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

speaker of a language has mastered and internalized a generative grammar that
expresses his knowledge of his language. (Chomsky, 1965, p. 8)
A sentence’s structural description is represented by using a phrase marker, which is
a hierarchically organized symbol structure that can be created by a recursive set of
rules called a context-free grammar. In a generative grammar another kind of rule,
called a transformation, is used to convert one phrase marker into another.
The recursive grammars that have been developed in linguistics serve two
purposes. First, they formalize key structural aspects of human languages, such
as the embedding of clauses within sentences. Second, they explain how finite
resources are capable of producing an infinite variety of potential expressions. This
latter accomplishment represents a modern rebuttal to dualism; we have seen that
Descartes (1996) used the creative aspect of language to argue for the separate, nonphysical
existence of the mind. For Descartes, machines were not capable of generating
language because of their finite nature.
Interestingly, a present-day version of Descartes’ (1996) analysis of the limitations
of machines is available. It recognizes that a number of different information
processing devices exists that vary in complexity, and it asks which of these devices
are capable of accommodating modern, recursive grammars. The answer to this
question provides additional evidence against behaviourist or associationist theories
of language (Bever, Fodor, & Garrett, 1968).
b
b
b
b
a
b
b
b
b
Write
Read
Instructions
State
State
Symbol
Machine Head
Figure 3-8. How a Turing machine processes its tape.
In Chapter 2, we were introduced to one simple—but very powerful—device, the
Turing machine (Figure 3-8). It consists of a machine head that manipulates the
symbols on a ticker tape, where the ticker tape is divided into cells, and each cell
is capable of holding only one symbol at a time. The machine head can move back
and forth along the tape, one cell at a time. As it moves it can read the symbol on the
current cell, which can cause the machine head to change its physical state. It is also
capable of writing a new symbol on the tape. The behaviour of the machine head—its
Elements of Classical Cognitive Science 69