The Language of Argument

1 7 4

C H A P T E R 7 ■ C a t e g o r i c a l L o g i c

than explicitly asserted. We do not feel called on to say many things that

are matters of common agreement. Before we can apply the theory of the

syllogism to everyday arguments, these things that are simply under-

stood must be made explicit. This is often illuminating, and sometimes

boring, but it usually involves a great deal of work. Second, the theory of

the syllogism applies to statements only in a highly stylized form. Before

we apply the theory of the syllogism to an argument, we must cast its

premises and conclusion into the basic A, E, I, and O forms. As we saw

earlier in this chapter, the needed translation is not always simple or obvi-

ous. It may not always be possible. For these and related reasons, modern

logicians have largely abandoned the project of reducing all reasoning to

syllogisms.

Why study the theory of the syllogism at all, if it is hard to apply in some

circumstances and perhaps impossible to apply in others? The answer to this

question was given at the beginning of Chapter 6. The study of formal logic

is important because it deepens our insight into a central notion of logic: va-

lidity. Furthermore, the argument forms we have studied do underlie much

of our everyday reasoning, but so much else is going on in a normal con-

versational setting that this dimension is often hidden. By examining argu-

ments in idealized forms, we can study their validity in isolation from all the

other factors at work in a rich conversational setting.

There is a difference, then, between the techniques developed in Chapters

1–5 and the techniques developed in Chapters 6 and 7. The first five chap-

ters presented methods of informal analysis that may be applied directly to

the rich and complex arguments that arise in everyday life. These methods

of analysis are not wholly rigorous, but they do provide practical guides for

the analysis and evaluation of actual arguments. The chapters concerning

formal logic have the opposite tendency. In comparison with the first five

chapters, the level of rigor is very high, but the range of application is cor-

respondingly smaller. In general, the more rigor and precision you insist on,

the less you can talk about.

1. What are the chief differences between the logical procedures developed in
   this chapter and those developed in Chapter 6 on propositional logic?


2. If we evaluate arguments as they occur in everyday life by using the ex-
   act standards developed in Chapters 6 and 7, we discover that our every-
   day arguments rarely satisfy these standards, at least explicitly. Does this
   show that most of our ordinary arguments are illogical? What else might it
   show?

Discussion Questions

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