The Mind's Arrows contains a few extended essays united by a proposition: psychology should use graphical causal models. Glymour begins with human causal inference, surveys cognitive neuropsychology, and finally indicts most of social statistics. By turns the book is introductory or advanced, minutely detailed or broadly impressionistic.

The first half moves from developmental psychology and causal discovery to adult judgments of causation, promoting Bayesian networks as the proper representation for human learning of causal relations. So much is largely available in other papers,Footnote ¹ but is presented here somewhat more broadly.

More ambitiously, the second part argues that psychological models from Wernicke and Freud onwards have been causal Bayes nets.

Using Bayes nets, Glymour explores what we can (and cannot) learn from case studies, group data, and lesioning neural nets. Although the results are ‘elementary’ applications of the basic theory of causal models, they surprise.

The final section attacks explicitly acausal methods like factor analysis and regression. The critique is strongest in the final chapter—an extended version of Glymour's well-known attack of Reference Herrnstein and MurrayThe Bell Curve (Glymour Reference Glymour1998).

In all three sections, Glymour argues that existing models and methods improperly handle what Bayes netters call ‘d-separation’—the conditions under which variables become uncorrelated. Most notably, they fail to model dependencies induced by conditioning on common effects.

First, are Bayes nets the arrows of the mind? Do graphical models capture the structure of human causal knowledge? Glymour's answer appears essentially to be, Yes. At least they alone seem to show how we can possibly learn causal relations. Glymour admits, however, that existing algorithms are poor models of how we do learn them.

Glymour opens by reinterpreting early childhood learning as learning causal structure. Chapter 3 introduces causal Bayes nets (CBNs) and the causal Markov condition, shows that CBNs can be learned from observation and experiment, and describes preliminary experiments supporting the idea that humans use the Markov property to learn and organize causal knowledge. People cannot plausibly use the processing-intensive algorithms in AI, but Glymour suggests that if we assume our own actions are free with respect to the effects we create, then we might be able to learn causal structure far more efficiently. Glymour's discussion of concept formation is less convincing. It establishes only that concept formation could possibly be modeled in Bayes nets.

Section 2 grounds the book. As a survey, it aspires to be neither complete nor representative. It omits ‘mechanism’ approaches such as that championed by Ahn and Bailenson (Reference Ahn and Bailenson1996) and Ahn et al. (Reference Ahn1995), and begins the covariation account not with Kelley (Reference Kelley1973), but with Baker et al. (Reference Baker1993). But then, Glymour wants to know how we even learn what a mechanism is, and Baker's theory nicely exemplifies the errors of the covariation approach.

Covariation accounts essentially pick a measure of causal strength as normative, and see how well humans approximate it. One obvious measure is ΔP, the change in probability of an effect E due to a cause C. $\Delta P=P(E\vert C) -P(E\vert \neg C) $ . As Glymour notes, variations on ΔP abound in the literature.

Glymour argues that rather than estimating causal strength, subjects are finding the proper causal structure to explain the dependencies and independencies. And because the real causal model may involve colliders (shared effects), causal Markov learning is the better tool. Glymour's analysis of Baker's camouflage experiment is strongly recommended.

Glymour treats one causal attribution theory at length. Patricia Cheng's mathematical theory of causal judgments (Cheng Reference Cheng1997; Glymour and Cheng Reference Glymour, Cheng, Oaksford and Chater1998) assumes that causal strength is a theoretical value. Although not directly observable, with some plausible assumptions, causal strengths can be estimated rather easily from frequencies.

Embedding Cheng's model in Bayes nets, Glymour shows how to extend it to more complicated graphs. Even so, Glymour points out that Cheng's theory is largely about estimating parameters given a known graph. According to Tenenbaum and Griffiths (Reference Tenenbaum, Griffiths, Leen, Dietterich and Tresp2001), subjects in her experiments are not estimating the strength of arc $C\rightarrow E$ given the background B, but choosing between two models, $E\leftarrow B$ and $C\rightarrow E\leftarrow B$ . Tenenbaum and Griffith's theory fared better overall, but there were cases where Cheng's dominated.

Metaphysically, Cheng's theory is very different from the usual interpretation of probabilistic causation. Normally we take probabilistic causation to mean determination of probabilities. But Cheng's causal power of C to cause E is the probability that C causes E, given $C=1$ —as if ‘causing’ is an extra switch. That distinction founds the recent strident debate between Cartwright on the one hand and Hausman and Woodward on the other. (See, for example, Hausman and Woodward Reference Hausman and Woodward2004.)

Glymour's discussion of ‘backward blocking’ is overly complicated. The main point is that psychologists have dismissed it as a bias, but CBN learning shows it to be normative.

The lesson from Part 1 is that previous theories ignored the dependencies induced by conditioning on colliders or their descendants, and therefore made mistakes. The lesson for Part 2 is largely the same: the usual methods of statistical inference and analysis also make no allowance for colliders, and therefore make the same mistakes.

In Part 3, Glymour argues that cognitive models are really graphical causal models, and that lesion-induced malfunctions should correspond to severing arcs or damaging nodes in the Bayes net. He then proves that with the usual simple assumptions about the parts of those models, different patterns of deficits could easily select among six plausible models of aphasias. However, if some capacities require more resources than others, we quickly lose the ability to rule out models.

If we add noisy data, the situation gets worse.

However, prior knowledge often does constrain theory choice, and Glymour argues that lesioning neural nets has explanatory power, because the independencies in the original graph will always be a subset of those in the lesioned graph.

The final chapter expands Glymour's well-known critique of The Bell Curve (Herrnstein and Murray Reference Herrnstein and Murray1994). Glymour does not target the authors, but rather the methods of social science, especially factor analysis and regression. In his view these procedures at best find the right parameters for the wrong models. In contrast, the AI literature has concentrated on algorithms that find the right model, partly by attending to dependencies induced by conditioning on colliders.

There are more cohesive, more introductory, and more thorough introductions to causal Bayesian networks. The Mind's Arrows, however, is useful reading for psychologists, philosophers of psychology, and perhaps philosophers of mind. Those unfamiliar with Cheng's work will appreciate Glymour's presentation. That and its broad view of the role of CBNs in neuropsychology are the book's main contributions.