### Hypothetical Syllogisms:Invalid Forms

There are two other possible forms of mixed hypothetical syllogism, both of them invalid:

DENYING THE ANTECEDENT

 If p, then q. If my car is out of gas, it will stop running. Not-p. My car is not out of gas. Therefore, not-q. Therefore, it will not stop running.

AFFIRMING THE CONSEQUENT

 If p, then q. If my car is out of gas, it will stop running. q. My car stopped running. Therefore, p. Therefore, it is out of gas..
In each case, the hypothetical premise says that being out of gas is sufficient to make my car stop running. Both arguments assume, however, that being out of gas is the only thing that can do so. That is not true, of course, and it is not implied by the hypothetical premise. Suppose I have a full tank but my battery is dead. That would make the premises of both arguments true, but the conclusion in each case would be false.

A valid deductive argument cannot have true premises and a false conclusion.

Affirming the antecedent | Denying the consequent
Invalid forms | Finding missing premises

Hypothetical Syllogisms