Modus Ponens

A rule in of inference in propositional logic. It's used to break up a conditional statement.

If you have a statement in the form "if x then y" and you have x, then you can validly conclude that y.

If P, then Q
P
Therefore, Q

If Socrates is a man, then he is mortal.
Socrates is a man.
Therefore Socrates is mortal.

Often abbreviated to MP. This is a simple one, but easily confused with Affirming the consequent.

Also see Modus Tollens, Disjunctive Syllogism and Hypothetical Syllogism.

Modus Ponens is an interesting beast, from a metalogical point of view. All argument and propositional logic depends upon MP, because every argument implies the following assumption:

If {set of propositions P} are all true, then {conclusion Q} is true
P are all true.
Therefore, Q is true.

As a result of this feature of logical argumentation it is impossible to prove that Modus Ponens is itself valid. Therefore our most important rule of inference is one we use just because it intuitively seems right.