Modus Ponendo Tollens
Also abbreviated MPT. One of the elementary (valid) logical conclusion figures. It is based on a contravalence and has the form:
A ⊻ B– (A or B, but not both)
A– (A [is true])
∴ ¬B– (therefore: not B)
For example, the following is a valid MPT:
A number is either even or odd (but not both).
x is even.
Therefore x is not odd.
Since contravalence is commutative, this also implies the following:
y is odd.
Therefore y is not even.
The name of this inference form can be loosely translated as “form of negation [of a statement] by affirmation [of the alternative]”.
- Conjunctive syllogism
As with other forms of logical reasoning, there are several fallacies that can on incorrect application of the MPT:
The following table compares the Modus Ponendo Tollens and the most important related fallacies:
| Modus ponendo tollens |
| Denying a Conjunct |
| Affirming a Disjunct
|Premise 1|| A ⊻ B |
(A or B, but not both)
| ⌐ (A ∧ B) |
(not both, A and B)
| A ∨ B
(A oder B)
|Premise 2||A||B||⌐A (not A)||⌐B (not B)||A||B|
|Konklusion||⌐B (not B)||⌐A (not A)||B||A||⌐B (not B)||⌐A (not A)|
- Modus ponendo tollens on Wikipedia