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, I call that an _universal_ predicate, which is predicated
of a subject totally and essentially, and considered as primarily
and inseparably inherent in that subject: for it does not follow
that a predicate, which is total, should be immediately universal;
for whiteness is affirmed of every swan, and blackness of every
crow, yet neither universally. In like manner, a substantial
predicate is not consequently an universal one; for the third mode
of essential predicates, and the two following (instanced before)
cannot be universal. Thus, colour, although inherent in superficies
essentially, is not inherent in every superficies, and consequently
not universally. Thus again, Socrates, Callias, and Plato, though they
exist essentially, are not universals, but particulars; and thus,
lastly, the drinking of poison was an essential cause of the death of
Socrates, but not an universal one, because Socrates might have died
by other means than poison. If then, we wish to render an accurate
definition of an universal predicate, we must not only say it is total
and essential, but that it is primarily present to its subject and no
other. Thus, the possession of angles equal to two right, primarily
belongs to a triangle; for this assertion is essentially predicated of
triangle, and is inherent in every triangle. This property, therefore,
is not universally in figure, because it is not the property of every
figure, not of a square, for instance; nor as universal in a scalene
triangle: for although it is contained in every scalene, and in every
equilateral, and isosceles triangle, yet it is not primarily contained
in them, but in triangle itself; because these several figures inherit
this property, not from the particular species to which they belong,
but from the common genus _triangle_. And thus much concerning
_total_, _essential_, and _universal_ predicates.
10. Concerning that which is universal, we are frequently liable to
err; often from a belief that our demonstration is universal, when it
is only particular; and frequently from supposing it particular when it
is, on the contrary, universal. There are three causes of this mistake;
the first, when we demonstrate any particular property of that which is
singular and individual, as the sun, the earth, or the world. For since
there is but one sun, one earth, and one world, when we demonstrate
that the orb of the earth possesses the middle place, or that the
heavens revolve, we do not then appear to demonstrate that which is
universal.
To this we answer: when we demonstrate an eclipse of the sun to arise
from the opposition of the moon, we do not consider the sun as one
particular luminary, but we deduce this consequence as if many other
suns existed besides the present.