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 [consequent statement] by affirmation [of the antecedent statement]”.
Other names
In the literature, one may also come across the following alternative names for this conclusion:
- Implication elimination
- Affirming the antecedent
- Modus ponendo ponens
- Affirmatio conditionis
Fallacies
Although the MP is intuitively understandable to most people, it is not uncommon for people to draw erroneous conclusions based on it.
The following table contrasts the modus ponens with its most common fallacies:
| 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 | | |
These fallacies can be summarized as follows:
- In case of an affirmation of the consequent, the direction of inference in the conditional statement is reversed: the consequent is thus made the antecedent and vice versa, which is not a valid transformation (illicit commutation).
- When denying the antecedent, one mistakenly assumes that a negated consequent can be inferred from a negated antecedent. This, too, is not a valid transformation.
Both fallacies are described in more detail in the linked articles.
See also
More information
- Modus ponens on Wikipedia