The term is used to express a variety of meanings which, although distinct in themselves, yet flow readily into one another. These meanings may best be grouped according as they have (1) an ontological objective value, or a logical subjective value; and (2) according as they are used antithetically to actuality or necessity. The antithetical point of view is the most convenient from which to begin.
Possibility may mean that something is (1) not actual, or (2) that, while it possesses actual existence, that existence lacks causal or rational necessity.
(1) As opposed to the actual, the phrase has again a double meaning. (a) Taken objectively, it may mean something as yet undeveloped, since not presenting itself in actually objectified form, but capable of doing so at some future time, when all the conditions of its realization occur: latent, potential being. This implies capacity for realization; and, if this capacity be taken in an active sense, connotes some inherent tendency to actuality, which, if not thwarted, leads to final completeness of being. This involves the active sense of potentiality, of force, etc. It is close to the literal sense of the term (posse, can be). This is the dominating sense in Greek philosophy, being connected with Aristotle’s teleological theory of development. (b) Taken logically, it denotes that there is some ground for asserting actuality, but not sufficient to justify a positive statement: may, as distinct from can, be. Thus, possibly it will rain tomorrow. It has to do with degrees of certainty in judging.
(2) As opposed to the necessary, the term has also a double sense. (a) It may mean chance, contingency, as an objective fact. Chance again, has a double meaning: (i) something not derivable or explainable causally by reference to antecedent facts. There are those who assert the reality of such chance. On this view there are many possibilities in store in the future which no amount of knowledge would enable us to foresee or forestall. Indeterministic theories of the will assert possibilities of this sort also. (ii) Chance may mean that which, while necessary causally, is not necessary teleologically; the unplanned, the fatalistic. From this point of view the “possible” is that which unexpectedly prevents the carrying-out of a purpose or intention. It leads up to the logical sense (b), according to which the possible, as opposed to the necessary, is anything whose existence cannot be derived from reason; that, the existence of which, rationally speaking, might be otherwise. It is opposed to mathematical or metaphysical necessity, where existence cannot be otherwise than as it is. In this sense the objective actual may be only (logically) possible; the present rain-storm is actual, but since it does not follow from a necessity of thought, but only from empirical antecedents, it is not necessary, and hence just a contingent possibility. [—] In the sphere of mathematics, logic, and metaphysics there is no possibility in the strict sense; all that exists exists of necessity. In the physical and practical spheres which deal with the space and time world the notion of possibility has full sway. Everything is possible which does not contradict the laws of reason; that which is inconceivable, which violates the law of reason, is impossible. The impossible is the self-contradictory.
The nominalistic definition (nominalistic in its real character, though generally admitted by realists, as Scotus, i. dist. 7, qu. unica) that that is possible which is not known not to be true in a real or assumed state of information is, like many nominalistic definitions, extremely helpful up to a certain point, while in the end proving itself quite superficial. It is not that certain things are possible because they are not known not to be true, but that they are not known not to be true because they are, more or less clearly, seen to be possible.