Possibles, as mere beings of reason, have neither actuality nor formal unity, except in intellectual conception; whence it follows that they do not constitute number, except in intellectual conception. This inference is evident. For every multitude is made up of distinct units; and therefore no real multitude can be conceived without real units really distinct. On the other hand, possible beings are not real, but conceptual, units, nor are they really, but only mentally, distinct from one another. As, however, they are distinctly conceived, and have a distinct ideal actuality in the intellect that conceives them, they constitute what may be called an ideal multitude. Such a multitude, as seen and exhaustively comprehended by God's intellect, is absolutely and positively infinite; for possibilities are nothing but the virtual degrees of being which God's infinite reality eminently contains, and which God's infinite power can produce outwardly. The range of possibilities is therefore co-extensive with God's infinity, and thus actually comprises an infinite (not an indefinite) multitude of distinct terms.
This infinite multitude is distinctly and positively known to God in the perfect comprehension of his own infinite being, which is the inexhaustible source of all possible beings; to our intellects, however, which cannot comprehend infinity, the same infinite multitude is known only negatively, inasmuch as we understand that the multitude of possible beings admits of no limit whatever. We have, in fact, no positive intuition of the infinite, but acquire a notion of it by means of abstraction only, as we remove the limits by which any finite reality directly perceived by us is circumscribed. In other terms, our [pg 292] notion of the infinite is not an intuitive idea, as the ontologists assume, but only an abstract concept.[86]
Thus far we have spoken of what is called intrinsic possibility. Besides this possibility, which is theoretical and absolute, there is also a relative possibility which is extrinsic and practical. Extrinsically possible we call that which is in the power of some being to do. With regard to God, all that is intrinsically possible is also extrinsically possible; for his omnipotence has no bounds. With regard to creatures, whose power is confined to the production of accidental acts, the range of extrinsic possibility is very limited, since it is reduced to acts of a determinate species, and depends on extrinsic conditions. Still, as the efficient power of created substances is never exhausted by exertion, creatures virtually contain in their own power a multitude of possible acts which has no limit but that of the multitude of terms or subjects which can be placed within the sphere of their activity. This amounts to saying that the active power of creatures can be exerted, not only successively, but even simultaneously, in the production of any number of accidental acts of a certain kind. Thus the attractive power of the sun sufficiently accounts for the possibility of innumerable movements which can take place at any time and at all times in any number of planets, comets, or particles of matter around it; so that the multiplication of the effects does not require the multiplication of the power, but only that of the number of subjects, or potential terms, in which the acts proceeding from that power must be received.
From what we have just said of real possibility, it will be easy to determine in what real impossibility consists. Really impossible we call that which cannot exist in nature. Now, nothing can exist in nature which is not an act completed by a suitable term, or a term actuated by a suitable act, or an actuality resulting from the conspiration of an act and a suitable term, as we have shown in a preceding article. That, therefore, is absolutely and intrinsically impossible in which this essential law of being is not fulfilled. Thus passion without action is absolutely and intrinsically impossible, because a term cannot be actuated without an act; whiteness with nothing white is absolutely impossible, because no mode of being is conceivable where there is no being; a material form actuating an intellectual term is absolutely impossible, because the one cannot give that kind of reality which the other should receive, and thus they cannot conspire into one essence; rotundity and triangularity in the same subject are absolutely impossible, because they exclude and destroy one another. Generally, whenever the assumed principles of a thing do not conspire into one essential ratio, the thing will have no essence, and consequently no possibility of existence. Hence everything is intrinsically impossible which lacks some constituent, or of which the constituents cannot meet together.
Things intrinsically impossible are no beings, not even ideal beings; for since they have no essence, they have no objective intelligibility. Nevertheless, they are said to be really, truly, entitatively impossible, inasmuch as they are the opposite of possible entity, reality, and truth.
Besides this intrinsic and absolute impossibility, there is a relative impossibility, which is styled extrinsic, arising from a deficiency or limitation of extrinsic power. It is evident that a thing intrinsically possible may be extrinsically impossible to causes possessing limited power. To God nothing is impossible. When we say that God cannot sin or make a square circle, we do not limit his power, but only point out the intrinsic impossibility of the thing. And let this suffice with regard to possibles and impossibles.
Principles of real relation.
Relative we call “that which connotes something else”—id quod se habet ad aliud. Thus the greater connotes the less, as nothing can be styled “greater” except as compared with something less; and, similarly, the less connotes the greater, as nothing can be styled “less” except as compared with something greater. Hence greater and less are both relative.
That one thing may connote another, there must be some link between them—that is, a communication in something that reaches them both, and thus connects the one with the other. Hence, to constitute a relative being, three things are required: 1st, that which is to be related, or the subject of the relation; 2d, that to which it is to be related, or the term of the relation; 3d, that through which it is related, or the foundation or formal reason of the relation.