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The Varieties of Necessity

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Necessity and Possibility
Necessity and possibility are intimately related: to say that a scenario is possible is to say that it is not necessary that it is not possible, while to say that a scenario is necessary is to say that it is not possible that it fails to be the case. Such type of relation is more thoroughly investigated by that branch of logic that goes under the label of modal logic: the term "modal" is owed to the fact that necessity and possibility are modes of existence of entities.

Necessity and possibility, however, are also key notions in metaphysics as well as in epistemology: it is from this perspective that, in the rest of this article, I shall distinguish different senses in which some scenario may be said to be necessary.

Nomic Necessity
Sometimes, we say that a scenario is necessary because it seems to follow from certain rules or laws of natural events. Thus, if right now you grab hold of an apple with your hand and you bring it at the height of your face to then let it go, observing the apple falling to the ground seems to be a necessary event, dictated by the law of universal gravitation.

This variety of necessity is indeed labeled nomic necessity, as it deals with laws – "nomos," in Greek.

Deontic Necessity
Not every necessity we express is nomic. A form of non-nomic necessity is the one related to ethical judgments. If I say that a person must not lie, I am expressing the moral necessity of a scenario not taking place. Of course, that someone lies is compatible with the laws of nature and, alas, it is quite common. Yet, to express that such a scenario is not verified in any circumstance that is free from moral blame, we indeed employ a variety of necessity: this is called deontic necessity, from the Greek "deontos," meaning "that which is proper."

Legal and Conventional Necessity
Other varieties of necessity are those expressed in conventions. When I say that, in soccer, a team cannot play with twelve players at once on the field, I am expressing a rule of soccer: of course, no law of nature violates there being twelve players on the field and not even any moral principle seems to be against it. Other examples of conventional necessity are, say, that you must stop when a traffic light is red, or that in chess you cannot move a bishop in vertical or horizontal directions.

Metaphysical Necessity
Sometimes, we may want to express the possibility that our universe could have functioned in accordance with different laws of nature from the ones we observed. Consider again holding your apple in your hand: once you let go of it, it will fall to the ground; and indeed, in some sense that was a necessary consequence of the law of gravitation. However, we may also imagine a scenario in which the law of gravitation does not hold. That is because the scenario of the apple falling is nomically necessary, it is not metaphysically necessary: our metaphysical intuitions, tells us that the apple may have not fallen. (Of course, not every metaphysician would agree to this!)

Logical Necessity
What are the limits of what is metaphysically possible? For some, those are fixed by that which is logically possible. In other words, if the description of a scenario seems to be non-contradictory, then it is possible. This means that only that which is logically necessary, is also metaphysically necessary. For instance, since it is logically necessary that a triangle has three sides, then it is also metaphysically necessary that a triangle has three sides. However, since it is not logically necessary that a triangle be greater than the universe, than such a triangle is possible.

Essences
Finally, we shall mention that variety of necessity that goes under the label of essence. The term, first introduced in Western philosophy by Aristotle, expresses not only the necessary property of an entity, but also the fact that such a property defines the identity of the entity in question. Thus, it is part of the essence of water that its chemical structure is H2O; or, it is part of the essence of a singleton of a set to be defined by such a set.

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