Logic Question

Question

If Paul was killed in an automobile accident then Paul is dead. Paul was not killed in an automobile accident. Therefore Paul is not dead.

1) What is the form of this argument?

2) Construct a counterexample to establish whether it is valid.

 

If Mark was killed in an automobile accident then Mark is dead. Mark is dead. So, Mark was killed in an automobile accident.

1) What is the form of this argument?
2) Construct a counterexample to establish whether it is valid.

3) Convert this passage into an enthymeme. Explain your results.

Answer 1

The first argument could be represented (in predicate logic) as:

 

Kp ⊃ Dp / ~Kp // ~Dp

 

The form of this argument is called "denying the antecedent." It is called this because the second premise, "Paul was not killed in an automobile accident" denies the antecedent of the conditional in the related premise. It is a known invalid form of argumentation is easily shown to be such with a simple truth table.

 

A simple counterexample would be if Paul was actually dead, but died from some cause other than a car accident (which is common enough).

 

The second argument could be represented as:

 

Km ⊃ Dm / Dm // Km

 

This form is known as "affirming the consequent." It is also a known invalid form.

 

Since Mark is already dead, it will be hard to construct a counterexample, since the best one would be to kill Mark some other way.

 

An enthymeme is an incomplete argument, so simply saying, "Mark is dead, so he must have been killed in a car accident," represents an enthymeme.