Necessity and sufficiency

A necessary condition and a sufficient condition are concepts from the theory of scientific explanations, divide the conditions into two different types. The different relationships between Bedingendem and Conditional also be treated in logic, especially in propositional logic.

Understood causal affect both terms the question of whether certain events are irreplaceable as causes of other events, and whether the other events inevitably one devices when certain events would be present (see also counterfactuality ).

Necessary condition

Considered logical statements is a necessary condition for B K a statement a statement that must be necessarily true ( satisfied), if K is true. It does not happen that K is fulfilled without B is satisfied.

The relationship is expressed by the symbolic notation, that is, " implies K B" or " K from the following B". The arrow symbolizes the connection is possible conclusion. If it is certain that K is met, one can be certain that B is true; It can therefore be concluded from K to B. It is irrelevant whether K takes place chronologically before or after B. Often it's just a matter of hiring from the presence of K a conclusion to the previous conditions. There are several necessary conditions that is considered as must all be met simultaneously if K is satisfied ( logical conjunction ):

Are there different from each other logically independent, necessary conditions, so that applies to all pairs of terms with j ≠ k, we can not be alone sufficient for himself that this would be the one that the others are required. A necessary condition is therefore indispensable for the occurrence of an event. But if she is not at the same time sufficiently, it is not enough to ensure that the event occurs. In other words: Without it there ( hence the term Latin conditio sine qua non, see also conditio sine - qua -non- formula ) is not, for the occurrence of K but is something else possibly needed.

Sufficient conditions

A sufficient condition ensures necessarily (or at least ceteris paribus ) for the occurrence of the related event. If the condition is not necessary at the same time, then there are other possible conditions that also the occurrence of the event might have led; means a sufficient, not a necessary condition is thus replaced or bypassed (multiple satisfiability ). In other words, if a sufficient condition is present, then the conditional event occurs a necessity; but the event has already occurred, it can be inferred only on his conditions necessary because if a contemplated sufficient condition is not necessary, it must always be other possible conditions that are sufficiently well. Which present the sufficient conditions can not be decided on the basis of the conditional event.

Considered statements Logical: Has a subjunction several sufficient conditions, that is true, it is sufficient if at least one is satisfied ( logical disjunction ), so K is considered.

Equivalent condition

A condition that is both necessary and sufficient is called equivalent condition. Statements is logical for the abbreviation iff - engl. if and only if usual; German -language correspondences are g d w. , abbreviated for exactly when and then and only then, symbols.

For each conditional, there can be only one at the same time necessary and sufficient condition -. If there were alternative sufficient conditions, it would not be necessary, there would be additional necessary conditions, so they would not be sufficient. Condition and are therefore contingent in the logical relation of Bikonditionals: they are equivalent.

Logical statements related

Necessary and sufficient conditions are closely related. Within the framework of propositional logic means KB (pronounced "K implies B"): If K is a sufficient condition for a situation B, then B is also a necessary condition for K.

Also, the reverse conclusion regarding the type of the condition is valid: If K is a necessary condition for B, then B is a sufficient condition for K. In the propositional logic can be necessary and sufficient conditions alone no further conclusions on the nature of the relationship between condition and conditional about. This requires further consideration and often empirical studies; see also paradoxes of material implication.

INUS condition

The INUS condition of the Australian philosopher John Leslie Mackie represents a nested concept: What is meant is not a sufficient, but necessary part of an unnecessary but sufficient condition. This concept will be especially of knowledge fair that rarely equivalent conditions can be identified for empirical events, even under ceteris paribus clauses.