## Foundations of Mathematics## Axiomatic System |

##
What is
modus ponens? |

The Latin term *modus ponens* means “mode that affirms,” or in the case of logic, stands for the rule of detachment. This rule (also known as a rule of inference) pertains to the “if…then” statement and forms the basis of most proofs: “If *p* then q,” or if *p* is true, then the conclusion *q* is true. Or simply, it is often seen as the following:

If p, then q.

p. Therefore, q.

To see this another way:

p ⇒ q: ‘If it is raining, then there are clouds in the sky.”

p: “It is raining.”

q: “There are clouds in the sky.”

There are several ways to break down the *modus ponens.* The argument form has two premises: The “if-then” (or conditional claim), or namely that pimplies q; and that p (called the antecedent of the conditional claim) is true. From these two premises it can be logically concluded that q (called the consequent of the conditional claim) must be true as well; in other words, if the antecedent of a conditional is true, then the consequent must be true.