Counterposition
Under contraposition (from latin contra against 'and lat. Positio , position', 'position', 'location') is understood in the logic to reverse an implication , d. H. the conclusion from “If A , then B ” to “If not B , then not A ”.
In fact, the statement “From A follows B ” is even equivalent to its counter-position “From not B does not follow A ”.
On the other hand, the conclusion “From B follows A ” or “From not A does not follow B ” is not permitted .
Examples
Everyday example
“When it rains, the pedestrian walkway is wet.” This statement (“From A follows B ”) is equivalent to its counter-position (“From not B does not follow A ”): “If the pedestrian walkway is not wet, then it does not rain . "
"From B follows A ", however, does not apply "if the walkway is wet", must it not rain necessarily. It can (still) rain; it can rain again; it is not raining; or the pedestrian path is wet for completely different reasons (street cleaning, children playing).
Mathematical example
Statement: a ≡ 1 mod 3 ⇒ a ² ≡ 1 mod 3 (with a ∈ Z )
It is the contraposition : a ² ¬≡ 1 mod 3 ⇒ a ¬≡ 1 mod 3
If a ² ≡ 1 mod 3 holds, no unequivocal statement can be made about a, since a ≡ 1 mod 3 or a ≡ 2 mod 3 can be.
See also
- Conversely , the contraposition as a legal method of interpretation
