We argue that Schilbach et al. have neglected an important part of the social neuroscience literature involving participants in social interactions. We also clarify some part of the models the authors discussed superficially. We finally propose that social neuroscience should take into consideration the effect of being observed and the complexity of the task as potentially influencing factors.

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.

Classical probability models of incentive response are inadequate in “large worlds,” where the dimensions of relative risk and the dimensions of similarity in outcome comparisons typically differ. Quantum probability models for choice in large worlds may be motivated pragmatically – there is no third theory – or metaphysically: statistical processing in the brain adapts to the true scale-relative structure of the universe.

In this response we address additions to as well as criticisms and possible misinterpretations of our proposal for a second-person neuroscience. We map out the most crucial aspects of our approach by (1) acknowledging that second-person engaged interaction is not the only way to understand others, although we claim that it is ontogenetically prior; (2) claiming that spectatorial paradigms need to be complemented in order to enable a full understanding of social interactions; and (3) restating that our theoretical proposal not only questions the mechanism by which a cognitive process comes into being, but asks whether it is at all meaningful to speak of a mechanism and a cognitive process when it is confined to intra-agent space. We address theoretical criticisms of our approach by pointing out that while a second-person social understanding may not be the only mechanism, alternative approaches cannot hold their ground without resorting to second-person concepts, if not in the expression, certainly in the development of social understanding. In this context, we also address issues of agency and intentionality, theoretical alternatives, and clinical implications of our approach.

Pothos & Busemeyer (P&B) argue that classical probability (CP) fails to describe human decision processes accurately and should be supplanted by quantum probability. We accept the premise, but reject P&B's conclusion. CP is a prescriptive framework that has inspired a great deal of valuable research. Also, because CP is used across the sciences, it is a cornerstone of interdisciplinary collaboration.

Quantum probability (QP) theory can be seen as a type of vector symbolic architecture (VSA): mental states are vectors storing structured information and manipulated using algebraic operations. Furthermore, the operations needed by QP match those in other VSAs. This allows existing biologically realistic neural models to be adapted to provide a mechanistic explanation of the cognitive phenomena described in the target article by Pothos & Busemeyer (P&B).

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.

The attempt to employ quantum principles for modeling cognition has enabled the introduction of several new concepts in psychology, such as the uncertainty principle, incompatibility, entanglement, and superposition. For many commentators, this is an exciting opportunity to question existing formal frameworks (notably classical probability theory) and explore what is to be gained by employing these novel conceptual tools. This is not to say that major empirical challenges are not there. For example, can we definitely prove the necessity for quantum, as opposed to classical, models? Can the distinction between compatibility and incompatibility inform our understanding of differences between human and nonhuman cognition? Are quantum models less constrained than classical ones? Does incompatibility arise as a limitation, to avoid the requirements from the principle of unicity, or is it an inherent (or essential?) characteristic of intelligent thought? For everyday judgments, do quantum principles allow more accurate prediction than classical ones? Some questions can be confidently addressed within existing quantum models. A definitive resolution of others will have to anticipate further work. What is clear is that the consideration of quantum cognitive models has enabled a new focus on a range of debates about fundamental aspects of cognition.