Thinking and Computation - Thinking as Computation - page 20

(Actually, there are good reasons to deviate somewhat from strict logical entailment
for this. See chapter 3.)
So computation over a knowledge base is the direction pursued in this topic, although
it deals with only tiny knowledge bases. The next chapter studies a procedure that
performs this computation for knowledge bases of a certain restricted form.
Want to read more?
This chapter introduced the connection between thinking and computation, an idea
that is the subject matter of the rest of this topic.
The starting point for this connection is the work of the philosopher Gottfried Leib-
niz. A good introduction to his thinking can be found in [59]. (His own work is
scattered in the thousands of letters he wrote.) There is not much in terms of details,
however, as Leibniz did not have the benefit of the modern notions of symbolic logic
or computation. These came along in the 1930s, and it took until the 1950s, when John
McCarthy, one of the founders of the field of artificial intelligence (AI) [11], became
the first person to propose the approach followed in this topic, representing what is
known as a collection of sentences and computing their logical entailments [47].
An excellent place to begin to explore what psychologists have to say about human
thinking is a book by Pinker [9] that is aimed at a broad audience. However, the
whole topic of human thinking remains highly controversial, and even Pinker has his
detractors [3]. Many find the notion of symbolic computation too limiting because
it downplays the effect of the rest of the body on the thinking process [2]. Among
the computationalists, many prefer symbolic structures other than sentences that can
represent knowledge in a more concrete way [5]. There are also researchers who feel
that a lot of thinking needs to be more pictorial or diagrammatic in nature [6].
The general notion of computation used here arose directly out of work on logic
in the 1930s. This account of computation is due to Alan Turing, widely considered
to be the father of computer science (John von Neumann is often called the father of
electronic computers). In 1936, Turing proposed a formal definition of what is here
called a procedure in terms of a very simple imaginary device: a Turing machine [12].
With this definition, one could now ask questions like whether it was even possible to
compute a certain result. Turing was the first to prove that there was a universal Turing
machine that could compute what any other one could, and remarkably enough, that
some results could not be computed by any Turing machine.