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
And thus, by taking away infinity from the reasoning art, we have
given a support to science, which the most vigorous efforts of subtle
sophistry can never finally subvert. We have set bounds to that
restless spirit of enquiry which wanders uncontrouled in the mind
unenlightened by science, by every where circumscribing its progress
within the limits of that which is most particular, and most universal,
a first predicate, and an ultimate subject: and finally, by asserting
that all the evidence of human knowledge results from the lustre
of primary and immediate principles, we have held up a steady and
permanent light, ever sufficient to direct our steps through the dark
mazes of ignorance and error, into the bright paths of certainty and
truth.
20. Let us next consider whether universal demonstration is preferable
to particular, or not. And first, in favour of particulars we may
say that their evidence is more exquisite and certain than that of
universals. Thus, the knowledge, from inspection, that Callias is a
rational animal, is superior to that acquired by a reasoning process
which infers his rationality, because every man is a rational animal.
By particular demonstration a thing is known as it is, by universal
only in common. Besides, particulars possess some solidity, universals
none: and the demonstration of things which have a real existence,
is more excellent than that of things which have none. And there are
no errors more frequent than those about universals; demonstration
considering them as things entirely abstracted from singulars. On
the contrary, particulars are usurped by the sight, grasped, as it
were, by the hand, and the general subject of every sense; so that
concerning these, demonstration affirms nothing false or inconstant.
But these reasons, however plausible, are easily confused. And,
first, the term essential is more closely connected with universals
than particulars. Thus the possession of three angles equal to two
right, is an affection more essential to the triangle itself, than
to one equilateral or scalene. Add too, that in the demonstration of
universals we always infer some property of a subject from its simple
existence, or because it is such a subject. Again, many affections are
contained in singulars assumed from no particular nature, but from
that which is universal; as rationality in Socrates, which is not
inferred from his existence as Socrates, but from his existence as man.
Farther, that demonstration is the more excellent which is derived
from the better cause: but an universal cause is more extended and
excellent than a particular one; since the arduous investigation of
the _why_ in any subject is stopt by the arrival at universals.
Thus, if we desire to know why the exterior angles of a triangle are
equal to four right ones, and it is answered, because the triangle
is isosceles; we again ask, But why because isosceles? And if it be
replied, because it is a triangle, we may again enquire, But why