Jones & Love (J&L) suggest that we should reject Bayesian Fundamentalism in favour of Bayesian Enlightenment, thus combining Bayesian analysis with mechanistic-level models. This raises two questions: Who are these Bayesian Fundamentalists and what is a mechanistic-level model?
First, let us go in search of Bayesian Fundamentalists. As I read the target article, I began to wonder how it could be that I’d never encountered a Bayesian Fundamentalist. If these ideas are so pervasive, then surely J&L could quote at least one author who has made a clear statement of the Bayesian Fundamentalist programme? From the first line of the abstract it appears that the main proponent of Bayesian Fundamentalism must be Anderson (Reference Anderson1990) with his Rational Analysis framework, and his suggestion that behaviour can often be explained by assuming that it is optimally adapted to its purpose and the environment. In criticising rational analysis, J&L argue that “Rather than the globally optimal design winning out, often a locally optimal solution . . . prevails. . . . Such non-behavioral factors are enormously important to the optimization process, but are not reflected in rational analyses, as these factors are tied to a notion of mechanism, which is absent in rational analyses” (sect. 5.3, paras. 3 and 5).
A similar concern about the limitations of rational analysis can be found in the following quotation: “My guess is that short-term memory limitations do not have a rational explanation. . . . [T]hey reflect the human trapped on some local optimum of evolution” (Anderson Reference Anderson1990, pp. 91–92). These cautionary words on the dangers of relying entirely on rational explanations were written by the arch-Fundamentalist himself. Is there really a difference, then, between these two positions?
Let's now move on to the second question: What is a mechanistic-level model? If we need to develop mechanistic models, then we need to know what such entities might look like. Nowhere do J&L define what they mean by a mechanistic-level theory. Perhaps we can get some clues from their other writings. Sakamoto et al. (Reference Sakamoto, Jones and Love2008) describe a “mechanistic model that principally differs from the aforementioned rational models in that the mechanistic model does not have perfect memory for the training items” (p. 1059). But here the mechanism is simply a specification of the computations that the model performs. That is, although the model is not as abstract as Marr's (Reference Marr1982) computational level, it is not as concrete as his algorithmic level, and certainly says nothing about implementation.
One might call this a process model, or a functional-level explanation. It specifies the functions, computations, and processes in a way that allows the model to be implemented as a computer program and to simulate behavioural data. The program performing the simulations must compute mathematical functions such as square roots, but presumably the exact algorithm or implementation used to compute a square root is not part of the theory. If this kind of functional explanation is indeed what J&L mean by a mechanistic theory, then I am wholeheartedly in favour of their approach. But I am not entirely sure that this is exactly what they have in mind. Elsewhere they talk about mechanistic issues “of representation, timing, capacity, anatomy, and pathology” (sect. 4.1, para. 3). If this is simply to echo Marr in wishing to bring together multiple levels of description and explanation, then few would disagree. However, I worry that J&L may be encouraging Mechanistic Fundamentalism: the belief that a good cognitive theory must do more than just describe processes and computations, and must also specify concrete mechanisms in terms of mechanical components such as nodes, activations, weights, and buffers. This view easily leads to the illusion of mechanism, whereby the mechanisms are mistaken for explanations.
Let's illustrate this by considering interactive activation networks, which are still at the core of many contemporary models. In these networks the activation of each node increases as a result of weighted input, and decreases as a result of inhibition from competing nodes. Activations roughly reflect the evidence for each node or hypothesis as a proportion of the evidence for all hypotheses. Although it is hard to specify exactly what computational function such networks perform, the general principle seems very much like Bayes’ theorem. However, for many psychologists the network model is to be preferred over a Bayesian explanation because the former seems to say something about mechanism. But this is the illusion of mechanism. Unless the precise implementation of the network is intended as a theoretical claim about how processes are implemented in the brain, the mechanism itself makes no contribution to the explanation. If it happened to be the case that the data could be fit by any “mechanism” that could compute Bayes’ theorem, then the explanation would be that the system behaves in an approximately optimal manner.
This immediately raises the problem of model equivalence. Unless candidate mechanisms produce testably different behaviours, the implementational details are not part of the explanation. To quote yet again from Anderson (Reference Anderson1990), “If two theorists propose two sets of mechanisms in two architectures that compute the same function, then they are proposing the same theory” (p. 26). One might protest that at least when studying the mind and the brain, there will always be some neurobiological data that could definitively distinguish between alternative mechanisms. Even ignoring the fact that such a view would imply that there is no distinctly psychological level of explanation, in practice such optimism is misplaced. Even the most productive cognitive theories rarely make any definitive commitment to implementational details. Again, this is apparent in connectionist models based on artificial neurons whose properties bear little resemblance to real neurons. But connectionist modellers are fully aware of this deliberate limitation, and it is hard to see that any of the insights from connectionist modelling are undermined by this simplification.
In conclusion, then, I suggest that most Bayesians are already enlightened; it is the Mechanistic Fundamentalists we should worry about.
You have
Access
Jones & Love (J&L) suggest that we should reject Bayesian Fundamentalism in favour of Bayesian Enlightenment, thus combining Bayesian analysis with mechanistic-level models. This raises two questions: Who are these Bayesian Fundamentalists and what is a mechanistic-level model?
First, let us go in search of Bayesian Fundamentalists. As I read the target article, I began to wonder how it could be that I’d never encountered a Bayesian Fundamentalist. If these ideas are so pervasive, then surely J&L could quote at least one author who has made a clear statement of the Bayesian Fundamentalist programme? From the first line of the abstract it appears that the main proponent of Bayesian Fundamentalism must be Anderson (Reference Anderson1990) with his Rational Analysis framework, and his suggestion that behaviour can often be explained by assuming that it is optimally adapted to its purpose and the environment. In criticising rational analysis, J&L argue that “Rather than the globally optimal design winning out, often a locally optimal solution . . . prevails. . . . Such non-behavioral factors are enormously important to the optimization process, but are not reflected in rational analyses, as these factors are tied to a notion of mechanism, which is absent in rational analyses” (sect. 5.3, paras. 3 and 5).
A similar concern about the limitations of rational analysis can be found in the following quotation: “My guess is that short-term memory limitations do not have a rational explanation. . . . [T]hey reflect the human trapped on some local optimum of evolution” (Anderson Reference Anderson1990, pp. 91–92). These cautionary words on the dangers of relying entirely on rational explanations were written by the arch-Fundamentalist himself. Is there really a difference, then, between these two positions?
Let's now move on to the second question: What is a mechanistic-level model? If we need to develop mechanistic models, then we need to know what such entities might look like. Nowhere do J&L define what they mean by a mechanistic-level theory. Perhaps we can get some clues from their other writings. Sakamoto et al. (Reference Sakamoto, Jones and Love2008) describe a “mechanistic model that principally differs from the aforementioned rational models in that the mechanistic model does not have perfect memory for the training items” (p. 1059). But here the mechanism is simply a specification of the computations that the model performs. That is, although the model is not as abstract as Marr's (Reference Marr1982) computational level, it is not as concrete as his algorithmic level, and certainly says nothing about implementation.
One might call this a process model, or a functional-level explanation. It specifies the functions, computations, and processes in a way that allows the model to be implemented as a computer program and to simulate behavioural data. The program performing the simulations must compute mathematical functions such as square roots, but presumably the exact algorithm or implementation used to compute a square root is not part of the theory. If this kind of functional explanation is indeed what J&L mean by a mechanistic theory, then I am wholeheartedly in favour of their approach. But I am not entirely sure that this is exactly what they have in mind. Elsewhere they talk about mechanistic issues “of representation, timing, capacity, anatomy, and pathology” (sect. 4.1, para. 3). If this is simply to echo Marr in wishing to bring together multiple levels of description and explanation, then few would disagree. However, I worry that J&L may be encouraging Mechanistic Fundamentalism: the belief that a good cognitive theory must do more than just describe processes and computations, and must also specify concrete mechanisms in terms of mechanical components such as nodes, activations, weights, and buffers. This view easily leads to the illusion of mechanism, whereby the mechanisms are mistaken for explanations.
Let's illustrate this by considering interactive activation networks, which are still at the core of many contemporary models. In these networks the activation of each node increases as a result of weighted input, and decreases as a result of inhibition from competing nodes. Activations roughly reflect the evidence for each node or hypothesis as a proportion of the evidence for all hypotheses. Although it is hard to specify exactly what computational function such networks perform, the general principle seems very much like Bayes’ theorem. However, for many psychologists the network model is to be preferred over a Bayesian explanation because the former seems to say something about mechanism. But this is the illusion of mechanism. Unless the precise implementation of the network is intended as a theoretical claim about how processes are implemented in the brain, the mechanism itself makes no contribution to the explanation. If it happened to be the case that the data could be fit by any “mechanism” that could compute Bayes’ theorem, then the explanation would be that the system behaves in an approximately optimal manner.
This immediately raises the problem of model equivalence. Unless candidate mechanisms produce testably different behaviours, the implementational details are not part of the explanation. To quote yet again from Anderson (Reference Anderson1990), “If two theorists propose two sets of mechanisms in two architectures that compute the same function, then they are proposing the same theory” (p. 26). One might protest that at least when studying the mind and the brain, there will always be some neurobiological data that could definitively distinguish between alternative mechanisms. Even ignoring the fact that such a view would imply that there is no distinctly psychological level of explanation, in practice such optimism is misplaced. Even the most productive cognitive theories rarely make any definitive commitment to implementational details. Again, this is apparent in connectionist models based on artificial neurons whose properties bear little resemblance to real neurons. But connectionist modellers are fully aware of this deliberate limitation, and it is hard to see that any of the insights from connectionist modelling are undermined by this simplification.
In conclusion, then, I suggest that most Bayesians are already enlightened; it is the Mechanistic Fundamentalists we should worry about.