Now, not only demonstration and belief and knowledge, but foreknowledge also, are used in a twofold manner. There is that which is scientific and certain, and that which is merely based on hope.
In strict propriety, then, that is called demonstration which produces in the souls of learners scientific belief. The other kind is that which merely leads to opinion. As also, both he that is really a man, possessing common judgment, and he that is savage and brutal,—each is a man. Thus also the Comic poet said that "man is graceful, so long as he is man." The same holds with ox, horse, and dog, according to the goodness or badness of the animal. For by looking to the perfection of the genus, we come to those meanings that are strictly proper. For instance, we conceive of a physician who is deficient in no element of the power of healing, and a Gnostic who is defective in no element of scientific knowledge.
Now demonstration differs from syllogism; inasmuch as the point demonstrated is indicative of one thing, being one and identical; as we say that to be with child is the proof of being no longer a virgin. But what is apprehended by syllogism, though one thing, follows from several; as, for example, not one but several proofs are adduced of Pytho having betrayed the Byzantines, if such was the fact. And to draw a conclusion from what is admitted is to syllogize; while to draw a conclusion from what is true is to demonstrate.
So that there is a compound advantage of demonstration: from its assuming, for the proof of points in question, true premisses, and from its drawing the conclusion that follows from them. If the first have no existence, but the second follow from the first, one has not demonstrated, but syllogized. For, to draw the proper conclusion from the premisses, is merely to syllogize. But to have also each of the premisses true, is not merely to have syllogized, but also to have demonstrated.
And to conclude, as is evident from the word, is to bring to the conclusion. And in every train of reasoning, the point sought to be determined is the end, which is also called the
