We highlight methodological and theoretical limitations of the authors' Dirac formalism and suggest the von Neumann open systems approach as a resolution. The open systems framework is a generalization of classical probability and we hope it will allow cognitive scientists to extend quantum probability from perception, categorization, memory, decision making, and similarity judgments to phenomena in learning and development.

The “Orch OR” theory suggests that quantum computations in brain neuronal dendritic-somatic microtubules regulate axonal firings to control conscious behavior. Within microtubule subunit proteins, collective dipoles in arrays of contiguous amino acid electron clouds enable “quantum channels” suitable for topological dipole “qubits” able to physically represent cognitive values, for example, those portrayed by Pothos & Busemeyer (P&B) as projections in abstract Hilbert space.

According to the foundations of economic theory, agents have stable and coherent “global” preferences that guide their choices among alternatives. However, people are constrained by information-processing and memory limitations and hence have a propensity to avoid cognitive load. We propose that this in turn will encourage them to respond to “local” preferences and goals influenced by context and memory representations.

Pothos & Busemeyer's (P&B's) query about whether quantum probability can provide a foundation for the cognitive modeling embodies so many underlying implications that the subject is far from exhausted. In this brief commentary, however, I suggest that the conceptual thresholds of the meaningful learning give rise to a typical Boltzmann's weighting measure, which indicates a statistical verisimilitude of quantum behavior in the human cognitive ensemble.

Typically, human decision making is emotionally “hot” and does not conform to “cold” classical probability (CP) theory. As quantum probability (QP) theory emphasises order, context, superimposition states, and nonlinear dynamic effects, one of its major strengths may be its power to unify formal modeling and realistic psychological theory (e.g., information uncertainty, anxiety, and indecision, as seen in the Prisoner's Dilemma).

We agree with Pothos & Busemeyer (P&B) that formal tools can be fruitfully employed to model human judgment under uncertainty, including well-known departures from principles of classical probability. However, existing findings either contradict P&B's quantum probability approach or support it to a limited extent. The conjunction fallacy serves as a key illustration of both kinds of problems.

Quantum probability models may supersede existing probabilistic models because they account for behaviour inconsistent with classical probability theory that are attributable to normal limitations of cognition. This intriguing position, however, may overstate weaknesses in classical probability theory by underestimating the role of current knowledge states and may under-employ available knowledge about the limitations of cognitive processes. In addition, flexibility in model specification has risks for the use of quantum probability.

In important ways, Clark's “hierarchical prediction machine” (HPM) approach parallels the research agenda we have been pursuing. Nevertheless, we remain unconvinced that the HPM offers the best clue yet to the shape of a unified science of mind and action. The apparent convergence of research interests is offset by a profound divergence of theoretical starting points and ideal goals.

Life is preserved and enhanced by coordinated selectivity in local neural circuits. Narrow receptive-field selectivity is necessary to avoid the curse-of-dimensionality, but local activities can be made coherent and relevant by guiding learning and processing using broad coordinating contextual gain-controlling interactions. Better understanding of the functions and mechanisms of those interactions is therefore crucial to the issues Clark examines.

It is often helpful to distinguish between a theory (Marr's computational level) and a specific implementation of that theory (Marr's physical level). However, in the target article, a single implementation of predictive coding is presented as if this were the theory of predictive coding itself. Other implementations of predictive coding have been formulated which can explain additional neurobiological phenomena.

Clark expresses reservations about Friston's reductive interpretation of action-oriented predictive processing (AOPP) models of cognition, but he doesn't link these reservations to specific alternatives. Neuroeconomic models of sub-cognitive reward valuation, which, like AOPP, integrate attention with action based on prediction error, are such an alternative. They interpret reward valuation as an input to neocortical processing instead of reducing it.

The brain is involved in theory-laden cognitive processes. But there are two different theory-laden processes. In cases where the theory is based on facts, more facts can either falsify or confirm a theory. In cases where the theory is about the choice of a benchmark or a standard, more facts can only make a theory either more or less warranted.

While the target article provides a glowing account for the excitement in the field, we stress that hierarchical predictive learning in the brain requires sparseness of the representation. We also question the relation between Bayesian cognitive processes and hierarchical generative models as discussed by the target article.

The sensory cortex has been interpreted as coding information rather than stimulus properties since Sokolov in 1960 showed increased response to an unexpected stimulus decrement. The motor cortex is also organized around expectation, coding the goal of an act rather than a set of muscle movements. Expectation drives not only immediate responses but also the very structure of the cortex, as demonstrated by development of receptive fields that mirror the structure of the visual world.

A behavioral drive directed solely at minimizing prediction error would cause an agent to seek out states of unchanging, and thus easily predictable, sensory inputs (such as a dark room). The default to an evolutionarily encoded prior to avoid such untenable behaviors is unsatisfying. We suggest an alternate information theoretic interpretation to address this dilemma.

The Bayesian brain hypothesis provides an attractive unifying framework for perception, cognition, and action. We argue that the framework can also usefully integrate interoception, the sense of the internal physiological condition of the body. Our model of “interoceptive predictive coding” entails a new view of emotion as interoceptive inference and may account for a range of psychiatric disorders of selfhood.

A quantitative theory of reproductive decisions (Gowaty & Hubbell 2009) says that individuals use updated priors from constantly changing demographic circumstances to predict their futures to adjust actions flexibly and adaptively. Our ecological/evolutionary models of ultimate causes seem consistent with Clark's ideas and thus suggest an opportunity for a unified proximate and ultimate theory of Bayesian animal brains, senses, and actions.

Why do brains have so many connections? The principles exposed by Andy Clark provide answers to questions like this by appealing to the notion that brains distil causal regularities in the sensorium and embody them in models of their world. For example, connections embody the fact that causes have particular consequences. This commentary considers the imperatives for this form of embodiment.

A radical interpretation of the predictive coding approach suggests that the mind is “seamless” – that is, that cancellation of error signals can propagate smoothly from highest to lowest levels of the control hierarchy, dissolving a distinction between belief and perception. Delusions of alien control provide a test case. Close examination suggests that while they are evidence of predictive coding within the cortex, they are not evidence for the seamless interpretation.

Clark advertises the predictive coding (PC) framework as applying to a wide range of phenomena, including attention. We argue that for many attentional phenomena, the predictive coding picture either makes false predictions, or else it offers no distinctive explanation of those phenomena, thereby reducing its explanatory power.