In my article Changing the Mind I had referred to a certain type of formal theories used within the research paradigm of cognitive science. The argument given there was that theories of cognition formulated in terms of such theories must be incomplete because they can be extended by new information that cannot be derived within the given theory.
However, I used this type of theories only as a peg for the argument. This argument of extensibility or programmability does not depend on the specific kind of formal theories like logic based or rule based systems used in some approaches of cognitive science and artificial intelligence that where in fashion in the 1960s, 1970s and 1980s. The same kind of argument works just as well if you use a connectionist approach where you describe cognition in terms of neural networks. You could build a simulation model based on simulated neurons (see
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