The Language of Argument

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6

Propositional Logic

This chapter begins our investigation of evaluating arguments by means of formal

deductive logic. The first part of the chapter will show how the crucial standard of

validity, which was introduced in Chapter 5, can be developed rigorously in one

area—what is called propositional logic. This branch of logic deals with connectives

such as “and” and “or,” which allow us to build up compound propositions from

simpler ones. Throughout most of the chapter, the focus will be theoretical rather

than immediately practical. It is intended to provide insight into the concept of

validity by examining it in an ideal setting. The chapter will close with a discussion

of the relationship between the ideal language of symbolic logic and the language we

ordinarily speak.

The Formal Analysis of Arguments

When we carry out an informal analysis of an argument, we pay close attention

to the key words used to present the argument and then ask ourselves

whether these key terms have been used properly. So far, we have no exact

techniques for answering the question of whether a word is used correctly.

We rely, instead, on linguistic instincts that, on the whole, are fairly good.

In a great many cases, people can tell whether an argument marker, such

as “therefore,” is used correctly in indicating that one claim follows from

another. However, if we go on to ask the average intelligent person why one

claim follows from the other, he or she will probably have little to say except,

perhaps, that it is just obvious. In short, it is often easy to see that one claim

follows from another, but to explain why can be difficult. The purpose of this

chapter is to provide such an explanation for some arguments.

This quality of “following from” is elusive, but it is related to the technical

notion of validity, which was introduced in Chapter 5. The focus of our

attention will be largely on the concept of validity. We are not, for the time

being at least, interested in whether this or that argument is valid; we want

to understand validity itself. To this end, the arguments we will examine

are so simple that you will not be able to imagine anyone not understand-

ing them at a glance. Who needs logic to deal with arguments of this kind?

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