Argument Forms

A.  Argument Forms and Validity

• Principle:  validity depends on argument forms and not on the truth of the statements in the argument.

• 4 common argument forms:

  • modus ponens

  • modus tollens

  • hypothetical syllogism

  • disjunctive syllogism

• Arguments which have one of these forms will always be valid

 

B.  Valid Argument Forms

 

1.  Modus Ponens

 

If P, then Q. P. Therefore Q.

If my pet hamster gave birth, then it must be female My pet hamster has given birth. Therefore it must be female.

 

1b.   Invalid Form of Modus Ponens

If P, then Q Q Therefore P

When the Dow Jones shows a decline for two months, we are in a recession We are in a recession, so the Dow Jones must have shown a decline for two months

 

2.  Modus Tollens

If P, then Q. - Q Therefore - P

If I owned property in Manhattan today, I would be rich. I am not rich. Therefore, I don't own property in Manhattan.

 

 

2b.  Invalid Form of Modus Tollens

 

If P, then Q -P Therefore, -Q

If I owned a hotel I would be rich. I don't own a hotel. Therefore, I am not rich.

 

3.  Hypothetical Syllogism

If P, then Q If Q, then R Therefore, if P then R

If I get an A on my calculus final, I will get an A in the course. If I get an A in the course, I will have a 3.5 average for the semester. Therefore, If I get an A on the final, I will get a 3.5 average for the semester.

 

4.  Disjunctive Syllogism

P or Q - Q Therefore, P

Either we should fight the Spartan or retreat until help comes. We cannot afford to retreat. Therefore, we should fight the Spartans.

       Ex.  3:  Identifying Argument Forms

Molloy College   |    Department of Philosophy     |    Sophia Project 

   © 2000, Michael S. Russo.       For more information contact:  mrusso@molloy.edu