The Language of Argument

9 6

cH A Pt eR 5 ■ D e e p A n a l y s i s

Suppressed Premises

Now that we understand validity and soundness, we can use those stand-

ards to determine which assumptions can fairly be added to deductive argu-

ments in order to complete them. If some extra premise is needed in order

for a deductive argument to be valid or sound, then that argument needs

that assumption in order to succeed as a deductive argument. That makes it

legitimate to add that extra premise to the argument even though the person

who gave that argument omitted that premise. The arguer did not openly

state the extra premise, but he did assume it.

For example, if we are told that Chester Arthur was a president of the

United States, we have a right to conclude a great many things about him—

for example, that at the time he was president, he was a live human being.

Appeals to facts of this kind lie behind the following argument:

Benjamin Franklin could not have been our second president, because he

died before the second election was held.

This argument obviously turns on a question of fact: Did Franklin die before

the second presidential election was held? (He did.) The argument would not

be sound if this explicit premise were not true. But the argument also depends

on a more general principle that ties the premise and conclusion together:

The dead cannot be president.

This new premise is needed to make the argument valid in the technical

sense.

This new premise is also needed to explain why the premise supports the

conclusion. You could have made the original argument valid simply by

adding this:

If Franklin died before the second election was held, then he could not

have been our second president.

Indeed, you can always make an argument valid simply by adding a condi-

tional whose antecedent is the premises and whose consequent is the con-

clusion. However, this trick is often not illuminating; it does not reveal how

the argument works. In our example, there is nothing special about Franklin,

so it is misleading to add a conditional that mentions Franklin in particular.

In contrast, when we add the general principle, “The dead cannot be presi-

dent,” this new premise not only makes the argument valid but also helps

us understand how the conclusion is supposed to follow from the premise.

5. Every argument with true premises and a false conclusion is invalid.


6. Every argument with a true conclusion is sound.


7. Every argument with a false conclusion is unsound.

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