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
We collect their necessity demonstratively, thus; he who does not
know a thing by the proper cause of its existence, cannot possess
science of that thing; but he who collects a necessary conclusion from
a medium not necessary, does not know it by the proper cause of its
existence, and therefore he has no proper science concerning it. Thus,
if the necessary conclusion _c_ is _a_, be demonstrated by
the medium B, not necessary; such a medium is not the cause of the
conclusion; for since the medium does not exist necessarily, it may
be supposed not to exist; and at the time when it no longer exists,
the conclusion remains in full force; because, since necessary,
it is eternal. But an effect cannot exist without a cause of its
existence; and hence such a medium can never be the cause of such a
conclusion. Again, since in all science there are three things, with
whose preservation the duration of knowledge is connected; and these
are, first, he who possesses science; secondly, the thing known; and
thirdly, the reason by which it is known; while these endure, science
can never be blotted from the mind, but on the contrary, if science be
ever lost, it is necessary some of these three must be destroyed.
If then you infer that the science of a necessary conclusion may be
obtained from a medium not necessary, suppose this medium, since
capable of extinction, to be destroyed; then the conclusion, since
necessary, shall remain; but will be no longer the object of knowledge,
since it is supposed to be known by that medium which is now extinct.
Hence, science is lost, though none of the preceding three are
taken away; but this is absurd, and contrary to the principles we
have just established. The thing known remains; for the conclusion,
since necessary, cannot be destroyed;--he who knows still remains,
since neither dead, nor forgetful of the conclusion:--lastly, the
demonstration by which it was known, still survives in the mind; and
hence we collect, that if science be no more after the corruption
of the medium, neither was it science by that medium before its
corruption; for if science was ever obtained through such a medium,
it could not be lost while these three are preserved. The science,
therefore, of a necessary conclusion can never be obtained by a medium
which is not necessary.