Philosophy Index

Modus ponens

Modus ponendo ponens, usually simply called modus ponens or MP is a valid argument form in logic. It is also known as "affirming the antecedent" or "the law of detachment".

The form of modus ponens is: "If P, then Q. P. Therefore, Q." It may also be written as:

P → Q, P infers Q

Examples of modus ponens

The following are examples of the modus ponens argument form:

If the cake is made with sugar, then the cake is sweet.
The cake is made with sugar.
Therefore, the cake is sweet.

If Sam was born in Canada, then he is Canadian.
Sam was born in Canada.
Therefore, Sam is Canadian.

Conditional elimination

Modus ponens, as a valid argument form, also serves as the basic conditional elimination rule (→E), one of the basic rules of inference, and may be labeled as such where appropriate.