Thinking and Deciding

TYPES OF LOGIC 81
The system of categorical logic is concerned with membership in categories. It
concerns the behavior of arguments with the words “all,” “some,” “none,” “not,” and
“no.” This is the type of logic most intensively discussed by the Greek philosopher
Aristotle, the main inventor of formal logic, and the type most studied by psychologists.
Here are two examples of valid arguments of this type:
All As are Bs.
All Bs are Cs.
Therefore all As are Cs.
Some A are B.
No B are C.
Therefore some A are not C.
The system of predicate logic includes both propositional and categorical logic.
It includes relations among terms as well as class membership. A “predicate” is
anything that is true or false of a term or set of terms. In the sentence “A man is a
scientist,” the word “scientist” is considered a “one-place predicate,” because it says
that something is true of the single term “man.” In the sentence “John likes Mary,”
the word “likes” is considered a “two-place predicate,” because it describes a relation
between two specific terms. In predicate logic, we can analyze such questions as
this: “If every boy likes some girl and every girl likes some boy, does every boy like
someone who likes him?”
Other systems of logic extend predicate logic in various ways. For example,
modal logic is concerned with arguments using such terms as “necessarily” and “possibly.”
The idea is not simply to capture the meanings of English words as they are
normally used but also, as in the “if” example described earlier, to develop formal
rules for particular meanings, usually the most conservative meanings. No sharp
boundary separates modern logic from “semantics,” the part of modern linguistics
that deals with meaning.
The various systems of logic I have listed constitute what I shall call “formal”
logic. These systems have in common their concern with validity, that is, the drawing
of conclusions that are absolutely certain from premises that are assumed to be
absolutely certain. (The next chapter considers “informal” logic.)
If we view formal logic within the search-inference framework, we see that formal
logic is concerned with the rules for drawing conclusions from evidence with
certainty. That is, it is concerned only with inference. It says nothing about how
evidence is, or should be, obtained. Formal logic, therefore, cannot be a complete
theory of thinking. Moreover, formal logic cannot even be a complete normative
theory of inference, for most inferences do not involve the sort of absolute certainty
that it requires.
Nonetheless, logic may be a partial normative theory of inference. Each system
of logic has its own rules that specify how to draw valid conclusions from a set of
evidence, or premises. These rules make up the normative model. Within logic,
there are many such systems of rules, and often there are many equivalent ways of
describing the same system. These rules are the subject matter of logic textbooks.