NECESSITY AND CAUSALITY.
[CHAPTER I.]
NECESSITY.
1. Beings are divided into two c∞∞lasses: necessary and contingent; necessary being is that which cannot but be; contingent is that which may be and cease to be. In these definitions every thing is said; but their laconism does not permit all that is expressed in them to be easily understood. Necessity and contingency may refer to different aspects and give rise to very diverse considerations. This makes a careful analysis of the ideas expressed by them necessary.
2. What is meant by necessity? In general that is called necessary which cannot but be; but the expression cannot, may be taken in different senses: in a moral sense, as when we say: I cannot but fulfil this duty; in a physical, as in this proposition; a paralytic cannot move himself; and in a metaphysical sense, as: A triangle cannot be a quadrilateral. In the first example, the obstacle is founded on a law; in the second, it arises from nature; in the third, it follows from the essence of the things. In all these suppositions, necessity implies the impossibility of the contrary, and this impossibility results from the necessity.
3. Hence it follows that the ideas necessity and impossibility are correlative, and that is metaphysically necessary whose opposite is metaphysically impossible. Impossibility consists in the exclusion of one thing by another; thus, "a circular triangle is impossible," means the same as "the nature of a triangle excludes the nature of a circle." In all impossibility, therefore, there is a term denied; as in all necessity there is a term affirmed; the metaphysically necessary is that whose opposite is contradictory; the existence of the absurd is impossible, the non-existence of the necessary is absurd. It is contradictory for a triangle to have four sides; and it is absurd for a triangle not to have three angles.
4. In the purely ideal order we see many necessities without any relation to existence; such are all geometrical truths. Even in the real order we conceive many hypothetical necessities in contingent beings: such are those which are obtained by applying absolute principles to any hypothesis furnished by experience. The principle of contradiction serves in an infinity of cases to found a certain necessity even in contingent beings. There is no absolute necessity of the existence of extended beings; but on the supposition that they exist, it is necessary for them to have the properties proceeding from extension.
5. In no finite being can there be an absolute necessity; the only necessity which it can have is hypothetical. The relation of its essential attributes is necessary; but, as its essence does not exist necessarily, whatever is necessary in it is so only hypothetically, that is, on the supposition that it exists.
6. We must then distinguish two necessities: one absolute, the other hypothetical. The latter relates to the essences of things, abstracting their existence, although implying it as a condition, and supposing another necessary as the ground of its possibility;[72] the former relates to the existence of the thing. The absolutely necessary is that whose existence is absolutely necessary.