# Online Encyclopedia

# Modus ponens

**Modus ponens** (Latin: *mode that affirms*) is a valid, simple argument form (often abbreviated to **MP**):

- If P, then Q.
- P.
- Therefore, Q.

or in logical operator notation:

where represents the logical assertion.

The argument form has two premises. The first premise is the "if-then" or *conditional* claim, namely that P implies Q. The second premise is that P, the *antecedent* of the conditional claim, is true. From these two premises it can be logically concluded that Q, the *consequent* of the conditional claim, must be true as well.

Here is an example of an argument that fits the form *modus* *ponens*:

- If democracy is the best system of government, then everyone should vote.
- Democracy is the best system of government.
- Therefore, everyone should vote.

The fact that the argument is valid cannot assure us that any of the statements in the argument are true; the validity of modus ponens tells us that the conclusion must be true if and only if all the premises are true. It is wise to recall that a valid argument within which one or more of the premises are not true is called an *unsound* argument, whereas if all the premises are true, then the argument is *sound*. In most logical systems, Modus ponens is considered to be valid. However, the instances of its use may be either sound or unsound.

- If the argument is modus ponens and its premises are true, then it is sound.
- The premises are true.
- Therefore, it is a sound argument.

A propositional argument using modus ponens is said to be deductive.

For an amusing dialog that problematizes modus ponens, see Lewis Carroll's "What the Tortoise Said to Achilles."