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In the first two ways, we considered more concrete and evident objects of contemplation, i.e., the causes of being and becoming. In the third way, we go even deeper, considering being qua being.
Contingency: Contingency, broadly speaking, is the "ability to not-be." It is important to note that this is distinct from "possibility" which is the ability to be.
Contingent being: This is a being which is indifferent in respect to "to-be" and "not to-be." Thus, concretely, each being that is contingent is also possible.
Necessity: Impossible to not be.
Necessary being: A being wherein it is impossible for it to not be. This can be of two kings. First, we can think of a certain "caused" or "hypothetical" necessity wherein, on the supposition of the creation of the being, the being is not contingent (intrinsically, i.e., does not have the principle of tending towards "not-be" in itself). Such are angels and souls. Second, we can think of an uncaused necessity, i.e., an absolutely necessary being.