Valid Argument Forms

The following are a few valid argument forms. That is to say, any deductive argument having any of the following forms is valid. Note that it is possible to combine these forms in any stretch of deductive argumentation and preserve validity. Also, this list is by no means exhaustive. There are other valid argument forms. These valid argument forms are, however, the forms we will encounter most often in this course.

Modus Ponens
  1 If P then Q  
  2 P  
3 Q 1&2

 

Modus Tollens
  1 If P then Q  
  2 not Q  
3 not P 1&2

 

Disjunctive Syllogism
  1 P or Q  
  2 not P  
3 Q 1&2

 

Hypothetical Syllogism
  1 If P then Q  
  2 If Q then R  
3 If P then R 1&2

 

Barbara Syllogism
  1 All A's are B's  
  2 All B's are C's  
3 All A's are C's 1&2

 

Reductio ad Absurdum
  1 P  
    ...  
n Q  
    ...  
m not Q  
m+1 not P 1,n&m

 

Replacement
  1 a is an F  
  2 a = b  
3 b is an F 1&2

 

Proof by Cases
  1 P or Q  
  2 If P then R  
  3 If Q then R  
4 R 1,2&3