Modus tollens literally means "the mode of denying."
If P, then Q. It is not the case that Q. Therefore, it is not
the case that P.
The symbolic form looks like this;
. If it is raining, then it is cloudy. It is not cloudy.
Therefore, it is not raining.
How does it work? Recall that "necessary" means that
whenever the antecedent is present, the it is necessary that the
consequent be present. So it logically follows that if the necessary
condition (the consequent) is NOT present, that the sufficient
condition (the antecedent) couldn't be present either. In our example,
you'll remember that there has to be at least a small cloud for
there rain, so we know that whenever there are no clouds, then
it is guaranteed that there is no rain.
It is called the mode of denying because it denies P by denying