Modus Tollens

Disciplines > Argument > Syllogisms > Modus Tollens

Description | Example | Discussion | See also

Description

If X is true then Y is true.

Y is false.

Therefore X is false.

Example

If there is smoke, there is fire. There is not fire, so there is no smoke.

If I am happy, then I smile. I am not smiling, therefore I am not happy.

Discussion

Modus Tollens is not as straightforward as its companion, Modus Ponens. Although common in argument, a Modus Tollens is not necessarily true, as the major premise (If X is true then Y is true) says nothing about falsehood. If, however, X and Y are bivalent (both can be either true or false) and X can only be true if Y is true, then the Modus Tollens stands.

Modus Tollens is the root of falsification, as proposed by Karl Popper and since used as the cornerstone of scientific proof.

This is also known as Denying the Consequent, as Y, the consequent is being denied as being true.