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

A device that can compute every possible input-output function does not exist.
The Turing machine was invented and used to prove that there exist some functions
that are not computable (Turing, 1936). However, the subset of functions that are
computable is large and important:
It can be proved mathematically that there are infinitely more functions than
programs. Therefore, for most functions there is no corresponding program that
can compute them. . . . Fortunately, almost all these noncomputable functions are
useless, and virtually all the functions we might want to compute are computable.
(Hillis, 1998, p. 71)
A major discovery of the twentieth century was that a number of seemingly different
symbol manipulators were all identical in the sense that they all could compute
the same maximal class of input-output pairings (i.e., the computable functions).
Because of this discovery, these different proposals are all grouped together
into the class “universal machine,” which is sometimes called the “effectively computable
procedures.” This class is “a large zoo of different formulations” that includes
“Turing machines, recursive functions, Post canonical systems, Markov algorithms,
all varieties of general purpose digital computers, [and] most programming languages”
(Newell, 1980, p. 150).
Newell (1980) proved that a generic physical symbol system was also a universal
machine. This proof, coupled with the physical symbol system hypothesis, leads
to a general assumption in classical cognitive science: cognition is computation,
the brain implements a universal machine, and the products of human cognition
belong to the class of computable functions.
The claim that human cognition is produced by a physical symbol system is a
scientific hypothesis. Evaluating the validity of this hypothesis requires fleshing out
many additional details. What is the organization of the program that defines the
physical symbol system for cognition (Newell & Simon, 1972)? In particular, what
kinds of symbols and expressions are being manipulated? What primitive operations
are responsible for performing symbol manipulation? How are these operations
controlled? Classical cognitive science is in the business of fleshing out these
details, being guided at all times by the physical symbol system hypothesis.
3.8 The Intentional Stance
According to the formalist’s motto (Haugeland, 1985) by taking care of the syntax,
one also takes care of the semantics. The reason for this is that, like the rules in a
logical system, the syntactic operations of a physical symbol system are constrained
to preserve meaning. The symbolic expressions that a physical symbol system
evolves will have interpretable designations.
82 Chapter 3