Green (1998) expresses dissatisfaction with contemporary connectionist models as theories of cognition. A reexamination of the historical distinction between hypothetical constructs and intervening variables and their relative roles in theory development reveals an important role for well-designed, parsimonious connectionist models in the study of cognition. Although realist theories (i.e., theories that include hypothetical constructs) are bolder and might provide more intellectual satisfaction to psychologists, instrumentalist theories (i.e., theories that include only intervening variables) can bring rigor and understanding to the enterprise of cognitive science.
2. In the pre-cognitive era of psychology, realist theories were considered largely prescientific; the inclusion of unobservable entities that were hypothesized to have an independent existence made a theory more speculative than its instrumentalist counterparts. Intervening variables were thus only to be used as convenient summaries of empirical relations because they have no physical or psychological reality. "The validity of intervening variables... cannot be called into question except by an actual denial of the empirical facts" (MacCorquodale & Meehl, 1948, p. 104). No finding at a different level of analysis (e.g., neurophysiology) could disprove a theory comprising intervening variables. Does this make such a theory worthless? On the contrary: if one has a well-defined and empirically verified set of intervening variables, a theory comprising those variables can be used as a convenient summary of the empirical data; the availability of a good summary is especially important to those researchers operating at different levels of analysis.
3. B.F. Skinner (1950) championed the use of intervening variables in psychological theories. He recognized the "need for a formal representation of the data reduced to a minimal number of terms. A theoretical construction may yield greater generality than any assemblage of facts" (p. 216). Thus, one advantage of an instrumentalist theory is its ability to summarize a body of empirical work. Although he advocated such theories in his 1950 article, Skinner concluded that "we do not seem to be ready for theory in this sense" (p. 216). Given Green's (1998) response to connectionist models, it appears we are still not ready nearly 50 years later.
4. Hypothetical constructs were assumed to have some reality within the theory in which they were proposed. They "involve terms that are not wholly reducible to empirical terms; they refer to processes or entities that are not directly observed" (MacCorquodale & Meehl 1948, p. 104). Green cites a number of theories that he feels teaches us more about a phenomenon of interest, and each of these theories is replete with hypothetical constructs. Theories containing hypothetical constructs, however ontologically appealing they may be, carry an additional burden: for the theory to be "true" its hypothetical constructs must be shown to exist at some level of analysis. Green is right when he asserts that such theories represent "bold conjectures" in the spirit of Popper, but there is no reason to presuppose that theories containing hypothetical constructs are the only ones that can teach us anything about the processes under investigation.
5. Pioneers like Edward Tolman and B.F. Skinner ruled out any hypothetical constructs in their own theorizing (e.g., Skinner, 1938; Tolman, 1938). Skinner's focus was on quantifying behavioral laws in the form of relations among observable entities. Despite the scarcity of hypothetical constructs, behaviorism succeeded in moving our knowledge of psychology forward. Nonetheless, I believe that behaviorism failed to be bold enough: Theories containing hypothetical constructs were held in disdain when behaviorism reigned, with theorists preferring to err on the side of caution. To maximize the likelihood of progress, a science should be willing to use any and all avenues that have a chance of success.
6. Green asks: "Are connectionist models theories of cognition?" A historical perspective leads me to conclude that they are, but they are theories that are largely devoid of hypothetical constructs (as Green eloquently and emphatically demonstrates). The absence of hypothetical constructs, however, does not mean connectionist models have no utility; rather, these models have a different burden that they must carry: Theories that contain intervening variables must be true to the data. If connectionist models are to prove useful, they must provide good summaries of the empirical relations observed in the world. One must be careful, however, to minimize the variables included in a theory. Introducing too many variables increases the theory's degrees of freedom, making it more likely that the theory will overfit the currently available empirical data. This overfitting will undermine the future validity of the theory. Just as the utility of mathematical formulations of empirical relations has been demonstrated in physics, analytical chemistry, mathematical psychology, and dynamical systems, connectionist models of cognition can further our knowledge of behavior to the extent that they encapsulate the known empirical data and predict the unknown.
7. By now, I hope the reader recognizes the utility of a parsimonious connectionist model to the study of cognition from a strictly instrumentalist perspective. Connectionist models, however, are often more than simply a complex mathematical instantiation of the empirical relations under investigation. The failure of the Perceptron (Minsky & Papert, 1969) to capture certain observed relations allowed us to "know" more about the types of relations that must be computable by the human brain and which mechanisms would prove insufficient to the task. More recently, research on the "binding problem" has revealed an inherent limitation to many neural network architectures (Singer, 1996; von der Malsberg, 1996), one that is not solved by the addition of nodes and connections to a model.
8. Like Green, I have concerns about modern theories of cognition: (a) Some contemporary theories are replete with hypothetical constructs with no rigorous specification of the proposed relations among these constructs, and (b) some connectionist models, while largely avoiding hypothetical constructs, fail to capture the observed empirical relations sufficiently closely without including too much flexibility, thus overfitting the data. Both these concerns have a common thread that is echoed in Green's (1998) final paragraph: too many degrees of freedom make a poor theory. Realists need to make bolder conjectures by specifying the mathematical relations among their constructs whereas instrumentalists need to ensure that their computational models are sufficiently parsimonious.
Green, CD. (1998) Are Connectionist Models Theories of Cognition? PSYCOLOQUY 9(4) ftp://ftp.princeton.edu/pub/harnad/Psycoloquy/1998.volume.9/ psyc.98.9.04.connectionist-explanation.1.green
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Minsky, M., & Papert, S. (1969). Perceptrons. Cambridge, MA: MIT Press.
Singer, W. (1996). Neuronal synchronization: A solution to the binding problem?. In R.R. Llinas & P.S. Churchland (Eds.), The mind-brain continuum: Sensory processes, (pp. 101-130). Cambridge, MA: MIT Press.
Skinner, B.F. (1938). Behavior of organisms. New York: Appleton-Century.
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Tolman, E. C. (1938). The determiners of behavior at a choice point. Psychological Review, 45, 1-41.
von der Malsberg, C. (1996). The binding problem of neural networks. In R.R. Llinas & P.S. Churchland (Eds.), The mind-brain continuum: Sensory processes, (pp. 131-146). Cambridge, MA: MIT Press.