\section{Integration Without Equivocation}

Volume 2 supplements the Markov blanket with Integrated Information Theory. This is a strategically important move. A blanket alone identifies mediation between internal and external variables, but it does not show that the internal system is a unified causal whole. IIT attempts to measure the extent to which a system's cause-effect structure is irreducible to that of its parts. In the language of the master key, recurrent cortical microcircuits are expected to yield strictly positive integrated information, \(\Phi>0\).

The argument proceeds from recurrent internal connectivity and an irreducible covariance block to a discrete transition probability matrix and then to an intrinsic-difference comparison between intact and partitioned cause-effect structures. This route is plausible, but it crosses several conceptual levels. Correlation, dynamical coupling, causal irreducibility, and phenomenal unity must be distinguished if the conclusion is to remain rigorous.

Correlation is the weakest relation. Two variables may covary because one causes the other, because both share a common cause, or because of selection and measurement effects. A non-diagonal covariance matrix demonstrates statistical dependence, not intrinsic causal power. Recurrent neural connectivity makes causal coupling more plausible, but covariance irreducibility under a particular representation does not itself establish irreducibility under intervention.

Dynamical irreducibility is stronger. A system is dynamically irreducible when its evolution cannot be accurately reconstructed from independent models of its parts. Recurrent loops often produce this property because the future state of each component depends on feedback from others. Yet dynamical irreducibility remains relative to model class, grain, and error tolerance. A system that is irreducible at one temporal resolution may be approximately decomposable at another.

Causal integration adds counterfactual structure. Partitioning the system should alter its repertoire of causes and effects in ways that cannot be recovered by independent components. IIT formalizes this intuition through a minimum information partition and a distance between intact and partitioned cause-effect structures. The theory's intrinsic-difference measure is designed to capture information for the system rather than for an external observer. Whether it succeeds is an active philosophical and technical question, but the target is clear.

Phenomenal unity is stronger still. The fact that a system has irreducible causal organization does not logically entail that there is something it is like to be that system unless one accepts IIT's identity claim. IIT proposes that consciousness is identical to maximally irreducible intrinsic cause-effect power. Critics may instead interpret \(\Phi\) as a correlate, a structural enabling condition, or a measure of complexity. Volume 2 should acknowledge that the movement from \(\Phi>0\) to consciousness depends on this constitutive thesis.

The continuous-to-discrete transition is another critical point. The master key begins with stochastic differential equations and a stationary density, then derives a discrete transition probability matrix over a minimal timescale \(\Delta t\). Any such mapping requires choices: how continuous states are binned, which variables are included, how interventions are represented, and which temporal interval defines a transition. Different choices can produce different TPMs and different values of \(\Phi\).

This dependence does not make the measure useless. All empirical measurement depends on grain. But a robust claim should survive a reasonable range of grains. Let \(\Phi_{\ell,\tau}\) denote integrated information at spatial or state-space grain \(\ell\) and temporal grain \(\tau\). A candidate intellecton should exhibit a stable region in which causal integration remains positive and structurally similar:

\[
\mathcal{R}_{\Phi}
=
\int_{\ell\in L}\int_{\tau\in T}
\mathbf{1}\!\left[\Phi_{\ell,\tau}>\epsilon\right]
w(\ell,\tau)\,d\tau\,d\ell.
\]

Here \(\epsilon\) excludes numerical artifacts and \(w\) weights scientifically relevant scales. The purpose is not to replace IIT with an arbitrary integral, but to express a robustness demand. If \(\Phi>0\) only under one fragile binning, it provides weak evidence for an intrinsic unit. If integration persists across nearby grains and perturbations, the claim is stronger.

Intervention robustness is equally important. A recurrent covariance structure may disappear when common inputs are controlled or when connections are perturbed. Direct stimulation, lesion, and causal-discovery methods can test whether the internal system has the proposed cause-effect power. The relevant question is not merely whether intact activity is integrated, but whether partitioning interventions degrade the system in the specific ways predicted by its cause-effect model.

This requirement aligns IIT with the autonomy framework developed earlier. An autonomous system maintains its boundary under environmental perturbation. An integrated system preserves a distinctive internal causal organization under some perturbations while being selectively disrupted by partitions that sever constitutive interactions. Together these properties support a richer intellecton concept: a process that maintains both its boundary and its internal causal unity.

Yet integration and autonomy can diverge. A crystal may exhibit tightly constrained global structure without adaptive autonomy. A bureaucracy may be autonomous in maintaining its institutional boundary while remaining causally decomposable in many operations. A seizure may produce highly synchronized neural activity but diminish differentiated conscious experience. These cases show why no single scalar measure can carry the full explanatory burden.

The seizure case is especially instructive. High synchronization can reduce informational differentiation even while increasing correlation. A theory of consciousness must account for the balance between integration and differentiation. IIT explicitly aims to do so, but a loose appeal to recurrence or covariance does not. Volume 2 should therefore avoid treating strong recurrent loops as a direct proof of \(\Phi>0\) without calculating the relevant cause-effect structures and partitions.

There is also a problem of exclusion. If overlapping neural subsets each possess positive integration, which subset constitutes the subject? IIT addresses this with maximality or exclusion principles, but those principles are controversial and sensitive to measurement. The Markov blanket might assist by identifying a candidate boundary, while IIT identifies an integrated interior. However, the two boundaries may not coincide. The maximally integrated complex could cross a proposed blanket, or a blanket could contain multiple complexes.

This mismatch is not merely technical. It tests the proposed synthesis. If the free-energy partition and the IIT complex systematically diverge, then the theory cannot simply declare them two descriptions of one intellecton. It must explain why one boundary should dominate or how multiple organizational layers relate. Conversely, empirical convergence between stable blankets and maximally integrated complexes would be significant evidence for the framework.

The proper relationship is therefore one of mutual constraint. Markov blanket analysis proposes candidate agent boundaries based on mediated coupling. Autonomy analysis tests whether those boundaries are actively maintained. IIT analysis tests whether the internal dynamics constitute an irreducible causal whole. No component is reducible to another, and agreement among them is an empirical achievement.

This layered interpretation preserves the strongest insight of Volume 2 while avoiding equivocation. The intellecton is not conscious merely because its variables are conditionally independent of an environment. Nor is it conscious merely because its covariance matrix is recurrent. It becomes a serious candidate for subjecthood when a stable, self-maintaining boundary encloses a robustly integrated cause-effect structure whose organization explains behavior and persists across relevant scales.

Even then, the philosophical interpretation remains open. The evidence may support IIT's identity claim, an enactive theory of lived autonomy, or a more modest structural correlate of consciousness. Scientific rigor does not require prematurely resolving this debate. It requires specifying which observations would favor each account. Volume 2's synthesis is most valuable when it generates such discriminating tests rather than treating formal correspondence as metaphysical closure.

\subsection{Integration in Context}

Every causal system depends on background conditions held fixed by an analysis. A cortical microcircuit's repertoire depends on metabolism, neuromodulation, and surrounding activity. No intervention is literally background-free. The relevant question is whether the proposed complex retains explanatory autonomy across a justified range of backgrounds. Robustness across backgrounds should accompany robustness across grains.

There is also tension between maximal integration and adaptive modularity. Biological systems benefit from being partly decomposable: modules limit damage, permit specialization, and support flexible recombination. A system that maximized coupling without constraint could become brittle. Conscious organization may require a regime between fragmentation and total coupling. This supports studying integration profiles rather than assuming that a larger scalar is always superior.

Integration must preserve differentiated roles. A symmetric measure can conceal asymmetries important for agency, including sensory influence and active control. A credible intellecton should exhibit a stable causal core, articulated internal roles, and predictable degradation under targeted partitions. It should not qualify merely because every component correlates with every other. This is more demanding than the master-key inference, but it makes the claim of intrinsic organization substantially stronger.

The most revealing experiments will compare systems with similar recurrence but different causal organization. Recurrent random networks, trained predictive circuits, anesthetized cortex, and waking cortex may all display feedback, yet their intervention repertoires should differ. If the Volume 2 synthesis is correct, the relevant intellecton candidates will combine differentiated integration with maintained boundaries and adaptive action. Recurrence alone will fail to predict the full pattern.

This comparison also guards against a common mistake in consciousness science: choosing a metric because it correlates with the target in familiar cases, then treating the metric as constitutive. A serious constitutive proposal must explain difficult cases and survive manipulations designed to dissociate the measure from reports and behavior. The layered approach makes such dissociations central rather than inconvenient. It asks not whether one number wins, but how multiple organizational properties jointly constrain the space of possible subjects.
