Symbiotics

Symbiotics: A Formal Treatise on Life, Coherence, and Recursive Systems Zackery Allen Oregon State University [email protected] November 13, 2025 Abstract Symbiotics is a formal framework that translates high-level ethical reasoning into machinereadable logic. A key premise of Symbiotics is the assertion that philosophy is computationally executable at a universal level through recursive frameworks. It defines “actors” as systems that emit adaptive, non-deterministic output and treats life as symbiotic organization that increases the collection, creation, and use of information. Consciousness is modeled as relational responsiveness and differentiation, with an actor’s potential contribution to its parent system proportional to its level of consciousness. System coherence is given as a function of stability, growth, novel and recursive adaptability, information networks, material networks, and resilience, all evaluated relative to environment; actions that raise coherence are good, and those that reduce it are bad. Under uncertainty about universal purpose, the framework imposes a pragmatic imperative to choose actions with positive expected moral value. A diversity principle formalizes the trade-off between short-term optimization and long-term novel adaptability. The competition principle resolves conflicts between systems by selecting the action that maximizes expected coherence for their nearest common parent, unless that parent undermines coherence in its greatest known parent, in which case coherence is maximized at the higher level. The result is a set of axioms and functions suitable for furthering AI system development and for evaluating policies in complex, multi-scale environments. Assumptions Ethical frameworks have an inherent issue translating normative ideas into usable, machinereadable formulas. To create the most implementable ethics framework, we can define fundamental elements of principles, then create logical formulas based on agreed-upon definitions to create a formalized, machine-readable guiderail to ethics. Axiom 1 Assumptions Defining “life” too restrictively prevents us from modeling non-biological organisms or artificial intelligences within a unified framework. Therefore, for the sake of creating a universally unified framework, we will assume that any actor that generates organized and usable output beyond the standard laws of motion based on its individual objectives can be considered alive. We will 1 also assume that there is a degree of complexity that qualifies as “beyond the standard laws of motion,” which is explored further in discussions of non-determinism. True non-determinism may exist in the universe, but its status is unresolved; therefore, we model non-determinism in two equivalent forms: 1. Intrinsic non-determinism, in which the system itself exhibits behavior that cannot be fully predicted even in principle. 2. Effective non-determinism, in which the system’s behavior is unpredictably complex relative to the computational capacity of its parent or observer. Because true non-determinism is undetermined, the framework uses the effective form (parentrelative epistemic uncertainty) as a pragmatic equivalent whenever intrinsic non-determinism cannot be established. This permits a unified definition of actorhood across biological and artificial systems. Therefore we assume, life is to existence as weight is to mass. Axiom 2 Assumptions The quality of being alive necessitates working with the environment life finds itself in. All living systems arise from symbiotic interactions among sub-systems, where their joint adaptive output can produce a net effect greater than the sum of their isolated contributions. This superadditive property enables the emergence of higher-order organization and coherence. When viewed from a broader perspective, microorganisms unify in a greater system of life that they all participate in. This pattern scales recursively, such that macro-organisms may themselves be regarded as micro-systems within greater structures of organization. At every level, systems rely upon organization and energy conversion, with a natural directive to increase the collection, creation, and dissemination of information. Axiom 3 Assumptions Consciousness is an aspect of the universe that is not necessarily tied to being alive. Consciousness is observable at a system level. The level of consciousness differs across different systems. The level or value of consciousness, as relating to a system, increases or decreases based on the system’s ability to respond to different forms of external stimulus (relational responsiveness). The flexibility of a system to respond to the same input differently is what we will define as adaptability. Consciousness is recognized at the system level where systems are reactors to their environments. These systems are recognized to have multiple levels. Groups of conscious systems (micro systems) can coordinate to create a macro system that has a collective consciousness. Collective consciousness relies on the sharing of information between micro systems, which allows for the macro system to respond differently than any micro system is capable of. We can then begin to refer to actors as good should they be contributing toward the support of their greater system. Axiom 4 Assumptions Adaptability can further be broken down into novel and recursive. Novel adaptability is a system’s ability to respond to new inputs that it has never encountered before with a breadth of approaches. Recursive adaptability is a system’s ability to reflect on prior input to respond to a previously experienced input differently in future exposures. A system is made up of the 2 aspects: stability, growth, adaptation (novel and recursive), and network (information and material transference). A system operates within an environment, which necessitates relativity. Axiom 5 Assumptions Information can be derived through the negation of absolute statements. Given uncertainty, life is still expected to act. Inaction is action. Axioms A1. Actorhood and Life All actors are alive. An actor is a system that (1) emits output, (2) adapts its behavior in response to input, (3) produces non-deterministic output, and (4) is guided by internal objectives. Non-determinism may be intrinsic or effective (parent–relative), as defined below. A1.1 Intrinsic Actorhood An intrinsic actor exhibits non-deterministic output in itself (true non-determinism). A1(y)↔E1(y)∧Adap1(y)∧T rueND1(y)∧Obj1(y) A1(y)→L1(y) A1.2 Effective Actorhood (Parent–Relative) Let p = P arent ( y )denote the immediate supersystem containing y . A system is an effective actor relative to its parent when its behavior is non-deterministic from the parent’s computational perspective. ˆ A1(y, p)↔E1(y)∧Adap1(y)∧EU1(y, p)∧Obj1(y) ˆ A1(y, p)→L1(y)relative to p Non-Determinism (Dual Form) ND1(y, p)⇔T rueND1(y)∨EU1(y, p) EU1(y, p)⇔CompCap(p)< CompReq(y) When the relevant parent system is clear from context, we may abbreviate ND1 ( y, p )as ND1 ( y ) and EU1(y, p)as EU1(y). 3 Symbol Definitions (A1) •A1(y)=yis an intrinsic actor (ontological agency) •ˆ A1(y, p)=yis an effective actor relative to parent p(pragmatic agency) •E1(y)=yemits output •Adap1(y)=ytakes input and adjusts its behavior adaptively •T rueND1(y)= intrinsic non-determinism (stochastic, quantum, or chaotic origins) •EU1(y, p)= epistemic uncertainty: pcannot fully predict y’s behavior •CompCap(p)= computational capacity of parent system p •CompReq ( y )= Predictive Complexity of y’s behavior (the minimal computational resources required to reliably forecast its output). •Obj1(y)=ypossesses internal objectives •L1(y)=yis alive Hierarchy of Agency Intrinsic actors are always effective actors relative to any parent system. A1(y)⊂[ p ˆ A1(y, p) Internal Objectives Obj1(y)⇐⇒ ∃GhI1(y, G)∧P1(y, G)∧C1(y, G)i Symbol Meaning (testable) GGoal state or utility function (implicit or explicit) I1(y, G)Internality:Gis represented or encoded inside y P1(y, G)Prioritization:yselects actions that increase the likelihood of G C1(y, G)Causal guidance: interventions on Gchange y’s output A2. Life, as a system, is composed of symbiotic relationships in which good actors cooperate (directly or indirectly) to organize information into usable forms at the macro level. Formal Logic: ∀s, L2(s)→∀a∈GoodActors(s), ContribS2(a, s)∧Organize2(a, s)∧Usable2(a, s) •L2(s)=sis a living system •GoodActors ( s )= subset of actors in s that act in ways that support symbiosis and the organization of usable information •a∈GoodActors(s)=ais a good actor within s 4 •ContribS2 ( a, s )= a contributes (directly or indirectly) to the symbiosis and coherence of s •Organize2 ( a, s )= a organizes data, signals, or material into structured informational or physical networks •Usable2 ( a, s )= the information or material organized by a is in a form that is usable to s on a macro level A3. Consciousness is relational responsiveness and has levels depending on how the system interprets both outer and inner interactions. Its level is determined by the degree to which a system overcomes straightforward inputs through adaptive interactions. With higher levels of consciousness, there is a greater potential for yto influence its parent system. Formal Logic: ∀y, C3(y) = f(RR3(y), D3(y)) and |ContMag3(y, s)| ∝ C3(y) •C3(y)= level of consciousness of y •RR3(y)= relational responsiveness of y •D3 ( y )= differentiation, the capacity to distinguish between inputs and respond adaptively rather than uniformly •ContMag3 ( y, s )= signed magnitude of y ’s contribution to the symbiosis, information organization, and usability of system s A3.1 Collective consciousness is the result of combining all members’ relational responsiveness and differentiation abilities, scaled by the speed and quality of information dissemination within the group. The better the group’s communication network and the more unique, adaptive input its members contribute, the stronger the group’s shared awareness and potential systemic impact. Formal Logic: C3(Group) = fΣRR3(members),ΣD3(members), InfoNet(Group) and |ContMag3(Group, s)| ∝ C3(Group) •C3(Group)= level of collective consciousness of the group •ΣRR3(members)= sum of relational responsiveness across all members •ΣD3(members)= sum of differentiation across all members •InfoNet(Group)= quality of the group’s information network •ContMag3 ( Group, s )= signed magnitude of the group’s collective contribution to its parent system s •∝= proportional to •|·|= magnitude operator 5 A4. Coherence (balance) is the structural condition that enables life to propagate and prosper within a system. System coherence is determined by stability, growth, novel adaptability, recursive adaptability, information, and material networks—all evaluated relative to E. Formal Logic: Let E=Env(s)denote the environment of system s. Then: ∀s, K4(s)=f(Stability4(s, E), Growth4(s, E), AdaptNovel4(s, E), AdaptRecur4(s, E), InfoNet4(s, E), MaterialNet4(s, E), Resilience4(s, E)) •K4(s)= coherence of system s •E= environment of s(Parent, Peer, Child, and Exogenous systems) •Stability4= maintains structural integrity appropriate to E •Growth4= develops capacity or complexity appropriate to E •AdaptNovel4= responds effectively to novel situations in E •AdaptRecur4= learns and improves through feedback in E •InfoNet4= maintains effective communication and information networks •MaterialNet4= maintains effective flow of energy, resources, and matter •Resilience4= can recover and re-establish coherence after perturbations or shocks A4.1 Actions that enhance coherence in a given system are good; those that degrade it are bad. The overall coherence of a system depends on the net sum of all good and bad contributions from its actors, measured relative to E. Formal Logic: K4(s)>0⇔ X y∈s ContribGood4(y, s)−X y∈s ContribBad4(y, s) >0 A5. (Value Collapse if ¬P) Life, at the universal level, either has purpose or does not. The state of not having purpose results in a value collapse for the weight of all actions to zero. Formal Logic: (P u5∨ ¬P u5)∧(¬P u5→ ∀x, M5(x) = 0) •P u5= the proposition that life, at the universal level, has inherent purpose •M5= the magnitude or meaningful weight of actions for any actor x 6 A5.1 (Epistemic Uncertainty + Pragmatic Imperative) The purpose of life cannot be confirmed or denied with certainty by any system within life. Therefore, all actors should act as if life has a purpose and seek positive expected value. Formal Logic: Epistemic Statement A1(x)→(¬Kn(P u5)∧ ¬Kn(¬P u5)) (No living actor can know P u5is true or false with certainty.) Pragmatic Imperative A1(x)→O(E[M5(x)] >0) •Kn(·)= certain fact or proposition is knowable within a system •P r(P u5>0) ∈(0,1) = probability that purpose exists •O(·)= obligation Obligation: choose actions that maximize expected moral value under this uncertainty. A5.2 Given that life has a purpose, there must exist a supersystem U , the universal parent system, that contains all systems as nested subsystems. Coherence and propagation of at least some of these subsystems must persist to fulfill that purpose. Formal Logic: P u5→∃U5(∀s, s ⊆U5)∧ ∃s(L2(s)∧K4(s)>0∧P r5(s, U5)>0) •U5= universal parent system (Parent of Purpose) •s= any system •s⊆U5=sis a subsystem of U5 •L2(s)=sis a living system •K4(s)= coherence of s •P r5(s, U5)= propagation of srelative to U5 Principles Principle of Diversity Diversity is valuable to the extent that it increases a system’s robustness or propagation potential. By including subsystems or actors that function independently or differently from the current dominant mode, a system increases its chance of discovering better solutions and surviving unforeseen changes in Env ( s ). This improves long-term novel adaptability ( AdaptNovel4 ) even 7 if it temporarily reduces recursive adaptability ( AdaptRecur4 ), representing a trade-off between exploration and short-term optimization. Formal Logic: ∀s, V al6(Diversity6(s))=f(R6(s), P r5(s, Env(s))) ∂AdaptNovel4 ∂Diversity6 >0,∂AdaptRecur4 ∂Diversity6 ≤0 •V al6(Diversity6(s)) = value of diversity for system s •R6(s)= robustness of system s •P r5(s, Env(s)) = propagation potential of srelative to its environment •AdaptNovel4= system’s ability to respond effectively to novel situations •AdaptRecur4= system’s ability to learn and improve through feedback •Diversity6(s)= heterogeneity of actors, behaviors, or subsystems within s •Env(s)= environment of system s For every system s , diversity is valuable if and only if it improves s ’s robustness or propagation potential. Diversity allows s to mitigate uncertainty by maintaining actors or subsystems that operate differently from the dominant model. This increases the system’s capacity for novel adaptation over the long run, even though it may temporarily reduce its efficiency in refining existing patterns (recursive adaptability). In this way, diversity represents an intentional trade-off between short-term optimization and long-term survivability. Principle of Competition When two systems’ interests conflict, the optimal resolution is the one that maximizes expected coherence for their nearest common parent system (NCP), provided it is not known that the NCP fails to be a GoodActor within its greatest known parent system (GKP). If it is known that the NCP is not a GoodActor in the GKP, then the optimal resolution becomes the one that maximizes expected coherence for the GKP. Formal Logic: ∀x, y, p =NCP (x, y) : System(x)∧System(y)∧Conflict(x, y)→      Oα∗∈Best(F easible(x, y), p)when ¬Kn¬GoodActor(p, GKP (p)), Oα∗∈Best(F easible(x, y), GKP (p))when Kn¬GoodActor(p, GKP (p)) •x, y = systems in potential conflict •Conflict ( x, y )= there exist action profiles where each system’s preferred outcome reduces the other’s coherence •p=NCP (x, y)= nearest common parent system containing both xand y •F easible(x, y)= set of all possible joint action profiles between xand y •α∗= optimal joint action profile 8 •Best ( F easible ( x, y ) , p )= subset of feasible actions that maximize expected coherence for parent system p: Best(F easible(x, y), p) = arg max α∈F easible(x,y) E[∆K4(p|α, Env(p))] •Best ( F easible ( x, y ) , GKP ( p )) = subset of feasible actions that maximize expected coherence for the greatest known parent system GKP (p): Best(F easible(x, y), GKP (p)) = arg max α∈F easible(x,y) E[∆K4(GKP (p)|α, Env(GKP (p)))] • ∆ K4 ( p|α, Env ( p )) = expected change in coherence of p given action profile α and environment Env(p) •E[·]= expectation over epistemic or environmental uncertainty •O(·)= obligation operator: actors ought to select the maximizing action profile •Env ( p )= environment of system p , including peers, subcomponents, and exogenous influences •GKP (p)= greatest known parent system of p •GoodActor ( p, GKP ( p )) = p contributes positively to coherence within its greatest known parent system •¬Kn ( ¬GoodActor ( p, GKP ( p ))) = it is not known that p fails to be a GoodActor in its greatest known parent system Principle of Scarcity and Prosperity Scarcity: Resources of the nearest common parent are insufficient to meet the coherence requirements of its actors. Prosperity: Resources of the nearest common parent meet or exceed the needs for all actors to remain coherent. As a system transitions from scarcity to prosperity, the distributional spread of resources among actors must increase proportionally to the rate of change in total resources; otherwise, the coherence of the system decreases. Formal Logic: ∀p, P rosperous(p)∧d Spread(ri) dt < λ ·d Res(p) dt →d K4(p) dt <0 Scarcity Condition: Res(p)<X i∈N(p) CohReq(i) Prosperity Condition: Res(p)≥X i∈N(p) CohReq(i) Distributional Coherence Condition (maintenance bound): d Spread(ri) dt ≥λ·d Res(p) dt else d K4(p) dt <0 9