Modus ponens
Latin: mode that affirms) is a valid, simple argument form:
- If P, then Q.
- P.
- Therefore, Q.
or in logical operator notation:
- <math> p \rightarrow q, <math>
- <math> p \quad <math>
- <math> \vdash q <math>
where <math>\vdash<math> 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.
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."
See also
