal belongs to a family of views that take organization, relations, and stable patterns seriously. Structural realism gives structure a central epistemic or ontological role (French, 2014; Ladyman, 1998; Worrall, 1989). Work on emergence emphasizes novelty, robustness, effective autonomy, and the compatibility of higher-level organization with lower-level realization (Anderson, 1972; Butterfield, 2011; Franklin & Robertson, 2024). Accounts of real patterns and robustness likewise explain why a scale-relative object can be more than an arbitrary description (Dennett, 1991; Wimsatt, 2007).

The present framework is not a synonym for structural realism. It draws on structural realism while adding a field-to-object account of cross-scale formation and a boundary-relative practical framework for conation and action.

It does not claim priority over those ideas individually. Its proposed contribution is their integration into one scale-indexed architecture with four linked distinctions:

1. field states are separated from the laws that transform them;
2. stabilization produces nodes and relations, but a higher-scale field requires approximate dynamical closure and constraint relevance rather than a network alone;
3. real structures are separated from fallible models of them; and
4. conation is represented as an emergent field-like organization whose goals, capacities, and models enter a law-constrained, feedback-driven account of action.

Sections 2-6 develop the ontological framework. Section 7 explains what must be added before that ontology can support an account of conation. Sections 8-11 formulate the three-field analysis of action, intervention, policy choice, and receding-horizon practice. Section 12 states the scope and limits of the complete framework.

2. A Definition of Field within the Framework

Within Field Structuralism, a field is neither an empty container in which objects are placed nor a metaphorical name for any environment.

Anything called a field must specify at least three elements:

$$\mathfrak F_\ell := \bigl( \Omega_\ell, \psi_\ell, \Lambda_\ell \bigr)$$

where:

• $\Omega_\ell$ is the domain, or set of degrees of freedom, at scale $\ell$;
• $\psi_\ell$ is the content distributed over that domain;
• $\Lambda_\ell$ is the structure of couplings, dependencies, and constraints among those contents.

Thus:

A field is an organized distribution of some type of content, together with its coupling relations, over a given domain.

The domain need not be geometric space. It may instead be a state space, network domain, or relational domain. Distributed content may consist of physical quantities, system states, transformation constraints, or the internal states of a goal-directed system. These types share the formal pattern of domain, content, and coupling, but they do not thereby belong to the same ontological level.

If a purported field lacks a specified domain, distributed content, and coupling structure, it cannot strictly be called a field within this framework. Conversely, merely possessing content and relations is not sufficient. For a first-order state field, an operational model must also specify its degrees of freedom, state representation, and whether and how changes propagate through the coupling structure at the selected scale. A second-order law field instead requires an indexed domain of conditional transformation constraints and a specified dependency structure among them.

To formalize this cross-scale recurrence, begin at a selected scale with a first-order state field:

$$\mathcal F_\ell(t) := \bigl( \Omega_\ell, \Phi_\ell(t), \Lambda_\ell(t) \bigr)$$

where $\Phi_\ell(t)$ is the distribution of states and differences, and $\Lambda_\ell(t)$ is the currently realized structure of interactions and couplings.

A first-order state field describes:

What differences exist at the present moment, and what coupling relations are currently realized.

A law describes:

Under what conditions those states are allowed to transform, and how.

For a first-order state field, therefore, the field is a state structure, whereas a law is a transformation structure. They must be distinguished but cannot be separated. The “law field” introduced later is a second-order constraint field: its distributed content consists of conditional transformation relations, while the state field supplies current boundary values, parameter values, and resources. It shares the general form of a field with state fields but is not of the same type.

The term law field is used only when operative transformation constraints can be indexed over a meaningful domain and their dependencies can be specified. Uniform laws are represented as constant distributions over that domain. If no meaningful domain, distributed content, or coupling among constraints can be identified, the relevant object should be called a law structure rather than a field.

Schematic transition relation. Rather than specifying a completed empirical law, write the evolution of a field as:

$$\mathcal F_\ell(t+\Delta t) = T_{\mathcal K_\ell} \bigl( \mathcal F_\ell(t), \xi_t \bigr)$$

where:

• $\mathcal K_\ell$ is the second-order constraint field, or more generally the operative law structure, at scale $\ell$;
• $T_{\mathcal K_\ell}$ is the transition operator induced by the operative transformation structure encoded by $\mathcal K_\ell$;
• $\xi_t$ is a real external input or stochastic disturbance relative to the chosen system boundary; it is not a residual of an internal model. If the object of inquiry is a whole with no external boundary, there is no external input, although law-governed intrinsic randomness may remain.

A concrete application must specify the state space, input space, and transition operator.

A fuller statement of the proposed ontology is therefore:

Field Structuralism represents reality in terms of field states evolving under relatively stable structures of transformation.

3. How Fields Form Nodes and Edges

A field can undergo change, but not every change produces an object. Change may generate structure, preserve it, or destabilize it.

Within this framework, a “point” is not a dimensionless geometric position. It is a relatively stable pattern within a field. To avoid confusion, it will be called a structural node.

For a pattern to count as a node, it must satisfy three basic conditions:

It must be distinguishable from its background and from other patterns; it must preserve continuity over some interval; and it must withstand a defined range of disturbances without immediately losing its principal characteristics.

A node can therefore be defined as:

A stable pattern of difference formed during field evolution that remains continuously identifiable at a given scale and within a given range of disturbances.

An “edge” is not a material line connecting two nodes. It is a persistent effective relation between them, extracted at the selected scale from the underlying couplings $\Lambda_\ell$. The edge set therefore does not add a second, independent layer of relations; it represents which underlying couplings remain effective among stabilized nodes.

A structural edge exists when two or more nodes stand in a stable, repeatable interaction, dependence, or constraint relation at the selected scale. Causal direction should be asserted only when supported by mechanistic or intervention evidence.

An edge may represent transfer of matter, exchange of energy, flow of information, causal influence, functional dependence, state transformation, or behavioral constraint. These relations can share the abstract form of an edge, but their type, direction, and temporal properties must be preserved. The set $E_\ell$ is therefore a typed relation set: a predictive edge does not by itself establish a causal or mechanistic edge. Relations that hold jointly among several nodes may be represented as hyperedges.

Unconditional or in-sample correlation alone is insufficient to establish an edge. A predictive edge requires a prespecified conditional dependence that remains stable in out-of-sample tests; a causal edge additionally requires appropriate mechanistic or intervention evidence.

Schematic extraction relation. Let $\mathfrak D_\ell$ denote the scale-relative process of differentiation, stabilization, and extraction:

$$\mathfrak D_\ell \bigl[ \mathcal F_\ell \bigr] = \mathcal N_\ell, \qquad \mathcal N_\ell := (V_\ell,E_\ell)$$

where:

• $\mathfrak D_\ell$ is the process of differentiation and stabilization;
• $V_\ell$ is the set of structural nodes;
• $E_\ell$ is the set of stable relations;
• $\mathcal N_\ell$ is the structural network at that scale.

The equation names the role of this process; it is not an independently specified detection algorithm.

Nodes and edges do not necessarily arise in a strict sequence in which points are formed first and relations are added afterward. A pattern often becomes a node precisely because its couplings with its surroundings differ from those of the background.

Thus:

The nonuniform evolution of a field simultaneously produces stable patterns and stable relations; the former are abstracted as nodes, and the latter as edges.

4. How a Structure Emerges as a New Field

A mere collection of nodes and edges does not automatically form a new field.

Within the framework, a structure warrants representation as an effective higher-scale field within a declared regime only if it has the following properties:

First, it can be described by a set of macroscopic states without requiring every lower-level node to be tracked individually.

Second, it is robust under some lower-level changes. Some nodes may be replaced or altered while the whole retains its principal characteristics.

Third, it has an effective mode of evolution at the higher scale: its macroscopic variables, together with specified effective inputs, can describe or predict its evolution within a stated error tolerance.

Fourth, its overall configuration objectively limits the feasible states and transition paths of lower-level nodes through boundary conditions, resource distributions, and relational structure.

To avoid treating every arbitrary macroscopic description as a new field, introduce a coarse-graining map $Q_{\ell\to\ell+1}$, an input projection $J_{\ell\to\ell+1}$, an effective higher-level transition $T^{\mathrm{eff}}_{\ell+1}$, and declared classes of admissible lower-level states and inputs.

Operational criterion (one-step approximate dynamical closure). After $Q_{\ell\to\ell+1}$, $J_{\ell\to\ell+1}$, $T^{\mathrm{eff}}_{\ell+1}$, $d$, $\varepsilon$, and the admissible regime have been fixed independently of the assessment data, require, for every admissible lower-level state $\mathcal F_\ell(t)$ and input $\xi_t$, that

$$d\!\left( Q_{\ell\to\ell+1} T_{\mathcal K_\ell}\!\left( \mathcal F_\ell(t),\xi_t \right), T^{\mathrm{eff}}_{\ell+1}\!\left( Q_{\ell\to\ell+1}\mathcal F_\ell(t), J_{\ell\to\ell+1}\xi_t \right) \right) \leq \varepsilon$$

Here, $T_{\mathcal K_\ell}$ is the lower-level transition, $J_{\ell\to\ell+1}$ projects lower-level inputs into the declared effective-input representation, $d$ measures differences between higher-level states, and $\varepsilon$ is the allowed approximation error. The maps, distance measure, error tolerance, admissible regime, and time horizon must be specified independently of the transitions used to assess closure. The bound must hold on new admissible states, inputs, and perturbations and should be compared with a lower-complexity baseline. Multi-step closure requires an analogous bound over a declared finite horizon; unbounded stochastic inputs require an expected or high-probability bound.

Approximate closure is necessary but not sufficient for a new field. The coarse-grained result must also identify a higher-level domain, distributed content, and effective coupling structure.

Definition (coarse-grained higher-scale representation). When the declared field criteria are satisfied, define a model of the effective higher-scale field by:

$$\widehat{\mathcal F}_{\ell+1}(t) := Q_{\ell\to\ell+1}\mathcal F_\ell(t) = \bigl( \Omega_{\ell+1}, \Phi_{\ell+1}(t), \Lambda_{\ell+1}(t) \bigr).$$

If the result supplies only macroscopic variables and an effective transition rule, it is an effective higher-level system or state model, not yet a field in the strict sense defined in Section 2.

If a higher-level state improves out-of-sample prediction or intervention across independent models or measurements, that improvement may provide defeasible evidence that the higher-level variable tracks an objective constraint; it is not itself the constraint. Downward constraint is not a mysterious force that violates lower-level laws, nor is it an additional force existing independently of lower-level structures. It consists in the restriction of lower-level possibilities realized when nodes enter a particular overall configuration (Bechtel, 2017; Bursten, 2021; Craver & Bechtel, 2007).

An operational test should compare matched systems or interventions that preserve the relevant local transition rules while varying a higher-level boundary, resource distribution, or organizational variable. A downward-constraint claim requires a repeatable change in the accessible lower-level transition set beyond what a prespecified baseline using local variables alone can explain.

The claim is not supported within the declared regime if the prespecified coarse-grained variables and error bound fail on new admissible states, perturbations, or interventions, or if they do not outperform the stated baseline under the selected predictive or intervention criterion.

The emergence of a structure as an effective higher-scale field can be represented schematically as:

$$\mathcal F_\ell \xrightarrow{\mathfrak D_\ell} \mathcal N_\ell \xrightarrow{\mathfrak C_\ell} \mathcal F_{\ell+1}$$

where $\mathfrak C_\ell$ denotes structural integration and organizational closure in the target process. A coarse-graining map does not generate that organization or establish its reality by definition; it represents the organization when the declared field criteria are satisfied. Robustness across independent models, measurements, and interventions provides defeasible support for treating the represented organization as objectively significant.

The arrows represent scale-relative explanatory mappings. Node stabilization, relational organization, and effective higher-level description may develop together; they need not be three sharply separated moments in chronological time.

Organizational closure does not mean complete isolation from the environment. It means that sufficiently stable interdependencies have developed within a structure for it to persist and exhibit coherent system-level dynamics. This broad usage should not be confused with the more specific closure-of-constraints account developed in theoretical biology (Montévil & Mossio, 2015). Approximate dynamical closure is a distinct modeling criterion: selected macroscopic variables must support effective evolution within a stated regime and error tolerance.

The central cross-scale generative schema is therefore $\mathcal F_\ell\rightarrow(V_\ell,E_\ell)\rightarrow\mathcal F_{\ell+1}$. A sufficiently integrated structure warrants representation as an effective higher-scale field only within the declared regime and under the stated robustness, closure, and constraint criteria. Cross-scale recurrence neither requires identical content nor presupposes an infinite hierarchy.

Part II: Conation, Intervention, and Feedback

7. From Emergent Structure to Conative Organization

The ontological framework and the practical framework answer different questions. Sections 2-6 ask under what conditions stable objects and higher-scale fields can arise. Sections 8-11 ask how directed action can be represented and organized once conative organization is present.

The second account is compatible with the first, but it is not deduced from it. Approximate dynamical closure and structural robustness do not by themselves produce valuation, cognition, or action. A crystal, vortex, or ecosystem may qualify as a higher-scale field-like organization without possessing conative organization. An account of directed action therefore requires additional functional conditions.

An organization qualifies as conative only if, at the selected scale and time horizon, it has:

1. a relatively persistent boundary that distinguishes internal from external states;
2. internal organization that forms or maintains goals and evaluates actual or possible states relative to them;
3. action capacities through which internal states can systematically alter external transitions;
4. an internal representation, however limited or implicit, that differentiates relevant conditions and consequences; and
5. feedback processes that can modify internal state and subsequent action.

These functional conditions are requirements of the practical model, not a complete theory of life, consciousness, or moral responsibility. Goals may arise through biological regulation, learning, social processes, reflection, or combinations thereof; neither consciousness nor subjective experience is presupposed. The field criteria of Sections 2 and 4 remain separately necessary for describing such organization as a conative field. Otherwise, it should be called a conative organization.

The transition from the general ontology to the practical framework can be summarized by the following schematic relation:

$$\begin{aligned} &\text{effective higher-scale field}\ &\quad +\ \text{goal-forming and evaluative organization}\ &\quad +\ \text{action-capable coupling}\ &\quad +\ \text{limited internal representation}\ &\quad +\ \text{feedback-sensitive revision}\ &\qquad \longrightarrow\ \text{conative field} \end{aligned}$$

The plus signs enumerate jointly required features, and the arrow denotes eligibility for conative-field modeling; neither is a numerical operation or a sufficient dynamical law.

The framework then introduces a boundary-relative analytical decomposition. Objective transformation conditions are represented as the law field $\mathcal K$; external states relative to the selected focal-system boundary are represented as the state field $R_t$; and goal- and action-relevant internal organization is represented as the conative field $P_t$. This division does not posit three disconnected regions of reality. Depending on the selected boundary, the same physical component may enter $R_t$ or $P_t$, while $\mathcal K$ constrains the transformations of both.

The practical model also adopts bounded rationality. Action proceeds through a limited model, a limited policy set, and limited computational and material capacities rather than through optimization over a completely known reality (Simon, 1955). Consequently, the framework distinguishes at every stage between actual states and their estimates, objective feasibility and estimated feasibility, and internal capacity and context-relative implementability. Hereafter, actual denotes quantities in the target process, a hat denotes model-based estimates, and objective is reserved for constraints not made true merely by the focal system’s current goals or representations.

8. The Three Fields of Action

Human beings do not stand outside field structures. When the declared criteria are met, a person may be modeled as a bounded focal system whose internal organization instantiates a conative field.

Relative to a selected focal-system boundary, three fields can be distinguished:

$$\mathscr S_t := \bigl( \mathcal K, R_t, P_t \bigr)$$

where:

• $\mathcal K$ is the law field;
• $R_t$ is the state field;
• $P_t$ is the conative field.

The state and conative fields are first-order state fields. In Part II, $\mathcal K$ is called a law field only when it satisfies the second-order law-field criteria of Section 2; otherwise it denotes the operative law structure. The following schema assumes that all three field conditions are satisfied:

$$\text{field} \bigl( \text{domain}, \text{distributed content}, \text{coupling structure} \bigr)$$

The three analytical roles are:

$$\begin{aligned} \mathcal K &: \text{admissible transformations and objective constraints},\ R_t &: \text{the current task-relevant external configuration},\ P_t &: \text{the internal organization supporting goals, capacities, models, and action}. \end{aligned}$$

8.1. Law Field: The Distribution of Transformation Conditions

The law field is written as:

$$\mathcal K := \bigl( \Omega_{\mathcal K}, \kappa, \Lambda_{\mathcal K} \bigr)$$

where:

• $\Omega_{\mathcal K}$ is the domain over which operative transformation constraints are indexed, including constraints on components represented in $P_t$;
• $\kappa$ is the distribution of transformation rules and feasibility constraints over that domain;
• $\Lambda_{\mathcal K}$ is the structure of dependencies among those rules and constraints.

The law field does not distribute current states. It distributes the conditions under which states may transform. It is therefore a second-order constraint field.

In this usage, the law field is an indexed representation of conditional transformation constraints across a domain, not an additional physical substance or an independent causal force.

“Objective” means that these transformation conditions are not made true merely by the focal system’s current goals or internal representations. They constrain both external and internal states, including realized actions.

The law field does not contain the focal system’s goals, capacities, or selected actions. It constrains which interventions are realizable and what consequences can follow from states and interventions.

Writing $\mathcal K$ without a time index assumes that the relevant transformation constraints remain stable over the current planning horizon. Modeling changing constraints requires an expanded state, for example $\widetilde X_t=(\mathcal K_t,R_t,P_t)$, together with an explicitly specified evolution rule for $\mathcal K_t$; that extension is outside the present schema.

The action $a_t$ is not itself a transformation rule within the law field, nor does the law field select an action. Nevertheless, how an action can be realized and what consequences it can have remain constrained by the law field.

8.2. State Field: The Current Environmental Configuration

The state field is written as:

$$R_t := \bigl( \Omega_R, \rho_t, \Lambda_R(t) \bigr)$$

where:

• $\Omega_R$ is the domain of the task-relevant environment delimited relative to the selected focal-system boundary;
• $\rho_t$ is the distribution of external states and differences at time $t$;
• $\Lambda_R(t)$ is the currently realized structure of relations and couplings among external components.

The state field can also be abbreviated as:

$$R_t := \left. \mathcal F_{\mathrm{ext}}^{(\ell)} \right|_t$$

Thus, the state field is a structural cross-section of the task-relevant environment at time $t$ and at the chosen scale $\ell$.

At the chosen scale, $R_t$ denotes the actual effective external state relative to the selected boundary. Its estimate $\widehat R_t$, introduced below, should include enough variables to support transition judgments within the declared task tolerance; this does not require enumerating every variable that could affect the future.

Other goal-directed systems do not require a fourth analytical field. Relative to the focal system, they may be represented as action-capable components of the external state field. Whether they also constitute effective subfields depends on the chosen scale and the field criteria stated above.

9. How Action Enters the State Field

A law structure constrains transitions but does not select an intervention. A complete account of practice must therefore explain how a control proposal becomes a realized action and how that action changes the coupled system-environment state.

Modeling schema (joint transition). With $X_t=(R_t,P_t)$ and $a_t=E_{\mathcal K}(R_t,P_t,u_t)$ as defined above, represent the post-action state before observation-mediated internal updating as:

$$X_{t+1}^{-} = T^X_{\mathcal K}\bigl(X_t,a_t,\xi_t\bigr).$$

In stochastic applications, the execution and transition maps may instead be represented by conditional kernels.

The intervention terminology emphasizes that realized action changes which transition occurs rather than merely recording a correlation. The operators below are schematic constructions of the present framework, not an adoption of any single formal theory of causal intervention (cf. Woodward, 2003).

Modeling assumption (optional two-stage decomposition). For systems admitting such a factorization, introduce a schematic intervention map for the first stage:

$$R_t^{+} = I_{\mathcal K} \bigl( R_t, a_t \bigr)$$

where:

• $I_{\mathcal K}$ is the action-intervention map constrained by the law field;
• $R_t^{+}$ is the state field after intervention.

The subscript $\mathcal K$ indicates that, although an action is not itself part of the law field, it can be realized only in ways permitted by the laws.

The state field then continues to evolve according to the laws, including background focal-system/environment coupling not summarized by $a_t$:

$$R_{t+1} = T^R_{\mathcal K} \bigl( R_t^{+}, P_t, \xi_t \bigr)$$

Combining the two expressions:

$$R_{t+1} = T^R_{\mathcal K} \Bigl( I_{\mathcal K}(R_t,a_t), P_t, \xi_t \Bigr)$$

This analytical separation distinguishes the change attributed to realized action from the subsequent law-governed evolution of the intervened state, including background coupling not summarized by $a_t$. It does not mean that laws temporarily cease to operate during action.

If the environmental component is represented by the two-stage intervention-transition decomposition above, the model assumes the following factorization:

$$\operatorname{proj}_{R} T^X_{\mathcal K}\bigl(X_t,a_t,\xi_t\bigr) = T^R_{\mathcal K} \Bigl( I_{\mathcal K}(R_t,a_t), P_t, \xi_t \Bigr)$$

This factorization is a modeling assumption, not an identity that every joint dynamics must satisfy. Here, $T^R_{\mathcal K}$ describes only the transition of the environmental state field; the argument $P_t$ retains background coupling not already summarized by $a_t$. The operator $T^X_{\mathcal K}$ instead describes the joint transition of the focal system and environment in the general spirit of an interaction loop (Sutton & Barto, 2018). Because their domains differ, the two operators must not be identified. In the joint equation, $\xi_t$ represents input or stochastic disturbance external to the selected boundary of $X_t$; omission and error within the internal model must instead be represented as model residuals.

Practice is therefore not an escape from laws. It is:

The process through which goal-directed control proposals produce law-constrained changes in the state field.

10. Policy Selection under the Constraints of the Three Fields

A practical trajectory can be represented as:

$$\gamma = \left( \left\{(R_s,P_s)\right\}_{s=t}^{T}, \left\{a_s\right\}_{s=t}^{T-1} \right).$$

The symbol $\gamma$ denotes an actual state-action trajectory. In a deterministic, fully observed model, policies can be compared through their induced trajectories. Under uncertainty with continuing feedback, policy selection is more general than commitment to a single open-loop trajectory. Let the actual and modeled observation processes be

$$\begin{aligned} o_s &= O(R_s,P_s,\eta_s), \ \widehat o_s &= \widehat O_t(\widehat R_s,\widehat P_s,\nu_s). \end{aligned}$$

Here, $\eta_s$ is actual observation noise and $\nu_s$ is its modeled counterpart. Because the proposal $u_s$ and realized action $a_s$ may differ, let $\widetilde a_s$ denote the execution record available to the focal system and define, for $s>t$,

$$h_s = (o_t,u_t,\widetilde a_t,o_{t+1},\ldots,u_{s-1},\widetilde a_{s-1},o_s), \qquad h_t=(o_t),$$

with an analogous modeled history $\widehat h_s$. If execution is fully summarized in the next observation, $\widetilde a_s$ may be omitted. A feedback policy has time-$s$ component

$$\pi_s:\mathcal H_s\to\mathcal U_s, \qquad u_s=\pi_s(h_s), \qquad s=t,\ldots,T-1.$$

Define the extended exogenous sequences $\boldsymbol\omega=(\boldsymbol\xi,\boldsymbol\eta)$ and $\widehat{\boldsymbol\omega}=(\widehat{\boldsymbol\xi},\boldsymbol\nu)$. During execution the policy acts on $h_s$; in a model rollout it acts on $\widehat h_s$. With the actual execution map and joint dynamics, $\gamma(\pi,\boldsymbol\omega)$ denotes the executed trajectory. It generally cannot be known prospectively because the future exogenous sequence is not yet available. The internal model instead generates $\widehat\gamma_{M_t}(\pi,\widehat{\boldsymbol\omega})$ using $\widehat E_t$ and the estimated dynamics in $M_t$. Predicted and executed trajectories need not coincide.

The more general policy formulation will be used below; deterministic path selection is a special case (Kaelbling et al., 1998; Puterman, 1994).

Let $\mathbb P_t$ be the proposal-policy space on which the execution map is defined. Within it, define the model-admissible and objectively implementable policy sets by

$$\widehat\Pi_t = \operatorname{Adm}_{M_t} \bigl( \widehat{\mathcal K}_t, \widehat R_t, \widehat P_t \bigr) \subseteq\mathbb P_t, \qquad \Pi_t = \operatorname{Adm} \bigl( \mathcal K, R_t, P_t \bigr) \subseteq\mathbb P_t.$$

These are set-generating relations, not claims that the admissibility maps are unique. Their dependence on $P_t$ and $\widehat P_t$ includes the capacity projections $C_t$ and $\widehat C_t$ while retaining any other internal state relevant to execution. The model-implied, actually executed, and objectively implementable trajectory sets are, respectively,

$$\widehat\Gamma_t := \left\{ \widehat\gamma_{M_t}(\pi,\widehat{\boldsymbol\omega}) \;\middle|\; \pi\in\widehat\Pi_t, \widehat{\boldsymbol\omega}\in\widehat{\mathcal W}_t \right\}.$$

$$\Gamma_t^{\mathrm{exec}} := \left\{ \gamma(\pi,\boldsymbol\omega) \;\middle|\; \pi\in\mathbb P_t, \boldsymbol\omega\in\mathcal W_t \right\},$$

$$\Gamma_t := \left\{ \gamma(\pi,\boldsymbol\omega) \;\middle|\; \pi\in\Pi_t, \boldsymbol\omega\in\mathcal W_t \right\}.$$

The horizon $T-t$ is implicit. Here, $\widehat{\mathcal W}_t$ is the exogenous uncertainty class represented in the internal model, and $\mathcal W_t$ is the actual admissible exogenous-sequence set relative to the selected boundary and granularity. Because $\widehat\Pi_t\subseteq\mathbb P_t$, every selected proposal policy has an executed trajectory, even when it lies outside $\Pi_t$ and produces failed or distorted actions. Equality between modeled and actual policy or trajectory sets cannot generally be assumed.

Definition (goal-relative trajectory evaluation). Given a declared evaluation structure associated with $G_t$, define the goal-relative trajectory-evaluation functional, also called the practical action functional, by:

$$S_{G_t}[\gamma] = \Phi_{G_t}(R_T,P_T) + \sum_{s=t}^{T-1} L_{G_t}(R_s,P_s,a_s,s)$$

where:

• $\Phi_{G_t}(R_T,P_T)$ measures the deviation of the terminal state from the goal;
• $L_{G_t}$ measures time, resources, risk, expenditure, and other goal-relevant costs along the path.

This temporarily assumes that the goal structure is relatively stable over the current planning horizon. If goals change through practice, write $G_s=\Pi_G(P_s)$ and reevaluate and replan after feedback.

Using a scalar functional requires either a declared scalarization or a numerical representation of the relevant preference ordering. When values remain vector-valued, lexicographic, or partially ordered, policy comparison must use the corresponding comparison rule. Hard constraints represent noncompensable limits; they do not by themselves represent every form of value incomparability.

Operational criterion (model-internal robust feasibility). Represent a limit that cannot be offset by ordinary benefits as a hard constraint on every trajectory induced within the modeled exogenous-input class:

$$H_{G_t,j}\bigl(\widehat\gamma_{M_t}(\pi,\widehat{\boldsymbol\omega})\bigr)\leq 0, \qquad \forall \widehat{\boldsymbol\omega}\in\widehat{\mathcal W}_t, \ \forall j.$$

As a model-internal ideal benchmark, policy selection under uncertainty is represented by:

$$\pi_{t:T-1}^\star \in \operatorname*{arg\,min}_{\substack{ \pi\in\widehat\Pi_t,\ \sup_{\widehat{\boldsymbol\omega}\in\widehat{\mathcal W}_t} H_{G_t,j}\bigl(\widehat\gamma_{M_t}(\pi,\widehat{\boldsymbol\omega})\bigr)\leq 0, \ \forall j }} \mathbb E_{M_t} \left[ S_{G_t}\!\left[\widehat\gamma_{M_t}(\pi,\widehat{\boldsymbol\omega})\right] \right]$$

Here, $\mathbb E_{M_t}$ is taken with respect to the probability model over exogenous sequences and any stochastic transitions or outcomes represented in $M_t$ (Bertsekas & Shreve, 1978). The first component of the selected horizon policy produces the present proposal, $u_t=\pi_t^\star(h_t)$. Defensible numerical probabilities may be unavailable; under ambiguity, the expectation may be replaced by a robust or minimax criterion, or by an interval-valued criterion equipped with an explicit ordering rule.

These are hard constraints relative to $M_t$ and $\widehat{\mathcal W}_t$, not guarantees about executed trajectories. Realized compliance depends on model adequacy, coverage of relevant exogenous inputs, and appropriate safety margins.

The benchmark does not imply computation of an exact global optimum. If the feasible set is nonempty but the minimum is not attained, the selection rule may return a feasible $\delta$-optimal or satisficing policy according to an explicitly stated tolerance. If the modeled feasible set is empty, the procedure must instead report infeasibility, invoke a prespecified safe fallback, or explicitly relax only constraints that have been designated as soft; no feasible approximate optimum then exists.

A constraint that permits violation with a specified probability is a chance or risk constraint rather than a robust hard limit (Ben-Tal et al., 2009; Charnes & Cooper, 1959). In a deterministic and fully observable situation, a policy reduces to path selection, and the expression reduces accordingly to a direct comparison over $\widehat\gamma\in\widehat\Gamma_t$.

11. Receding-Horizon Practice

In the partially observed and evolving settings targeted here, future trajectories generally cannot be predicted exactly. Estimates of laws may be incomplete, the external state changes, other goal-directed systems respond, and internal capacities, models, and goals may change. Policy selection is therefore implemented as a repeatedly updated cycle:

$$\text{observation} \rightarrow \text{modeling} \rightarrow \text{policy search} \rightarrow \text{action} \rightarrow \text{feedback} \rightarrow \text{recalculation}$$

To make the temporal order explicit, decompose the post-action transition and observation-mediated update as

$$\begin{aligned} X_{t+1}^{-} &= T^X_{\mathcal K}(X_t,a_t,\xi_t),\ R_{t+1} &= \operatorname{proj}_{R}X_{t+1}^{-},\ P_{t+1}^{-} &= \operatorname{proj}_{P}X_{t+1}^{-},\ o_{t+1} &= O(R_{t+1},P_{t+1}^{-},\eta_{t+1}),\ P_{t+1} &= U_P(P_{t+1}^{-},o_{t+1}),\ M_{t+1} &= \Pi_M(P_{t+1}). \end{aligned}$$

Here, the superscript $-$ denotes the state after action and background dynamics but before the current observation is incorporated into the internal model. $U_P$ represents the internal update induced by observation; it may be the identity when observation produces no additional internal change. Learning, resource expenditure, and other internal changes may occur in either the joint transition or the observation-mediated update, but they must not be counted twice.

The schematic cycle can be written as:

$$M_t = \bigl( \widehat{\mathcal K}_t, \widehat R_t, \widehat P_t \bigr) \rightarrow \pi_{t:T-1}^\star \rightarrow u_t \rightarrow a_t \rightarrow (R_{t+1},P_{t+1}^{-}) \rightarrow o_{t+1} \rightarrow (P_{t+1},M_{t+1})$$

The internal model has no direct and complete access to the actual post-action state; it is updated through $o_{t+1}$. A finite-horizon problem is solved from current information, only the first action or a short initial segment is executed, and the problem is recalculated after observation. The general formulation may produce a feedback policy; classical model-predictive control commonly produces an open-loop sequence whose first control is implemented before replanning (Mayne et al., 2000). This yields a receding-horizon procedure in which planning sets direction and feedback supports correction.

12. The Scope and Limits of the Framework

Field Structuralism is presented as an ontological and practical framework, not as a completed empirical theory.

A generalized structural field is not identical to a physical field; the quantum-field example motivates a direction of explanation but does not establish a shared physical dynamics across domains.

Not every change forms a node, not every correlation forms an edge, and not every network warrants representation as a new field. Stable patterns, persistent effective relations, organizational integration, approximate dynamical closure, and constraint relevance determine whether an organization warrants treatment as an effective higher-scale field within a declared regime.

Although the law field, state field, and conative field share a common formal framework, they do not distribute the same kind of content. The law field distributes transformation conditions, the state field distributes external states, and the conative field distributes the internal states and couplings relevant to goal formation, evaluation, and action.

Policy selection by a goal-relative trajectory-evaluation functional is not an unconditional natural law of human behavior. It cannot generate goals from the formalism alone or guarantee optimality under limited information. It provides a disciplined modeling structure for distinguishing goals, internal capacities, context-relative implementability, states, and laws; comparing policies and predicted trajectories; and revising choices after feedback.

Applying the framework to a concrete domain requires explicit definitions of the variables in each field, criteria for nodes and edges, coarse-graining maps and error tolerances, law-governed operators, observation and probability models, a declared trajectory-evaluation rule, and empirical tests capable of disconfirming the proposed representation.

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Abstract

Conatism asks not what, specifically, a subject pursues, but why anything can become an end for a subject at all. It is developed here as a theory of self-preservation.

In this paper, self-persistence denotes the continuing unity of organized continuity and actualization: the exercise and development of constitutive capacities, the pursuit of ends, and the realization of possibilities. Self-preservation names the immanent striving through which a subject sustains that unity. Conatism's central thesis is that every particular motive is a context-specific determination of this striving, rather than an independent starting point outside it.

A subject can genuinely pursue another subject, knowledge, a work, or a shared undertaking. Conatism holds that every difference in value capable of stably motivating a subject’s action is ultimately grounded in how a state bears, or is taken to bear, on the subject’s continuity or actualization. This bearing may be actual, anticipated, learned, relationally constituted, or historically mediated; it does not imply that every motive consciously aims at, actually advances, or remains functionally subordinate to self-preservation.

Keywords: conatism; conatus; self-persistence; self-preservation; subjecthood; purposive action; motivation; diachronic continuity

Status and Method

This paper offers a constructive, conceptual reconstruction of Spinoza’s conatus, not a historical exegesis, a freestanding empirical law, or a complete ethics. Its distinctive claim is that self-preservative organization makes subject-relative stakes possible while bodily, psychological, relational, historical, and institutional processes give particular motives their content and stable force.

Autopoietic and enactive accounts explain how self-maintaining organization can generate endogenous norms (Barandiaran et al., 2009; Di Paolo, 2005; Maturana & Varela, 1980). Planning theory explains diachronic coordination (Bratman, 1987), while self-constitution explains how agency and identity are organized through action (Korsgaard, 2009). Accounts of group agency supply stronger criteria for treating organizations as agents (List & Pettit, 2011). Conatism draws on but does not replace these domain-specific theories: it asks how possibilities become non-neutral for a subject and how motives formed from that practical field can acquire relatively autonomous objects and functions. The cited accounts locate the proposal; they do not by themselves verify it.

The account is defeasible. A Conatist explanation must identify the subject and its continuity and actualization independently of the motive being explained, then specify an intelligible path showing why the relevant state bears, or was taken to bear, on those conditions. Mere post hoc redescription does not count. Stable counterexamples for which no such path can be established, or which are better explained without it, would require revision. The notation used below is schematic and clarificatory rather than a quantitative model.

Introduction: Where Do Ends Come From?

Every subject, insofar as it acts purposively, tends toward something in one way or another.

A subject may pursue survival, knowledge, another subject, creative activity, or a shared undertaking. These ends differ from one another, but the more fundamental question is not what a subject pursues. It is: why can anything become an end for a subject?

Ends do not arise from nothing.

A state can acquire the power to motivate action only if it is not neutral for the subject. Integrity differs from injury, possibility from closure, continuation from termination. Because these differences concern the subject itself, the world ceases to be a mere collection of facts and begins to present stakes and directions.

The subject thereby approaches, avoids, chooses, persists, and changes.

Conatism offers a fundamental explanation:

Self-preservation is not one desire among many, nor is it the thought “I want to stay alive” constantly appearing in consciousness. The subject is not an already completed entity that subsequently decides to protect itself. Its identity as a subject is formed and sustained through the continuous organization, maintenance, and actualization of itself.

The subject is not already complete prior to its endeavor of self-preservation; it exists in its endeavor to continue becoming itself.

I. The Subject

A subject is a relatively unified whole with its own boundary, endogenous stakes, and temporal continuity: certain states constitute gains or losses for it, and on that basis it can form, revise, and organize directions of action.

This statement identifies the phenomenon to be explained; it does not infer subjecthood from the particular motive under examination. For a Conatist explanation, the subject’s boundary, temporal continuity, and capacities for registering differences, retaining their effects, and revising activity must be specified independently of that motive. These are necessary rather than sufficient conditions, and the account does not claim to settle every borderline case between minimal agency and simple control.

Having its own boundary means that the subject can distinguish what belongs to itself from what comes from the environment. This boundary need not be a fixed physical shell; it may also be constituted by a body, memory, identity, relationships, or institutions.

Endogenous stakes mean that a state counts as beneficial or harmful not merely because an external observer judges it so, but because it enters into the subject’s own continuity and structure of action.

Temporal continuity means that the subject can preserve a certain identity through change. A subject may change, yet it remains the bearer of that change: the past enters the present, and the present opens onto its own future.

Animals, persons, and organizations are forms that subjects can take across different substrates and structures. In the organizational case, the claim presupposes integrated procedures for forming and revising goals rather than goals merely assigned by an observer (List & Pettit, 2011).

The following action sequences are idealized patterns rather than exhaustive laws. Sentient subjects organize action primarily through feeling, desire, and intention:

Feeling → Desire → Intention → Action

Feeling presents differences within a situation; desire points toward a positively valued possibility; intention organizes a path of action for realizing that possibility; action brings intention into reality.

Organizational subjects organize action through information, goals, and decisions:

Information → Goal → Decision → Action

Their mechanisms of actualization differ, yet they share the basic form of subjecthood: both can transform differences concerning themselves into directions of action and maintain relative unity over time.

II. Self-Preservation and Conatus

The philosophical concept carried forward by “self-preservation” is Spinoza’s conatus.

Spinoza argues that each thing strives, as far as it can by its own power, to persevere in its being, and that this striving is the thing’s actual essence (Spinoza, 1677/1985, Ethics IIIp6-p7). In human beings, considered in relation to mind and body, this striving is appetite; when appetite is conscious, it is desire (IIIp9 schol.).

Conatism inherits this central judgment and reconstructs it as a theory of the subject. This is a constructive use of conatus, not a claim that the present account reproduces Spinoza’s argument without revision (Garrett, 2002):

“Actual powers” here means the subject’s effective capacity to maintain its continuity, exercise its capabilities, form goals, act, and respond to change.

Self-preservation is neither an external end that commands the subject from the future nor a not-yet-realized result that pulls it from ahead. It is the present existence of the subject itself insofar as that existence is directed toward its own self-persistence.

The core claim of Conatism is therefore not:

The subject already exists as a completed entity and later develops a desire to survive.

It is instead:

The subject's existence as a subject is constituted by its striving to sustain organized continuity and actualize its capacities, ends, and possibilities.

It is within self-preservation that the subject maintains its identity, forms ends, and enters into action.

III. The Principle of Self-Preservation

Every motive presupposes a non-equivalence among states.

If all states were entirely equivalent for the subject, it would have no reason to approach anything or avoid anything. The formation of a motive requires that some states carry positive value while others carry negative value.

Conatism explains this non-equivalence as follows:

On this basis, the theory proposes its fundamental principle:

This is not a logical necessity automatically deduced from the mere existence of differences among states. It is the foundational explanation proposed by Conatism. Here, “grounded” means that the subject’s self-preservative organization makes motivational force possible and that an intelligible path of formation explains why a state acquired significance in relation to continuity or actualization. The bearing may be actual, anticipated, learned, relationally constituted, or historically mediated; a historical connection counts only when it helps explain this differential significance. Grounding does not mean that self-preservation is the conscious object of the motive, that the action actually benefits the subject, or that the motive remains functionally subordinate to self-preservation after it has formed.

The argument is constitutive rather than deductive. First, a motive requires that possible states be non-neutral for a subject. Second, such non-neutrality requires an independently identifiable subject whose continuity or actualization - its capacities, ends, and possibilities - can be promoted, impeded, or understood as being at stake. Third, perception, learning, relationship, history, and reflection transform these differences into determinate motives. Self-preservation therefore grounds the possibility of motivational force without dictating the object, outcome, or present function of every motive.

Here, “motive” is understood broadly as an internal structure that moves the subject to form a direction of action. In sentient subjects it appears as desire and intention; in organizational subjects it appears as goals and decisions.

A motive is “stable” when it persists or recurs across time or situations sufficiently to organize action, rather than appearing only as a momentary reflex or accidental impulse.

Therefore:

Let the self-preservative endeavor of subject $s$ be $K_s$, its particular situation be $\sigma$, and its particular motive be $m$. Then:

Here, $\mathrm{𝒟}(K_s,\sigma )$ denotes the possible determinations that the endeavor of self-preservation may assume in that situation.

The notation is schematic. It expresses a dependence of possible motives on the subject’s self-preservative organization and situation; it does not define a quantitative function, a prediction rule, or a complete causal model.

The formula states that a particular motive does not arise from nothing. As a determination of self-preservative striving, it is formed through the subject's self-preservative organization within a particular body, set of relationships, history, and environment.

Through different situations, that striving may assume the form of avoidance, attachment, exploration, creation, persistence, or relinquishment.

Roots, Objects, and Outcomes

To understand Conatism accurately, three concepts must be distinguished:

Root of Motive ≠ Object of Motive ≠ Outcome of Action

The root of a motive answers why a motive can form and acquire motivating force.

The object of a motive, that is, its particular end, answers what the subject genuinely seeks to realize here and now.

The outcome of an action answers what change the action ultimately produces.

A motive may be rooted in the subject’s self-preservation while genuinely directed beyond the subject. A subject can care directly about another person, knowledge, a work, or a community without treating them merely as instruments of personal interest.

When another person enters the subject’s identity, decisions, and future through a stable and non-instrumental relationship, that person’s existence becomes a genuine stake within the subject’s structure of self-preservation. Yet this relational inclusion need not turn two subjects into one, nor make the other person the property of the self.

Conatism does not claim that a subject can ultimately pursue only itself. It claims that a subject can genuinely move toward others precisely because self-preservation is not closed self-protection; through relationships, understanding, and creation, it can open outward into the world.

The root may be one; the ends may be many.

IV. The Structure of Self-Preservation

For a subject to sustain its self-persistence involves two inseparable aspects:

Here, $C_s$ denotes the subject’s continuity, $A_s$ its actualization, and ${\Pi }_s$ its overall state of self-persistence.

The notation is schematic rather than metric: it names two inseparable dimensions without presupposing a particular measure, rule of commensuration, or aggregate score. It does not rule out later domain-specific operationalization.

Continuity

Continuity is the subject’s maintenance of its organized identity over time.

This identity does not require the subject to remain unchanged. On the contrary, a subject often has to learn, repair itself, and change in order to continue being itself.

Genuine continuity does not freeze a particular state; it allows change to remain borne by the same subject. The past enters the present, the present opens onto the future, and the consequences of action still belong to this subject.

Continuity answers the question:

Does this subject still exist?

Actualization

Actualization is the degree to which a subject exercises and develops its capacities, advances its ends, and brings its possibilities into reality. The capacities, ends, and possibilities relevant to an explanation must be specified independently of the particular motive under examination. An end may be newly formed and still belong to actualization, but it cannot be included merely by redescribing the focal motive as already belonging to the subject's actualization.

A subject needs not only to continue existing but also to be able to exercise the capacities that constitute it. If a subject has not yet ceased to exist, yet its capacities, ends, and possibilities are continually closed off, its self-persistence is correspondingly diminished.

Actualization answers the question:

To what extent can this subject exercise its capacities, advance its ends, and unfold its possibilities?

Continuity enables the subject to persist; actualization enables it to unfold. Together they constitute self-persistence.

Three Typical Phenomena of Personal Self-Preservation

Survival, pleasure, and meaning are three typical phenomena of self-preservation in personal life. They are neither an exhaustive classification nor stages in a hierarchy of subjecthood.

Survival is the basic preservation of the subject’s continuity. It prevents the subject from being interrupted and ensures that long-term ends still have a bearer.

Pleasure is the positive experience that arises when a desire is satisfied, a tension is released, or the subject’s activity proceeds smoothly. It may accompany the exercise of the subject’s capacities, but it need not mean that those capacities have achieved lasting growth. Pleasure is therefore a possible signal that self-preservation is proceeding well, not sufficient proof of its success.

Meaning is the reflective subject’s organization of its long-term direction of actualization. It integrates desires, relationships, actions, and the future into a whole that can be understood, chosen, and assumed as one’s responsibility.

Thus:

The basic structure of self-persistence remains continuity and actualization. Survival, pleasure, and meaning are different manifestations of self-preservative striving in personal life.

Other kinds of subjects also possess continuity and actualization, though they manifest and organize self-preservation in different ways.

V. Self-Preservation Among Multiple Subjects

Subjects do not exist in isolation.

The continuity and actualization of one subject often depend on other subjects, its environment, and larger structures. Self-preservation does not mean self-sufficiency. It means that what is maintained and actualized is this subject itself, even though the conditions of that process may be distributed beyond it.

Different subjects may support one another or come into conflict.

One subject’s continuity may become a condition of another subject’s actualization; one subject’s development may also constrict another’s capacities and future.

Self-preservation is therefore not a single harmonious will in the world, but the direction in which each of many subjects continuously actualizes itself.

The coexistence of multiple subjects consequently creates problems of coordination: whether their directions of self-preservation are compatible, and how conflicts among them should be limited.

Judgments on these questions belong to ethics, not to Conatism itself. The theory explains how conflicts can arise by identifying their structural conditions, but the fact of self-preservation alone does not determine whose claims should take priority.