Hypothetical Syllogisms:
Denying the Consequent (Modus tollens)

Consider the argument:

If p, then q. If God had wanted us to fly, He would
   have given us wings.
Not-q.
He has not given us wings.
Therefore, not-p. Therefore, He did not want us to fly.

If we assume that q is false, we can infer that p is false--for if p were not false (i.e., if it were true), then q could not have been false either.

In this case, we denied the consequent, and that allowed us to deny the antecedent. Once again, the conclusion is a categorical proposition.


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

Hypothetical Syllogisms

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