In everyday language, one describes something as necessary if one believes ("considers it necessary") that it is needed or must be present in order to achieve a certain state or a certain result . Sometimes the words “most necessary”, urgently needed etc. are used to indicate the priority of a measure.
Often, necessity is also used in the sense of a (basic) requirement .
In scientific and systematic linguistic usage, the words "necessary" and "necessity" have two main uses:
- In the sense of a necessary condition that expresses that a state of affairs must be given so that another state of affairs can only occur. In this sense, for example, the presence of oxygen is necessary for a combustion process to take place. See also necessary and sufficient condition .
- In the sense of logical necessity , which expresses that a statement must be true regardless of the actual state of the world. Within logic, necessity is thematized in this sense by modal logic .
Gottfried Wilhelm Leibniz defines necessity as truth in all possible worlds. For him, contingent is a statement if it is true in at least one possible world and false in at least one possible world. The formal semantics of many logical systems fall back on this idea (see modal logic ).
In political thinking Niccolò Machiavelli the need (taking necessità ) play a key role. Political action should be based on the necessity of a situation.
Logical necessity is a property of statements. A statement is logically necessary if and only if it is impossible that this statement is false. But this phrase is a description, not a definition. The usual formal definition of necessity goes back to Leibniz and his concept of possible worlds: a statement is considered necessary if and only if it is true in all possible worlds, i.e. if reality could in no way be such that the objective statement can be made can be wrong.
The counterpart to logical necessity is the logical possibility: A statement is possible if and only if it is not necessarily false, i.e. H. if the reality could be such that the statement was true.
An extremely banal, but catchy example of a logically necessary statement is the sentence “There are mammals or there are no mammals”. Regardless of how the reality is, one of the two alternatives must apply, so the statement is true.
Logical necessity and possibility in modal logic are thematized and more precisely (and also somewhat more generally) defined.
Logic and math
Like the other sciences, logic and mathematics use the notion of necessity. They have a special role insofar as they consciously use both forms of necessity (sufficient condition and logical necessity) intensively and formalize both forms.
The sufficient condition is expressed or specified more precisely in formal logic through the material implication (better: conditional or subjunction). One writes that P and Q are arbitrary statements to express that P is a sufficient condition for Q or - which is the same thing - that Q is a necessary condition for P.
The subject of investigation becomes necessity in a general sense, the necessity of statements in modal logic. For this purpose it uses and formalizes the modal operators it is necessary that and it is possible that .
- Propositional Logic # Sufficient and necessary condition
- De re and de dicto
- Necessary and sufficient condition
- Kurt Kluxen : The concept of necessità in Machiavelli's thinking , dissertation, Bensberg 1949.