Inside-out determination and the authorship of an occurrence

Choosing a determining slice does not create a chooser. Full-state mathematical determination differs from the power exercised by a fragment of a world. This chapter engages the block-compatible freedom arguments directly, proves the required factorization and uniqueness statements, and gives an explicit reversible history with a usable forward command. It identifies what an account of settlement still owes without erasing practical authorship.

5 Inside-out determination and the authorship of an occurrence

The block-compatible defense of freedom deserves more than the reply that all choices already occur in a block. Its central challenge is that mathematical determination need not run from an independently privileged remote past toward a passive present. Hoefer asks why bidirectional state determination should assign all explanatory authority to an initial boundary. Brennan replies that changing the location of determining data does not by itself establish agential control. Both points survive close examination. Their combination motivates a stronger account of constituted agency: explain the work of the organization that decides, while refusing to obtain its independent sourcehood from the coordinate location of data.

5.1 What Hoefer proposes and what Brennan challenges

Hoefer distinguishes logical determination from causation and explanation. Under suitable laws a complete intermediate state can determine earlier and later states. Selecting the Big Bang rather than an intermediate slice as data is mathematically convenient, but is not itself a proof that the earlier slice exercises power over the later one (Hoefer 2001, author preprint pp. 4-6). He also discusses one-way deterministic, many-to-one laws, so the proposal should not be reduced to a claim that every physical law must be invertible (Hoefer 2001, preprint pp. 6-7).

The claim about human freedom needs more. Hoefer proposes that scattered macroscopic choices constrain the block while remaining compatible with a macroscopically fixed past. Changes in compatible microscopic detail need not be changes in that macroscopic past. His harmony argument is a plausibility argument about compossibility, not a general existence theorem for arbitrary collections of choices (Hoefer 2001, preprint pp. 10-12 and n. 14). He also expressly leaves a positive account of freedom undeveloped (Hoefer 2001, preprint p. 15 n. 18). The 2001 author preprint is the fully inspected original used for these locators; the final publication is Hoefer (2002). The editions must not be assigned interchangeable page numbers.

Brennan reconstructs the proposal sympathetically before isolating three difficulties. First, the symmetry of determination concerns complete data, not an arbitrary fragment containing a person’s choice (Brennan 2007, 211). Second, logical entailment in both temporal directions is not the relation between acting on a goal and bringing it about. Setting an alarm now to ring at six tomorrow differs from trying now to make it have rung in the past (Brennan 2007, 212-14). Third, even if freely selected acts could serve as boundary constraints, the existence of those acts and the power of selecting them still need an explanation. Calling a value free data does not supply that explanation (Brennan 2007, 215-17).

These criticisms have different targets. The first corrects a mathematical inference. The second requires an account of directional efficacy. The third requires an agent-level explanation and challenges the proposed explanatory priority of arbitrarily selected choice data. They do not establish that a block contains no ordinary decision authors, or that control requires indeterministic laws. Brennan’s own tentative reconstruction constrains compatible earlier and later states rather than literally changing an actual past (Brennan 2007, 214). We can retain that consistency insight while providing the missing operational distinctions.

5.2 Full-state uniqueness is not fragmentary power

Let $\mathcal H_L$ be a nominated space of complete physical histories satisfying laws $L$, with gauge-equivalent descriptions identified. Let

$$e_\Sigma:\mathcal H_L\longrightarrow\mathcal D_\Sigma$$

give complete admissible data at a chosen Cauchy surface, in a regime where such a surface and comparison map are available. The data and history equivalences, including the initial embedding or other required markings, must make this map well defined. Here complete data means fully specified data, not a geodesically complete initial metric.

Whole-history uniqueness means that $e_\Sigma$ is injective: agreeing on those data fixes the entire nominated history, including its past. This is stronger than forward uniqueness. Let $r_\Sigma^+$ restrict a history to its future development under the same initial-data-preserving gauge identifications. Forward uniqueness requires only

$$e_\Sigma(h)=e_\Sigma(h') \ \Longrightarrow\ r_\Sigma^+(h)=r_\Sigma^+(h'), \qquad \ker e_\Sigma\subseteq\ker r_\Sigma^+,$$

where $\ker f$ denotes the relation of having equal images under $f$. For example, over the declared finite interval $\{-1,0,1\}$, the deterministic update $F(0)=F(1)=0$ admits histories $(0,0,0)$ and $(1,0,0)$. Their present data and futures agree although their pasts differ. The example concerns that declared interval, without asserting that both histories extend to a bi-infinite trajectory.

Surjectivity of $e_\Sigma$ additionally requires existence, for every declared datum, of a history in the same specified domain or development class. In the general-relativistic application, the maximal-development theorem supports comparison of maximal globally hyperbolic developments up to initial-embedding-preserving isometry. Arbitrary truncated developments with the same data need not be identical. These are properties of a comparison family, not powers possessed by a datum or an experimenter.

Proposition 5.1 (History parametrization and fragment determination). If $e_\Sigma$ and $e_{\Sigma'}$ are bijective on the same history family, their data descriptions are related by the bijection $e_{\Sigma'}e_\Sigma^{-1}$. For any fragment $a:\mathcal H_L\to\mathcal A$ and target $Y:\mathcal H_L\to\mathcal Y$, a rule $\bar Y:a(\mathcal H_L)\to\mathcal Y$ satisfying $Y=\bar Y\circ a$ exists exactly when $Y$ is constant on each $a$-fibre.

Proof. The first map is a composition of bijections, with inverse $e_\Sigma e_{\Sigma'}^{-1}$. For the second claim, factorization makes equal fragment values imply equal targets. Conversely, define $\bar Y(a(h))=Y(h)$; constancy on the fibre makes this well defined on the image of $a$. ◻

The second clause is an application of the canonical descent result, not a new theorem replacing it. The first clause states a redescription equivalence. Neither clause establishes causal or explanatory priority for either slice. Brennan’s schematic biconditionals between actual complete-state propositions should therefore be read through a cross-history uniqueness condition of this kind. A material biconditional between two true actual propositions would be too weak to express deterministic evolution.

For a finite counterexample let $\mathcal H_L=\{(i,j):i,j\in\{0,1\}\}$, let complete data be $(i,j)$, and let the purported determining choice be $a(i,j)=i$. The target $Y(i,j)=j$ is not determined by the choice, although complete data determine everything in this family. The target $Y'(i,j)=i$ does descend. This directly answers the whole-to-fragment inference while showing why its failure does not eliminate all target determination. Causal control requires the additional operative relations specified in the next example.

The fragment’s causal reach must also be distinguished from its domain of dependence. In $1+1$ dimensions with signal speed $c$, an initial interval $|x|\lt r$ determines a shrinking diamond $|x|+c|t|\lt r$ under an appropriate local hyperbolic law. Signals emitted within that interval can nevertheless affect events outside the diamond, whose other incoming data are not supplied by the interval. A small brain region’s inability to determine a complete distant state therefore does not establish inability to contribute to a distant goal. Brennan’s use of domain-of-dependence limits is strongest against total state determination, and needs environmental and channel premises to become a bound on ordinary goal-directed influence.

5.3 A reversible history with directional command efficacy

An exact four-register example separates symmetric full-state determination from an available forward command. Prepare

$$(R,A,C,F)=(r,0,a,0),\qquad r,a\in\{0,1\}.$$

Execute a controlled NOT $R\to A$, swap $A$ with $C$, and execute a controlled NOT $A\to F$. The resulting history is

$$(r,0,a,0)\ \longrightarrow\ (r,r,a,0)\ \longrightarrow\ (r,a,r,0)\ \longrightarrow\ (r,a,r,a).$$

The raw map on all sixteen states is

$$(R,A,C,F)\longmapsto(R,C,A\oplus R,F\oplus C),$$

which is bijective. Every complete intermediate slice therefore determines the others. Across the admitted preparations with $r$ fixed, changing the command $a$ changes the later record $F$ while leaving the earlier record $R$ unchanged. Ready scratch registers, the command carrier and the schedule are explicit enabling conditions. If $F$ is initially one, the final record is instead $1-a$.

This is conditional command efficacy. It compares preparations with different initial $C$, so it is no counterexample to uniqueness from a fixed complete past. It nevertheless refutes an inference from two-way full-state entailment to the absence of an asymmetric command contract. A participant has access to some carriers at some stages, not arbitrary power to overwrite a complete Cauchy slice. Archives and actuators earn their roles through actual routes. Section 15 supplies a far more detailed version of those obligations for acquired recognition, including local routing and fresh ingress.

The example also makes Brennan’s demand constructive. A positive account must specify who or what carries a command, what preparation permits, which changes count as admitted operations, and which target changes through the route. It need not infer an independent author from a bare logical parameter. The apparatus does not decide whether a human’s deliberation has the relevant semantic and historical properties, but it identifies the additional account that mere block geometry lacks.

5.4 From an actual complete history to a limitation on authorship

Three comparisons now separate. Fixing the complete actual history fixes its act trivially. Fixing laws and complete earlier data fixes the act only under a uniqueness premise. Fixing accessible records, a macrostate or an environment may leave several acts compatible even under deterministic microphysics. Using one comparison in the premises and another in the conclusion creates a false proof.

Proposition 5.2 (Conditional prior-data exclusion). Let $A:\mathcal H_L\to\mathcal A$ be a nominated decision or action target that factors through the physical future development: $A=\alpha\circ r_\Sigma^+$ for some $\alpha$. If forward uniqueness holds, two histories with the same complete prior data cannot have different values of $A$. Whole-history injectivity of $e_\Sigma$ is a stronger sufficient condition. More generally, for any nominated target the same conclusion holds whenever $A$ is constant on every $e_\Sigma$-fibre, even if other future features are not uniquely determined.

Proof. Equal prior data give equal future restrictions by forward uniqueness, hence equal values after applying $\alpha$. Whole-history injectivity identifies the histories themselves. The final claim follows directly from target constancy on the prior-data fibre. ◻

Forward uniqueness therefore need not reconstruct the past, and target constancy can be weaker still. Failure of whole-history uniqueness might concern only differing pasts; it does not by itself establish an open future choice. Conversely, if other future features vary while the act remains fixed, the nominated decision has no same-data alternative even though the entire future is not unique.

The conclusion excludes settlement between different acts while the declared complete prior data and laws remain fixed. It does not exclude the person’s settling a practical question through the uniquely realized deliberation, nor alternatives that hold the environment fixed while varying the person’s own organization. Ismael explicitly uses that latter comparison and accepts complete-state fixation in her deterministic treatment (Ismael 2016, 107-8; p. 230 n. 9). A compatibilist who calls that organized deliberation authorship has not contradicted the proposition. A libertarian who requires alternatives under the same complete prior physical conditions has instead challenged either uniqueness, the completeness of the nominated physical data, or the necessity of that comparison. The factorization premise must also be warranted for the intended target. A registered action value need not exhaust every alleged mental or sourcehood fact. An account locating freedom in an actual initiating relation rather than in a second value of this target raises the separate token-causal constitution dispute.

The strongest embedded agent-causal rival grants that its act occupies a complete block and that its power has an unchosen constitution. It claims that the person nevertheless determines which lawful continuation becomes actual. A space of complete histories can represent such an interpretation: include two histories with the same prior data and different acts, and attribute their difference to personal settlement. Geometry alone does not exclude it. Stochastic laws alone also do not establish it. If the additional personal relation changes no operational law, the represented causal structure underdetermines that metaphysical interpretation. If it changes an observable law, its consequences must be specified and tested.

There is therefore a stronger conditional result, with visible dependencies. Shared constitution removes an absolutely independently constituted personal source. Inheritance plus well-founded authorization obstruct ultimate authorship of the entire enabling basis. Appropriate complete-data uniqueness excludes a particular same-prior-data alternative. Token-causal constitution excludes a further irreducible initiating relation in a nominated regime. These are cumulative, distinguishable claims; the block contributes the coherent complete occurrence within which they can be assessed, rather than a replacement proof of all four.

Brennan’s final demand for an explanation of brute free data remains pertinent (Brennan 2007, 215-17). Yet his suggestion that inside-out reasoning becomes irrelevant unless it is necessary for the supplemental freedom theory is too restrictive. Removing a false picture of the past as a second agent can clarify a constituted account even when it does not prove that account. The constructive answer is to explain deliberation, model acquisition and warranted commitment as activities within the history. That reply accepts the need for a positive mechanism while refusing an unsupported claim that choosing a determining slice creates ultimate explanatory authority.

5.5 Thyssen’s libertarian reconstruction and the remaining selection problem

Thyssen’s Chapter 4, coauthored with Sylvia Wenmackers, explicitly limits its central analysis to alternative possibilities, a necessary rather than sufficient condition on its intended freedom; intentional control is largely set aside (Thyssen 2020, 129 n. 5). Its classification usefully separates deterministic and probabilistic constraints on dynamics from constraints on boundary data. It therefore resists the false dichotomy that a decision must be either a deterministic consequence or an independently sampled random event.

The proposed repair to Hoefer takes two forms that should be distinguished. The pruning ladder treats a macrostate as actually multiply realized by a bundle of histories, with choices narrowing the bundle and its compatible past. The final presentation, under its simplifying unique-history assumption, withdraws that actual bundle, restores one deterministic microhistory, and locates alternatives in hypothetical macrohistories (Thyssen 2020, 156-59). Thyssen also allows that a residual thin bundle might remain (Thyssen 2020, 158 nn. 39, 42); that qualification does not supply a selection mechanism. Earlier, mere epistemic or counterfactual alternatives were judged insufficient for the intended libertarian reading (Thyssen 2020, 154-55). The final appeal to hypothetical alternatives therefore leaves an obligation: identify what makes their availability more than coarse-grained compatibility.

The thesis’s general conclusion candidly lists stronger assumptions, including inside-out priority, boundary-condition indeterminacy, downward causation and actual multiple realization (Thyssen 2020, 164). These are not identical to the restored deterministic microhistory formulation. On the stronger reading, the selection power is an additional metaphysical and causal premise; on the weaker reading, a branching coarse description has not yet established libertarian settlement. The issue is not settled by dismissing macrolevel explanation. Macrolevel reasons and commitments can be real and effective. The issue is which modal and operative relations the alternatives actually possess. The next section strengthens the proposal’s consistency side while keeping that selection obligation explicit.