The second species of analysis is as follows: It is necessary to make the thing investigated the subject of hypothesis; to survey such things as are prior to it; and to demonstrate these from things posterior, ascending to such as are prior, till we arrive at the first thing and to which we give our assent. But beginning from this, we descend synthetically to the thing investigated. Of this species, the following is an example from the Phaedrus of Plato. It is inquired if the soul is immortal; and this being hypothetically admitted, it is inquired in the next place if it is always moved. This being demonstrated, the next inquiry is if that which is always moved, is self-moved; and this again being demonstrated, it is considered whether that which is self-moved is the principle of motion, and afterwards if the principle is unbegotten. This then being admitted as a thing acknowledged, and likewise that what is begotten is incorruptible, the demonstration of the thing proposed is thus collected. If there is a principle, it is unbegotten and incorruptible. That which is self-moved is the principle of motion. Soul is self-moved. Soul therefore (i.e. the rational soul) is incorruptible, unbegotten, and immortal.
Of the third species of analysis, which proceeds from the hypothetical to that which is unhypothetical, Plato has given a most beautiful specimen in the first hypothesis of his Parmenides. For here, taking for his hypothesis that the one is, he proceeds through an orderly series of negations, which are not privative of their subjects, but generative of things which are as it were, their opposites, till he at length takes away the hypothesis that the one is. For he denies of it all discourse and every appellation. And thus evidently denies of it not only that it is, but even negation. For all things are posterior to the one; viz. things known, knowledge, and the instruments of knowledge. And thus, beginning from the hypothetical, he ends in that which is unhypothetical, and truly ineffable.
Having taken a general survey, both of the great world and the microcosm man, I shall close this account of the principal dogmas of Plato, with the outlines of his doctrine concerning Providence and Fate, as it is a subject of the greatest importance, and the difficulties in which it is involved are happily removed by that prince of philosophers.