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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.

Note: numbers can also be neither even nor odd (e.g. rational numbers). If such possibilities are not excluded (e.g. by considering only natural numbers), one can easily fall for the fallacies mentioned below.


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


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:

See also

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Ad Hominem Info is a project to explain and categorize the most common systematic fallacies and fallacies. On this page, you will find a background article that briefly explains an important logical concept, which may be needed to better understand another article in this area.
For more information, please see the main category “logic

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