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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.


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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