Modus Ponens is a rule of inference in propositional logic. It is used to break up a conditional statement. Modus Ponens says that if you have a statement in the form of "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.

The full name of this function is modus ponendo ponens, being Latin for "the way that affirms by affirming". It is often abbreviated to MP. This is a simple rule, but easily confused with Affirming the consequent.

Back up to Rules of Inference

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.

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