Modus Ponens
Also abbreviated MP or MPP, is one of the most elementary (valid) logical inferences. It is based on a conditional and the affirmation of its antecedent.
A → B–if A, then B.
A–A is true.
∴ B–therefore B [is true].
The following is an example of a valid Modus Ponens:
If it is raining, [then] the street will get wet.
It is raining,
Therefore: The street will get wet.
Name
The full name of this form is “Modus ponendo ponens”. Loosely, this could be translated as the “mode of inferring an affirmative [statement] by affirmation [another statement]”.
Other names
- Implication elimination
- Affirming the antecedent
- Affirmatio conditionis
Fallacies
Although the MP is intuitively comprehensible for most people, it is not uncommon to make fallacious conclusions on it.
The following table contrasts the modus ponens with its most common errors:
| Modus ponens (valid inference) | Affirming the consequent (formal fallacy) | Denying the antecedent (formal fallacy) |
||
|---|---|---|---|---|
| Premise 1 | A → B (if A, then B) | A → B (if A, then B) | A → B (if A, then B) |
|
| Premise 2 | A | B | ⌐A (not A) | |
| Conclusion | B | | |
See also
More information
- Modus ponens on Wikipedia