What premise can we add that will be plausible and fitting and make the argu- ment valid?
This premise will do: “Administering a punishment to criminals that does not deter crime is immoral.” The argument then becomes:
1. Administering a punishment to criminals that does not deter crime is immoral.
2. The use of capital punishment does not deter crime.
3. Therefore, the use of capital punishment is immoral.
Now the argument is valid, and trying to make it valid has helped us find at least one premise that might work. Moreover, if we know that the argu- ment is valid, we can focus our inquiry on the truth of the premises. After all, if there is something wrong with a valid argument (that is, if the argu- ment is not sound), we know that the trouble is in the premises—specifically, that at least one premise must be false. To put it another way, whether or not such an argument is a good argument depends entirely on the truth of the premises.
As it turns out, our added premise is a general moral principle. And like many implied premises, it is questionable. Deterrence is not necessarily the only reason for administering punishment. Some would say that justice is a better reason; others, that rehabilitation is. (The second premise is also dubious, but we won’t worry about that now.)
In any case, if the supplied premise renders the argument valid, and the premise is plausible and fitting, we can then conclude that we have filled out the argument properly. We can then examine the resulting argument and either accept or reject it. And if we wish to explore the issue at greater depth, we can overhaul the argument altogether to see what we can learn. We can radically change or add premises until we have a sound argument or at least a valid one with plausible premises.