nucleation

CLAIM-354: Freedom of will and autonomy come in degrees along several dimensions, among them viable reachability, control cost, robustness to disturbance, governance reconfigurability, revisability and motivational integration, and agents compare by inclusion of what they can viably reach under matched conditions: a partial order with incomparable pairs, not a scalar, and a gradient only of a declared measure

9 min read

Properties11
StatusProposed
Version2
Rolethesis
Warrantinterpretive
Tagsfree-will, self-governance, agency
Linewill-organization
Rests onCLAIM-079 — Stability does not entail viability: a system can occupy a stable regime while losing access to trajectories that keep satisfying its constraints, CLAIM-025 — An operative regime, the governing organization among regimes, and the capacity to transform that organization can persist or fail separately, CLAIM-345 — Equal controllability rank does not fix the cost of control: for x_{t+1} = x_t + b·u the least quadratic effort for a displacement Δ is Δ²/b², unbounded as b → 0 while the system stays controllable, and in general the least effort is Δxᵀ W_T^† Δx, set by the Gramian and not by its rank
GroundsTHEORY-134 — Whether a system can persist is a question about a constraint set fixed independently of its dynamics: a set is viable when from each of its states some evolution can stay in it, and when it is not, its viability kernel is the largest part that is, from the rest of which every evolution leaves in finite time, THEORY-054 — A regulation is autonomous to the degree it is integrated with one's other values and needs: autonomy is graded, and is not set by the order of the attitude that endorses it, THEORY-411 — In Sen's capability approach the weighting of functionings is left to public reasoning, and evaluation can still guide action without agreement on weights: where every weighting in an agreed range, or every view by its own argument, ranks one option above another, that ranking holds, so the approach is deliberately incomplete and yields a partial ordering, THEORY-654 — For full-state linear-quadratic regulation of a single-input plant, the return-difference identity keeps the sensitivity at or below 1 at every frequency, so the loop tolerates any gain increase, a gain cut to one half and at least 60° of phase error for any Q ≥ 0 and r > 0; the guarantee does not carry over when the state is replaced by an observer's estimate
ComplementsCLAIM-128 — No single ranking of translations holds across tasks: where distortion profiles trade off, only a task's priorities rank them, and the theory of fidelity fixes no weighting, CLAIM-122 — Will-organization is not one more higher-order preference: changing the conditions of efficacy changes behaviour while the competing preferences stay fixed, CLAIM-027 — Which of an agent's available regimes becomes effective depends on maintained relations — accessibility, precedence, persistence, jurisdiction, suspension and transformation — that are not reducible to the contents of the competing regimes, whatever mechanisms realize them, CLAIM-352 — Sen's two aspects of freedom divide along the record's line between what an agent can viably reach and the organization that selects among it: viable reachability can stand for the opportunity aspect only through a map from trajectories to valued functionings, which control theory does not supply, and will-organization gives a causal account of part of the process aspect, not of its fairness or legitimacy, CLAIM-410 — Removing a constraint on an organization's members does not move it along one scale of more or less governance: it changes a profile of who holds rule-making, monitoring, enforcement, appeal and revision, in which the authority the constraint held can be eliminated, distributed or transferred, and the members' first-order options and their share in revising the conditions of their action can move in opposite directions
Cited as “complements” byCLAIM-527 — Viable reach, valence and emotion are three quantities in an organization, not one: an emotion is a claim to precedence, system valence is movement along the ordering that wins the negotiation, and a change in what the organization can viably reach is neither, so an organization can run ahead along its prevailing ordering while its viable reach contracts, CLAIM-535 — An organization that acts on what it observes has a policy acceptable in every circumstance exactly when, for each observation, the circumstances it cannot tell apart share an acceptable action; so every circumstance having an acceptable action does not give a policy, a finer observation never removes one, and where acceptable actions overlap the coarsest observations that suffice are several and incomparable, so which distinctions must be made legible depends on which acceptable action the organization commits to, CLAIM-537 — In tolerance-bounded compatibility on a graph with disturbed offsets, |Dx − a₀ − w| ≤ δ for |w_e| ≤ η_e, a compatible configuration exists for every disturbance exactly when |cᵀa₀| + Σ η_e|c_e| ≤ Σ δ_e|c_e| on every cycle, and one configuration serves every disturbance exactly when η ≤ δ and |cᵀa₀| ≤ Σ(δ_e − η_e)|c_e|; an agent that chooses its configuration from what it observes needs the second condition within each class of disturbances it cannot tell apart, so whether a compatible state can be selected lies between the two and depends on what the agent can read, CLAIM-542 — Sensitivity does not fix the allocation or the authorship of control: linearized, every input reaches the final state through the same transition operator, ∂x_T/∂w_t = Φ(T, t)B_w(t), so systems with the same Lyapunov spectrum can differ arbitrarily in what an agent's own channel, an outside party's channel and noise each reach and at what least energy; and along one unstable direction a larger exponent λ lowers the least effort to reach a displacement, since W_T = b²(e^{2λT} − 1)/2λ grows with λ, while a constant open-loop input against white noise entering the same direction has terminal signal-to-noise ratio tending to (bu/σ)√(2/λ), which falls as λ grows, so only feedback that observes the state turns cheaper control into reliable direction
Cited as “rests on” byCLAIM-533 — The sensitivity that formal chaos gives a will's dynamics is not control over them: in Kane's self-forming actions, chaotic amplification keeps the outcome open, but it magnifies the agent's efforts, uncontrolled fluctuations and outside inputs alike, so what would make the outcome the agent's is how its own control couples to the amplifying directions, relative to noise and to other parties' inputs and with what feedback, which sensitivity does not supply; and under weak noise what amplification touches lasts only where it reaches the slow modes, CLAIM-545 — Freedom of will, in the operational sense, is an agent's governance of its own governability: the extent to which its own organization makes the relevant distinctions legible, gives the demands they raise practical efficacy, directs its transitions, and revises the relations that govern those three, including under another's interference; openness, sensitivity and controllability of outcomes each fall short of it, and domination is another's capacity to govern those same relations, used or not

Graph View

The claim

The owner, U9 of the exchange of 2026-10-17: “controllability of a system isn’t binary, and neither is sensitivity to perturbation. I’m wondering if our account equips us to make concrete statements about gradations (perhaps even gradients/spectra?) of freedom of will/autonomy”.

The record held graded autonomy in one sense only: integration (THEORY-054, Ryan and Deci), and its own graded-ownership thesis, CLAIM-016, is Deferred with the authenticity line. Nothing in it graded control authority by reach, cost or robustness. The owner’s idea is new to the record.

A9 §3 built the object. Given a set K of conditions the organization must keep satisfying, R_T^K(s₀; E) is the set of states it can reach within horizon T, staying in K, with control expenditure at most E. That is CLAIM-079 put to work: what counts is the viable alternatives, not the stable ones. Then: “We can compare systems by set inclusion … Under matched states, costs, controls, and environmental conditions, that means A has at least all of B’s viable alternatives. But when reachable sets overlap without containing one another, the systems are incomparable, rather than one being objectively freer.” And: “This gives us a partial order of freedom, which seems much more defensible than a universal ranking.”

The dimensions vary separately, each for its own reason:

  • Viable reachability against control cost. Equal controllability rank leaves the cost of a transition free (CLAIM-345). A9: a person “might genuinely be able to reorganize a habit, but the cognitive, social, emotional, or material effort needed could be prohibitively large.”
  • Robustness to disturbance. A9 §4: “an option available only when the environment cooperates is different from one the organization can reliably realize under resistance.” The robust set asks for a policy that works against every admissible disturbance (∃π ∀w). THEORY-654 is a case on file: the LQR margins hold with the full state and are lost with an observer, so a plant can be controllable and observable and still fragile.
  • Governance. A9 §4: “A remotely operated robot can have an enormous reachable state space while its actions are determined entirely by someone else.” What is reachable is not what the organization’s own governance can select (CLAIM-027, CLAIM-122).
  • Revisability against reliable execution. A9 §7: “strong habits can improve control economy while reducing revisability.” That is CLAIM-025 and CLAIM-099: the operative regime, its governance and the capacity to transform it persist or fail separately.
  • Motivational integration. Added by A15 §8.1, F = (R, C, V, G, I, E_f, R_v), from THEORY-054. A15 conceded what SDT already holds: “The novelty is not that autonomy comes in degrees.”

A9 and A10 also list the efficacy of a higher-order attitude on governance (A9’s “endorsement efficacy”, E_d). It is a candidate dimension, an influence: A9, “It measures influence, not the normative validity of endorsement.”

On the owner’s “gradients”, A9 §8: a declared measure J(θ) of the viable options has a gradient ∇_θ J, “But it wouldn’t be an objective gradient of free will. It would be the gradient of a declared operational measure, under a declared model.” A10 §7 the same: “It would not be an objective, context-free gradient of metaphysical free will.” So there is a gradient once a task or value fixes the measure, and a profile, compared by dominance, before one does.

The shape is on file in another line. CLAIM-128 and TERM-043: transport profiles that trade off “are incomparable until a task fixes weights”. THEORY-411: Sen’s approach “is deliberately incomplete and yields a partial ordering”. QUESTION-115 has A12 of 2026-10-16 on individuation: “There isn’t yet a justified single scalar objective”. This claim is the same shape for freedom of will.

What it does not say

  • Not metaphysical free will, and not responsibility. A9’s three senses: “Degrees of effective agency”, “Degrees of autonomous governance”, and “Freedom of will in the metaphysical sense”. “The first two look amenable to quantitative characterization. They may help clarify the third, but they don’t settle questions about determinism, moral responsibility, or ultimate sourcehood.” The claim is about the first two. On Fischer and Ravizza (THEORY-121), responsibility needs guidance control and not regulative control over alternatives, so a larger reachable set does not make a more responsible agent.
  • Not that more reachable is freer. Inclusion orders one dimension. A11 §4: “A person who restricts access to a distraction might reduce immediate behavioral flexibility while increasing their ability to pursue an endorsed project.” That is the reluctant writer (CASE-013). The precommitment shrinks the reachable set and lowers the cost and raises the robustness of the endorsed project. So the writer before and after are compared dimension by dimension, and may be incomparable. Reachable-set size is not monotone with autonomy.
  • Not endorsement in the record’s sense. The record’s endorsement (TERM-053) is any effect one process has on another’s share of future influence, and it is not Frankfurt’s. A9’s “endorsement” is the reflective attitude. Here it is called higher-order volition.
  • Not that the dimensions are measured. A9: “a Gramian is not automatically a meaningful psychological measure”, and the profile’s symbols “denote dimensions, not yet fully specified measurements.”
  • Not that reachable states are valuable. A11: “a control system’s reachable states are not automatically valuable human opportunities.” That is CLAIM-352’s point and CLAIM-075’s.
  • Not that K is the agent’s own. The comparison is relative to a viability set given from outside the dynamics (THEORY-134, CLAIM-195). Who fixes K is still open.
  • Not ownership. Integration enters as one dimension. Whether a will is its own to a degree is CLAIM-016’s question, which stays Deferred.

Note of 2026-10-21: a strategic route to non-monotonicity

A18 of the exchange of 2026-10-20 gave a strategic route to this claim’s non-monotonicity. In a prisoner’s dilemma, with a rule enforcing cooperation at (3, 3), removing the rule enlarges each player’s action set, and the unique equilibrium becomes (1, 1): “Expanded individual action sets ⇏ Pareto-improved equilibrium outcomes”. Checked. The sharp edge already says precommitment can shrink the set and make an endorsed project realizable. The PD is the two-agent form, in which the shrinking is imposed and not chosen. That bears on autonomy, which this claim does not settle. CLAIM-410 uses the example.

Note of 2026-10-31: “augmented ability to act” assumes a comparison this claim makes partial

The parent paper filed on this date defines agency by a transition “from a lesser to an augmented ability to act” (LIT-1902, p. 1354; THEORY-1280). That verdict assumes two abilities can be ranked. On this claim they compare by inclusion, and pairs that overlap without containment are incomparable. The paper’s own case is one. In the MSF meeting (pp. 1359–1363), MSF takes on an “ad hoc training program” it first resisted (“[they] are not here as educators”), while declining formal teaching (p. 1363). It gains a joint activity with the health department. And by the paper’s own account it may be “becoming a ‘university’” (p. 1363), the direction Robert had tried “to protect the organization from” (p. 1362). The paper counts the outcome as transindividuation, “augmented ability to act” (p. 1362). Without a declared measure, this claim would class it as a change, not an augmentation. NOTE-1484 found the same gap (“Building augmentation into ‘agency’ makes a verdict depend on a judgment of whose capacity counts”). This claim gives the reason in general. CLAIM-527 separates the quantity from valence and emotion.

No status, title or warrant changes.

Note of 2026-11-02: what the profile lacks, and a corrected reachable set

In the exchange “Assess SDT Coverage” (2026-11-02) the replies rebuilt this claim three times without saying so: A16’s reachable set and Gramian, A21’s “robust reachability” and A22’s three levels. Three points add to it.

  • Non-domination (Pettit, LIT-1614). An agent can be unfree because another holds an effective, unaccountable channel it never uses. The “governance” dimension, the remote-operated robot, covers actual external determination, not that counterfactual capacity. Formally it is the robust reachable set taken against an adversary class that includes the unused channel.
  • The allocation of control across channels, and its history (A21 §8, A22 §3). A slow state that changes the agent’s own gain, an outsider’s and the noise gain makes susceptibility itself governable. That extends governance reconfigurability from what the agent can do to what can be done to it. The demonstrated part is CLAIM-542.
  • A25 §7’s reachable set of governance and legibility configurations, ∃π_s ∀π_e. It ranges over every feedback policy. Against A25’s own model it should range over the policies the current organization can carry out that read only what its legibility regime makes usable. Otherwise legibility drops out of the set.

A26 identified freedom with the whole profile under reflexive revision. That is filed as CLAIM-545, Proposed, resting on this claim. The claim is unchanged.

Note of 2026-11-03: legibility-limited policies, stated

This claim’s note of 2026-11-02 said a reachable set should range over the policies an organization can carry out on what it can read. Two demonstrated claims from U30 to U33 of the exchange “Assess SDT Coverage” (2026-11-02) state it: CLAIM-535 in general (a policy acceptable everywhere exists exactly when the circumstances an observation cannot separate share an acceptable action), and CLAIM-537 for tolerance-bounded compatibility. The motivational integration this claim names is given a positive account in CLAIM-534.

The claim is unchanged.

Note of 2026-11-03 (later): empowerment and information, read

Empowerment (Klyubin et al. 2005, 2008; NOTE-1511, NOTE-1514) is a task-free number for perceivable reach, but it is open-loop, depends on the horizon and ignores cost and viability, so it does not collapse this claim’s profile to a scalar. Its maxima in the cart-pole cannot be reached and held, against what the agent can sustain (CLAIM-079). Ben-Tal et al.’s Table 2 (NOTE-1503) is a quantitative case of legibility-limited policies: cost 34,583 with on-line information, 35,121 with past demands, infeasible with a four-period delay or none.

The claim is unchanged.

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