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
constitute the best syllogisms derive all their force and efficacy from
these.
And on this account, above all others, they merit the title of
the principles of demonstration. But here it is worth observing,
that these primary propositions are not the first in the order of
our conceptions; but first to nature, or in the nature of things.
To us, that which is first is particular, and subject to sensible
inspection; to nature, that which is universal, and far remote from
the apprehension of sense. Demonstration does not submit itself to the
measure of our ingenuity, but, with invariable rectitude, tends to
truth as its ultimate aim; and without stopping to consider what our
limited powers can attain, it alone explores and traces out the nature
of a thing, though to us unperceived and unknown.
This demonstrative syllogism differs not a little from others, by the
above property; the rest can as well educe a true conclusion from false
premises, which is frequent among the rhetoricians, as that which is
prior from that which is posterior; such as, Is every syllogism derived
from conjecture?
With respect to the rest, as we have already confessed, they may be
formed from principles that are true, but not from such as are proper
and peculiar; as if a physician should endeavour to prove an orbicular
wound the most difficult to coalesce and heal, because its figure is of
all others, the most capacious; since the demonstration of this is not
the province of the physician, but of the geometrician _alone_.
5. That proposition is called immediate, which has none superior to
itself, and which no demonstration whatever can confirm: such as these
are held together by the embraces of universals. There are some,
indeed, united from that which is sensible and particular: thus, that
the garment is white, is an immediate proposition, but not of that
kind whose principles require to be demonstrative ones; the cause
of which we shall hereafter investigate. Of immediate propositions
subservient to the purposes of demonstration, some are of such a
superior nature, that all men possess a knowledge of them without any
previous instruction; and these are called axioms, or general notions;
for without these all knowledge and enquiry is vain. Another species
of immediate propositions is position; incapable of being strengthened
by demonstration, yet not necessarily foreknown by the learner, but
received from the teacher. With respect to the genus of position, one
of its species is definition, and another hypothesis. Definition is an
oration, in which we neither speak of the existence, nor non-existence
of a thing; but alone determine its nature and essence. It is common to
every hypothesis, not to be derived from nature, but to be the entire
result of the art of the preceptor.