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]”.
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 (valid inference) | Denying a Conjunct (fallacy) | Affirming a Disjunct (fallacy) |
|||||
|---|---|---|---|---|---|---|---|
| Premise 1 | A ⊻ B (A or B, but not both) | ⌐ (A ∧ B) (not both, A and B) | A ∨ B (A oder B) |
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| 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) | |