THE
PHILOSOPHICAL and MATHEMATICAL
COMMENTARIES OF PROCLUS,
ON
THE FIRST BOOK OF EUCLID’S ELEMENTS.
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.
IN TWO VOLUMES.
[Illustration]
VOL I.
LONDON, PRINTED FOR THE AUTHOR:
And Sold by T. PAYNE and SON; B. WHITE and SON; J. ROBSON; T. CADELL;
LEIGH and CO.; G. NICOL; R. FAULDER; and T. and J. EGERTON. 1792.
[Price Two Guineas in Boards.]
_Extracts from Curiosities of Literature._ Second Edition.
Printed for Murray. Page 385.
Mr. _T. TAYLOR_, the Platonic Philosopher and _the modern Plethon_,
consonant to that philosophy, professes Polytheism.[1]
The Reader is requested to correct the following Errors.
Page 4. of the Dissertation, Vol. I. line 8. for _admitted_,
read _omitted_. Page 16. line 8. for _from_, read _form_. Page
51. Vol. I. of the Commentaries, line 16. instead of _They are
surely not the_, &c. read _For surely it cannot be said that
there are_, &c. Line 17. for _but we_, read _but that we_. And
line 19. for _is by much prior to_, read _is by a much greater
priority_.
Vol. II. page 18. line 26. for _and one is_, read _and one part
is_. And line 27. for _another_, read _the other_. Page 114.
line 13. for _The angle_, read _Let the angle_; and instead
of _is bisected_, in the same line, read _be bisected_. Page
411. line 2. for _is filled with intellect_, read _fills
intellect_. And line 3. for _it also participates_, read _also
it participates_.
TO
THE SACRED
MAJESTY
OF
TRUTH.
PREFACE.
The design of the present work is to bring us acquainted with
the nature and end of Mathematics in general, and of Geometry in
particular: and in the execution of this design our Author has
displayed an uncommon elegance of composition, and a most valuable
store of recondite learning. He is not content with every where
unfolding the full, and most accurate meaning of Euclid; but he
continually rises in his discourse, and leads us into the depths of the
Pythagoric and Platonic philosophy. We are surprised to find an use in
Geometry, which at present it is by no means suspected to afford. For
who would conceive that it is the genuine passage to true theology, and
the vestibule of divinity? This, indeed, is by no means the case when
it is studied for lucre, and applied to mechanical purposes; for then
the soul is neither elevated nor enlightened; but degraded and filled
with material darkness. Hence these Commentaries are alone valuable
to the liberal part of mankind, who look beyond _sense_ for
certainty; and who prefer things desirable for their own sakes, before
such as minister to the necessities of life.
The translation of this work is attended with great difficulty and
labour; not only from the sense of the philosopher, which is always
profound, and frequently obscure, but from the great incorrectness of
the Greek edition, in which, exclusive of numberless typographical
errors, entire sentences, essential to the connection, are frequently
omitted; and in one place two pages of the Latin translation are
wanting in the original, as will be shewn in our following notes.
Indeed, the Latin translation of Francis Barocius the Venetian, (Patav.
1560.) which was made from a variety of manuscripts, is inconceivably
valuable; for the diagrams, so necessary to a work of this kind, but
which are omitted in the Greek, are here inserted; and the version
is every where faithful, and sufficiently perspicuous to those who
are conversant in the ancient philosophy. Barocius justly cautions
the reader not to compare his version with the printed Greek, which
he observes is rather lacerated than printed; as indeed, without his
translation, it is impossible for any one to read the half of this
invaluable work, even though he should be as perfect in Greek as in
his native tongue. If I had not, therefore, fortunately acquired this
translation, which is at present very rare, I would have by no means
engaged in this arduous undertaking. Barocius, indeed, gives evident
proofs of his possessing the philosophical genius, by the excellence of
his translation, and his preface to the reader; and it is greatly to
be lamented that he did not adorn his version with explanatory notes,
which this profound work frequently demands, and which he was doubtless
well qualified to accomplish. This defect I have endeavoured, as far
as I was able, to supply; and at the same time have been cautious
neither to weary the reader by prolixity, nor by too much brevity to
leave him destitute of proper information. In the distribution of
the first book of this work into chapters, I have followed the order
of Barocius, because it is natural and obvious; and must beg leave
to solicit the reader’s indulgence for using the words _partible_
and _impartible_, differently from their common signification. These
words I have generally employed to express the meaning of μεριστός[2]
and αμεριστος[3] in the Greek, as I do not conceive that the words
_divisible_ and _indivisible_ always convey their full signification.
I have likewise used _quadrangle_ instead of square, and _quinquangle_
for the word pentagon. For if τρίγωνος be rendered _triangle_, why
should not τετραγώνος be rendered _quadrangle_? And, as Barocius
observes, why, for a similar reason, should not πεντάγωνος and
ἑξάγωνος be rendered _quinquangle_ and _sexangle_; and so of the rest?
Uniformity is always desirable when it can be obtained; and is no where
so necessary as in scientifical disquisitions.
It is likewise necessary to inform the reader, that though I have
always endeavoured to give the faithful meaning of my Author, yet I
have occasionally paraphrased his sense, when most obscure, and added
such elucidations of my own, as I either thought necessary to the
full comprehension of his matter; or which were naturally excited by
the fire and spirit of the Original. If it shall appear that I have
succeeded in the execution of this work, and rendered it intelligible
to the lovers of truth, I shall rejoice in my success, and consider
my labours sufficiently rewarded. The applause of the multitude I am
neither likely nor desirous to gain; but I am anxious to procure the
approbation of the discerning few, who know that the age of philosophy
is past; and who esteem the works of her ancient heroes as the most
precious treasures which have escaped the ravages of time.
* * * * *
Time, indeed, is like a deep and rapid river; whatever is trifling and
light, is precipitately borne on its surface, and what is valuable and
weighty, sinks to its bottom. Hence, the superficial observer collects
nothing more than the rubbish, which it is forever devolving into the
abyss of oblivion; while the profound and contemplative genius explores
the depths of the stream, and accounts himself happy if he can gather
any of the pearl which its bottom contains. Thus the discoveries of
experimental philosophy, float like straws on the surface, while
the wisdom of Pythagoras and Plato lies concealed in the depths of
the river. I am well aware it will be said, that the reverse of this
similitude is true; that the modern philosophy is the pearl, and
the ancient the stubble; and that the former will be celebrated by
posterity, and increase in reputation when the latter shall scarcely
be known. But let us attentively examine the truth of this assertion,
and shut our ears to the unsubstantial echoes of popular applause. Is
it reasonable to suppose that men of such exalted abilities, as the
Pythagoric and Platonic philosophers possessed, even in the estimation
of their opponents, accompanied with the greatest advantages of birth
and fortune, and the most unwearied attention, have discovered nothing
valuable, and have left nothing behind them, but jargon and reveries?
Is it to be supposed, that in an age when philosophy was almost
adored; when it was esteemed by kings, cultivated by noblemen, and
even reverenced by the vulgar; when empire was relinquished for its
pursuit, and every danger encountered for its possession: is it to be
supposed, that nothing but delusion was the offspring of so glorious a
period, and nothing but folly the reward of such generous endurance?
Or shall we say, that the discovery of truth was reserved for the age
of experiment; and that she is alone to be apprehended in the infinite
labyrinth of particulars? That she is to be investigated with the
corporeal senses, and not with the powers of intellect; and that
the crucible, the alembic, and the air-pump, are the only mediums of
detection? If this be the case, truth is material, and may be calcined,
distilled, and rarefied, like any other corporeal substance. It is
no longer eternal and immutable, but perishable and fluctuating; the
phantastic subject of sensible inspection, and not the steady and real
object of the permanent energies of science. Shall we call this the
age of philosophy, in which talents are prostituted for sustenance,
and learning submits to the impudence of wealth? Shall we say that we
have strengthened the cause of philosophy, by demolishing her schools;
and increased her independence, by enlarging the empire of commerce?
Where shall we find the man, who is at present reverenced for the
profession of teaching speculative truth, or indeed who teaches it
at all? Or should we chance to meet with such an obsolete character,
shall we find him supported by the profession? It is a well known fact,
that men formerly lived in the highest esteem by its propagation: it
is equally as notorious, that a man at present would starve by such an
attempt. Dare we assert, that the reason of this difference must be
ascribed to the greater liberality, and more philosophical spirit of
the present age? Shall we not rather say, that the period, in which
these ancient heroes lived, was the golden age of philosophy;--a
period so different from the present, as to appear fabulous on the
comparison? For mark the distinguishing characteristics of our
inferiority. The great object of ancient philosophy, was an accurate
speculation of principles and causes: but that of the modern, is a
confused investigation of effects. And if pursuits participate of the
nature of their subjects, and causes are more noble than effects, the
ancient philosophy must undoubtedly be more elevated than the modern.
Again, the object of the Pythagorean and Platonic philosophy was to
make its possessors wise and virtuous; and to elevate them above the
common frailties and imperfections of degraded humanity; and this end
was happily accomplished in its votaries, as their lives abundantly
evince: but the object of modern philosophy, is a promotion of the
conveniencies and refinements of life, by enlarging the boundaries
of traffic; and the Mathematical Sciences are studied solely with a
view to this enlargement. The design of the ancient philosophy was
to remove the causes of wonder, by contemplating effects in their
causes: the grand object of the modern, is to increase admiration, by
attempting to investigate causes through the infinity of particular
effects. So that philosophy, as Mr. Harris justly observes, now
ends where it formerly began. For either there is no such thing as
science, or if its existence be admitted, it can never be obtained by
experimental enquiries; as these must be liable to all the inaccuracy
and imperfection of their material subjects.
In short, the philosophy of Pythagoras and Plato will be found, when
impartially considered, to contain every thing which can enlighten the
mind, improve the morals, and exalt the character of man. It is built
on the steady basis of truth, and will survive the wreck of ages. Its
foundation is deep, and its summit reaches the heavens. It is a mighty
rock, which modern systems _may_ assail, like a raging sea; but,
like stormy waves, they will only be broken about its impenetrable
sides. To war against wisdom is folly; for opposition in this case is
the destruction of its author. The moderns may, indeed, expect, because
their merit is raised by the present age, above that of the ancients,
to appear as giants in the eyes of posterity; but they will only verify
the elegant observation of the poet[4], that
Pygmies are Pygmies still, though perch’d on Alps,
And Pyramids are Pyramids in vales.
A
DISSERTATION
ON THE
PLATONIC DOCTRINE OF IDEAS, &c.
SECTION I.
The Platonic doctrine of Ideas has been, in all ages, the derision of
the vulgar, and the admiration of the wise. Indeed, if we consider
that ideas are the most sublime objects of speculation, and that their
nature is no less bright in itself, than difficult to investigate, this
opposition in the conduct of mankind will be natural and necessary;
for, from our connection with a material nature, our intellectual eye,
previous to the irradiations of science, is as ill adapted to objects
the most splendid of all, “as the eyes of bats to the light of day[5].”
And yet (as I presume, it will appear from the following discourse),
unless the existence of these lucid beings is admitted, there can
be no such thing as science; nor, indeed, any genuine knowledge at
all. Hence, an enquiry concerning their nature and reality, is highly
proper, as an introduction to the ensuing Commentaries, in which they
are considered as the stable pillars of all truth, and the prolific
principles of the universe.
But previous to this enquiry, it is proper to observe, that Plato
was not the inventor, though he was a strenuous asserter, of ideas;
for, in the Sophista he affirms, that ideas were the discovery of men
who excelled in wisdom and piety, and who contended for an invisible
essence. Diogenes Laërtius, indeed, asserts, that Plato received
the doctrine of ideas from Epicharmus. But Epicharmus was not their
inventor, because Pythagoras, and others of still higher antiquity,
were well acquainted with ideas; so that it may be affirmed, with much
greater truth, that Plato was instructed in their nature by Philolaus
his preceptor, and the disciple of Pythagoras. For Pythagoras, after
his mysterious manner, signified ideas by numbers. But, prior to
Pythagoras, Orpheus was an asserter of ideas, and called Jupiter, or
the dimiurgus of the world, “the idea of all things.” And, according
to Syrianus, the mundane sphere, celebrated by Empedocles, is no other
than the ideal world; so that the doctrine of ideas is as ancient as
that of wisdom itself.
But to begin with our enquiry: in the first place, without universals
there can be no science; for the flowing and perishing nature of
particulars is perfectly foreign from that stability and duration which
is requisite to objects of invariable truth. Neither is it possible,
that infinite individuals can exist without the subsistence of one
cause endued with infinite power; for all multitude must necessarily
originate from one, and must resemble its cause in as great a degree of
perfection as its nature can admit; by a diffused infinity, shadowing
forth that infinite power which subsists in indivisible union. Hence,
if this be the case, and if infinite men, horses, and a multitude
of other univocals, are produced in an infinite time, an unity of
infinite power must be the source of each, according to which they are
generated in a terminated manner to infinity in the universe. Again,
all animals are transmuted from that which is in capacity (i. e. seed),
into energy. But if this be true, it is requisite there should be some
animal in the universe, subsisting in ever-vital energy, which may
call forth that which is concealed in dormant capacity, into perfect
actuality. Thirdly, the celestial orbs would not perpetually revolve
in the same spaces, and after the same manner, unless one and the same
universal number, or idea, ruled in each. So, likewise, there is a
natural number in every animal; or those of the same species, would
not always (when perfect) be distinguished with the same invariable
organs; nor would they be subject to puberty and old age, at the same
time, unless they were detained by the same measure of nature. Besides,
the participation of universals, is evident in every sensible object.
Thus, the rational nature is united with every individual man. Thus,
animal subsists in a lion and a horse, in a man and a dog. And thus
the pentad, or number five, is participated in the five fingers, and
the duad in the nostrils, eyes, hands, and feet. But since these do
not subsist without a cause, but are perfected by certain determinate
natures, it is necessary there should be an universal animal, in the
whole of nature, separate from sensibles, by means of which this
sensible animal is generated. And that there should subsist in nature
a pentad, through which the hands are always adorned with that number
of extremities; and a duad, from which the two eyes and nostrils are
derived. But if nature does not possess these numbers from herself, as
she is not the first cause of all, but derives them from another cause,
in the same manner as matter from nature, it is necessary there should
be universals and numbers prior to nature, subsisting in far greater
purity and perfection.
Again, we may demonstrate the existence of ideas as follows: if the
Deity, in fabricating the universe, operated essentially (and there
is no other way in which we can conceive him to operate), he must
fabricate the universe, an image of Himself. But, if this be the case,
he contains in himself, in the manner of an exemplar, the causes of
the universe; and these causes are no other than ideas. Besides, this
consideration is not to be omitted, that the perfect must necessarily
antecede and preside over the imperfect; unity over multitude; the
impartible over the partible; and that which is perpetually the same,
over that which admits of variation and change. From whence it may be
inferred, that things do not originate from baser natures, but that
their gradual processions end in these; and that they begin from the
most perfect, best, and most beautiful natures. But let us pursue this
reasoning more minutely, as it affords the strongest arguments for the
existence of ideas.
When the Deity fabricated the various species of animals, and bestowed
on them the different senses, it was doubtless with a view to the
benefit of their possessors, as he foresaw, that without these, the
animal could neither provide for its own support, nor defend itself
from surrounding dangers. But may we not enquire from whence this
previous perception originated? For it is not to be supposed, that he
first made animals destitute of senses, and so, being admonished by
their sudden destruction, afterwards assigned them to their nature.
Shall we say, this foreknowledge was the result of a reasoning process?
But then, we again ask, What were the principles of this ratiocination?
For if they originated from other reasonings, it is necessary, at
length, to arrive at something prior to these discursive operations,
on which they ultimately depend; since all reasoning must be founded
on indemonstrable principles. Was sense, then, or intellect the
principle of this previous perception? But, sense, in the present
instance, had not then a being, for it could not exist prior to the
animal nature: it was, therefore, intellect. But if intellect be the
repository of certain propositions, and the conclusion be science, it
must follow, that there could not then be a consultation of any thing
sensible. For the principle and the conclusion must both depend on
something intelligible. Besides, may we not ask, how such a habit of
thought arose before the existence of a sensible nature! It is absurd
in the extreme, to say from chance, and to resolve it into a sudden
volition of the Deity, is an assertion that may, indeed, satisfy vulgar
minds, but can by no means quiet the restless spirit of philosophical
investigation. Since, to suppose the cause of the universe, actuated by
sudden volitions, is to place him on a level with the vilest natures,
and subject him to the irrational impulses of the brute. Hence we
infer that the formation of animals, and by the same arguments of
the world, was not the result of any reasoning process. For, indeed,
argument and foreknowledge cannot with propriety be attributed to
the Deity; but when they are ascribed to him, we must consider it as
nothing more than an indication of his constituting particulars, in a
manner somewhat similar to the providence of a wise man, in inferior
concerns. For, in subordinate natures, whose operations cannot take
effect prior to enquiry, reason is necessary, on account of the
inferiority of that power which precedes the reasoning energy. In
like manner, foreknowledge is necessary, because a power is wanting
to its possessor, which might render him superior to its use. For
foreknowledge is directed to this end, that one particular circumstance
may take place in preference to another. But if it be requisite that
every energy in the Deity should be void of defect, and if it is not
lawful that any thing should be present with him, which is not total
and universal, it is necessary that all things should be contained in
every thing essential to the nature of the Deity. Hence, since even
futurity is with him present, there is nothing in him posterior; but
what is present in him becomes posterior, by its participation in
another. If then futurity be present with the Deity, it is necessary it
should be so present, as if foreknown in a posterior nature; that is,
in such a manner that nothing may be wanting to any being; and that is,
lastly, so that every thing may be complete.
Besides, reasoning cannot, by any means, belong to an eternal essence
like the deity; for if this be admitted, he must be forgetful of his
former operations. And if, in consequence of reasoning, he produces
more perfect natures afterwards, his works could not be perfectly
beautiful before: but if they were beautiful before, they must be
co-existent with their cause, i.e. they must be eternally beautiful,
antecedent to the reasoning energy. Again, if we suppose the supreme
intellect, the demiurgus of the world, to operate by enquiry, his
energy could not be spontaneous, and truly his own; but his essence
would be similar to that of the artificer, who does not derive his
productions from himself, but procures them as something adventitious
by learning and enquiry. But if the universe was not formed by
deliberation, it must be co-existent with its cause, and reside in
his essence; for if it be not co-existent there must have been some
particular time, in which its artificer determined on its production;
and this determination must have been the result of a reasoning
process, concluding that it would not be good to produce it before
that particular time, (from whence, by the way, we infer the eternity
of the world.) And if the universe be co-existent with its author, it
must perpetually emanate from his nature, and be dependent on it, like
the shadow on its forming substance. But in this case, its archetype
must be contained in the essence of its author; for every cause is
that primarily, which its effect is secondarily. And hence we infer,
that if the sensible universe be replete with forms of every kind, the
exemplars of those forms, must subsist in immaterial perfection, in the
artificer of the world.
If this sensible world, then, be formed according to the exemplar of
that which is intelligible; may we not say, with the great Plotinus,
that it is requisite universal animal should there primarily subsist in
perfect vital energy, containing all things in its omniform essence.
“Hence (says he[6]) the heavens are there a divine animal, replete with
ideal stars. Earth too does not there subsist solitary, but is much
more vital than this corporeal earth, for it is full of intellectual
life. The sea too is there, and all water subsisting in life, and an
ever-abiding stream. For how is it possible that any thing not vital,
can be the progeny of life itself? He, therefore, who enquires from
whence animals originate in the intelligible world, might as well
enquire from whence all life, and soul, and universal intellect, arose.
For here there is nothing indigent nor defective, but every thing is
perfect and exuberant. Here they all flow from one fountain, not as
from a certain spirit, or heat, but as if from an universal quality,
possessing and preserving in itself, all qualities; such as sweetness,
accompanied with fragrance of smell, the vigour of wine, and the
strength of all juices, bright colours, and whatever is perceived by
the taste.”
3. Such then are the arguments which the Platonic philosophy affords
in defence of ideas; the existence of which was so evident to Plato,
that, in the Sophista, he compares those who oppose the friends of
ideas to the giants of old, warring, as it were, on celestial souls,
and such as are engaged in sublime investigations. Let us now consider
to what universals these lucid beings are confined; since, according to
the Pythagoreans and Platonists, there are not ideas of all universal
conceptions. “For, in the first place (says Syrianus[7]), there are no
ideas of things evil and base, because these subsist in nature rather
by a privation and absence of ideas. And, on this account, they are
said to exist contrary to nature. Nor, secondly, of negations, for
these are destructive of the bound and limitation which is attributed
to every thing from the unifying and comprehending nature of ideas;
and hence, separation is rather the result of material infinity than
of that which is formal or ideal. Nor again, are there any ideas of
things which at different times receive a variety of conditions. For
these participate of transmutation from a moveable cause, but not from
the immoveable and stable illustration of ideas. Nor again of parts,
such as the hand, head, fingers, and the like. For the causes of
things existing entire, produce whole species and forms; not divided
about the parts of these, like the reasons of nature. But neither did
these wise men place in intellect the determinate causes of accidents
in bodies, such as sweetness and whiteness. For they considered that
natural reasons were sufficient for the production of accidents.
Nor again, of composites, as of a wise man. For since ideas are
simple, they preside over the simple essence of every thing. But the
composition and division of things is the business of our intellect;
ideas, at the same time, and that intellection which is co-ordinate
to ideas, being exempt from all these, on account of superlative
simplicity. Neither, therefore, must we establish ideas of things
generated from dissimilars, such as mules; nor of fruit produced by
engrafting from different trees. For all these have a posterior and
adventitious generation, and are not the work of nature alone, nor
of nature proceeding according to her own reasons, but, as it were,
compelled to labour contrary to her own determinations. Hence it is
manifest, that all art, which imitates nature, and alone ministers
to the use of mortal life, is separated from the cause of ideas. But
neither are the works which, depending on the purpose of the soul, are
perfected by a concourse of many causes, and which we are accustomed
to call the operations of fortune, to be conjoined to the cause of
ideas. For things which are there perfected, are eternal, and subsist
perpetually the same, free from the nature of contingent events. It
remains, therefore, that ideas must be confined to universal and
perfect essences, and to whatever confers to their natural disposition;
as for instance, to man, and every thing perfective of man, such as
wisdom and virtue. For ideas existing as the generative and energetic
causes of the perfection of every thing, distribute being to essences,
and convert them to the inexhaustible plenitude of their own omniform
natures.”
4. But let us now consider the nature of numbers; for as every form
is a number, according to the Pythagoreans[8], a speculation of this
kind must afford no small light to the arduous investigation of ideas.
Will it not, therefore, be proper, in the first place, to enquire,
with the great Plotinus[9], whether multitude is not a departure and
distance from _one_, so that infinity itself is a separation
from unity in the extreme, because it is no other than innumerable
multitude; that on this account it becomes evil; and that we contract a
similar nature when departing from intellectual unity, we are divided
by sensible multitude? For a being then properly becomes many, when no
longer able to remain collected in itself, the same, it is diffused
abroad, and thus, being dispersed, is variously extended; so that
when, by diffusion, it is absolutely deprived of unity, it becomes
perfect multitude, destitute of that universal cement, which unites
one part with another. But whenever the conciliating one is present,
then that which was scattered and diffused, becoming permanent by its
bounding power, passes into magnitude. But if any one should deny the
subsistence of unity, asserting that one is no where to be found,
which is not some particular one; and should hence affirm, that what
is called one abstractedly, is only a certain affection of the soul
towards any being; we ask, what prohibits the appellation of essence,
from being nothing more than an affection of the soul, and consequently
the existence of _being_, a delusion? For we predicate unity of
particulars with as great propriety as being. I am well aware, that
philosophers of the present day will answer, that we have an evident
proof of the reality of being, from its agitating the soul, and
becoming apparent in the phantasy: to which we reply, that in like
manner, the soul is agitated, and the imagination influenced about the
_one_. For every individual as much excites the perception of one,
as of being.
Besides, it is necessary to enquire whether we behold this passion and
conception of the soul, as one or multitude. And again, when we say
not one, we do not then possess one from the thing itself; for we say
that one is not contained in that individual. And hence we must possess
one in our own nature, and this must reside in the soul, separate
from that which is denominated some particular one. But here it may
be objected, that the one we possess is received from externals, and
is nothing more than a conception of the mind, produced by the thing
itself. For it will be said, that as multitude is nothing besides a
number of individuals, which are called many, so one is nothing besides
one thing; and is formed by thought separating that one particular from
others. To this we reply as follows:
How can it be consonant to reason to suppose that the conception of
_one_ arises from the sensation of some one particular subject?
For one particular man, who is discerned by sense, is by no means the
same with one itself, since, if this were the case, thought could never
predicate one of that which is not a man. Besides, as cogitation, on
beholding the different positions of things, affirms that this is here
or there, so when it perceives an individual, pronounces one; for that
passion is not vain, nor does it assert one of a non-entity. Nor must
we think it predicates ones, because this individual is different from
another; for when cogitation affirms such a thing is this, and not
another, it declares, in the mean time, that the other is _one_.
Likewise when it affirms that any thing is this _alone_, it then
declares, that what is alone is one: on which account, it predicates
one, prior to alone. Besides, if there be multitude, it is necessary
that one should antecede; since when it predicates _many_, it
pronounces more than one. And when it affirms that an army contains a
multitude of men, it conceives the soldiers reduced to one order.
For thought, indeed, does not permit multitude to remain perfect
multitude, destitute of the conciliating power of unity; in which
very circumstance, the subsistence of one is evinced; for acutely
and swiftly perceiving the one which results from order, it reduces
the nature of the many into one. Besides, we affirm that a house and
an army are each one, but that a house is more one than an army, on
account of the continuity of its parts. If therefore, one is contained
more in that which is continued than in that which is discrete, and
still more in what is perfectly indivisible, it is evident that _the
one_ is a certain nature, and has a real being. For it is impossible
that the more and the less should take place among things which have no
subsistence. If then it be not possible to understand any thing without
one or two, or some other number, it is by no means proper to deny
existence to that, without which we cannot comprehend the existence
or properties of any being: but it is requisite _that_ nature
should antecede all discourse, and intelligence, which is every where
necessary to their existence.
Again, if unity has no real subsistence, and is nothing more than
a name or conception of the mind, it may be destroyed without the
destruction of its subject. The unity, therefore, of a house may be
taken away, without the ruin of a house. But if a house is nothing more
than certain materials, reduced into one form, this is impossible. And,
on the contrary, the alteration of that subject, of which unity is
predicated, can make no real alteration in unity (on this hypothesis)
any more than the death of a man can affect his name. When, therefore,
a body, of which _one_ was predicated, is divided into a multitude
of parts, there is no real alteration made in the unity of the body,
because unity is nothing more than a name.
It was in consequence of this reasoning, and perceiving that unity
was participated by every being, that the Pythagoreans placed a
super-essential one at the top of the universe, intelligibly abstracted
from all beings in simplicity and excellence of nature. For they
considered, that unless there was a self-subsisting one in all things,
there could neither be universals nor particulars. Not the first,
because they are by nature _one_ and _many_. But it is requisite that
the one itself, should preside over that which is not one alone.
Nor again, the second, because they are many and one, (that is,
they participate more of multitude than unity, and their nature is
determined more by the _many_ than the _one_.) And because of things
in participation, unless an unparticipated one is added, there can
be no cause of union to beings; in the same manner as the cause of
essence to beings, is taken away by those who deny that being itself,
is the principle of all essence. For as the good itself, is the one
principle of good to the universe, and is nothing besides good; and
as a self-motive nature, which is nothing besides self-motion, is the
cause of motion to all things; so all things proceed from being itself,
and all united natures receive their union from _the one_, abstracted
from all things.
Hence (such is the absolute dominion of unity), continued quantities
would have no existence without its participation; for when they are
divided, so far as they lose unity, they change their being into some
other form. Hence, the bodies of plants or animals, which are each of
them one, when they fly from unity, and are dissipated into multitude,
immediately lose the essence they formerly possessed, and become
something else; which new state of being they likewise possess so far
as they are one. Add too, that health then flourishes in the corporeal
frame, when the body is conciliated into one; then beauty flourishes,
when the power of one connects the members into proportion and consent;
and then virtue reigns in the soul, when the soul is reduced into one
similitude with that which is divine.
5. But let us now investigate the nature of numbers. All number,
according to the Pythagoreans, originates from unity and the indefinite
duad; the first having the relation of form, and the second, that
of matter to all the orders of numbers. But they likewise divided
number into two kinds, essential and monadic. The essential number
they considered as first subsisting in the intelligible world,
together with being, and from thence distributed into all the various
gradations of forms. But the monadic, or that which is composed from
certain units, they justly considered as nothing more than the image
of essential number. And with respect to the numbers which the human
soul participates, these from its imperfect condition have a middle
subsistence; i. e. they exist in a vital, gnostic, and speculative,
but not in an operative manner. Hence, when receiving one thing with
another, we affirm, that they are two, as a dog and a man, or two men;
or when we compute more than two, as ten, and say that there is a decad
of men, this number is not essential to the two or ten individuals,
nor is it to be conceived as subsisting in sensible natures; but it
is purely quantity. But when we distribute this ten, into units,
we produce the principle of quantity, and generate a subject in
opinion[10], capable of participating the essential decad of our soul.
But when, considering man in himself, we affirm that he is a certain
number, as the duad, composed of animal and rational, we do not observe
one mode in this predication; but so far as by a discursive operation
of the soul, we numerate, we effect a particular quantum; but so far as
the subjects are two, and at the same time both one (since one fills
the essence of both, and in both unity is contained), we pronounce
another, and an essential number: and this duad is not of a posterior
origin, nor alone signifies a certain quantity, external to the
subject, but a duad subsisting in the essence of man, and containing
his nature. For here we do not produce a number by a discursive
operation, while we pursue essential natures. But when we number any
ten things, which are not connected by any conciliating unity, like
a choir, or an army, then this decad, which we predicate of the ten
particulars, subsists alone in our numerating soul, which renders
the ten individuals in opinion, a definite quantum. But in a choir,
or an army, essential number is participated exclusive of that which
subsists in our soul. And if it be enquired how number subsists in the
human soul, we must say, that the soul, by her self-moving energies,
procreates number, while she numerates, and by this energy, causes the
existence of quantity; in the same manner as in walking, we give rise
to a certain motion. Thus, monadic number, or a collection of units of
various kinds, subsists in opinion, in a manner correspondent to that
of geometrical figures; and by this means participates the essential
number of the soul. For as a triangular figure in the phantasy, is the
recipient of a triangular nature, or of triangle itself; so every three
units in opinion, receive the essential triad of the soul, and, by this
means, form a definite quantum.
In short, as in every being we may discern the resemblances of matter
and form, so in the pentad, or any other number, the five units, which
are the subject of participation, and the quantity of the number,
originate from the duad; but the form, that is the pentad itself, from
unity. For every form is an unity, which unites its subject quantity,
and connects it with its ideal species. It is, therefore, requisite
to understand, that the two principles of mathematical numbers are
resident in our souls, with which every mathematical number is
co-existent; I mean unity, comprehending in itself all the forms of
numbers, and which corresponds to unity in intellectual natures; and
the duad, endued with a generative power, of a formless nature, and of
infinite virtue; and which is called boundless, on account of its being
the image of never-failing and intelligible duality. Hence, the unity
of the soul, with a never-ceasing energy, continually distinguishes and
forms all the orderly processions of her numbers, suffers no vacuum
to intervene, and leaves no quantity formless and innumerable. Hence
too, no essential number of the soul, as for instance, the pentad,
is composed from substance and accident, as a white man; nor from
genus and difference, as man from animal and biped; nor again, from
five unities mutually touching each other, like a bundle of wood; nor
from things mixt, like water and wine, nor from things subsisting
by position, in the manner that stones compose a house; nor lastly,
does it subsist like things numerable; for it is not because they are
composed from indivisible units, that they possess any thing besides
units. For many points are indivisible, yet quantity is not produced
on this account; but because they participate of two natures, the one
corresponding to matter, and the other to form. Lastly, it is not
proper to say, that the number seven (and so of any other number), is
composed from the triad and the tetrad; for units, indeed, composed
with units, form a subject adapted to the reception of the heptad,
or the ideal and essential number seven; but the definite numerical
quantity seven, is formed from so many units, and the ideal heptad.
Hence, as the soul of the shipwright gives form to the timber, from her
inherent art; so the numerative soul, from the unity endued with the
relation of a principle which she possesses, gives form and subsistence
to all her inherent numbers. But there is this difference between the
two, that the shipwright’s art is not essential to our nature, and
requires manual operation, because it is conversant with sensible
matter; but the numerative art is essentially inherent in the soul,
and is therefore present with all men, and possesses an intellectual
matter, which it easily forms without the assistance of time. And
this, perhaps, is what deceives many, who think that the heptad is
nothing more than seven units. For the imagination of the vulgar,
unless it first perceives a thing destitute of ornament, and afterwards
the operations of the adorning artificer supervening its nature; and
lastly, beholds the thing perfect, and invested with form, cannot be
persuaded that it possesses two natures, the one formless, but the
other endued with an energetic and forming power.
And here it is necessary to observe, that though unity is the form
of all arithmetical forms, yet it is chiefly the form of the decad.
For what unity is simply to all the series of numbers, that the decad
is to the following hundreds, thousands, and millions; from whence,
according to a secondary progression, it is denominated unity. As
intellect, therefore, is the form of all things, but especially of the
soul, so unity, though it is the idea of all numbers, yet especially
of the decad. But the reason why the Pythagoreans extended ideal
numbers no farther than ten, is because this number is the ultimate
perfection of beings, containing all things in its omniform nature.
For all proportion subsists within the number ten; the arithmetical in
a natural progression of numbers from unity; the geometrical in the
numbers 1, 2, 4, and 1, 3, 9, and the harmonical in the numbers 2,
3, 6, and 3, 4, 6. And since the causes of all things are contained
in numbers, as far as to the decad[11], it is superfluous to suppose
exemplars of the following numbers.
If it should be asked in what manner we must conceive number as
subsisting in the intelligible world, we answer, with the great
Plotinus, that we must conceive it as subsisting in being itself,
with a power of impelling it to the production of multitude. “Hence
(says he, Ennead vi. lib. vi.) number is either the essence or the
energy of being, and animal itself, and intellect is number. But,
perhaps, we must call being, number united (ἀριθμὸς ηνωμένος),
but beings, number evolved, or unfolded; (ἐξεληλεγμένος ἀριθμὸς)
intellect, number moving in itself; (ἀριθμὸς ἐν ἐαυτῶ κινούμενος)
and lastly, animal, number comprehending (ἀριθμὸς περιέχων.“) It
was in consequence of this reasoning, that the Pythagoreans called
ideas numbers; because the gradual evolution of these from ineffable
unity, produced all the beautiful variety of forms. Their exalted
conceptions of numbers, likewise, originated from the same sublime
theory. Hence, [12]Pythagoras, in the sacred discourse, calls number
“_the ruler of forms and ideas_.” But [13]Philolaus, “_the
commanding and self-begotten container of the eternal duration of
mundane concerns_.” And [14]Hippasus, and all those who were
called ἀκουσματικοὶ (or such as were yet under the probation of the
quinquennial silence), “_the first exemplar of the mundane fabric,
and the judiciary instrument of its artificer_.”
6. And here I cannot but take notice, with regret, of the very
unphilosophical mistake committed by that great mathematician Dr.
Barrow[15]: I say, with regret, on account of the extraordinary
obligations I am under to his writings, for my proficiency (whatever it
may be) in mathematical learning. But respect must yield to the truth.
“Unity, says he, is not indivisible. (For how ex. gr. can 2/6 added
to 4/6 be equal to unity, if unity be indivisible and incomposed, and
represent a point) but rather only unity is properly divisible, and
numbers arise from the division of unity.” Here the Doctor evidently
confounds sensible units, which are the subjects of vulgar practical
arithmetic, with those units which are the objects of science.
Every individual sensible object, is indeed an unit, so far as it
participates the connecting and conciliating power of an immaterial
_one_: but the unity which stands at the top of speculative
arithmetic, is perfectly indivisible, or arithmetic would cease to be a
science. The truth of this is evident from Euclid’s definition: “Unity
(says he) is that according to which each of the things which are, is
called one.” But if unity be a composite, the definition is false;
since a composite, or a certain multitude, can never be the cause of
unity, but the contrary. And that this immaterial _one_ subsists
in sensible natures, has, I hope, been sufficiently proved in the
preceding part of this discourse. But the Platonic Theo[16] of Smyrna,
fully establishes the indivisibility of unity, as follows: “Unity is
terminating quantity, the principle and element of numbers, which
remains undiminished by the most immense multitude of subtractions,
and being deprived of all number, continues firm and fixt, because
it is impossible for division to proceed beyond the bound of unity.
Thus, if we separate any one corporeal substance into parts, the
_one_ again becomes _many_; and by subtracting the several
parts, we end in one part; and from this remaining part, again divided,
arises multitude; and by taking away every part, we again arrive at
_one_. So that _one_, considered as _one_, is incapable
of diminution, and perfectly indivisible. On the contrary, every
number is diminished by division, and is separated into parts less
than itself; as the number 6 into 3 and 3, or into 4 and 2, or into 5
and 1. But unity in sensible particulars, if divided, is diminished
after the manner of body, and by section is distributed into parts less
than itself: but it receives increase after the manner of number; for
instead of the one, multitude is produced. In this sense, therefore,
is unity indivisible; for nothing is divided into parts greater than
itself. But that which is cut into parts greater than the whole,
and into parts equal to the whole, is divided as number. Thus, for
instance, if any one sensible body is divided into six parts, 1, 1, 1,
1, 1, 1, these shall be equal to the whole; but by a section into 4
and 2, it is divided into parts greater than the whole, considered as
_one_; for 4 and 2 considered as numbers, exceed unity, and the
body was supposed to be one. Unity, therefore, as number is perfectly
indivisible. But unity is called by the Greek word μονάς, only, or
alone, either because it remains immoveable, and does not desert
itself, nor surpass the bounds of its nature (for it remains the same,
however multiplied into itself, through an infinite progression) or
because it is placed separate and apart from the multitude of other
numbers, it is denominated the _monad_, or _one_.”
In consequence of this very mistaken hypothesis, which opposes not
only all the wisdom of antiquity, but the sublimest truths, the Doctor
asserts, that an arithmetical cypher is the principle of numbers; and
that it is analogous to a point in geometry. Just as if a cypher, which
is nothing more than a mark expressive by its position with numbers,
of a certain quantity, had a real existence, and was productive of
number: when, at the same time, any other arbitrary character would
serve the same purposes, if applied in a similar manner. It must surely
afflict every thinking mind, to see how dreadfully the mechanical
system of philosophy, which has been so long in fashion, enslaves and
perverts the minds of its votaries; for there cannot, I think, be a
more egregious instance of its fatal tendency, than the present, in
which _nothing_ is considered as the foundation of that noble
science, arithmetic; which was deservedly placed by the ancients, in
the first rank of the mathematical disciplines. Such a foundation,
indeed, _may be_ proper to the _mechanical philosophy_, but
is very ill adapted to support the solid fabric of the arithmetical
science. But let us attend to the arguments of this most learned man,
in defence of so strange an assertion, “A cypher, or arithmetical
nothing (says he) is really the bound of every number coming between
it and the numbers next following, but not as a part. A cypher being
added to, or taken from a number, does neither increase nor diminish
it; from it is taken the beginning of computation, while itself is not
computed; and it bears a manifest relation to the principal properties
of a geometrical point.” But in what manner are we to conceive the
_nothing_ which intervenes between any two numbers, to be their
term or boundary? For Euclid defines a term to be the extremity of
any thing; implying by the extremity, something belonging to that of
which it is the bound. But how can a cypher, or _nothing_, in any
respect belong to number, or _something_? For if _nothing_
be a boundary, merely from its intervention, a point existing between
any two disjoined lines, though at the greatest distance from each,
must be their common boundary, which is evidently absurd. Besides, what
relation does it bear to a point, which is endued with a generative
power, by its flux forming the simple extension of a line, and, at
the same time, every where limiting its progression, and subsisting
in infinite capacity in its every part? Where are the real and divine
properties to be found in an arithmetical nothing, which Proclus,
in the following Commentaries, exhibits in a point? And how can
computation originate from a mere non-entity?
But a little consideration will convince us, that this Saracen, or
Indian cypher, is nothing more than an arbitrary character, invented
for the purpose of facilitating computation. For, suppose the letter
(_a_) to be placed in its stead, and to signify, when connected
with the mark for unity, ten, or ten multiplied by one; when connected
with the mark for two, ten multiplied by two, and so on. And again,
when placed twice after unity, let it express the second power of ten,
or one hundred, in this manner, _a a_; when thrice connected,
one thousand, or the third power of ten, and so on: shall we say, in
consequence of this, that (_a_) is the bound of numbers, and
the principle of arithmetic? Or, shall we not rather say, that it is
an arbitrary symbol, like any other algebraic character, having no
real connection with numbers, and depending, for its existence and
application, entirely on the will of its inventor. But this opinion is
too absurd to need any farther refutation.
7. It may here, perhaps, be expected, that I should explain how, in the
language of Syrianus[17], “divine number proceeds from the immortal
retreats of unity, until it arrives at the divine tetrad[18];” and
that I should unfold the properties of the tetractys, according to
the Pythagoreans; but an undertaking of this kind, would not only far
exceed the limits of this dissertation, but, perhaps, in the present
age, might be justly deemed, by the lovers of wisdom, a prostitution
and profanation of the most exalted truths. Enough, I hope, has been
said to excite the curiosity, and rouse the attention of the thinking
and liberal part of mankind; and those who understand what is here
briefly delivered, may apply themselves, with advantage, to Proclus on
Plato’s Theology, where they will find all the mysteries of numbers
unravelled; and to the works of the great Plotinus, who will lead them
into the penetralia of the most recondite wisdom. But, in perusing
the works of these great men, the reader must not expect to find the
sublimest truths explained in a familiar manner, and adapted, like
many modern publications, _to the meanest capacities_. For this,
indeed, is impossible to be effected. “Mankind (says Petvin[19]),
are not to be made any more truly knowing than happy by another’s
understanding.--There is no man can at once convey light in the higher
subjects, to another man’s understanding. It must come into the mind
from its own motions, within itself: and the grand art of philosophy,
_is to set the mind a-going_; and, even when we think nothing
of it, to assist it in its labour.” After which he observes, that
“the ancients never attempt to lead us into knowledge, by a continued
chain of reasoning; on the contrary, they write in such a manner,
as to force us to think for ourselves.” And, previous to this, he
remarks, “that there are certain truths acquired by a long exercise
of reason, both in _particular_, and likewise in those subjects
that are most _general_, as much, perhaps, out of the reach of the
greatest mathematician, as Sir Isaac Newton’s speculations are above
the capacity of some that are now called mathematicians.” The truth of
this observation is sufficiently evinced, in Plato’s definition of a
philosopher (in his Sophista), “The philosopher (says he) is the man
who sufficiently sees one idea every way extended through many, every
one of them lying apart; and many ideas different from one another,
externally comprehended under one.--And farther, one idea, throughout
all manys, wrapt up in one; and many ideas, every way separate or
discreet. This is to have the knowledge to discern how ideas, as they
are general, agree and disagree.” Now, he who thinks that a perception
of this kind may be acquired by barely reading an accurate discourse
on the nature of ideas, composed in intelligible terms, without, at
the same time, employing a long course of profound meditation, and
patient thought, knows but little the difficulty of the task, and
until he changes his opinion will never be the wiser. But the folly
and presumption of men, with respect to this sublime philosophy, is
really unpardonable; for there are very few who conceive that much
previous instruction is requisite to its acquisition; but almost
every man decides peremptorily on the most abstract speculations, and
reckons himself sufficient for the most profound investigations. In the
sciences and arts they are willing to proceed to perfection by gradual
advances; but they consider philosophy as easy, of instant access, and
hastily approach to her embraces with an assured confidence of success.
Though, like unhappy Ixion, through their presumption, instead of a
goddess, they grasp nothing but an empty cloud. Plato was so sensible
of this truth, that, in his seventh epistle to Dion, he expressly
affirms, that he neither has written, nor ever will write explicitly
concerning these sublime speculations; “For a thing of this kind (says
he) cannot be expressed by words, like other disciplines, but by a
lasting familiarity, and conjunction of life, with this _divine
object_, a bright light[20] on a sudden, as it were leaping from
a fire, will illuminate the soul, and there preserve and nourish its
splendor. He adds, that a publication of such concerns, is alone
useful to a few of mankind, who from some small vestiges previously
demonstrated, are sufficiently sagacious to their invention. But it
will fill others partly with a base contempt, and partly with a rash
and vain confidence, as if they had now learned some very excellent
things.” He then subjoins the following instance of the difficulty
attending such an undertaking: “There are three things (says he),
from which science must necessarily be produced; but the fourth is
science itself. And it is requisite to establish the fifth as that
which is the object of knowledge, and has a true existence. One of
these is the name of a thing; the second its definition; the third
the resemblance; the fourth science. Now take each of these, desiring
to learn what we have lately asserted, and think concerning them all,
in a similar manner. A circle is called something, whose _name_
we have just expressed. After this follows its definition, composed
from nouns and verbs. For that which every where is equally distant
from the extremes to the middle, is the definition of that which we
signify by the name of a round, and a circumference, and a circle. But
the third is the circle which may be painted, or blotted out, which
may be made by a wheel, or destroyed. None of which affections, the
circle itself, which each of these respects, suffers, as being of a
different nature. But the fourth is science, and intellect, and true
opinion about these. And this again must be established as one whole,
which neither subsists in voice, nor in corporeal figures, but in
intellect and intelligence. It is therefore manifest, that this fourth
is different from the nature itself of the circle, and again different
from the three we have previously mentioned. But among the number of
these, intellect, by its relation and similitude, proximately adheres
to the fifth, while the rest are more remote from its nature. The same
may likewise be affirmed of a straight and crooked figure, of colour,
and of the good, the beautiful, and the just. And again, of every
body, whether fashioned by the hand, or the work of nature, whether
fire or water, and the rest of this kind; likewise of every animal,
and the manners of animals; and of all actions and passions. For
unless, among these, some one, after a manner, receives that fourth,
he will never perfectly participate the science about the fifth.” He
then proceeds to shew in what respect each of the preceding four are
different from the fifth. “Every circle (says he) which by the hands
of men is either painted, or fashioned by a wheel, is plainly contrary
to our fifth. For it every where participates of the right-line. But
we must affirm, that the circle itself has neither more nor less of
any thing whatever; that is, it possesses in itself, nothing of a
contrary nature. Besides, none of these are endued with any stability
of name. For nothing hinders our applying the appellation of straight
to that which we now denominate round, and calling the straight by
the denomination of the round; nor will there be any less stability
in these, when their names are changed into the contrary. The same
reasoning is likewise true of definition, since it is composed from
nouns and verbs, which possess no stability. And in a variety of ways,
it may be proved, that no one of these four is certain and firm.” Now,
this fifth division of Plato’s entirely respects ideas, considered as
flourishing in intellect; by a conjunction with which, we acquire true
intelligence, and the perfection of human knowledge. The first three of
the preceding are obnoxious to various mutations; the fourth less; but
the last is perfectly stable and invariable. The three first are rather
conversant about the qualities of things, about the image and shadow;
the fourth raises us to the participation of truth; but the fifth to
truth itself, and permanent essence. In the first degrees almost all
are conversant; in the fourth a few; in the fifth, all the gods, but a
very small part of mankind, as it is asserted in the Timæus. The four
first may be known, indeed, without the fifth, confusedly; but from
the knowledge of the fifth they become perfectly manifest, as effects
from the knowledge of their cause. But we cannot, by any means, attain
to the apprehension of the fifth, unless we have been first accurately
conversant with the rest; for from our imperfect condition we are
compelled to rise from difference to identity, from multitude to unity,
and from shadow to substance. While we investigate the knowledge of
things, if we are alone desirous to apprehend their resemblance (which
is the case with the multitude) we shall be placed in the third degree,
and may easily acquire the object of our pursuit. But if we should
fortunately possess the true philosophical genius, which is rare in the
extreme, and aspiring to the fifth degree, should, by a happy event,
attain to its conjunction, though such a contact is clearer and more
certain than all knowledge; yet it is difficult to express it in words,
and to manifest it to others. And the reason of this is obvious: first,
because words are wanting, which exactly correspond to the essence of a
thing, since these are only the symbols of shadows. Secondly, because
we speak with those, who are alone conversant with shadows, and are on
this account derided by them, when they find that our fifth does not,
by any means, accord with material resemblances, which they consider as
the only realities.
8. And here a question very naturally presents itself for our solution,
whether the soul, while united with the body, is able to perceive
ideas, without the assistance of the phantasy, For it seems difficult
to apprehend how the soul, thus depressed and weighed down with the
terrene mass, should be able to raise herself to the supernal light
of ideas, and become united with their refulgence. The opinion of the
Peripatetics is well known, that some phantasm must always accompany
intelligence; but this is denied by the Platonists, and I think with
great reason. For the operations of intellect are not dependent on
the phantasy, though the perceptions of the latter proceed from the
energies of the former. Besides, as Plotinus beautifully observes, our
most vigorous energies are accompanied with the least animadversion;
and there is no absurdity in supposing that by increasing the force of
intellectual energy, we may speculate free from all imagination; since
the phantasms attending our conceptions, became weak in proportion
as the intellectual sight increases in vigour. On this account, the
Platonists affirm, that the moral virtues free us from the vehemence
of perturbations; but the contemplative from imagination, and the
senses. Hence too, the sciences may be called living waters; in which
the wings of the soul being dipt, her feathers, which were either
separated or broken by her lapse into body, are repaired, and restored
to a resemblance of their former perfection. For the wings are the
powers of the soul, leading to intelligibles: but the feathers are as
well the natural instincts to good and truth, as reasons inserted in
the soul; which either fall off, or are broken by her descent into
body, and conjunction with its ruinous bonds. But these are repaired
and invigorated by the sciences, which, like living streams, flowing
from the fountains of ideas, restore life and perfection to the soul.
Hence Plato, in the Phædrus, asserts that these wings of the soul
are increased by every thing which confers to supernal elevation; as
beauty, wisdom, and the like; and by a convenient metaphor, in the same
dialogue, he considers the chariot of the souls lives, her charioteer,
and the horses by which her car is drawn; and lastly, every thing which
contributes to the elevation of the soul, and her conjunction with
intellect and ideas. We may therefore conclude, that this conjunction
is possible to be effected, though it is rarely obtained; and that it
is a flight too arduous and sacred for the groveling and sordid; a
splendor too bright for the sensible eye; and a contact too ineffable
to be described by the unstable composition of words.
But I cannot conclude this section, without soliciting the reader’s
attention to a comparison of the difference between the ancient
philosophy, and that invented by Mr. Locke, and the moderns. According
to Mr. Locke’s system ideas are formed from sensible particulars, by a
kind of mechanical operation; so that truth is something by its nature,
posterior to sensation, and entirely dependent on it for existence.
According to Plato, ideas are eternal and immaterial beings, the
originals of all sensible forms, and the fountains of all evidence
and truth; so that on this system truth ranks among the first, and
not in the last of things; and would still retain its nature, though
the corporeal senses were no more. According to Mr. Locke, the soul
is a mere _rasa tabula_, an empty recipient, a mechanical blank.
According to Plato, she is an ever-written tablet, a plenitude of
forms, a vital and intellectual energy. On the former system, she is
on a level with the most degraded natures, the receptacle of material
species, and the spectator of delusion and non-entity[21]. Hence,
her energies are nothing but somnolent perceptions, and encumbered
cogitations; for all her knowledge terminates in sense, and her science
in passion. Like a man between sleeping and waking, her visions are
turbid and confused, and the phantoms of a material night, continually
glide before her drowsy eye. But on the latter system, the soul is the
connecting medium of an intelligible and sensible nature, the bright
repository of all middle forms, and the vigilant eye of all cogitative
reasons. Hence she is capable of rousing herself from the sleep of a
corporeal life, and emerging from this dark Cimmerian land, into the
regions of light and reality. At first, indeed, before she is excited
by science, she is oppressed with lethargy, and clouded with oblivion;
but in proportion as learning and enquiry stimulate her dormant powers,
she wakens from the dreams of ignorance, and opens her eye to the
irradiations of wisdom. On Mr. Locke’s system, the principles of
science and sense are the same, for the energies of both originate
from material forms, on which they are continually employed. Hence,
science is subject to the flowing and perishable nature of particulars;
and if body and its attributes were destroyed, would be nothing but
a name. But on the system of Plato, they differ as much as delusion
and reality; for here the vital, permanent, and lucid nature of ideas
is the fountain of science; and the inert, unstable, and obscure
nature of sensible objects, the source of sensation. On Mr. Locke’s
system, body may be modified into thought, and become an intelligent
creature; it may be subtilized into life, and shrink, by its exility,
into intellect. On that of Plato, body can never alter its nature by
modification, however, it may be rarefied and refined, varied by the
transposition of its parts, or tortured by the hand of experiment. In
short, the two systems may be aptly represented by the two sections of
a line, in Plato’s Republic. In the ancient, you have truth itself, and
whatever participates of the brightest evidence and reality: in the
modern, ignorance, and whatever belongs to obscurity and shadow. The
former fills the soul with intelligible light, breaks her lethargic
fetters, and elevates her to the principle of things; the latter
clouds the intellectual eye of the soul, by increasing her oblivion,
strengthens her corporeal bands, and hurries her downwards into the
dark labyrinths of matter.
Nor is it wonderful there should be so great a difference between the
two systems, and so much in favour of the ancients, if we consider the
great advantages these ancients possessed over the moderns in every
thing which contributes to the advancement of philosophy. For, in
the first place, they lived in an age when abstract investigations
were in the greatest request, and the professors of such pursuits in
the highest estimation. Besides this, they united the most exalted
abilities with the most unwearied attention and obstinate perseverance;
they devoted their whole lives to the search of truth; and relinquished
every thing which might be an obstacle to its acquisition. We may
add, likewise, the advantages of a language extremely philosophical;
and a freedom from the toil of learning any tongue but their own. Now
the reverse of all this is the portion of the moderns: for in the
present age, abstract speculations are ridiculed; and its professors
despised. The pursuit of truth is considered as perfectly consistent
with ordinary avocations, and is rather prosecuted as a relief from
the toils of business than as a thing desirable for its own sake,
and of the greatest dignity and worth. Hence, a few years desultory
application at a college, where language is one of the first objects
of attention, qualifies a modern for philosophy, raises him above
Pythagoras and Plato, and persuades him, with presumptuous confidence,
to enter the lists against these venerable heroes. And lastly, all
modern languages are barbarous with respect to the Greek; falling far
short of its harmony and energy, its copiousness and propriety. If
such then be the true state of the case, what judgment must we form
of men who, with all these disadvantages, philosophized without the
assistance of the ancients, despising their works, and being ignorant
of their contents? Shall we call it prudence or presumption, wisdom
or folly? Truth will certainly pronounce the latter; and the general
voice of posterity will confirm her decision. There are two egregious
instances in our own country of this daring presumption; I mean Bacon
and Locke. The former of these is celebrated for having destroyed the
jargon of the schoolmen, and brought experimental enquiries into
repute; and for attempting to investigate causes through the immensity
of particular effects. Hence, he fondly expected, by experiment piled
on experiment, to reach the principle of the universe; not considering
that his undertaking was as ridiculous as that of the giants of old,
who attempted to invade the heavens, by placing Ossa upon Pelion, and
Olympus upon Ossa; and ignorant that
Heaven still, with laughter, the vain toil surveys,
And buries madmen in the heaps they raise.
The latter of these, Mr. Locke, is applauded for having, without
assistance from the ancients, explained the nature, and exhibited
the genuine theory of human understanding. But that this applause
is false, the preceding comparison between his and the ancient
philosophy, may evince; and the variety of other self-taught systems
which, like nocturnal meteors, blaze for a while, and then vanish
in obscurity, abundantly confirms. Had these men, indeed, when they
justly derided the barbarous writings of the schoolmen, explored the
works of antiquity, penetrated the wisdom they contain, and enriched
their native language with its illustration, they had doubtless been
celebrated by the latest posterity: but, desirous of becoming masters
in philosophy by intuition, they disdained the instruction of the
ancients, and vainly attempted to soar on artificial wings to the
very summit of science. They are, however, destined, like Icarus, to
a precipitate fall; for the influence of time, which is continually
dissolving the cement of their plumes, is likewise continually
weakening their force, and will at last effect their final separation.
And thus much concerning the doctrine of ideas, and numbers, according
to Pythagoras and Plato.