Claiming that it is not clear how many theoretical terms a connectionist model has to be built of is one of Green's (1998a) main arguments for referring to (a) a lack of correspondence of the theoretical entities of connectionist models to any type of empirical entity and (b) the resulting abundance of degrees of freedoms in the connectionist modelling of cognition. A more brain-oriented modelling approach might yield the desired theoretico-empirical mapping but it does not reduce a model's degrees of freedom.
2. Green accordingly argues that connectionist models should only be considered as theories of cognition when their "units DO correspond to something closely related to the cognitive domain; viz., the neurons of the brain" (para. 18) or, more generally, when they are interpreted "as literal models of the brain activity that underpins cognition" (para. 20). This interposes the human brain as a hidden layer between connectionism and cognition. While one might agree that this layer makes a model's terms interpretable, it does not solve the "degrees of freedom" problem.
3. In para. 11, Green says that it would be ridiculous or almost meaningless that 326 units govern a specific activity in the cognitive domain. However, assigning these (or even more) units to neurons or "brain units" of whatever type makes this statement even more questionable. If connectionism is to model how the human brain processes information, there cannot be much doubt that many more units must be involved. Thus, modelling the brain's activity does not reduce a model's number of terms, it increases them.
4. This particularly applies when it is intended to model the activity of a "true brain" whose behaviour is not only determined by simple and standardized neurons, but also by, for example, glial cells, different types of synapses, area-specific variations in neuron-density and types of neurons, etc. Taking all these different variables into account would be a prerequisite (Crick, 1989; Orbach, 1998) for a connectionist model to be a LITERAL brain activity model -- especially when one wants to deal with the brain's implementation of cognition. Although this certainly accords with Green's intention (as also becomes evident in one of his replies, Green, 1998b), the immediate result will be an exponential explosion of the number of units/terms of a model.
5. One might argue that there is no such increase of degrees of freedom because now it is the brain that is modelled and not cognition itself. But in most cases it will still be the behaviourally observable processes during a specific cognitive task (e.g., reading, speaking) on which a model will be tested, whereas a true modelling of brain-implemented cognition could only be tested against the recorded activity of the brain doing this specific task. However, the language of brain processes is not the language of cognition (Gevins & Cutillo, 1995). Brain-activity oriented models of cognition accordingly need to "speak" both of these rather complicated languages. This could result in a "falling between the stools," one chair being the "degrees of freedom" and the other the testing against the brain's activity proper, perhaps unintentionally moving the models farther away from cognition itself.
Crick, F. (1989) The Recent Excitement About Neural Networks. Nature, 337, 129-132.
Gevins, A.S., & Cutillo, B.A. (1995) Neuroelectric Measures of Mind. In: Neocortical Dynamics And Human EEG Rhythms, ed. Nunez, P. L., Oxford University Press.
Green, C.D. (1998a) 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
Green, C.D.(1998b) Lahley's Lesson Is Not Germane. Reply to Orbach on Connectionist-Explanation. PSYCOLOQUY 9 (7) ftp://ftp.princeton.edu/pub/harnad/Psycoloquy/1998.volume.9/ psyc.98.9.07.connectionist-explanation.4.green
Orbach, J. (1998). Do wires model neurons? PSYCOLOQUY 9 (5) ftp://ftp.princeton.edu/pub/harnad/Psycoloquy/1998.volume.9/ psyc.98.9.05.connectionist-explanation.2.orbach