[a] Page 1.—“_But others from opinion in conjunction with reason_;”—which
in the original is, τα δε και δοξῃ, μετα λογου. But Ocellus is not
accurate in what he here asserts, as is evident from what Plato says in
his Timæus. For the divine philosopher having, in the former part of this
dialogue, proposed to consider “what that is which is always being, but
is without generation, and what that is which is generated [or consists
in becoming to be], but is never [really] being,” adds: “The former of
these, indeed, is comprehended by _intelligence in conjunction with
reason_, since it always subsists with invariable sameness; but the
latter is perceived _by opinion in conjunction with irrational sense_,
since it is generated and corrupted, and never truly is.” Τι το ον μεν
αει, γενεσιν δε ουκ εχον· και τι το γιγνομενον μεν, ον δε ουδεποτε· το
μεν δη, νοησει μετα λογου περιληπτον, αει κατα ταυτα ον· το δ’αυ δοξῃ
μετ’ αισθησεως αλογου, δοξαστον, γιγνομενον και απολλυμενον, οντως δε
ουδεποτε ον. Plato, as is evident from what is said in the Introduction
to this work, had seen this tract of Ocellus, and corrects him in what he
here says, as he also did the opinions of other philosophers anterior to,
or contemporary with him. For if Ocellus had spoken accurately, he should
have said, “that he had learnt some things through clear arguments from
nature herself, but others from opinion in conjunction with irrational
sense.” For, as Proclus admirably demonstrates in his Commentary on
the above passage from the Timæus of Plato, truly existing being is
only to be apprehended by us through illuminations from an intellect
superior to the human, in conjunction with the energy of _the summit of
our reasoning power_; for such is the accurate meaning of λογος in this
place. But opinion is a knowledge of sensibles conformable to reason,
yet without being able to assign the cause of what it knows; and sense
is an irrational knowledge of the objects to which it is passive, and
the instrument of sense is passion only. See the first volume of my
translation of the Commentaries of Proclus on the Timæus of Plato, p.
202, &c.
Ocellus adds, “that it is his intention [in this treatise On the
Universe] to derive what is _probable_ from intellectual perception.” For
in physiological discussions we must be satisfied with probability and
an approximation to the truth. Hence, Proclus, in his Commentary on that
part of the Timæus in which Plato says, “What essence is to generation,
that truth is to faith,” admirably observes as follows: “The faith of
which Plato now speaks is rational, but is mingled with irrational
knowledge, as it employs sense and conjecture; hence, it is filled with
much of the unstable. For receiving from sense or conjecture the ὁτι, _or
that a thing is_, it thus explains causes. But these kinds of knowledge
have much of the confused and unstable. Hence, Socrates, in the Phædo,
reprehends sense in many respects, because we neither hear nor see
anything accurately.
“How, therefore, can the knowledge which originates from sense possess
the accurate and the irreprehensible? For the powers which use science
alone, comprehend the whole of the thing known with accuracy; but those
that energise with sense, are deceived, and deviate from accuracy, on
account of sense, and because the object of knowledge is unstable. For,
with respect to that which is material, what can any one say of it?
since it is always changing and flowing, and is not naturally adapted
to abide for a moment. But that which is celestial, in consequence of
being remote from us, is not easily known, nor can it be apprehended
by science, but we must be satisfied in the theory of it with an
approximation to the truth, and with probability [instead of certainty].
For everything which is in place requires the being situated there, in
order to a perfect knowledge of its nature. The intelligible, however,
is not a thing of this kind, since it is not apprehended by us in
place; for, wherever any one establishes his reasoning energy, there,
truth being everywhere present, he comes into contact with it. But if
it is possible to assert anything firm and stable about that which is
celestial, this also is possible, so far as it participates of being,
and so far as it can be apprehended by intelligence. For, if anything
necessary can be collected concerning it, it is alone through geometrical
demonstrations which are universal. But so far as it is sensible, it is
difficult to be apprehended, and difficult to be surveyed.”—See the first
volume of my translation of Proclus on the Timæus of Plato, p. 291.
In p. 293, he also observes, “that perfectly accurate arguments, and such
as are truly scientific, are not to be expected in physical discussions,
but such as are assimilated to them. It is besides this requisite
to know, that as the world is mingled from physical powers, and an
intellectual and divine essence; for “physical works, as the [Chaldean]
Oracle says, co-subsist with the intellectual light of the father;”
thus, also, the discussion of the world makes a commixture of faith and
truth. For things which are assumed from sense participate largely of
conjectural discussion; but things which commence from intelligibles,
possess that which is irreprehensible, and cannot be confuted.” And,
lastly, in p. 296, he adds, “that the want of accuracy in the theory of
the images of being, arises from our imbecility; for, to the knowledge of
them we require imagination, sense, and many other organs. But the Gods
contractedly contain these in their unity and divine intellection; for,
in sublunary natures, we are satisfied in apprehending that which, for
the most part, takes place on account of the instability of their subject
matter. But again, in celestial natures, we are filled with much of the
conjectural, through employing sense and material instruments. On this
account we must be satisfied with proximity in the apprehension, of them,
since we dwell remotely at the bottom, as it is said, of the universe.
This also is evident from those that are conversant with them, who
collect the same things respecting them from different hypotheses; some
things, indeed, through eccentrics, others through epicycles, and others
through evolvents, [in all these] preserving the phænomena.”
Shuttleworth, in his Astronomy, has demonstrated that the celestial
phænomena may be solved by the hypotheses of Ptolemy and Tycho Brahe,
equally as well as by those of Copernicus. But astronomers of the present
day, from not being skilled in the logic of Aristotle, are not aware that
true conclusions may be deduced from false premises; and hence, because
their theory solves the phænomena, they immediately conclude that it
is true. Aristotle, in his Posterior Analytics, has incontrovertibly
shown, that the things from which demonstrative science consists, must
be necessarily true, the causes of, more known than, and prior to
the conclusion. But where the premises of a syllogism are false, the
conclusion is not _scientifically_, i. e. _necessarily_, true. Thus in
the syllogism, Every stone is an animal; every man is a stone; therefore
every man is an animal,—the conclusion is true, but not _scientific_.
_Note to p. 14._—Ocellus is wrong in ascribing two powers only to each
of the elements, instead of three, as is clearly shown by Proclus, in
the following extract from his admirable Commentary on the Timæus of
Plato. “There are some physiologists (says he) who ascribe one power to
each of the elements; to fire indeed heat, to air frigidity, to water
moisture, and to earth dryness; in so doing, entirely wandering from the
truth. In the first place, because they subvert the world and order. For
it is impossible for things to be co-adapted to each other, when they
possess the most contrary powers, unless they have something in common.
In the next place, they make the most contrary natures allied to each
other, viz. the hot to the cold, and the moist to the dry[26]. It is
necessary, however, to make things which are hostile more remote than
things which are less foreign. For such is the nature of contraries. In
the third place, therefore, the first two powers will have no sympathy
whatever with the rest, but will be divulsed[27] from each other. For it
is impossible to say what is common to humidity and frigidity. And in
addition to all these things, as the elements are solids, they will not
be conjoined to each other by any medium. It has however been shown that
it is not possible for solids to be conjoined through one medium. Nor can
they be conjoined without a medium. For this is alone the province of
things that are perfectly without interval.
“But some others, as Ocellus, who was the precursor of Timæus, attribute
two powers to each of the elements; to fire indeed heat and dryness; to
air, heat and moisture; to water, moisture and coldness; and to earth,
coldness and dryness. And these things are written by this man in his
treatise On Nature. In what, therefore, do these err who thus speak? In
the first place, indeed, wishing to discover the common powers in the
elements, in order that they may preserve the co-arrangement of them with
each other, they no more assign communion than separation to them, but
equally honour their hostility and their harmony. What kind of world,
therefore, will subsist from these; what order will there be of things
which are without arrangement and most foreign, and of things which are
most allied and co-arranged? For things which in an equal degree are
hostile and peaceful, will in an equal mode dissolve and constitute
communion. But this communion being similarly dissolved, and similarly
implanted, the universe will no more exist than not exist. In the second
place, they do not assign the greatest contrariety to the extremes, but
to things most remote from the extremes; though we everywhere see, that
of homogeneous natures, those which are most distant have the nature of
contraries, and not those which are less distant. How likewise did nature
arrange them, since they are most remote in their situation from each
other? Was it not by perceiving their contrariety, and that the third
was more allied than the last to the first? How, also, did she arrange
the motions of them, since fire is most light and tends upward, but
earth is most heavy and tends downward? But whence were the motions of
them which are most contrary derived, if not from nature? If, therefore,
nature distributed to them most contrary motions, it is evident that they
are themselves most contrary. For as the motions of simple beings are
simple, and those things are simple of which the motions are simple,
thus also those things are most contrary of which the motions are most
contrary. And this may occasion some one to wonder at Aristotle, who, in
what he says about motion, places earth as most contrary to fire; but in
what he says about powers, he makes the most remote of similar natures
to be more friendly than those that are proximate, when they are moved
with most contrary motions. For, as the elements have contrary places in
their positions, as they have contrary motions in lations, as they have
contrary powers, gravity and levity, through which motions subsist in
their forms, thus also they have contrary passive qualities. Aristotle
himself likewise manifests that earth is contrary to fire. For wishing to
show that it is necessary there should be more bodies than one, he says:
“Moreover, if earth exists, it is also necessary that fire should exist.
For in things, one of the contraries of which naturally is, the other
likewise has a natural subsistence.” So that neither was he able after
any other manner to show that there are more elements than one, than by
asserting that fire is contrary to earth.
“Further still, as the elements are solids, how can they be bound
together through one medium? For this is impossible in solids, as we
have before observed. Hence those who assert these things, neither
speak mathematically nor physically, but unavoidably err in both these
respects. For physical are derived from mathematical entities. _Timæus
therefore alone, or any other who rightly follows him, neither attributes
one or two powers alone to the elements, but triple powers; to fire
indeed tenuity of parts, acuteness, and facility of motion; to air,
tenuity of parts, obtuseness, and facility of motion; to water, grossness
of parts, obtuseness, and facility of motion; and to earth, grossness of
parts, obtuseness, and difficulty of motion._ But this is in order that
each of the elements may have two powers, each[28] of which is common to
the element placed next to it, and one power which is different, in the
same manner as it was demonstrated in mathematical numbers and figures;
this different power being assumed from one of the extremes; and also in
order that earth, according to all the powers, may subsist oppositely
to fire; and that the extremes may have two media, and the continued
quantities two; the latter having solids for the media, but the former,
common powers. For let fire indeed be attenuated in its parts, acute, and
easily moved. For it has an attenuated essence, and is acute, as having
a figure of this kind [i. e. a pyramidal figure], and on this account is
incisive and fugitive[29], and permeates through all the other elements.
It is also moved with facility[30], as being most near to the celestial
bodies, and existing in them. For the celestial fire itself is moved
with celerity, as is likewise sublunary fire, which is perpetually moved
in conjunction with it, and according to one circle, and one impulse.
Since, therefore, earth is contrary to fire, it has contrary powers, viz.
grossness, obtuseness, and difficulty of motion, all which we see are
present with it. But these being thus hostile, and being solids, are also
similar solids. For their sides and their powers are analogous. For as
the gross is to the attenuated, so is the obtuse to the acute, and that
which is moved with difficulty, to that which is moved with facility. But
those are similar solids of which the sides that constitute the bodies
are analogous. _For the sides are the powers of which bodies consist._
Hence, as fire and earth are similar bodies, and similar solids, two
analogous media fall between them; and each of the media will have two
sides of the extremes situated next to it, and the remaining side from
the other extreme. Hence, since fire has for its three physical sides the
triple powers, tenuity, acuteness, and facility of motion, by taking away
the middle power, acuteness, and introducing instead of it obtuseness, we
shall produce air, which has two sides of fire, but one of earth, or two
powers of fire, but one of earth; as it is fit that what is near should
rather communicate with it, than what is separated in the third rank from
it.
“Again, since earth has three physical powers, contrary to the powers of
fire, viz. grossness of parts, obtuseness, and difficulty of motion; by
taking away difficulty of motion, and introducing facility of motion, we
shall produce water, which consists of gross parts, is obtuse, and is
easily moved; and which has indeed two sides or powers common with earth,
but receives one from fire. And thus these media will be spontaneously
conjoined with each other; communicating indeed in twofold powers, but
differing in similitude by one power; and the extremes will be bound
together by two media. Each element also will thus be in a greater
degree conjoined to, than separated from, the element which is near to
it; and one world will be perfectly effected through all of them, and
one harmonious order, through the predominance of analogy. Thus also, of
the two cubes 8 and 27, the medium 12 being placed next to 8, will have
two sides of this, but one side of 27. For 12 is produced by 2 × 2 × 3.
But it is vice versâ with 18. For this is produced by 3 × 3 × 2. And the
side of 27 is 3, in the same manner as 2 is the side of 8. The physical
dogmas, therefore, of Plato, about the elements of the universe, accord
with mathematical speculations.”
In the Introduction to my Translation of the Timæus of Plato, I have
added the following numbers, for the purpose of representing this
beautiful distribution of the elements, by Proclus, arithmetically.
Let the number 60 represent fire, and 480 earth; and the media between
these, viz. 120 and 240, will correspond to air and water. For, as 60 :
120 :: 240 : 480. But 60 = 3 × 5 × 4, 120 = 3 × 10 × 4, 240 = 6 × 10 ×
4, and 480 = 6 × 10 × 8. So that these numbers will correspond to the
properties of the elements as follows:
Fire. Air.
3 × 5 × 4 3 × 10 × 4 ::
Subtle, acute, moveable. Subtle, blunt, moveable.
Water. Earth.
6 × 10 × 4 : 6 × 10 × 8.
Dense, blunt, moveable. Dense, blunt, immoveable.
“Hence,” Proclus adds, “these things being thus determined, let us
physically adapt them to the words of Plato. We call a [physical]
plane or superficies, therefore, that which has two powers only, but a
[physical] solid that which has three powers. And we say, that if we
fashion bodies from two powers, one medium would conjoin the elements
to each other. But since, as we assert, bodies possess triple powers,
they are bound together by two media. For there are two common powers of
the adjacent media, and one power which is different. And the extremes
themselves, if they consisted of two powers, would be conjoined through
one medium. For let fire, if you will, be alone attenuated and easily
moved; but earth, on the contrary, have alone grossness of parts and
immobility. One medium, therefore, will be sufficient for these. For
grossness of parts and facility of motion, and tenuity of parts and
difficulty of motion, are all that is requisite to the colligation of
both. Since, however, each of the elements is triple, the extremes
require two media, and the things themselves that are adjacent are bound
together through two powers. For solids, and these are things that have
triple contrary powers, are never co-adapted by one medium.”