Necessity

In everyday language, is referred to as something necessary if one believes ( " necessary hold " ) that it is required and must be present in order to achieve a particular state or a particular result. Sometimes called the increase " most needed ", is urgently needed, etc. used to indicate the priority of a measure.

Frequently need is also in the sense of ( basic) used condition.

In the scientific and systematic usage, the words are "necessary" and " necessity" mainly in two uses:

Philosophy

In the ontology is the (absolute ) need the antonym for contingency.

Gottfried Wilhelm Leibniz defines necessity as truth in all possible worlds. Quota is a statement for him, if it is false in at least one possible world and true in at least one possible world. The formal semantics of many logical systems takes up this idea back (see modal logic ).

In Niccolò Machiavelli's political thinking the need ( necessità ) plays a key role. Political action should be based on the necessity of a situation.

Logical necessity

Logical necessity is a property of statements. A statement is logically necessary if and only if it is impossible that this statement is false. However, this formulation is a description, not a definition. The usual formal definition of necessity going to Leibniz and his concept of possible worlds back: A statement is accurate then considered necessary if it is true in all at all possible worlds, if reality could therefore be such not mean that the objective statement may be wrong.

The counterpart of the logical necessity is the logical possibility: A statement is exactly possible when it is not necessarily wrong, that is, when the reality could be such that the statement would be true.

A very banal, but catchy example of a logically necessary statement is the sentence " There are mammals, or there are no mammals ". Regardless of how reality is constituted, must be one of the two alternatives are true, the statement is so true.

Be defined more precisely identifies and (and also somewhat more general ) logical necessity and possibility in modal logic.

Logic and mathematics

Like the other sciences use logic and mathematics the concept of necessity. A special role they have in that they deliberately use both forms of need ( sufficient condition and logical necessity ) intensive and formalize both forms.

The sufficient condition is in formal logic by the material implication (better: Conditional or subjunction ) expressed or clarified. One writes, where P and Q are any statements to express that P is a sufficient condition for Q or - what is the same - that Q is a necessary condition for P.

To the object of investigation is necessary in a general sense, the need for statements in modal logic. They are used and for this purpose the modal formalized, it is necessary and it is possible, dass