Mind, Body, World- Foundations of Cognitive Science, 2013a

Bever, Fodor, and Garrett (1968) used this result to conclude that associationism
(and radical behaviourism) was not powerful enough to deal with the embedded
clauses of natural human language. As a result, they argued that associationism
should be abandoned as a theory of mind. The impact of this proof is measured
by the lengthy responses to this argument by associationist memory researchers
(Anderson & Bower, 1973; Paivio, 1986). We return to the implications of this argument
when we discuss connectionist cognitive science in Chapter 4.
While finite state automata cannot accept the recursive grammar used by
Bever, Fodor, and Garrett (1968), Turing machines can (Révész, 1983). Their ability
to move in both directions along the tape provides them with a memory that enables
them to match the number of leading bs in a string with the number of trailing bs.
Modern linguistics has concluded that the structure of human language must be
described by grammars that are recursive. Finite state automata are not powerfulenough
devices to accommodate grammars of this nature, but Turing machines are.
This suggests that an information processing architecture that is sufficiently rich to
explain human cognition must have the same power—must be able to answer the
same set of questions—as do Turing machines. This is the essence of the physical
symbol system hypothesis (Newell, 1980), which are discussed in more detail below.
The Turing machine, as we saw in Chapter 2 and further discuss below, is a universal
machine, and classical cognitive science hypothesizes that “this notion of symbol
system will prove adequate to all of the symbolic activity this physical universe of
ours can exhibit, and in particular all the symbolic activities of the human mind”
(Newell, 1980, p. 155).
3.5 Underdetermination and Innateness
The ability of a device to accept or generate a grammar is central to another computational
level analysis of language (Gold, 1967). Gold performed a formal analysis
of language learning which revealed a situation that is known as Gold’s paradox
(Pinker, 1979). One solution to this paradox is to adopt a position that is characteristic
of classical cognitive science, and which we have seen is consistent with its Cartesian
roots. This position is that a good deal of the architecture of cognition is innate.
Gold (1967) was interested in the problem of how a system could learn the
grammar of a language on the basis of a finite set of example expressions. He considered
two different situations in which the learning system could be presented
with expressions. In informant learning, the learner is presented with either valid
or invalid expressions, and is also told about their validity, i.e., told whether they
belong to the grammar or not. In text learning, the only expressions that are presented
to the learner are grammatical.
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