There is a paradox at the heart of cognitive science. Human beings (and some animals) seem to have abstract, hierarchical, structured representations of the world. These representations allow us to make a wide range of novel predictions and produce a wide range of novel behaviors. And these representations seem to be accurate – they capture the structure of the world, and they improve as we learn more about the world. But the information provided by our senses, our one direct source of evidence about the world, is very different from these representations. It is a noisy, probabilistic, and chaotic set of contingencies among specific concrete inputs, apparently far removed from the true structure of the world itself.

In the past 2000 years of western philosophy, and the past 50 years of cognitive science, there have been two very different approaches to resolving this paradox. One tradition (nativist, rationalist, propositional, “East Coast”) argues that cognition does indeed involve abstract, hierarchical, structured representations. It only appears, however, that we infer these representations from the evidence of our senses. In fact, these representations must be there innately, and are only slightly modified by learning. Small details may be filled in by experience, or alternative parameters may be triggered by different experiences. But the fundamental structure of the representations is there from the start. The alternative tradition (empiricist, associationist, connectionist, “West Coast”) argues that it only appears that we have abstract, hierarchical, structured representations. In fact, our novel predictions and behaviors are based on the complex contingency patterns among individual sensory inputs, patterns that we extract through associative mechanisms.

There have sometimes been arguments for a kind of dismissive co-existence between these two approaches. The rationalists say that most cognition is the result of innate abstract representations, but mere associationist processes may play a role in very automatic, low-level kinds of behavior. The empiricists say that associations are responsible for most cognition, but there may be explicit, conscious, and sophisticated propositional reasoning layered on top. These two-process views both suggest that there is some relationship between the sophistication, power, and likely domain of the representations and their computational character – associations are “low-level” and propositions are “high-level.” They just disagree on whether most cognition falls on one side or the other.

The target article is in this general tradition, though it endorses the idea that propositional representations can account for even classical associationist phenomena, such as conditioning. But Mitchell et al. also argue that the propositional representations they endorse are resource-intensive, subject to conscious reflection, and can be understood as beliefs – they are “high-level.”

In cognitive development, going back to Piaget, there has been a long tradition of trying to elude the rationalist/empiricist dichotomy with “constructivist” theories. A constructivist account should allow us to actually infer highly structured representations accurately from patterns of contingency in the data. The most recent constructivist project has been the “theory theory” – the idea that children develop intuitive theories from evidence in the way that scientists do. But the theory theory, like earlier constructivist theories, has suffered from a lack of computational precision and specific learning mechanisms.

However, in the last 10 years or so there has been increasing excitement about a new theoretical view that provides a computationally rigorous basis for the constructivist project. This approach might be called “rational probabilistic modeling.” This view, unlike classical empiricist views, proposes structured, abstract, hierarchical representations. But unlike classical rationalist views, it sees those representations as probabilistic and learned. Moreover, the kind of learning that is involved is not the simple method of association, but is a form or rational probabilistic induction, often involving Bayesian methods. This general theoretical approach has been applied to a very wide range of kinds of cognition, including “low-level” automatic cognition such as vision, motor control, and syntax, as well as “high-level” conscious cognition such as category and word learning and causal learning. (For some recent examples and reviews of this work see Chater & Manning Reference Chater and Manning2006; Chater et al. Reference Chater, Tenenbaum and Yuille2006; Gopnik & Schulz Reference Gopnik and Schulz2004; Gopnik & Tenenbaum Reference Gopnik and Tenenbaum2007; Gopnik et al. Reference Gopnik, Glymour, Sobel, Schulz, Kushnir and Danks2004; Reference Gopnik and Schulz2007; Regier & Gahl Reference Regier and Gahl2004, Tenenbaum et al Reference Tenenbaum, Griffiths and Kemp2006; Xu & Tenenbaum Reference Xu and Tenenbaum2007; Yuille & Kersten Reference Yuille and Kersten2006).

Causal knowledge and learning, one of the foci of the target article, has been a particularly fruitful venue for these new theories. In our own work, we have shown that even very young children represent the causal structure of the world and reason about those representations in a rational way, in accordance with the principles of causal Bayes nets (Gopnik et al. Reference Gopnik, Glymour, Sobel, Schulz, Kushnir and Danks2004). As Mitchell et al. mention, this “causal Bayes net” approach seems to be very convergent with the approach that is presented here. But there is one important difference. The computations that are involved in rational probabilistic models have no necessary link to issues of high- versus low-level, animal versus human, conscious versus unconscious, or resource-dependent versus automatic.

Indeed, many of these models have their conceptual roots in vision science. At least since Irv Rock and arguably since Helmholz, vision scientists have seen vision as a process of hypothesis generation and testing. The visual system inferentially reconstructs an accurate representation of the visual world; it solves “the inverse problem.” We know that these inferential processes are much more constrained and complex than simple associations, and they have been well-modeled as a kind of Bayesian inference. But they are unconscious, automatic, and low-level (see Yuille & Kersten Reference Yuille and Kersten2006).

Thinking about the issue developmentally also makes this point vivid. We know that even very young babies are capable of sophisticated kinds of statistical and inductive reasoning – reasoning capacities that go far beyond simple associative mechanisms. In fact, arguably infants have more powerful learning capacities than adults. It seems unlikely, however, that infant resource allocation or consciousness parallels that of adults, though undoubtedly infants are conscious. From a computational point of view, propositional reasoning does indeed go all the way down, as Mitchell et al. argue. The same kinds of rational computations play an essential role in cognition from vision to causation, and from infancy to adult science. But this is orthogonal to the question of how those computations are related to resource management or phenomenology.