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.
Name
The name of this inference form can be loosely translated as “form of negation [of a statement] by affirmation [of the alternative]”.
Other names
- Conjunctive syllogism
Fallacies
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) |
||||
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) |
See also
More information
- Modus ponendo tollens on Wikipedia