We can illustrate these methods of deep analysis by examining the difficult question of the constitutionality of capital punishment. It has been argued that the Supreme Court should declare the death penalty unconstitutional because it is a cruel and unusual punishment. The explicitly stated argu- ment has the following basic form:
(1) The death penalty is a cruel and unusual punishment.
(2) The death penalty should be declared unconstitutional. (from 1)
The argument plainly depends on two suppressed premises:
SP1: The Constitution prohibits cruel and unusual punishments.
SP2: Anything that the Constitution prohibits should be declared unconstitutional.
So the argument, more fully spelled out, looks like this:
(1) The death penalty is a cruel and unusual punishment. (2) SP: The Constitution prohibits cruel and unusual punishments.
(3) The Constitution prohibits the death penalty. (from 1–2) (4) SP: Anything that the Constitution prohibits should be declared
unconstitutional.
(5) The death penalty should be declared unconstitutional. (from 3–4)
This reconstruction seems to be a fair representation of the intent of the original argument.
We can now turn to an assessment of this argument. First, the argument is valid: Given the premises, the conclusion does follow. All that remains is to determine the truth of the premises one by one.