The target article by Jones & Love (J&L) is another entry to the recent debate contrasting the merits of Bayesian and more mechanistic modeling perspectives (e.g., Griffiths et al. Reference Griffiths, Chater, Kemp, Perfors and Tenenbaum2010; McClelland et al. Reference McClelland, Botvinick, Noelle, Plaut, Rogers, Seidenberg and Smith2010). Regrettably, much of this debate has been tainted by a subtext that presupposes the approaches to be adversarial rather than allied (see, e.g., Feldman Reference Feldman2010; Kruschke Reference Kruschke2010). J&L are correct in asserting that research agendas pitched at different levels of analysis will investigate different research questions that lead to different theoretical solutions (e.g., Dennett Reference Dennett1987; Marr Reference Marr1982/2010). However, any complete psychological theory must account for phenomena at multiple levels of analysis and, additionally, elucidate the relations between levels (e.g., Schall Reference Schall2004; Teller Reference Teller1984). We also note that the various levels of analysis are causally interrelated and are thus mutually constraining (Rumelhart & McClelland Reference Rumelhart and McClelland1985). It follows that refinement of a model at one level of analysis focuses the search for theoretical solutions at another. We therefore view theoretical pluralism among researchers as an efficient means of developing more complete psychological theories.
We suggest that findings from the so-called “Bayesian Fundamentalist” perspective have highlighted core issues in developing more complete psychological theories, and that discoveries by individual “Fundamentalist” researchers may actually facilitate discipline-wide “Enlightenment” by sharpening questions and generating novel insights that stimulate research (e.g., Shiffrin et al. Reference Shiffrin, Lee, Kim and Wagenmakers2008). J&L's admonishment of Bayesian Fundamentalism, depending on whether it is directed at psychological science as a whole, or to individual researchers, is either a) powerful but directed at a largely non-existent opponent, or (b) misguided insofar that the collaborative nature of scientific progress offsets the narrow focus of individual scientists.
Contrary to J&L, we argue the “breadth-first” approach adopted by many Bayesian theorists, rather than stifling theoretical progress, actually facilitates cross-talk between levels of analysis. That contemporary Bayesian theorists are aware of, and aspire to resolve this tension, is reflected in recent work that has sought to reconcile rational accounts with more traditional process models. For example, to the extent that models of cognitive processing implement sampling algorithms to approximate full Bayesian inference, models at different levels of analysis can be mutually informative. Shi et al. (Reference Shi, Griffiths, Feldman and Sanborn2010) illustrate how exemplar models (e.g., Nosofsky Reference Nosofsky1986) can be interpreted as an importance sampling algorithm, and, similarly, Sanborn et al.(Reference Sanborn, Griffiths and Navarro2010a) explored the particle filter algorithm as a way of leveraging a process interpretation of Anderson's (Reference Anderson1991b) rational model. Lewandowsky et al.(Reference Lewandowsky, Griffiths and Kalish2009) used iterated learning (Griffiths & Kalish Reference Griffiths and Kalish2007; Kalish et al. Reference Kalish, Griffiths and Lewandowsky2007), an experimental paradigm motivated by technological advances in sampling techniques used to approximate Bayesian posteriors, to decisively reject a sparse-exemplar model of predicting the future. Kruschke (Reference Kruschke2006; Reference Kruschke2008) contrasted globally and locally Bayesian approaches to associative learning, the latter of which can be construed as carrying very direct process implications concerning selective attention. J&L acknowledge the potential of these approaches for transcending computational level theories but do not acknowledge the role of the computational theories for driving research in this direction.
One area where Bayesian perspectives appear particularly more illuminating than mechanistic approaches is in explaining individual differences. For example, work from within the knowledge partitioning framework has repeatedly found large differences in transfer performance in tasks that can be decomposed into a number of simpler sub-tasks (e.g., Lewandowsky et al. Reference Lewandowsky, Kalish and Ngang2002; Reference Lewandowsky, Roberts and Yang2006; Yang & Lewandowsky Reference Yang and Lewandowsky2003). Mechanistic modeling of these results has highlighted the importance of modular architecture (Kalish et al. Reference Kalish, Lewandowsky and Kruschke2004; Little & Lewandowsky Reference Little and Lewandowsky2009), selective attention (Yang & Lewandowsky Reference Yang and Lewandowsky2004), and their interaction (Sewell & Lewandowsky Reference Sewell and Lewandowsky2011) in accounting for such individual differences. However, a significant limitation of a mechanistic approach is that the solutions have been built into the models. By contrast, recent Bayesian modeling of knowledge partitioning has showed that many aspects of the individual differences observed empirically emerge naturally if one assumes that people are trying to learn about their environment in a rational manner (Navarro Reference Navarro, Lafferty, Williams, Shawe-Taylor, Zemel and Culotta2010).
J&L draw uncharitable parallels between “Bayesian Fundamentalism” on the one hand, and Behaviorism, connectionism, and evolutionary psychology on the other. In response, we note that theoretical setbacks in those paradigms have clarified our understanding of how the mind does and does not work. Consequently, cognitive science has emerged with a more refined theoretical toolkit and new, incisive research questions. For Behaviorism, a restrictive theoretical stance solidified the need to consider more than just the history of reinforcement in explaining behavior (Neisser Reference Neisser1967). The inability of the perceptrons to handle nonlinearly separable problems forced connectionists to consider more powerful model architectures (Thomas & McClelland Reference Thomas, McClelland and Sun2008). Likewise, controversies that have erupted in evolutionary psychology over the propagation of cognitive modules have forced theorists to refine and reevaluate classical notions of modularity (cf. Barrett & Kurzban Reference Barrett and Kurzban2006; Fodor Reference Fodor1983). Thus, the failures of the precedents chosen by J&L actually constitute successes for the field; for example, the cognitive revolution was propelled and accelerated by the spectacular failure of Behaviorism.
We close by considering how J&L's critique of Bayesian Fundamentalism relates to scientific activity in practice. If they address the scientific community as a whole, their criticism is powerful, but lacks a real target. Alternatively, if J&L's concerns are directed at individual scientists, their plea overlooks the fact that scientific progress, being inherently distributed across multiple research groups, “averages out” individual differences in theoretical dispositions. That is, the aggregate outcomes produced by the scientific community are unlikely to be reflected in the individual outcomes produced by a given scientist (Kuhn Reference Kuhn1970).
Whereas a complete level-spanning theory will always be the goal of science, the approach toward that collective goal will be incremental, and those pursuing it will tend to focus on a particular level of analysis. The important question for any individual researcher is whether an adopted theoretical framework sharpens questions, provides insight, and guides new empirical inquiry (Shiffrin et al. Reference Shiffrin, Lee, Kim and Wagenmakers2008); recent Bayesian modeling of cognition undoubtedly fulfills these requirements.
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The target article by Jones & Love (J&L) is another entry to the recent debate contrasting the merits of Bayesian and more mechanistic modeling perspectives (e.g., Griffiths et al. Reference Griffiths, Chater, Kemp, Perfors and Tenenbaum2010; McClelland et al. Reference McClelland, Botvinick, Noelle, Plaut, Rogers, Seidenberg and Smith2010). Regrettably, much of this debate has been tainted by a subtext that presupposes the approaches to be adversarial rather than allied (see, e.g., Feldman Reference Feldman2010; Kruschke Reference Kruschke2010). J&L are correct in asserting that research agendas pitched at different levels of analysis will investigate different research questions that lead to different theoretical solutions (e.g., Dennett Reference Dennett1987; Marr Reference Marr1982/2010). However, any complete psychological theory must account for phenomena at multiple levels of analysis and, additionally, elucidate the relations between levels (e.g., Schall Reference Schall2004; Teller Reference Teller1984). We also note that the various levels of analysis are causally interrelated and are thus mutually constraining (Rumelhart & McClelland Reference Rumelhart and McClelland1985). It follows that refinement of a model at one level of analysis focuses the search for theoretical solutions at another. We therefore view theoretical pluralism among researchers as an efficient means of developing more complete psychological theories.
We suggest that findings from the so-called “Bayesian Fundamentalist” perspective have highlighted core issues in developing more complete psychological theories, and that discoveries by individual “Fundamentalist” researchers may actually facilitate discipline-wide “Enlightenment” by sharpening questions and generating novel insights that stimulate research (e.g., Shiffrin et al. Reference Shiffrin, Lee, Kim and Wagenmakers2008). J&L's admonishment of Bayesian Fundamentalism, depending on whether it is directed at psychological science as a whole, or to individual researchers, is either a) powerful but directed at a largely non-existent opponent, or (b) misguided insofar that the collaborative nature of scientific progress offsets the narrow focus of individual scientists.
Contrary to J&L, we argue the “breadth-first” approach adopted by many Bayesian theorists, rather than stifling theoretical progress, actually facilitates cross-talk between levels of analysis. That contemporary Bayesian theorists are aware of, and aspire to resolve this tension, is reflected in recent work that has sought to reconcile rational accounts with more traditional process models. For example, to the extent that models of cognitive processing implement sampling algorithms to approximate full Bayesian inference, models at different levels of analysis can be mutually informative. Shi et al. (Reference Shi, Griffiths, Feldman and Sanborn2010) illustrate how exemplar models (e.g., Nosofsky Reference Nosofsky1986) can be interpreted as an importance sampling algorithm, and, similarly, Sanborn et al.(Reference Sanborn, Griffiths and Navarro2010a) explored the particle filter algorithm as a way of leveraging a process interpretation of Anderson's (Reference Anderson1991b) rational model. Lewandowsky et al.(Reference Lewandowsky, Griffiths and Kalish2009) used iterated learning (Griffiths & Kalish Reference Griffiths and Kalish2007; Kalish et al. Reference Kalish, Griffiths and Lewandowsky2007), an experimental paradigm motivated by technological advances in sampling techniques used to approximate Bayesian posteriors, to decisively reject a sparse-exemplar model of predicting the future. Kruschke (Reference Kruschke2006; Reference Kruschke2008) contrasted globally and locally Bayesian approaches to associative learning, the latter of which can be construed as carrying very direct process implications concerning selective attention. J&L acknowledge the potential of these approaches for transcending computational level theories but do not acknowledge the role of the computational theories for driving research in this direction.
One area where Bayesian perspectives appear particularly more illuminating than mechanistic approaches is in explaining individual differences. For example, work from within the knowledge partitioning framework has repeatedly found large differences in transfer performance in tasks that can be decomposed into a number of simpler sub-tasks (e.g., Lewandowsky et al. Reference Lewandowsky, Kalish and Ngang2002; Reference Lewandowsky, Roberts and Yang2006; Yang & Lewandowsky Reference Yang and Lewandowsky2003). Mechanistic modeling of these results has highlighted the importance of modular architecture (Kalish et al. Reference Kalish, Lewandowsky and Kruschke2004; Little & Lewandowsky Reference Little and Lewandowsky2009), selective attention (Yang & Lewandowsky Reference Yang and Lewandowsky2004), and their interaction (Sewell & Lewandowsky Reference Sewell and Lewandowsky2011) in accounting for such individual differences. However, a significant limitation of a mechanistic approach is that the solutions have been built into the models. By contrast, recent Bayesian modeling of knowledge partitioning has showed that many aspects of the individual differences observed empirically emerge naturally if one assumes that people are trying to learn about their environment in a rational manner (Navarro Reference Navarro, Lafferty, Williams, Shawe-Taylor, Zemel and Culotta2010).
J&L draw uncharitable parallels between “Bayesian Fundamentalism” on the one hand, and Behaviorism, connectionism, and evolutionary psychology on the other. In response, we note that theoretical setbacks in those paradigms have clarified our understanding of how the mind does and does not work. Consequently, cognitive science has emerged with a more refined theoretical toolkit and new, incisive research questions. For Behaviorism, a restrictive theoretical stance solidified the need to consider more than just the history of reinforcement in explaining behavior (Neisser Reference Neisser1967). The inability of the perceptrons to handle nonlinearly separable problems forced connectionists to consider more powerful model architectures (Thomas & McClelland Reference Thomas, McClelland and Sun2008). Likewise, controversies that have erupted in evolutionary psychology over the propagation of cognitive modules have forced theorists to refine and reevaluate classical notions of modularity (cf. Barrett & Kurzban Reference Barrett and Kurzban2006; Fodor Reference Fodor1983). Thus, the failures of the precedents chosen by J&L actually constitute successes for the field; for example, the cognitive revolution was propelled and accelerated by the spectacular failure of Behaviorism.
We close by considering how J&L's critique of Bayesian Fundamentalism relates to scientific activity in practice. If they address the scientific community as a whole, their criticism is powerful, but lacks a real target. Alternatively, if J&L's concerns are directed at individual scientists, their plea overlooks the fact that scientific progress, being inherently distributed across multiple research groups, “averages out” individual differences in theoretical dispositions. That is, the aggregate outcomes produced by the scientific community are unlikely to be reflected in the individual outcomes produced by a given scientist (Kuhn Reference Kuhn1970).
Whereas a complete level-spanning theory will always be the goal of science, the approach toward that collective goal will be incremental, and those pursuing it will tend to focus on a particular level of analysis. The important question for any individual researcher is whether an adopted theoretical framework sharpens questions, provides insight, and guides new empirical inquiry (Shiffrin et al. Reference Shiffrin, Lee, Kim and Wagenmakers2008); recent Bayesian modeling of cognition undoubtedly fulfills these requirements.