Jones & Love (J&L) contend that the Bayesian approach should integrate process constraints with abstract computational analysis. We agree, but argue that the fundamentalist/enlightened dichotomy is a false one: Enlightened research is deeply intertwined with – and to a large extent is impossible without – the basic, fundamental work upon which it is based.

Rather than worrying about Bayesian Fundamentalists, I suggest that our real concern should be with Mechanistic Fundamentalists; that is, those who believe that concrete, but frequently untestable mechanisms, should be at the heart of all cognitive theories.

Describing a cognitive system at a mechanistic level requires an engineering task analysis. This involves identifying the task and developing models of possible solutions. Evolutionary psychology and Bayesian modeling make complimentary contributions: Evolutionary psychology suggests the types of tasks that human brains were designed to solve, while Bayesian modeling provides a rigorous description of possible computational solutions to such problems.

Rational models vary in their goals and sources of justification. While the assumptions of some are grounded in the environment, those of others – which I label probabilistic models – are induced and so require more traditional sources of justification, such as generalizability to dissimilar tasks and making novel predictions. Their contribution to scientific understanding will remain uncertain until standards of evidence are clarified.

We distinguish between literal and metaphorical applications of Bayesian models. When intended literally, an isomorphism exists between the elements of representation assumed by the rational analysis and the mechanism that implements the computation. Thus, observation of the implementation can externally validate assumptions underlying the rational analysis. In other applications, no such isomorphism exists, so it is not clear how the assumptions that allow a Bayesian model to fit data can be independently validated.

The breadth-first search adopted by Bayesian researchers to map out the conceptual space and identify what the framework can do is beneficial for science and reflective of its collaborative and incremental nature. Theoretical pluralism among researchers facilitates refinement of models within various levels of analysis, which ultimately enables effective cross-talk between different levels of analysis.

A central claim of Jones & Love's (J&L's) article is that Bayesian Fundamentalism is empirically unconstrained. Unless constraints are placed on prior beliefs, likelihood, and utility functions, all behaviour – it is proposed – is consistent with Bayesian rationality. Although such claims are commonplace, their basis is rarely justified. We fill this gap by sketching a proof, and we discuss possible solutions that would make Bayesian approaches empirically interesting.

In advocating Bayesian Enlightenment as a solution to Bayesian Fundamentalism, Jones & Love (J&L) rule out a broader critique of rationalist approaches to cognition. However, Bayesian Fundamentalism is merely one example of the more general phenomenon of Rationalist Fundamentalism: the tendency to characterize human judgments as rational and optimal in a post hoc manner, after the empirical data are already known.

Mathematical developments in probabilistic inference have led to optimism over the prospects for Bayesian models of cognition. Our target article calls for better differentiation of these technical developments from theoretical contributions. It distinguishes between Bayesian Fundamentalism, which is theoretically limited because of its neglect of psychological mechanism, and Bayesian Enlightenment, which integrates rational and mechanistic considerations and is thus better positioned to advance psychological theory. The commentaries almost uniformly agree that mechanistic grounding is critical to the success of the Bayesian program. Some commentaries raise additional challenges, which we address here. Other commentaries claim that all Bayesian models are mechanistically grounded, while at the same time holding that they should be evaluated only on a computational level. We argue this contradictory stance makes it difficult to evaluate a model's scientific contribution, and that the psychological commitments of Bayesian models need to be made more explicit.