The Language of Argument

1 3 1

B a s i c P r o p o s i t i o n a l C o n n e c t i v e s

The labeling not only shows that the argument form is invalid, it also

shows why it is invalid. Each line that is marked “Invalid” shows a combina-

tion of truth values that makes the premises true and the conclusion false.

Row 6 presents the combination in which Valerie is not a doctor, is a lawyer,

and is not a stockbroker. With these assignments, it will be true that she is

either a doctor or a lawyer (premise 1), and also true that she is not both a

lawyer and a stockbroker (premise 2), yet false that she is a doctor (the con-

clusion). It is this possibility that shows why the argument form is not valid.

In sum, we can test a propositional argument form for validity by follow-

ing these simple steps:

1. Provide a column for each premise and the conclusion.


2. Fill in truth values in each column.


3. Underline each row where all of the premises are true.


4. Mark each row “OK” if the conclusion is true on that row.


5. Mark each row “Invalid” if the conclusion is false on that row.


6. If any row is marked “Invalid,” the argument form is invalid.


7. If no row is marked “Invalid,” the argument form is valid.

Using the truth table technique outlined above, show that argument forms

1–2 in the above section on process of elimination are valid and that argument

forms 3–4 in the same section are invalid.

Exercise XIII

Is the following argument valid in our technical sense? Explain why or why

not. Could it be sound? Explain why or why not.

(1) Frogs are green.

(2) Frogs are not green.

∴ (3) I am president. (from 1–2)

Exercise XIV

Using the truth table technique outlined above, test the following argument

forms for validity:

1 . ~ p ∨ q 2 . ~ (p ∨ q)

p ∴~q

∴~q

Exercise XV

(continued)

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