The Language of Argument

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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

matter of logical form. There are, in fact, some obviously valid arguments

that have yet to be shown to be valid in terms of their form. Explaining

validity by means of logical form has long been an ideal of logical theory, but

there are arguments—many of them quite common—where this ideal has

yet to be adequately fulfilled. Many arguments in mathematics fall into this

category. At present, however, we will only consider arguments in which the

strategy we used for analyzing conjunction continues to work.

Are the following arguments valid by virtue of their propositional form? Why

or why not?

1. Donald owns a tower in New York and a palace in Atlantic City.
   Therefore, Donald owns a palace in Atlantic City.


2. Tom owns a house. Therefore, Tom owns a house and a piece of land.


3. Ilsa is tall. Therefore, Ilsa is tall, and Ilsa is tall.


4. Bernie has a son and a daughter. Bernie has a father and a mother.
   Therefore, Bernie has a son and a mother.


5. Mary got married and had a child. Therefore, Mary had a child and got
   married.


6. Bess and Katie tied for MVP. Therefore, Bess tied for MVP.

Exercise V

For each of the following claims, determine whether it is true or false. Defend

your answers.

1. An argument that is a substitution instance of a valid argument form is
   always valid.


2. An argument that is a substitution instance of an invalid argument form
   is always invalid.


3. An invalid argument is always a substitution instance of an invalid
   argument form.

Exercise VI

Is a valid argument always a substitution instance of a valid argument form?

Why or why not?

Discussion Question

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