Modus tollens

Modus tollens (Latin for: Mode of fuss, literally aufhebender mode), mode actually tollendo tollens (as opposed to mode ponendo tollens ) is a final figure, which is also used in several calculi of classical logic as a rule of inference.

He says that from the premises B and if A, then B can not be closed to non- A.

The tollendo tollens mode is thus a counterpart to the mode ponendo ponens.

The premises

So let the Conclusion

Pull.

The Latin name mode tollendo tollens, " by canceling canceling circuit manner " explained by the fact that it is a final figure ( mode) is that, given the first premise A → B, by the " picked up " ( tollendo ) of the set B, so by setting its negation, ¬ B, another set, namely a, also " pick up " ( tollens ), ie its negation, ¬ a leads.

As a statement

Although the mode tollendo tollens a rule of inference, then, is a meta-linguistic concept, the term " mode tollens " occasionally used for object- language expressions with the following structure:

However, since inference rules and statements are completely different concepts, it is scientifically rather unfortunate to call them with the same name. Generally, the mixing property and the metalanguage is problematic and should normally be avoided.

Example

From the conditions when it rains, the road is wet and the road is not wet can be the logical conclusion It is not raining draw. In contrast, the circuit direction The road is wet, so it rains inadmissible and wrong.

Evidence

The logical equivalence of the statements A → B and ¬ B → ¬ A follows from the definitions of subjunction and the negation.

Left side:

Right side:

Importance of tollens mode

After the critical rationalism of the mode is tollens the basis of scientific research. Where A is an abstract hypothetical theory, B is a set of observations, which follows from the theory. Scientific experiments have the function determine by observation whether B is true or false. If B is false, then its underlying theory, this is then falsified.