The philosophical and mathematical commentaries of Proclus on the first book of Euclid's elements (Vol. 1 of 2) : $b To which are added, A history of the restoration of Platonic theology, by the latter Platonists: And a translation from the Greek of Proclus's Theological elements — Plato — John Shaqi
The philosophical and mathematical commentaries of Proclus on the first book of Euclid's elements (Vol. 1 of 2) : $b To which are added, A history of the restoration of Platonic theology, by the latter Platonists: And a translation from the Greek of Proclus's Theological elements
Plato · en
Again, we have already proved that all demonstration consists of
such principles as are prior in the nature of things; and from
hence we infer, that it is the business of no science to prove its
own principles, since they can no longer be called principles if
they require confirmation from any thing prior to themselves; for,
admitting this as necessary, an infinite series of proofs must ensue.
On the contrary, if this be not necessary, but things most known
and evident are admitted, these must be constituted the principles
of science. He who possesses a knowledge of these, and applies them
as mediums of demonstration, is better skilled in science, than he
who knows only posterior or mediate propositions, and demonstrates
from posterior principles. But here a doubt arises whether the first
principles of geometry, arithmetic, music, and of other arts, can ever
be demonstrated? Or shall we allow they are capable of proof, not by
that particular science which applies them as principles or causes
of its conclusions? If so, this will be the office of some superior
science,--which can be no other than the first philosophy, to whose
charge the task is committed; and whose universal embrace circumscribes
the whole circle of science, in the same manner as arithmetic
comprehends music, or geometry optics.--This is no other than that
celebrated _wisdom_ which merits the appellation of science in
a more simple, as well as in a more eminent degree than others: not,
indeed, that all causes are within its reach, but such only as are the
principal and the best, because no cause superior to them can ever be
found. Hence the difficulty of knowing whether we possess science or
not, from the difficulty of understanding whether it is founded on
peculiar or common principles; since it is necessary that both these
should be applied in the constitution of all real knowledge and science.