# Modus Tollens

Abbreviated MT or MTT. One of the most elementary (valid) logical inferences. It is based on a conditional and then denying its consequent.

`A → B`   – if A, then B.
`¬B`   –   not B.
`∴ ¬A`   –  therefore: not A

For example, the following is a valid Modus Tollens:

If it is raining, [then] the street will be wet.
The street is not wet.
Therefore it does not rain.

## Name

The full name of this inference is “modus tollendo tollens”. This could be loosely translated as “mode of inferring a denying [statement] by denying [another statement]”.

### Other names

• Modus tollendo tollens
• Denying the consequent
• Negatio consequentiae

## Fallacies

Since the Modus Tollens does not necessarily correspond to the colloquial meaning of statements of the type “if … then”, it is usually perceived as less intuitive than, for example, the Modus Ponens. This may be the reason why erroneous conclusions based on the MT are not uncommon.

The following table compares the Modus Tollens and the most important related fallacies: