Case Study: Other Ways of Thinking - Thinking as Computation - page 240

5. Shako is a polar bear, and Shako is white.
6. Peppy is a polar bear, and Peppy is white.
One might want to generalize from these and surmise that all polar bears are white.
Again, this sort of thinking is not deductive. The facts about the individuals do not
logically entail that all polar bears are white; the very next polar bear could turn out
to be a different color. C. S. Peirce called this type of nondeductive thinking induction :
from (2) and (3) (and others like it), one can induce (1). This is the sort of reasoning
that underlies a form of learning : from observing the color of polar bears Thornton,
Shako, Peppy, and perhaps others, one learns that as a rule, polar bears are white.
So, to summarize:
from (1) and (2), one can deduce (3);
from (1) and (3), one can abduce (2);
from (2) and (3), one can induce (1).
Finally, suppose (7) is added:
7. Freddy is a either a polar bear or a swan.
Based on what is known, one can conclude (that is, deduce) that Freddy is white. This
is logically entailed by (1), (4), and (7). If (7) is true, then there are only two possi-
bilities, and in either case, given (1) and (4), the color must be white. However, this
conclusion could not be drawn using the current thinking procedure, back-chaining.
There is no way to even represent a sentence like (7), since it is neither an atomic
sentence nor a conditional. This chapter also explores what is involved with this
sort of thinking, called propositional reasoning . (It is sometimes also known as Boolean
reasoning.) Back-chaining is a special case.
The chapter is divided into four sections. The first section reexamines back-chaining
as the starting point for discussing the other ways of thinking. Sections 2, 3, and 4
discuss explanation, learning, and propositional reasoning, respectively.
There is something of a paradox in using Prolog and back-chaining to look at
new ways of thinking that go beyond back-chaining. And as the paradox is resolved,
thinking itself will end up becoming the subject matter of the thinking. This reinterpre-
tation will require a major conceptual shift, and this chapter is the most technically
challenging one in the topic.