1 3 5C o n d i t i o n a l sconnectives. When this is so, it is possible to test for validity in a purely me-
chanical way. This can be done through the use of truth tables. Thus, in this
area at least, we are able to give a clear account of validity and to specify
exact procedures for testing for validity.
This truth-functional approach might seem problematic in another area:
conditionals. We will argue that an important group of conditionals can be
handled in much the same way as negation, conjunction, and disjunction.
We separate conditionals from the other connectives only because a
truth-functional treatment of conditionals is more controversial and faces
problems that are instructive.
Conditionals have the form “If ______, then _______.” What goes in the
first blank of this pattern is called the antecedent of the conditional; what
goes in the second blank is called its consequent. Sometimes conditionals ap-
pear in the indicative mood:
If it rains, then the crop will be saved.
Sometimes they occur in the subjunctive mood:
If it had rained, then the crop would have been saved.
There are also conditional imperatives:
If a fire breaks out, then call the fire department first!
And there are conditional promises:
If you get into trouble, then I promise to help you.
Indeed, conditionals get a great deal of use in our language, often in argu-
ments. It is important, therefore, to understand them.
Unfortunately, there is no general agreement among experts concerning
the correct way to analyze conditionals. We will simplify matters and avoid
some of these controversies by considering only indicative conditionals. We
will not examine conditional imperatives, conditional promises, or subjunctive
conditionals. Furthermore, at the start, we will examine only what we will call
propositional conditionals. We get a propositional conditional by substituting in-
dicative sentences that express propositions—something either true or false—
into the schema “If ____, then ______.” Or, to use technical language already
introduced, a propositional conditional is a substitution instance of “If p, then
q” in which “p” and “q” are propositional variables. Of the four conditional
sentences listed above, only the first is clearly a propositional conditional.
Even if we restrict our attention to propositional conditionals, this will not
avoid all controversy. Several competing theories claim to provide the correct
analysis of propositional conditionals, and no consensus has been reached
concerning which is right. It may seem surprising that theorists disagree
about such a simple and fundamental notion as the if-then construction, but
they do. In what follows, we will first describe the most standard treatment of
propositional conditionals, and then consider alternatives to it.97364_ch06_ptg01_111-150.indd 135 15/11/13 10:15 AM
some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materiallyCopyright 201^3 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights,
affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.