And Homer indeed excellently well places first things that are present,
and afterwards what is future and past. For by the very nature of
the connection the argument is based on that which now is. Thus, “if
this is, that preceded;” and again, “if this is, that shall be.” For
the knowledge of the consequence is, as has been said, an artificial
and rational thing; but sense gives the assumption to reason. Whence
(though it may seem indecent to say it) I will not be afraid to
aver this, that the tripod of truth is reason, which recognizes the
dependence of the consequent on the antecedent, and then, assuming the
reality of the antecedent, infers the conclusion of the demonstration.
If then the Pythian Apollo delights in music, and is pleased with
the singing of swans and the harmony of the lute, what wonder is it
that, for the sake of logic, he embraces and loves this argumentative
particle, which he sees the philosophers so much and so frequently to
use? Hercules indeed, not having yet unbound Prometheus, nor conversed
with the sophisters that were with Chiron and Atlas, but being still a
young man and a plain Boeotian, at first abolished logic and derided
this word _ΕΙ_; but afterwards he seemed by force to have seized on the
tripod, and contended with our God himself for the pre-eminence in this
art; for being grown up in age, he appeared to be the most expert both
in divination and logic.
7. Theon having ended his speech, I think it was Eustrophus the
Athenian who said to us: Do you not see how valiantly Theon vindicates
logic, having, in a manner, got on the lion’s skin? So it is not right
even for us—who comprehensively place all the affairs, nature, and
principles of things both divine and human in number, and make it
most especially the author and lord of honest and estimable things—to
be at quiet, but we must willingly offer the first-fruits of our
dear mathematics to the God; since we think that this letter Ε does
not of itself differ from the other letters either in power, figure,
or expression, but that it has been preferred as being the sign of
that great number which has an influence over all things, called the
Quinary (or Pemptas), from which the Sages have expressed the art of
numbering by the verb πεμπτάζειν (signifying _to account by fives_).
Now Eustrophus spake these things to us, not in jest, but because I did
at that time studiously apply myself to the mathematics, and perhaps
also in every thing to honor that saying, “Nothing too much,” as having
been conversant in the Academy.
8. I answered therefore that Eustrophus has excellently solved the
difficulty by number. For (said I) since all number is distributed into
even and odd, unity is in efficacy common to them both,—for that being
added to an even number, it makes it odd, and to an odd, it makes it
even, two constituting the beginning of the even, and three of the odd.
Now the number of five, composed of these two, is deservedly honored,
as being the first compound made of the first simple numbers, and is
called the marriage, for the resemblance of the odd with the male,
and the even with the female. For in the divisions of the numbers
into equal parts, the even, being wholly separated, leaves a certain
capacious beginning and space in itself; but in the odd, suffering the
same thing, there always remains a middle, of generative distribution,
by which it is more fruitful than the other, and being mixed is
always master, never mastered. For by the mixture of both, even and
odd together, there is never produced an even number but always an
odd. But which is more, either of them added to and compounded with
itself shows the difference; for no even joined with another even ever
produced an odd, or went forth of its proper nature, being through
weakness unable to generate another and imperfect. But odd numbers
mixed with odd do, through their being every way fruitful, produce many
even ones. Time does not now permit us to set down the other powers
and differences of numbers. Therefore have the Pythagoreans, through a
certain resemblance, said that five is the marriage of the first male
and the first female number. This also is it for which it is called
Nature, by the multiplication of itself determining again into itself.
For as Nature, taking a grain of wheat for seed and diffusing it,
produces many forms and species between, by which she brings her work
to an end, but at last she shows again a grain of wheat, restoring the
beginning in the end of all; so, while the rest of the numbers, when
they are multiplied into others, terminate by the increase only those
of five and six, multiplied by themselves, bring back and preserve
themselves. For six times six makes thirty-six, and five times five
makes twenty-five. And again, six does this once, and only after one
manner, to wit, when it is squared. But this indeed befalls five both
by multiplication and by composition with itself, to which being added,
it alternatively makes itself and ten; and this as far as all number
can extend, this number imitating the beginning or first Cause which
governs the universe. For as that first Cause, preserving the world by
itself, does reciprocally perfect itself by the world, as Heraclitus
says of fire,
Fire turns to all things, and all things to fire;
and as money is changed for gold, and gold for money; so the congress
of five with itself is framed by Nature to produce nothing imperfect
or strange, but has limited changes; for it either generates itself or
ten, that is, either what is proper to itself, or what is perfect.
9. Now if any one shall say, What is all this to Apollo? we will
answer, that it concerns not Apollo only, but Bacchus also, who has
no less to do with Delphi than Apollo himself. For we have heard the
divines, partly in verse partly in prose, saying and singing, that the
God is of his own nature incorruptible and eternal, but yet, through
a certain fatal decree and reason, suffers changes of himself, having
sometimes his nature kindled into a fire, and making all things alike,
and otherwhiles becoming various, in different shapes, passions, and
powers, like unto the World, and is named by this best-known of names.
But the wiser, concealing from the vulgar the change into fire, call
him both Apollo from his unity[207] and Phoebus from his purity and
unpollutedness. But as for the passion and change of his conversion
into winds, water, earth, stars, and the various kinds of plants and
animals, and its order and disposition, this they obscurely represent
as a certain distraction and dismembering; and they now call him
Dionysus, Zagreus, Nyctelius, and Isodaetes, exhibiting and chanting
forth certain corruptions, disparitions, deaths, and resurrections,
which are all riddles and fables suited to the said mutations. To
Dionysus or Bacchus they sing dithyrambic verses, full of passions and
change, joined with a certain wandering and agitation backwards and
forwards; for, as Aeschylus says,
The dithyramb, whose sounds are dissonant,
’Tis fit should wait on Bacchus.
But to Apollo they sing the well-ordered paean and a discreet song.
And Apollo both in their sculptures and statues they always make to
be young and never declining to old age; but Dionysus they represent
in many shapes and forms. Lastly, to the one they attribute equality,
order, and unmixed gravity; but to the other, a certain unequal mixture
of sports, petulancy, gravity, and madness, surnaming him,
Evius Bacchus, who to rage incites
Women on tops of mountains, and delights
In frantic worship.
Thus they not unfitly touch the property of both changes. Now because
the time of the revolutions in these changes is not equal, but that of
the one which they call Koros (that is, _satiety_) is longer, and that
of the other named Chresmosyne (or _want_) shorter; observing in this
the proportion, they all the rest of the year use in their sacrifices
the paean; but at the beginning of winter, rousing up the dithyramb,
and laying the paean to rest, they do for three months invocate Bacchus
instead of Apollo, esteeming the creation of the world to be the same
in proportion of time to the conflagration of it as three to one.
10. But these things have perhaps had more than sufficient time spent
on them. This, however, is evident, that they properly attribute
to this God the number of five, saying that it sometimes of itself
produces itself like fire, and other whiles the number of ten, like
the world. But do we think that this number is not also concerned with
music, which is of all things most acceptable to this God? For the
chiefest operation of harmony is, as one may say, about symphonies.
Now that these are five and no more, reason convinces even him who
will by his senses without reasoning make trial either on strings or
pipe-holes. For all these accords take their original in proportions
of number; and the proportion of the symphony diatessaron is
sesquitertial, of diapente sesquialter, of diapason duple, of diapason
with diapente triple, and of disdiapason quadruple. But as for that
which, transcending all measures, the musicians add to these, naming
it diapason with diatessaron, it is not fit we should receive it,
gratifying the unreasonable pleasure of the ear against proportion,
which is as the law. I may therefore let pass the five positions of
the tetrachords, and also the five first,—whether they are to be
called tones, tropes, or harmonies,—according to the changes of which
by rising or falling, either to more or less, the rest are bases or
trebles. And, whereas there are many or rather infinite intervals, are
not five of them only used in music, to wit, diesis, hemitonion, tonos,
triemitonion, and ditonon? Nor is there in the voice any other space,
either greater or less, that, being distinguished by base or treble,
comes into melody.
11. Passing by many other such like things, said I, I will produce only
Plato; who says, that there is but one world, but that if this were not
alone, so that there were others besides it, they would be in all five
and no more. For indeed, though there is but this one only world, as
Aristotle is also of opinion, yet this world is in some sort composed
and assembled of five, of which one indeed is of earth, another of
water, the third of fire, the fourth of air, and the fifth, being
heaven, some call light and others the sky; and some also name this
same the fifth essence, which alone of all bodies is naturally carried
about in a circle, and not of necessity or otherwise by accident.
Wherefore Plato, knowing that, of the figures which are in Nature,
there are five most excellent and perfect,—to wit, the pyramid, the
cube, the octahedron, the icosahedron, and the dodecahedron,—has fitly
accommodated each of them to each of these worlds or bodies.
12. There are some also who apply the faculties of the senses, being
equal in number, to these five first bodies, seeing the touch to be
firm and earthly, and the taste to perceive the qualities of savors by
moisture. Now the air being struck upon is a voice and sound to the
ear; and as for the other two,—the scent, which the smell has obtained
for its object, being an exhalation and engendered by heat, is fiery;
and the sight, which shines by reason of its affinity to the sky and
light, has from them a temperature and complexion equally mingled of
both. Now neither has any animal any other sense, nor the world any
other nature simple and unmixed; but there has been made, as appears, a
certain wonderful distribution and congruity of five to five.
13. Having here stopped a little, and made a small pause between, I
said: What a fault, O Eustrophus, were we like to have committed,
having almost passed by Homer, as if he were not the first that
distributed the world into five parts, who assigned the three which
are in the midst to three Gods, and left the two extremes, Olympus
and the Earth—of which one is the limit of things above, the other of
things below—common and undistributed.[208] But we must, as Euripides
says, return to our discourse. For those who magnify the quaternary,
or number of four, teach not amiss, that every solid body had its
generation by reason of this. For since every solid consists in length
and breadth, having withal a depth; and since before length there is
extant a point, answerable to unity, and length without breadth is
called a line and consists of two; and the motion of a line towards
breadth exhibits also the procreation of a superficies in the number
three; and the argumentation of this, when depth is added to it, goes
on to a solid in the number four; it is manifest to every one, that
the quaternary, having carried on Nature hitherto, and even to the
perfecting of a body and the exhibiting it tangible, massy, and solid,
has yet at last left it wanting the greatest accomplishment. For that
which is inanimate is, to speak sincerely, orphan-like, imperfect,
and fit for nothing at all, unless there is some soul to use it; but
the motion or disposition introducing a soul, being a change made by
the number five, adds the consummation to Nature, and has a reason
so much more excellent than the quaternary, as an animal differs in
dignity from that which is inanimate. Moreover, the symmetry and power
of this number five, having obtained greater force, has not permitted
the animate body to proceed to infinite sorts, but has exhibited five
species of all things that have life. For there are Gods, Genii, and
heroes, and then after them the fourth sort is men, and the fifth and
last the irrational and brutish animal. Furthermore, if you divide
the soul itself according to its nature, its first and most obscure
part or faculty is the vegetative, the second the sensitive, then
the concupiscible, after that the irascible; and having brought on
and perfected Nature in the faculty of the rational, it rests in this
fifth, as in the top of all.
14. Now the generation of this number, which has so many and so great
faculties, is also beautiful,—not that which we have already discoursed
of, from two and three, but that which the first principle joined
with the first square has exhibited. For the principle of all number
is unity, and the first square is the quaternary; now the quinary is
composed of these, as of form and of matter which has attained to
perfection. And if it is right, which some hold, that unity is also
square, as being the power of itself and terminating in itself; the
quinary, being made of the first two squares, could not have a more
noble original.
15. But as for its greatest excellency, I fear, lest being spoken
it should press our Plato as much as he himself said Anaxagoras was
pressed by the name of the moon, when he made a certain opinion
concerning her illuminations, which was very ancient, to be an
invention of his own. For has he not said this in his dialogue entitled
Cratylus?[209]
Yes indeed, answered Eustrophus; but I see not any thing that has
fallen out like it. And yet you know, that in the Sophister[210] he
demonstrates five principal beginnings, to wit, that which _is_, or
Ens (τὸ ὄν), the _Same_, the _Different_, adding to these, for a
fourth and fifth, _Motion_ and _Rest_. Again, in his dialogue called
Philebus,[211] using another manner of division, he says, that there
is one thing Infinite, and another the End; and that all generation
consists of these two mixed together. Then he puts the cause by which
they are mixed for the fourth kind; and has left us to conjecture
the fifth, by which the things that were mixed have again a division
and dissipation. Now I am of opinion that these last are delivered
as the images or representations of those before,—to wit, the things
engendered of Ens, the Infinite of Motion, the End of Rest, the Mixing
Principle of the Same, and the Separating Principle of the Different.
But if these are different from those, yet both that way and this
way these principles are still distinguished into five kinds and
differences. Now some one, said he, being persuaded of these things
and seeing them before Plato, consecrated to the God two Ε Ε, for a
mark and symbol of the number of all things. And having perhaps further
understood that good also appears in five kinds, of which the first
is the mean, the second the commensurate, the third understanding,
the fourth the sciences, arts, and true opinions in the soul, and the
fifth a certain pleasure, pure and unmixed with sorrow; he stops there,
subjoining that of Orpheus:
In the sixth age stay your desire of singing.
16. After what I have spoken to you, I said, Yet one short word to
those about Nicander,
I’ll sing to men of skill.
For on the sixth day of the new moon, when you introduce the Pythia
into the Prytaneum, the first of the three lots tends with you towards
five, casting neither three, nor two, one to another.[212] For is not
this so?
It is so, said Nicander; but the cause is not to be told to others.
Well then, said I smiling, till such time as the God admits us, being
consecrated, to know the truth, this also shall be added to those
things that have been spoken concerning the quinary. This end, as
I remember, had the discourse of the arithmetical and mathematical
encomiums of Ε.
17. But Ammonius, who had himself also bestowed not the worst part
of his time in mathematical philosophy, was delighted with what had
been spoken, and said: It is not meet too eagerly to oppose these
young men about these things, except by saying that every one of the
numbers will afford you, if you desire to praise it, no small subject
of commendations. And what need is there to speak of others? For the
septener, sacred to Apollo, will take up a day’s time, before one can
in words run through all its powers. We shall therefore pronounce, that
the Sages do at once contest both against common law and a long series
of time, if, throwing the septenary out of its seat, they consecrate
the quinary to the God, as being more suitable to him. I am therefore
of opinion, that this syllable signifies neither number, order, nor
connection, nor any other of the deficient parts, but is a self-perfect
appellation and salutation of the God, which brings the speaker to the
conception of the power of the God at the very moment of uttering it.
For the God in a manner calls upon every one of us who comes hither,
with this salutation, Know thyself, which is nothing inferior to All
hail. And we again, answering the God, say to him Εἶ, _thou art_;
attributing to him the true, unfeigned, and sole appellation of being,
as agreeing to him alone.
18. For we indeed do not at all essentially partake of being; but every
mortal nature, being in the midst between generation and corruption,
exhibits an appearance, and an obscure and weak opinion of itself.
And if you fix your thought, desiring to comprehend it,—as the hard
grasping of water, by the pressing and squeezing together that which
is fluid, loses that which is held,—so when reason pursues too evident
a perception of any one of the things subject to passion and change,
it is deceived and led away, partly towards its generation and partly
towards its corruption, being able to apprehend nothing either
remaining or really subsisting. For we cannot, as Heraclitus says,
step twice into the same river, or twice find any perishable substance
in the same state; but by the suddenness and swiftness of the change,
it disperses and again gathers together, comes and goes. Whence what
is generated of it reaches not to the perfection of being, because the
generation never ceases nor is at an end; but always changing, of seed
it makes an embryo, next an infant, then a child, then a stripling,
after that a young man, then a full-grown man, an elderly man, and
lastly, a decrepit old man, corrupting the former generations and
statures by the latter. But we ridiculously fear one death, having
already so often died and still dying. For not only, as Heraclitus
said, is the death of fire the generation of air, and the death of
air the generation of water; but you may see this more plainly in men
themselves; for the full-grown man perishes when the old man comes, as
the youth terminated in the full-grown man, the child in the youth, the
infant in the child. So yesterday died in to-day, and to-day dies in
to-morrow; so that none remains nor is one, but we are generated many,
according as matter glides and turns about one phantasm and common
mould. For how do we, if we remain the same, delight now in other
things than we delighted in before? How do we love, hate, admire, and
contemn things contrary to the former? How do we use other words and
other passions, not having the same form, figure, or understanding? For
neither is it probable we should be thus differently affected without
change, neither is he who changes the same. And if he is not the same,
neither is he at all; but changing from the same, he changes also his
being, being made one from another. But the sense is deceived through
the ignorance of being, supposing that to be which appears.
19. What then is it that has really a being? That which is eternal,
unbegotten, and incorruptible, to which no time brings a change. For
time is a certain movable thing appearing in connection with fleeting
matter, always flowing and unstable, like a leaky vessel full of
corruption and generation; of which the sayings “after” and “before,”
“it has been” and “it shall be,” are of themselves a confession that
it has no being. For to say that what not yet is or what has already
ceased to be is in being, how foolish and absurd is it. And as for
that on which we chiefly ground the understanding of time,—saying,
the instant, present, and now,—this again reason wholly rejects and
overthrows; for it is lost between the future and the past, like a
flash of light, and is separated into two when we will behold it.
Now if the same thing befalls Nature, which is measured by time, as
does the time which measures it, there is nothing in it permanent or
subsistent, but all things are either breeding or dying, according to
their commixture with time. Whence also it is not lawful to say of any
thing which is, that it was or shall be; for these are inclinations and
departures and changes of that whose nature is not to continue in being.
20. But God, we must say, _is_, and he is not in any time, but in
eternity, which is immovable without time, and free from inclination,
in which there is nothing first, or last, or newer; but being one, it
has filled its eternal duration with one only “now”; and that only
_is_ which is really according to this, of which it cannot be said,
that it either was or shall be, or that it begins or shall end. Thus
ought those who worship to salute and invocate this Eternal Being, or
else indeed, as some of the ancients have done, with this expression
Εἶ ἕν, _Thou art one_. For the Divinity is not many, as every one of
us is made of ten thousand differences in affections, being a confused
heap, filled with all diversities. But that which is must be one, as
one must have a being. But diversity, which is esteemed to be different
from being, goes forth to the generation of that which is not. Whence
both the first of his names agrees rightly with this God, as do also
the second and third. For he is called Apollo, as denying plurality and
rejecting multitude; and Ieïos, as being only one; and Phoebus was the
name given by the ancients to every thing that is pure and chaste; as
the Thessalians even to this day, if I am not mistaken, say of their
priests, when on vacant days they abstain from the temples and keep
themselves retired, that they purify themselves (φοιβονομεῖσθαι). Now
that which is one is sincere and pure. For pollution is by the mixture
of one thing with another; as Homer, speaking of a piece of ivory dyed
red, said it was “polluted” by the dye, and dyers say of mixed colors
that they are corrupted, and call the mixture itself corruption. It is
therefore always requisite for that which is incorruptible and pure to
be one and unmixed.
21. Now, as for those who think Apollo and the Sun to be the same,
they are to be caressed and loved for their ingenuity, as placing the
notion of God in that which they most reverence, of all things that
they know and desire. And now, as if they were dreaming of God the
most glorious dream, let us stir up and exhort them to ascend higher,
and to contemplate his reality and his essence; but to honor also this
his image (the Sun), and to venerate that generative faculty he has
placed in it, since it exhibits in some sort by its brightness—as far
as it is possible for a sensible thing to represent an intellectual,
and a movable thing that which is permanent—certain manifestations and
resemblances of his benignity and blessedness. But as for those his
sallyings out and changes, when he casts forth fire, ... and when he
again draws himself in, afterwards extending himself into the earth,
sea, winds, animals, and strange accidents both of animals and plants,
they cannot so much as be hearkened to without impiety; or else God
will be worse than the child in the poet,—who made himself sport with
a heap of sand, first raised and then again scattered abroad by
himself,—if he shall do the same in respect of the universe, first
framing the world when it was not, and then destroying it when made.
On the contrary, whatsoever of him is in any sort infused into the
world, that binds together its substance, and restrains the corporeal
weakness which tends to corruption. And it seems to me that this word
is chiefly opposed to that doctrine, and that Εἶ, _Thou art_, is spoken
to this God, as testifying that there is never in him any going forth
or change. But to do and suffer this agrees to one of the other Gods,
or rather Daemons, ordained to take care about Nature in generation
and corruption; as is immediately manifest from their names, being
wholly contrary and of different significations. For the one is called
Apollo (or _not many_), the other Pluto (or _many_); the one Delius
(from _clearness_), the other Aidoneus (from _obscurity_); the one
Phoebus (or _shining_), the other Scotius (or _dark_); with the one
are the Muses and Mnemosyne (or _song_ and _memory_) with the other
Lethe and Siope (or _forgetfulness_ and _silence_). The one is (from
_contemplating_ and _showing_) named Theorius and Phanaeus; the other is
Prince of dark night and sluggish sleep, whose fate
Is that men him most of all Gods do hate.