Valid form
Modus ponens
Also known as affirming the antecedent, modus ponendo ponens or conditional elimination
Modus ponens (Latin modus ponendo ponens, “the way that affirms by affirming”; in English, affirming the antecedent) is the most basic valid inference from an if-then statement. If “if P, then Q” is true, and P is true, then Q must be true.
It’s valid by its form alone. You don’t need to know what P and Q stand for: any argument with this shape and true premises has a true conclusion.
Example
If it’s a weekday, the library opens at 9. It’s a weekday. So the library opens at 9.
In “if P, then Q”, P is called the antecedent and Q the consequent. Modus ponens affirms the antecedent (P is true) and concludes the consequent.
Valid isn’t the same as true
A valid argument only guarantees its conclusion if its premises are true.
If the moon is made of cheese, mice could live on it. The moon is made of cheese. So mice could live on it.
That’s a perfectly valid modus ponens with a false conclusion, because a premise is false. An argument that is valid and has true premises is called sound. So when an argument has this form, the reasoning isn’t the problem. The question is whether the premises are true.
Look-alikes
Four forms that look similar. Two are valid, two are not.
| Form | Valid? |
|---|---|
| If P, then Q. P. So Q. | Yes: modus ponens (affirming the antecedent) |
| If P, then Q. Not Q. So not P. | Yes: Modus tollens (denying the consequent) |
| If P, then Q. Q. So P. | No: Affirming the consequent |
| If P, then Q. Not P. So not Q. | No: Denying the antecedent |
Sources
- Irving M. Copi, Carl Cohen and Kenneth McMahon (2011). Introduction to Logic (14th edition). Pearson.
Last reviewed 2026-09-13.