One Game of Oughts

Persistence, coupling, and the structure of biological normativity

Theoretical and formal paper · biological normativity, viability, maintenance, and coupled systems

Andraž Đurič

Version 1 · 22 September 2026

Abstract

A living system's conditions of continuation need not be represented by that system to constrain its possible futures. This paper develops that distinction in a shared-world setting. It separates the bearer of a persistence-relative requirement from the systems supplying its enabling conditions, the controller capable of changing those conditions, and the observer evaluating their significance. Using a finite-horizon stochastic model, it defines indexed continuation events, distinguishes actual performance from available viability, and establishes a dependency-transfer bound: when continuation without an enabling event has probability at most ε throughout a specified policy class, achieving continuation probability α requires that enabling event with probability at least α − ε. Such requirements compose along genuine dependency chains, but generic beneficial influence does not. Constructed examples show how maintaining another system can sustain one's own continuation, why substitute providers make contribution nonadditive, and why individually achievable continuation requirements can be jointly infeasible. A further distinction separates maintenance expenditure from adverse persistence impact. The biological interpretation inherits Epistemic Forge's persistence-indexed account of functional oughts; it is not proved by the probability calculus. The proposal is a formal synthesis concerning interacting, locally indexed requirements—not a derivation of a universal moral scalar, a claim that organisms maximize one metric, or the discovery that biological normativity precedes reflective thought.

Keywords: biological normativity; persistence; viability; organizational autonomy; ecological dependence; maintenance; semantic information; coupled systems.

In plain language

A plant does not need to think about being damaged for damage to threaten its continued existence. Nor do I have to notice my dependence on another system for that dependence to obtain.

But these are not isolated facts about isolated things. What one living system does can help maintain—or destroy—the conditions under which another continues. An organism's physical boundary is not the boundary of its persistence conditions.

The resulting structure is neither a universe with one objective nor a collection of unrelated private problems. It is a shared causal world containing different bearers, different continuation requirements, and interactions that connect their consequences. Supporting another system can sometimes be part of sustaining oneself. In other cases, continuation interests conflict. The mathematics must preserve both possibilities.

That is the defensible starting meaning of one game of oughts: one interacting world of locally indexed continuation requirements. Whether that structure supports a stronger unification is a question to investigate, not a result to insert into the title.

1. The plant and the change in the map

I was standing beside a pavement, trying to kick away a plant growing from the curb. I thought it was dry and dead. After several attempts, its bending made me reconsider. It might still be alive.

Then a thought appeared without a deliberate reconstruction of the argument: I was probably harming its persistence. More exactly, I was presently one of the conditions acting against its continuation.

The plant's living status was not independently established. The episode therefore does not demonstrate that I injured a living organism. What it makes visible is a distinction in the structure of the assessment. My estimate changed; the relation I was estimating did not wait for my estimate to exist.

If the plant was alive, damage could have affected its continuation before either of us represented that consequence. Its capacity to articulate an ought was not the relevant variable. My recognition was a possible addition to the causal situation, not the original source of the plant's requirements.

The same separation appears when looking in the other direction. Some of the systems on which I depend might be sustaining me without my awareness. My model can omit them; my functioning cannot thereby dispense with them.

The question is not merely whether living things have requirements. It is how those requirements relate when the activities of one system enter the continuation conditions of another.

2. What is inherited, and what is being added

This paper does not introduce nonreflective ought-bearers into Epistemic Forge for the first time. Value as Persistence already permits minimal regulatory models without conscious or propositional representation. The Natural History of Fidelity discusses a bacterium's functional ought without assigning it reflective moral reasoning. [F1–F2]

Two further commitments are inherited. First, an ought in the relevant sense remains indexed to a bearer and its continuation conditions; universal scope does not remove that index. Second, persistence enabling continued valuation is not, by itself, a proof that every value reduces in content to persistence. Relata-Indexed Objectivity and Universal Is Not Categorical keep the normative interpretation and the stronger reduction claim distinguishable. [F3–F4]

The work attempted here is more specific. It connects bearer-relative continuation requirements through explicit dependencies, identifies when that connection licenses a further requirement, and identifies several tempting inferences that it does not license. A common framework should explain both external maintenance and conflict without silently changing the beneficiary of the analysis.

Three levels of claim will remain separate. The stochastic model describes possible continuation under specified conditions. Elementary results establish consequences inside that model. The interpretation of some of those relations as functional oughts is a philosophical commitment, defended below and inherited from the corpus. None acquires the standing of the other merely by appearing beside it.

3. Position in the literature

There is substantial prior work on precisely the terrain into which this argument enters.

Di Paolo distinguishes autopoietic self-production from the additional adaptive capacities needed for richer accounts of agency and value. His account matters here because maintaining organization, regulating threats to it, and exhibiting richer agency should not be compressed into one capacity. [1]

Mossio, Saborido, and Moreno develop an organizational account of biological functions through contributions to differentiated self-maintaining organization. This supplies a serious predecessor for grounding functional assessment in the organization of the system rather than in an observer's arbitrary preference. [2]

The closest formal predecessor is Barandiaran and Egbert. They distinguish norm-establishing dynamics from norm-following behavior, model metabolic viability and precariousness, and construct a normative field specifying environmental changes relevant to continued existence. They also discuss nested processes and possible higher-dimensional formulations. Neither normativity before reflective thought nor a mathematically represented normative landscape is new here. [3]

The mathematical foundation comes from viability theory. Aubin, Bayen, and Saint-Pierre develop constraint-based continuation; Doyen and De Lara formulate stochastic viability and viable controls through probability constraints and dynamic programming. The present use of finite-horizon continuation probabilities belongs to that established apparatus. [4–5]

Béné and Doyen explicitly examine biodiversity contributions relative to ecological and economic viability in numerical models. Their work is an important precedent for context-dependent contribution rather than a fixed, context-free value assigned to each provider. Holling's cross-scale framework provides a further background for nested, changing dependencies, without establishing that every connected collection is itself an organism. [6–7]

Kolchinsky and Wolpert investigate information whose system–environment correlations causally contribute to a selected viability measure, using interventions on those correlations. Sowinski and colleagues instantiate this approach in resource-gathering agents, relating sensor degradation to modeled lifetime. These connect informational fidelity to continuation without making explicit deliberation necessary. [8–9]

The normative interpretation remains contested. Corti argues that counterfactual dependence and organizational closure do not, on their own, establish the normative force sometimes claimed for them. Li's later relational account instead emphasizes a system-relative standard and fragile self-maintenance. These are competing philosophical treatments, not two empirical measurements whose disagreement can be removed by averaging. [10–11]

The intended contribution is therefore an explicit synthesis and development: separate indices, connect their requirements through conditional dependency results, account for costs and substitution, and preserve the difference between individual and joint viability. No priority claim is made for the component concepts or the elementary mathematics.

4. Bearers, conditions, providers, and controllers

Four roles need to be distinguished before writing an equation.

A bearer is the system whose continuation is being assessed. A condition is something necessary or contributory to that continuation. A provider helps realize that condition. A controller can alter part of the relevant dynamics. An observer can describe all four roles without occupying any of them.

The roles can overlap. A system can regulate itself and supply something another system requires. They need not overlap. Water can be an enabling condition without being a living ought-bearer. A nonliving device can regulate a condition without acquiring every property of the organism it supports.

For the biological application, a working bearer is an individuated living organization whose activities and retained capacities participate in sustaining its continuity. This characterization permits dependence: requiring outside resources or support does not make the bearer unreal. It also permits inactivity during part of a lifecycle. It does not settle every boundary case by definition.

A bare boundary is insufficient. We need an account of what continues through changes in material composition and state. Here the target is the continuity of a specified organizational process, not preservation of every molecule or an exact configuration. The corpus's distinction between a continuing process-token and a merely similar replacement remains relevant. [F5]

Nested systems require more than drawing boxes. A component and a larger system may both be legitimate objects of functional assessment, but they have different continuity criteria. The larger system's persistence must not be silently substituted for that of a component. Nor does recording both as bearers automatically justify counting them twice in an aggregate moral total.

The extension to all life is a substantive scope hypothesis: wherever a living individual can be identified, its organization supplies nonindifferent continuation conditions even without propositional representation. Cells, dormant stages, colonies, symbiotic systems, and dependent biological entities test the individuation criterion. A disputed case is a reason to specify the bearer more carefully, not to award every physically bounded object an independent moral status.

The formalism below is deliberately broader than this biological interpretation. It can assess a chosen physical system whether or not that system qualifies as a living bearer. Mathematical applicability alone therefore cannot decide the scope of biological normativity.

5. The normative commitment

The proposed interpretation can be stated directly:

Persistence-indexed functional normativity: relative to an identified living organization, conditions and activities can count as sustaining or defeating its continuation independently of whether the organization, a controller, or an observer represents or endorses that relation.

Calling the sustaining requirements oughts for that bearer is the normative commitment inherited here. It is not the claim that the organism ought to persist only because it happens to desire persistence. The index concerns the organization whose continuation is at issue, not an optional preference report.

There are reasons to use the functional vocabulary. The target is not chosen as freely as an arbitrary score in a game. It is constrained by what makes this system the continuing organization under examination. A regulatory process can fail relative to that organization even while obeying physics perfectly. Actual behavior, felt preference, and successful continuation need not coincide.

An observer can be wrong about the requirements. A bearer can fail to detect them. A controller can detect them but fail to act accordingly. These possibilities help distinguish a standard of functional success from a description of whatever happens.

Nevertheless, identifying those asymmetries is not a deductive proof that every ordinary or moral use of “ought” reduces to them. Corti's objection is relevant exactly at that step: a causal dependence does not automatically supply the full normative significance one might attach to it. [10] This paper keeps the interpretive premise visible rather than hiding it in a definition of a probability.

The proposal is neither contentless stipulation nor a completed reduction. It is a reconstruction whose value depends on whether the chosen reference can be identified nonarbitrarily, whether it supports accurate functional distinctions, and whether further normative claims can be derived without changing the index. A reader can reject this reconstruction while accepting the mathematical results. Conversely, accepting it does not exempt the causal model from testing.

It is also necessary to distinguish three claims: something is required for the plant's continuation; the plant can regulate in relation to it; I am obligated to protect it. The first need not await the second. The third requires an account of my relation to the plant and of the relevant normative standard. Coupling can establish part of that relation, but not by making the indices disappear.

6. A model of indexed continuation

Consider a finite sequence of times $t=0,\dots ,H$. For the formal results, use finite state and action spaces. This avoids unnecessary measure-theoretic assumptions; it is not a claim that biological reality is literally a finite-state machine.

Let $z_t$ encode the relevant joint state: the bearer, other modeled systems, resource stocks, and environmental variables. Its dynamics are

$$z_{t+1}\sim T_t(\cdot \mid z_t,u_t).$$

(1)

A joint policy $\pi$ determines actions from the information available to the modeled controllers. The nonempty admissible class $\mathrm{\Pi }$ includes constraints on observation, action, resources, and coordination. Describing a joint policy does not imply that any single real agent can choose everyone else's behavior.

Overlapping and nested bearers can be represented by different observables of $z_t$. There is no assumption that each bearer occupies a statistically or causally independent factor of the state space.

For bearer $i$, let $K_i(t)$ specify states compatible with its constitutive continuity. Define the continuation event

$${\mathrm{\Phi }}_i^H=\{z_t\in K_i(t)\text{ for every }t=0,\dots ,H\}.$$

(2)

Where continuity depends on history, augment the state with the necessary history or use a trajectory predicate directly. A stage transition may be included without counting it as death. An actual termination of the chosen process-token cannot be erased by later producing a similar token.

The sets $K_i$ are not viability kernels. They specify what counts as continuing at each time; viability additionally depends on whether available policies can keep the trajectory there. A system can still be alive while no available response prevents its later termination.

Under model $M$, initial state $z_0$, and policy $\pi$, define

$$v_i^{\pi }(M,z_0,H)=\underset{M}{\overset{\pi }{Pr}}({\mathrm{\Phi }}_i^H\mid z_0).$$

(3)

This is one operational persistence measure, not a universal measure of value. It distinguishes continuation probabilities, but can leave differences in reserves, damage, welfare, and recovery capacity unresolved when they do not change the selected event or horizon.

Actual-policy performance must also be separated from available performance:

$$V_i(M,z_0,H;\mathrm{\Pi })=\underset{\pi \in \mathrm{\Pi }}{sup}{v}_i^{\pi }.$$

(4)

A low actual value and a low attainable value are different diagnoses. The first may permit correction. The second may reflect constraints no available policy can overcome.

For a stated reliability target ${\alpha }_i\in [0,1]$, define

$${\mathrm{\Pi }}_i({\alpha }_i)=\{\pi \in \mathrm{\Pi }:v_i^{\pi }\ge {\alpha }_i\}.$$

(5)

The target is an explicit modeling or practical parameter. Physics has not, through this definition, prescribed a uniquely correct risk tolerance. If this set is empty, a continuation requirement can remain unsatisfied as a structural fact; emptiness does not entail that every action becomes obligatory or that an impossible action becomes available.

Equations (1)–(5) instantiate the distinction between constraints, policies, and probabilistic viability developed in the control literature. [4–5] The interpretive work lies in identifying a real bearer and its constitutive conditions, not in renaming every chosen constraint a biological ought.

7. Dependency transfer

The central result concerns a necessary enabling condition, allowing a bounded exception. Hold the model, initial state, and horizon fixed; their arguments are suppressed below. Exception bounds are nonnegative.

Let $Q$ be an event: for example, some enabling function is adequately supplied during the interval in which it is needed. It need not be the survival of a particular provider throughout the whole horizon.

Proposition 1. Approximate dependency transfer

Suppose that, for every policy $\pi$ in a specified admissible class,

$$\stackrel{\pi }{Pr}({\mathrm{\Phi }}_i^H\cap Q^c)\le \epsilon .$$

(6)

Then every such policy satisfies

$$v_i^{\pi }\le \stackrel{\pi }{Pr}(Q)+\epsilon .$$

(7)

Consequently, a policy achieving $v_i^{\pi }\ge {\alpha }_i$ must satisfy

$$\stackrel{\pi }{Pr}(Q)\ge max\{0,{\alpha }_i-\epsilon \}.$$

(8)

Proof. Split the continuation event into the disjoint events ${\mathrm{\Phi }}_i^H\cap Q$ and ${\mathrm{\Phi }}_i^H\cap Q^c$. The first has probability at most $\stackrel{\pi }{Pr}(Q)$; the second is bounded by (6). Adding gives (7), and rearranging gives (8). $◻$

When $\epsilon =0$, $Q$ is necessary for the selected continuation event within the modeled policy class. When , continuation without it has a bounded probability. A policy making $Q$ impossible yields $v_i^{\pi }\le \epsilon$, provided the dependency bound remains valid for that policy.

The qualification matters. An intervention that adds a replacement mechanism can invalidate the original dependency premise. A theorem about one transition structure cannot be exported to a changed structure without checking its premises again.

This is elementary probability, not a new probability theorem. Its use is to make a cross-system inference exact. If $Q$ is supplied by another system, sufficiently reliable continuation of $i$ requires sufficiently reliable provision of $Q$. No equal weighting of organisms has been assumed. Nor has concern for the other system been introduced as an optional desire.

Under the persistence-indexed interpretation, $Q$ enters the requirements for $i$. Whether controller $c$ ought to take a particular action concerning $Q$ additionally depends on what $c$ can change and which alternative actions remain. A necessary condition of an outcome is not automatically an executable instruction.

Proposition 2. Composition of necessary dependencies

Suppose, throughout the same policy class,

$$\stackrel{\pi }{Pr}({\mathrm{\Phi }}_i^H\cap Q^c)\le \epsilon ,\stackrel{\pi }{Pr}(Q\cap R^c)\le \delta .$$

(9)

Then

$$\stackrel{\pi }{Pr}({\mathrm{\Phi }}_i^H\cap R^c)\le \epsilon +\delta ,$$

(10)

and achieving continuation probability ${\alpha }_i$ requires

$$\stackrel{\pi }{Pr}(R)\ge max\{0,{\alpha }_i-\epsilon -\delta \}.$$

(11)

Proof. The event ${\mathrm{\Phi }}_i^H\cap R^c$ is contained in the union of ${\mathrm{\Phi }}_i^H\cap Q^c$ and $Q\cap R^c$. Apply the union bound, then Proposition 1. $◻$

The result extends along a chain by summing the exception bounds, although a long chain can make the resulting bound uninformative. No independence assumption is needed.

This is not a rule that every favorable influence propagates favorably through every network. Generic increases in one system's persistence can have mixed or opposing effects elsewhere. What composes here is a stated necessary-event relation, not an unspecified positive association.

A special case illustrates the distinction. If ${\mathrm{\Phi }}_i^H$ entails ${\mathrm{\Phi }}_j^H$, then ${\mathrm{\Pi }}_i(\alpha )\subseteq {\mathrm{\Pi }}_j(\alpha )$. But the real necessary event may instead be a service from $j$ delivered before some earlier time. A stored resource can remain useful after its provider no longer exists. Keeping the event precise prevents instrumental dependence from becoming an indiscriminate command to preserve every provider forever.

8. Costs and external maintenance

A resource budget can be represented schematically as

$$r_{i,t+1}=r_{i,t}+I_i(z_t,u_t)-E_i(z_t,u_t),$$

(12)

where influx $I_i$ and expenditure $E_i$ use the same physical units. “Cost” can refer to expenditure, foregone alternatives, or a reduction in continuation prospects. These are related but nonidentical quantities.

In microbial modeling, maintenance includes nongrowth demands on energy or substrate. Wang and Post show that different maintenance formulations involve different assumptions and parameter interpretations; their coefficients should not be casually interchanged. [12] The relevant lesson is not that all expenditure is beneficial. It is that absence of immediate growth does not make expenditure irrelevant to continued functioning.

Repair may consume resources while improving continuation prospects. Refusing to repair can save resources while making future failure more likely. Thus minimizing expenditure and sustaining the system are different objectives.

The distinction also prevents double-counting. If a continuation probability already reflects the depletion caused by an action, subtracting that same depletion again as an additional persistence penalty counts one mechanism twice. A resource budget can remain a separate constraint, but it should not be silently duplicated inside the outcome measure.

An exact constructed example

Consider two systems with integer reserves $a_t$ and $b_t$, initially

$$(a_0,b_0)=(2,1).$$

Positive reserves are required for continuation; reaching zero is absorbing termination. While alive, system $A$ pays one unit per step for its own maintenance and may spend a further unit $u_t\in \{0,1\}$ supporting $B$. While $B$ is alive, it supplies a service worth two reserve units per step to $A$. System $B$ also spends one unit per step and receives $u_t$.

For live systems, the updates are

(13)

$$b_{t+1}=max\{0,b_t-1+u_t\}.$$

(14)

Dead systems remain at zero. Support is permitted only when both systems are alive and $A$ can fund it. The service depends on the provider's state at the beginning of the step. The two-unit return is an environmental inflow enabled by the provider, not resources created from nothing. These timing and supply assumptions are part of the model.

With no support, the four-step trajectory is

$$(2,1)\to (3,0)\to (2,0)\to (1,0)\to (0,0).$$

With support at every step, it is

$$(2,1)\to (2,1)\to (2,1)\to (2,1)\to (2,1).$$

Supporting the other system consumes resources but preserves the supporter across this horizon. The policy spending less terminates $A$ at the fourth step. External maintenance can therefore be part of self-maintenance without assigning the two systems equal moral weight.

This example establishes a possibility, not a biological estimate. Continuous support is not the only policy preserving $A$ through four steps. Stored reserves allow some histories in which $B$ terminates late while $A$ survives the selected horizon. The choice of horizon is doing real work.

Now add a substitute providing the same service independently of $B$. The instrumental requirement to support this particular $B$ disappears from $A$'s four-step continuation problem. $B$'s own termination remains terminal relative to $B$. A change in one beneficiary's dependence is not a change in the identity of the other beneficiary.

The general point is not “preserve every dependency.” It is “include the maintenance of external enabling conditions in the model of self-maintenance.”

9. Contribution is indexed, interventional, and often nonadditive

To assess the contribution of another system, specify a contrast. Let $I$ and $I_0$ be well-defined interventions or policy configurations. Define

$${\mathrm{\Delta }}_i(I,I_0\mid \mathrm{\Gamma })=\stackrel{I}{Pr}({\mathrm{\Phi }}_i^H)-\stackrel{I_0}{Pr}({\mathrm{\Phi }}_i^H),$$

(15)

where $\mathrm{\Gamma }$ records the bearer, continuity criterion, horizon, initial conditions, dynamics, response policies, and available substitutes.

The intervention must be specified causally. Removing a provider while allowing compensation is a different contrast from removing it while freezing every controller. Comparing one condition's optimal response to another condition's unrevised response is not a neutral test unless that asymmetry is itself the question.

The result is a contribution to this continuation measure, not a context-free moral weight. Observational association does not establish it: a third process might produce both the provider and the observed continuation.

Substitution makes a single global coupling coefficient especially hazardous. Suppose either of two providers, $B$ or $C$, suffices for an enabling service:

$$Q=B\vee C.$$

(16)

When both are available, removing one leaves the service intact. Removing both destroys it. The individual deletion effects can each be zero in the original context while the joint deletion is decisive.

If provider availability is independently distributed with probabilities $p_B$ and $p_C$, then

$$Pr(Q)=1-(1-p_B)(1-p_C).$$

(17)

The drop caused by deleting $B$ is $p_B(1-p_C)$. Its size depends on the remaining provider. Independence is an assumption of this illustration, not a universal property of biological suppliers.

This is why “one plant makes little difference to me” cannot establish “the systems supplying that function are dispensable to me.” It is also why not every individual loss should be redescribed as equally consequential to every bearer. Context-sensitive contribution preserves both conclusions. Viability-based biodiversity valuation already investigates such system- and constraint-relative contributions. [6]

Some dependencies are represented better by sets of jointly adequate providers or failure cut sets than by fixed pairwise links. A necessary event might be “at least one of these providers remains functional,” not the persistence of any specific member. The framework should preserve that structure rather than force all coupling into additive scores.

Under model uncertainty, even the sign of ${\mathrm{\Delta }}_i$ can be unresolved. A robust positive claim over a stated model class $\mathcal{M}$ requires

(18)

This supplies a demanding test, not a guarantee that the model class contains reality. Agreement among badly specified models does not validate their shared omissions.

10. Shared world, distinct feasibility problems

For a collection $G$ of bearers with specified targets, define the joint policy requirement

$${\mathrm{\Pi }}_G(\mathit{\alpha })=\bigcap _{i\in G}{\mathrm{\Pi }}_i({\alpha }_i).$$

(19)

Every individual set can be nonempty while their intersection is empty. Consider one indivisible resource and two systems, each requiring the entire unit to continue. Either can be sustained alone; both cannot be sustained under the stipulated constraints. Coupling has produced a coordination and allocation problem, not a proof of harmony.

Separate probability targets also differ from simultaneous success. A policy that allocates the unit randomly with equal probability gives each system continuation probability one half, while the probability that both continue is zero. For a finite group, the elementary union bound gives

$$\stackrel{\pi }{Pr}\left(\bigcap _{i\in G}{\mathrm{\Phi }}_i^H\right)\ge max\{0,1-\sum _{i\in G}(1-v_i^{\pi })\}.$$

(20)

When simultaneous continuation is the target, evaluate it directly or impose an adequate joint constraint. Do not assume that separate marginal assessments already answer that question.

Nor is a physically feasible joint policy necessarily available to any individual controller. The analysis must distinguish coordinated control, the policies actually implemented, and guarantees achievable when other systems respond differently. One shared state space is not one shared decision-maker.

These distinctions constrain the meaning of “one game.” The bearers participate in one interacting causal structure, but they need not share an objective. Where a policy improves all selected continuation measures, that is a form of Pareto improvement relative to those measures. It does not automatically improve every dimension of welfare or settle every obligation. Where effects conflict, an aggregation rule or an alternative conflict procedure requires additional justification.

For example, policies with continuation vectors $(1,0)$ and $(0,1)$ are not ranked by the vector alone. A weighted sum ranks them only after its weights are supplied. The formalism neither discovers those weights nor proves that no defensible scalar can exist. The corpus's stronger scalar hypothesis remains a separate research commitment. [F6]

Nested organization does not remove this issue. The continuation of a larger organization and that of its members can differ. A legitimate higher-level bearer needs its own constitutive account; it cannot be inferred simply from observing many interactions. Shared causation connects the consequences without making the bearers interchangeable.

11. Representation, noise, and the availability of correction

The model contains a continuation criterion before specifying how much of it a controller represents. Four situations are therefore distinguishable: a requirement obtains; regulation responds to something correlated with it; a system represents the relation; a reflective process examines and revises the policy through which that representation affects action.

They are not interchangeable achievements. Accurate stored information can fail to influence action. An automatic controller can respond adequately without explicit deliberation. A reflective process can be expensive or wrong.

An elementary information result states precisely one advantage of increased access.

Proposition 3. Costless informational refinement cannot reduce optimal performance

Suppose a refined observation arrangement permits every policy available under a coarser arrangement, with the same dynamics and resource costs. Thus ${\mathrm{\Pi }}_{\mathrm{coarse}}\subseteq {\mathrm{\Pi }}_{\mathrm{fine}}$. Then

$$\underset{\pi \in {\mathrm{\Pi }}_{\mathrm{fine}}}{sup}{v}_i^{\pi }\ge \underset{\pi \in {\mathrm{\Pi }}_{\mathrm{coarse}}}{sup}{v}_i^{\pi }.$$

(21)

Proof. The supremum over a set cannot be smaller than the supremum over its subset. $◻$

The result concerns attainable performance and permits the controller to ignore additional information. It does not say every implemented policy improves when given more input. Nor does it apply unchanged when sensing, processing, or acting consumes additional resources.

Kolchinsky and Wolpert explicitly evaluate information relative to viability and intervention choices; their framework also makes dependence on the selected viability measure visible. [8] Sowinski and colleagues' resource-gathering model illustrates why some sensor degradation can have little effect while crossing a threshold has a large effect. That is evidence from a specified model, not a universal noise threshold for life. [9]

The appropriate target is not maximal representation of everything. It is adequate access to persistence-relevant distinctions, coupled to useful regulation at a cost the system can sustain.

My plant episode is consistent with a previously developed concept influencing rapid recognition. It does not establish the cognitive mechanism that produced the thought. Its role here is narrower: awareness of a relation and the relation itself can come apart. Reflection may later alter which relations become salient without creating those relations from nothing.

12. What the common structure does—and does not—explain

The framework permits a conditional explanation of cross-system preservation. When another system supplies an irreplaceable enabling condition, sustaining that condition belongs to the first system's continuation requirements. This explains why concern beyond a body's boundary need not be foreign to self-maintenance.

It also permits indifference relative to a specific index. An intervention may make no difference to $i$'s selected continuation measure while terminating $j$. That is not a contradiction. The model contains two bearers. Treating the smaller external effect as proof that the terminated bearer's own loss was small would switch indices mid-argument.

The same structure permits conflict. One system's persistence can depend on activities incompatible with another's. Calling both living does not remove the incompatibility. The concept of a local functional ought is therefore not an automatic warrant for every action serving the bearer. An agent's functional interest and another agent's moral justification are not synonyms.

Biological ought-bearing also does not establish conscious suffering. A termination event identifies failure of the specified continuity condition; it does not measure experience. The paper neither assigns every organism equal moral weight nor concludes that beings without established conscious experience have no normative significance of any kind. Those claims require additional arguments.

Finally, the account does not say organisms always maximize $v_i$, or that evolution optimizes this exact individual-level quantity. A formal measure of continuation need not be the objective actually implemented by any organism. Reproduction, lineage continuation, component functioning, and individual survival require distinct indices. Switching from one to another when a counterexample appears would protect a slogan rather than test a theory.

13. Failure conditions and empirical use

The formal results are only as applicable as their premises. A useful application would identify a bearer and its continuity criterion before comparing interventions, specify the relevant environment and response capacities, and justify the selected horizon. It would then test the proposed enabling mechanism while distinguishing removal, compensation, and replacement.

The dependency claim in Proposition 1 is particularly exposed. If continuation without $Q$ occurs more often than the proposed exception bound permits, the stated dependency model fails. If an intervention changes the mechanism supplying $Q$, the original bound may no longer apply. These are different outcomes and should not be recorded as the same kind of correction.

The toy model in Section 8 yields exact results because its dynamics are stipulated. Establishing comparable claims for a plant, organism, or ecological community requires empirical measurement. The paper does not contain that calibration. Existing viability and information models provide methodological precedents, not a shortcut around measuring the particular system. [5–6, 9]

The bearer criterion is separately exposed. A model that labels every useful part as a separate organism, excludes dormant continuity by requiring constant overt activity, or counts replacement as the original process continuing needs revision. Robustness across reasonable descriptions matters: a supposedly decisive ranking that reverses under equally defensible boundaries or horizons should be reported as unresolved.

The normative interpretation has its own test. Does it preserve the difference between success and mere occurrence? Can it explain a functional requirement independently of an observer's preference without covertly importing a global objective? Does it retain distinct bearers when their requirements conflict? If not, the vocabulary has concealed rather than clarified the problem.

There are also limits to the selected probability measure. At a horizon beyond every attainable lifetime, all continuation probabilities can vanish. That does not make every earlier trajectory identical. One can examine a profile over horizons, expected duration, reserves, or other justified measures. Choosing among them is substantive. “Persistence” should organize that inquiry, not conceal its choices.

A complete evaluation must therefore distinguish a faulty proof, a wrong biological model, a disputed continuity criterion, and rejection of the normative interpretation. They are not interchangeable failures, and none can be repaired merely by increasing confidence in another layer.

14. Standing of the proposal

The dependency bound, its composition, the joint-success bound, and the information-refinement inequality follow from the stated finite probabilistic framework. Their mathematical certainty is conditional on those premises. They are elementary results organized for this application, not advertised as discoveries in probability theory.

The supporting biological and philosophical literature establishes a substantial prior field: self-maintenance, organizational functions, norm-establishment distinct from norm-following, viability-based contribution, and information relevant to continuation. This paper's combination and interpretation remain open to comparison with further work. The literature pass does not establish exclusive novelty.

The broader all-life scope depends on defensible individuation. The inference from functional oughts to interpersonal moral duties is not completed here. A uniquely justified scalar across bearers is neither derived nor disproved. The claim that all value reduces to persistence is not used as a premise.

What the paper supplies is a disciplined intermediate result: given indexed continuation criteria and a defensible dependency model, some cross-system requirements follow without equalizing bearers, positing a global organism, or assuming conscious representation. Costs, substitution, uncertainty, and conflict are part of that result's domain, not exceptions added after it fails.

The contribution is strongest where those distinctions prevent an actual inference error. One plant's loss need not matter much to me to be terminal for it. My limited dependence on one provider need not make its collective function dispensable. Supporting another system need not be a departure from self-maintenance. And shared participation in a causal world need not supply a unique common objective.

15. One game, many indices

The sidewalk event began with an error in my map: I may have treated a living plant as dead material. The correction made a relation visible. My action could be moving another organization toward termination.

The more general insight is not that minds project oughts onto an otherwise indifferent world. Under the interpretation defended here, living organizations already have conditions under which they continue or fail. Minds can represent those conditions, miss them, distort them, or become capable of changing them.

Those conditions are realized together. The activity of one system can supply another's enabling function. Support can return through a dependency. A substitute can remove a particular dependence. A collective loss can matter where an isolated loss does not. Requirements can align or conflict, and their alignment can change as the dynamics change.

Local does not mean isolated. Shared does not mean identical.

That is the structure this paper has formalized. It is not yet a complete mathematics of morality. It is a mathematics of indexed continuation and dependency, accompanied by a defended proposal about the functional normativity those relations express.

All life may inhabit that common structure without every living thing knowing it, without every participant having the same stakes, and without the whole acquiring one will.

One game of oughts. Not one ought for everything.

---

References

External literature

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   Author manuscript consulted: https://xabier.barandiaran.net/wp-content/uploads/2012/05/barandiaran_egbert_-_2012_norm-establishing_norm-following_jal_revised-2.pdf
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Internal lineage

1. [F1]
   Đurič, A. (2026). Value as Persistence: Agent-relative oughts under coupling, nesting, uncertainty, and open-ended time. Epistemic Forge. Version 2, 10 July 2026; June publication URL. https://epistemicforge.blogspot.com/2026/06/value-as-persistence-agent-relative.html
2. [F2]
   Đurič, A. (2026). The Natural History of Fidelity. Epistemic Forge. Version 1, July 2026; especially Section 17. https://epistemicforge.blogspot.com/2026/07/the-natural-history-of-fidelity.html
3. [F3]
   Đurič, A. (2026). Relata-Indexed Objectivity. Epistemic Forge. Version 1, July 2026. https://epistemicforge.blogspot.com/2026/07/relata-indexed-objectivity.html
4. [F4]
   Đurič, A. (2026). Universal Is Not Categorical. Epistemic Forge. Version 1, 28 August 2026. https://epistemicforge.blogspot.com/2026/08/universal-is-not-categorical.html
5. [F5]
   Đurič, A. (2026). What You Actually Are. Epistemic Forge. Version 4, July 2026 page. https://epistemicforge.blogspot.com/2026/07/what-you-actually-are.html
6. [F6]
   Đurič, A. (2026). Reality Alignment. Epistemic Forge. Version 2, July 2026. https://epistemicforge.blogspot.com/2026/07/reality-alignment.html

Authorship, provenance, and scope

Author: Andraž Đurič, Slovenia.

Developed from the author's reported episode, the Epistemic Forge corpus, and dialogue with ChatGPT (OpenAI), with an external literature review and checks of the constructed formal examples. The author retains responsibility for the claims, framing, synthesis, and final text. Contributions are assessed by their content rather than their origin.

Source access: The internal lineage draws on the cited corpus and recorded reading of it; several original pages could not be reopened during preparation. Where complete external articles were unavailable, the review relied on publisher abstracts or selected sections. Citation does not certify every claim made in the cited works.

Formal and empirical status: The examples are constructed, not empirically calibrated. Finite executable checks were used to check their arithmetic and counterexamples. These checks do not replace the written proofs, independently verify the biological or normative interpretation, or constitute peer review. The assumptions, limitations, and failure conditions remain explicit in the paper.

License: CC BY 4.0.