Something to Reckon With: The Logic of Terms

Charles R. Crawford, formerly an associate professor of computer science
at York University, is a computer-programming and mathematics
consultant.

Like many areas of philosophy and mathematics, systems of formal logic
have been difficult to apply to certain practical problems. The first
part of this book describes how Aristotle’s syllogisms, Boolean
algebra, and symbolic methods from Frege, Quine, and others have been
used in the teaching of undergraduate courses in logic and critical
thinking. As the author points out, each of these systems can be easily
applied to simple arguments, and some are successful at analyzing
complex technical arguments in mathematics. However, all fail when
applied to complex natural-language arguments such as political debates.


In the second part of his book, Professor Englebretsen describes “a
system of formal logic that is (1) natural ... (2) as powerful as the
standard system ... and (3) provided with a symbolic algorithm that is
easy to learn, simple to manipulate, and effective.” By
“effective” he means that the system can be applied to a “serious
piece of argumentation in natural language” and evaluate its validity.
The description of this system and its associated algorithm is detailed
and includes numerous examples, but it is difficult to say whether or
not the system avoids all the weaknesses of the others. While it is
arguably better able than conventional symbolic logic to deal with
natural-language arguments, since none of the examples presented could
be considered “a serious piece of argumentation,” the extent to
which it is both “simple” and “effective” is uncertain.