and prior to these the definitive method, and the divisive prior to this.
On the contrary, the merely logical method, which is solely conversant
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.