Setting up “Bayesian Fundamentalism” as a straw man for criticism, which is what Jones & Love (J&L) do in their target article, is counterproductive for two related reasons. The first reason is both substantive and didactic. The only viable general formulation of perception, cognition, and action is statistical inference under uncertainty, which proceeds from prior experience to probabilistic models that can support principled decision-making and control, and thereby make informed behavior possible. Branding the realization that the modus operandi of any mind is fundamentally Bayesian as “fundamentalist” is akin to condemning Hamiltonian mechanics for its reliance on a single overarching principle. This is not a good idea, if even a single reader decides after reading the target article that some kind of pluralism ideal should trump a genuine insight into the workings of the world.

In the Enlightenment-era natural philosophy and in the sciences that grew out of it, the insight that singles out statistics as the only possible conceptual foundation for a sound theory of how the mind works can be traced back to Hume's Treatise: “All knowledge resolves itself into probability” (Hume Reference Hume1740, Part IV, sect. I). More recently, J. J. Gibson (Reference Gibson1957) noted in a book review, from which we borrowed the title of the present commentary, that “perception is always a wager.” By now, it has become incontrovertibly clear that not only perception, but thinking and action too, indeed take the form of statistical inference (Glimcher et al. Reference Glimcher, Camerer, Poldrack and Fehr2008; Heit Reference Heit2000; Knill & Richards Reference Knill and Richards1996; Körding & Wolpert Reference Körding and Wolpert2006; for a brief overview, see Chater et al. Reference Chater, Tenenbaum and Yuille2006).

Statistical inference is indispensable in cognition because informed behavior requires a degree of foresight; that is, anticipating and planning for the future. Foresight, in turn, is possible because the world is well-behaved (the past resembles the future often enough to support learning from experience), but can be only probabilistic because the regularities in the world's behavior manifest themselves as merely statistical patterns in sensorimotor data (Edelman Reference Edelman2008b).

The rich theory of statistical learning from experience developed over the past several decades, all of which ultimately relies on this view of cognition, is very diverse. Many of the techniques that it encompasses have been inspired by particular classes of problems, or solution methods, that on the face of it have no bearing on the Bayesian debate. For instance, insofar as perception is ill-posed in the formal sense that a given problem typically admits multiple solutions, it needs to be regularized by adding extra constraints (Poggio Reference Poggio1990; cf. Tikhonov & Arsenin Reference Tikhonov and Arsenin1977). Likewise, modeling problems in motor control can be approached via function approximation (Mussa-Ivaldi & Giszter Reference Mussa-Ivaldi and Giszter1992) and control theory (Kawato Reference Kawato1999).

At the same time, because the normative way of performing statistical inference is Bayesian (Howson & Urbach Reference Howson and Urbach1991; Schervish Reference Schervish1995; Wasserman Reference Wasserman2003), one would expect that all such methods would ultimately reduce to Bayesian inference, and indeed they do. In particular, perceptual regularization can be given a statistical formulation (Marroquin et al. Reference Marroquin, Mitter and Poggio1987), and so can function approximation – be it classification or regression (Bishop Reference Bishop2006; Hastie et al. 2003/2009). More generally, various popular theoretical approaches in cognitive science, too numerous to mention here, which may appear refreshingly pluralistic when contrasted to the big bad Bayes, do in fact draw their justification from Bayesian considerations (Bishop Reference Bishop2006; Hastie et al. 2003/Reference Hastie, Tibshirani and Friedman2009).

This brings us to the second reason to shun the distinction between Bayesian Fundamentalism and Bayesian Enlightenment, which is that the latter builds upon the former rather than supplanting it. It used to be possible to produce good work in computer vision or natural language engineering without giving much thought to the ultimate justification of the methods one uses, and it may still be the case in some isolated corners of those fields. Likewise, in cognitive modeling, where theoretical confusion – especially conflation of Marr's levels of understanding – is often endemic (cf. Edelman Reference Edelman2008a; Reference Edelman2008c), modelers may happily use “backpropagation networks” without giving much thought to the fact that they are doing function approximation, which in turn rests on Bayesian principles. Although it is always good to know exactly why your model works as it does (or does not), in practice focusing on the more problematic levels, such as coming up with a good theory of the hypothesis space that applies to the learning task at hand, may actually lead to progress that would elude someone who is concerned exclusively with the fundamentals.

Thus, Bayesian theorists worth their salt (do we need to worry about others?) know that a full-fledged theory has many aspects to it that must be addressed, including, in addition to the just-mentioned issue of the structure of the hypothesis space, various questions regarding the nature of inference and decision-making algorithms that have to be computationally tractable and biologically feasible. Crucially, they also know that the very need for statistical inference and the constraint of having to deal incrementally with a stream of environmental data are non-negotiable. If this earns them the label of fundamentalism, we should all be eager to share it with them, normatively. After all, we owe to it our survival.