with opinion, is deprived of the incontrovertible reasonings of demonstration. The following is a specimen of the analytical method of Plato's dialectic. Of analysis there are three species. For one is an ascent from sensibles to the first intelligibles; a second is an ascent through things demonstrated and subdemonstrated, to undemonstrated and immediate propositions; and a third proceeds from hypothesis to unhypothetical principles. Of the first of these species, Plato has given a most admirable specimen in the speech of Diotima in the Banquet. For there he ascends from the beauty about bodies to the beauty in souls; from this to the beauty in right disciplines; from this again to the beauty in laws; from the beauty in laws to the ample sea of beauty (Greek: to polu pelagos tou kalou); and thus proceeding he at length arrives at the beautiful itself. 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.