CHAPTER XXXII.

ANALOGIES OF PHYSICAL AND RELIGIOUS PHILOSOPHY.

1. Any assertion of analogy between physical and religious philosophy

will very properly be looked upon with great jealousy as likely to

be forced and delusive; and it is only in its most general aspects

that a sound philosophy on the two subjects can offer any points of

resemblance. But in some of its general conditions the discovery of

truth in the one field of knowledge and in the other may offer certain

analogies, as well as differences, which it may be instructive to

notice; and to some such aspects of our philosophy I shall venture to

refer.

For the physical sciences--the sciences of observation and

speculation--the progress of our exact and scientific knowledge, as

I have repeatedly said, consists in reducing the objects and events

of the universe to a conformity with Ideas which we have in our own

minds:--the Ideas, for instance, of Space, Force, Substance, and the

like. In this sense, the intellectual progress of men consists in the

Idealization of Facts.

2. In moral subjects, on the other hand, where man has not merely to

observe and speculate, but also to act;--where he does not passively

leave the facts and events of the world such as they are, but tries

actively to alter them and to improve the existing state of things,

his progress consists in doing this. He makes a moral advance when he

succeeds in doing what he thus attempts:--when he really improves the

state of things with which he has to do by removing evil and producing

good:--when he makes the state of things, namely, the relations between

him and other persons, his acts and their acts, conform more and

more to Ideas which he has in his own mind:--namely, to the Ideas of

Justice, Benevolence, and the like. His moral progress thus consists in

the realization of Ideas.

And thus we are led to the Aphorism, as we may call it, that _Man's

Intellectual Progress consists in the Idealization of Facts, and his

Moral Progress consists in the Realization of Ideas_.

3. But further, though that progress of science which consists in

the idealization of facts may be carried through several stages, and

indeed, in the history of science, has been carried through many

stages, yet it is, and always must be, a progress exceedingly imperfect

and incomplete, when compared with the completeness to which its nature

points. Only a few sciences have made much progress; none are complete;

most have advanced only a step or two. In none have we reduced all the

Facts to Ideas. In all or almost all the unreduced Facts are far more

numerous and extensive than those which have been reduced. The general

mass of the facts of the universe are mere facts, unsubdued to the rule

of science. The Facts are not Idealized. The intellectual progress

is miserably scanty and imperfect, and would be so, even if it were

carried much further than it is carried. How can we hope that it will

ever approach to completeness?

4. And in like manner, the _moral_ progress of man is still more

miserably scanty and incomplete. In how small a degree has he in this

sense realized his Ideas! In how small a degree has he carried into

real effect, and embodied in the relations of society, in his own acts

and in those of others with whom he is concerned, the Ideas of Justice

and Benevolence and the like! How far from a complete realization of

such moral Ideas are the acts of the best men, and the relations of

the best forms of society! How far from perfection in these respects

is man! and how certain it is that he will always be very far from

perfection! Far below even such perfection as he can conceive, he will

always be in his acts and feelings. The moral progress of man, of each

man, and of each society, is, as I have said, miserably scanty and

incomplete; and when regarded as the realization of his moral Ideas,

its scantiness and incompleteness become still more manifest than

before.

Hence we are led to another Aphorism:--_that man's progress in the

realization of Moral Ideas, and his progress in the Scientific

idealization of Facts, are, and always will be, exceedingly scanty and

incomplete_.

5. But there is another aspect of Ideas, both physical and moral,

in which this scantiness and incompleteness vanish. In the Divine

Mind, all the physical Ideas are entertained with complete fulness

and luminousness; and it is because they are so entertained in the

Divine Mind, and it is because the universe is constituted and framed

upon them, that we find them verified in every part of the universe,

whenever we make our observation of facts and deduce their laws.

In like manner the Moral Ideas exist in the Divine Mind in complete

fulness and luminousness; and we are naturally led to believe and

expect that they must be exemplified in the moral universe, as

completely and universally as the physical laws are exemplified in the

physical universe. Is this so? or under what conditions can we conceive

this to be?

6. In answering this question, we must consider how far the moral,

still more even than the physical Ideas of the Divine Mind, are

elevated above our human Ideas; but yet not so far as to have no

resemblance to our corresponding human Ideas; for if this were so, we

could not reason about them at all.

In speaking of man's moral Ideas, Benevolence, Justice, and the like,

we speak of them as belonging to man's _Soul_, rather than to his

_Mind_, which we have commonly spoken of as the seat of his physical

Ideas. A distinction is thus often made between the intellectual and

the moral faculties of man; but on this distinction we here lay no

stress. We may speak of man's _Mind_ and _Soul_, meaning that part of

his being in which are all his Ideas, intellectual and moral.

And now let us consider the question which has just been asked:--how we

can conceive the Divine Benevolence and Justice to be completely and

universally realized in the moral world, as the Ideas of Space, Time,

&c. are in the physical world?

7. Our Ideas of Benevolence, Justice, and of other Virtues, may be

elevated above their original narrowness, and purified from their

original coarseness, by moral culture; as our Ideas of Force and

Matter, of Substance and Elements, and the like, may be made clear

and convincing by philosophical and scientific culture. This appears,

in some degree, in the history of moral terms, as the progress of

clearness and efficacy in the Idea of the material sciences appears in

the history of the terms belonging to such sciences. Thus among the

Romans, while they confined their kindly affections within their own

class, a stranger was universally an enemy; _peregrinus_ was synonymous

with _hostis_. But at a later period, they regarded all _men_ as having

a claim on their kindness; and he who felt and acted on this claim was

called _humane_. This meaning of the word _humanity_ shows the progress

(in their Ideas at least) of the virtue which the word _humanity_

designates.

8. And as man can thus rise to a point of view where he sees that man

is to be loved as man, so the humane and loving man inevitably assumes

that God loves all men; and thus assumes that there is, or may be, a

love of man in man's heart, which represents and resembles in kind,

however remote in degree, the love of God to man.

But as in man's love of man there are very widely different stages,

rising from the narrow love of a savage to his family or his tribe,

to the widest and warmest feelings of the most enlightened and loving

universal philanthropist;--so must we suppose that there are stages

immeasurably wider by which God's love of man is more comprehensive and

more tender than any love of man for man. The religious philosopher

will fully assent to the expressions of this conviction delivered by

pious men in all ages. "The eternal God is thy refuge, and beneath

thee are the everlasting arms." "When my father and my mother forsake

me the Lord taketh me up," is the expression of Divine Love, consistent

with philosophy as well as with revelation. But as the Divine Love is

more comprehensive and enduring than any human love, so is it in an

immeasurably greater degree, more enlightened. It is not a love that

seeks merely the pleasure and gratification of its object; _that_

even an enlightened human love does not do. It seeks the good of its

objects; and such a good as is the greatest good, to an Intelligence

which can embrace all cases, causes, and contingencies. To our limited

understanding, evil seems often to be inflicted, and the good of a

part seems inconsistent with the good of another part. Our attempts to

conceive a Supreme and complete Good provided for all the creatures

which exist in the universe, baffle and perplex us, even more than our

attempts to conceive infinite space, infinite time, and an infinite

chain of causation. But as the most careful attention which we can

give to the Ideas of Space, Time, and Causation convinces us that

these Ideas are perfectly clear and complete in the Divine Mind, and

that _our_ perplexity and confusion on these subjects arise only from

the vast distance between the Divine Mind and our human mind, so is

it reasonable to suppose the same to be the source of the confusion

which we experience when we attempt to determine what most conduces to

the good of our fellow-creatures; and when, urged by love to them, we

endeavour to promote this good. We can do little of what Infinite Love

would do, yet are we not thereby dispensed from seeking in some degree

to imitate the working of Divine Love. We can see but little of what

Infinite Intelligence sees, and this should be one source of confidence

and comfort, when we stumble upon perplexities produced by the seeming

mixture of good and evil in the world.

9. But when we ask the questions which have already been stated:

Whether this Infinite Divine Love is realized in the world, and if

so, How: I conceive that we are irresistibly impelled to reply to the

former question, that it is: and we then turn to the latter. We are

led to assume that there is in God an Infinite Love of man, a creature

in a certain degree of a Divine nature. We must, as a consequence of

this, assume that the Love of God to man, necessarily is, in the end,

and on the whole, completely and fully realized in the history of the

world. But what is the complete history of the world! Is it that which

consists in the lives of men such as we see them between their birth

and their death? If the minds or souls of men are alive after the death

of the body, that future life, as well as this present life, belongs to

the history of the world;--to that providential history, of which the

totality, as we have said, must be governed by Infinite Divine Love.

And in addition to all other reasons for believing that the minds and

souls of men do thus survive their present life, is this:--that we thus

can conceive, what otherwise it is difficult or impossible to conceive,

the operation of Infinite Love in the whole of the history of mankind.

If there be a Future State in which men's souls are still under the

authority and direction of the Divine Governor of the world, all that

is here wanting to complete the scheme of a perfect government of

Intelligent Love may thus be applied: all seeming and partial evil may

be absorbed and extinguished in an ultimate and universal good.

10. The Idea of Justice as belonging to God suggests to us some of the

same kind of reflexions as those which we have made respecting the

Divine Love. We believe God to be just: otherwise, as has been said,

He would not be God. And as we thus, from the nature of our minds and

souls, believe God to be just, we must, in this belief, understand

Justice according to the Idea which we have of Justice; that is, in

some measure, according to the Idea of Justice, as exemplified in

human actions and feelings. It would be absurd to combine the two

propositions, that we necessarily believe that God is just, and that by

_just_, we mean something entirely different from the common meaning of

the word.

But though the Divine Idea of Justice must necessarily, in some

measure, coincide with our Idea of Justice, we must believe in this,

as in other cases, that the Divine Idea is immeasurably more profound,

comprehensive, and clear, than the human Idea. Even the human Idea of

Justice is susceptible of many and large progressive steps, in the way

of clearness, consistency, and comprehensiveness. In the moral history

of man this Idea advances from the hard rigour of inflexible written

Law to the equitable estimation of the real circumstances of each case;

it advances also from the narrow Law of a single community to a larger

Law, which includes and solves the conflicts of all such Laws. Further,

the administration of human Law is always imperfect, often erroneous,

in consequence of man's imperfect knowledge of the facts of each case,

and still more, from his ignorance of the designs and feelings of the

actors. If the Judge could see into the heart of the person accused,

and could himself rise higher and higher in judicial wisdom, he might

exemplify the Idea of Justice in a far higher degree than has ever yet

been done.

11. But all such advance in the improvement of human Justice must

still be supposed to stop immeasurably short of the Divine Justice,

which must include a perfect knowledge of all men's actions, and all

men's hearts and thoughts; and a universal application of the wisest

and most comprehensive Laws. And the difference of the Divine and of

the human Idea of Justice may, like the differences of other Divine

and human Ideas, include the solution of all the perplexities in which

we find ourselves involved when we would trace the Idea to all its

consequences. The Divine Idea is immeasurably elevated above the human

Idea; in the Divine Idea all inconsistency, defect, and incompleteness

vanish, and Justice includes in its administration every man, without

any admixture of injustice. This is what we must conceive of the Divine

administration, since God is perfectly just.

12. But here, as before, we have another conclusion suggested to us. We

are, by the considerations just now spoken of, led to believe that, in

the Divine administration of the world is an administration of perfect

Justice;--that is, such is the Divine Administration in the end and on

the whole, taking into account the whole of the providential history of

the world. But the course of the world, taking into account only what

happens to man in this present life, is not, we may venture to say, a

complete and entire administration of justice. It often happens that

injustice is successful and triumphant, even in the end, so far as the

end is seen here. It happens that wrong is done, and is not remedied

or punished. It happens that blameless and virtuous men are subjected

to pain, grief, violence, and oppression, and are not protected,

extricated, or avenged. In the affairs of this world, the prevalence of

injustice and wrong-doing is so apparent, as to be a common subject of

complaint: and though the complaint may be exaggerated, and though a

calm and comprehensive view may often discern compensating and remedial

influences which are not visible at first sight, still we cannot regard

the lot of happiness or misery which falls to each man in this world

and this life as apportioned according to a scheme of perfect and

universal justice, such as in our thoughts we cannot but require the

Divine administration to be.

13. Here then we are again led to the same conviction by regarding the

Divine administration of the world as the realization of the Divine

Justice, to which we were before led by regarding it as the realization

of the Divine Love. Since the Idea is not fully or completely realized

in man's life in this present world, this present world cannot be the

whole of the Divine Administration. To complete the realization of the

Idea of Justice, as an element of the Divine Administration, there

must be a life of man after his life in this present world. If man's

mind and soul, the part of him which is susceptible of happiness and

misery, survive this present life, and be still subject to the Divine

Administration, the Idea of Divine Justice may still be completely

realized, notwithstanding all that here looks like injustice or

defective justice; and it belongs to the Idea of Justice to remedy

and compensate, not to prevent wrong. And thus by this supposition

of a Future State of man's existence, we are enabled to conceive

that, in the whole of the Divine Government of the universe, all

seeming injustice and wrong may be finally corrected and rectified,

in an ultimate and universal establishment of a reign of perfect

Righteousness.

14. Admitting the view thus presented, we may again discern a

remarkable analogy between what we have called our _physical_ Ideas

(those of Space, Time, Cause, Substance, and the like), and our _moral_

Ideas, (those of Benevolence, Justice, &c.). In both classes we must

suppose that our human Ideas represent, though very incompletely and at

an immeasurable distance, the Divine Ideas. Even our physical Ideas,

when pursued to their consequences, are involved in a perplexity

and confusion from which the Divine Ideas are free. Our Ideas of

Benevolence and Justice are still more full of imperfections and

inconsistency, when we would frame them into a complete scheme, and

yet from such imperfections and inconsistency we must suppose that

the Divine Benevolence and Justice are exempt. Our physical Ideas we

find in every case exactly exemplified and realized in the universe,

and we account for this by considering that they are the Divine Ideas,

on which the universe is constituted. Our moral Ideas, the Ideas of

Benevolence and Justice in particular, must also be realized in the

universe, as a scheme of Divine Government. But they are not realized

in the world as constituted of man living this present life. The Divine

Scheme of the world, therefore, extends beyond this present life of

man. If we could include in our survey the future life as well as the

present life of man, and the future course of the Divine Government, we

should have a scheme of the Moral Government of the universe, in which

the Ideas of Perfect Benevolence and Perfect Justice are as completely

and universally exemplified and realized, as the Ideas of Space, Time,

Cause, Substance, and the like, are in the physical universe.

15. There is one other remark bearing upon this analogy, which seems

to deserve our attention. As I have said in the last chapter, the

scheme of the world, as governed by our physical Ideas, seems to point

to a Beginning of the world, or at least of the present course of the

world: and if we suppose a Beginning, our thoughts naturally turn to

an End. But if our physical Ideas point to a Beginning and suggest an

End, do our Ideas of Divine Benevolence and Justice in any way lend

themselves to this suggestion?--Perhaps we might venture to say that in

some degree they do, even to the eye of a mere philosophical reason.

Perhaps our reason alone might suggest that there is a progression in

the human race, in various moral attributes--in art, in civilization,

and even in humanity and in justice, which implies a beginning. And

that at any rate there is nothing inconsistent with our Idea of the

Divine Government in the supposition that the history of this world has

a Beginning, a Middle and an End.

16. If therefore there should be conveyed to us by some channel

especially appropriated to the communication and development of moral

and religious Ideas, the knowledge that the world, as a scheme of

Divine Government, has _a Beginning_, _a Middle_, and _an End_, of

a Kind, or at least, invested with circumstances quite different

from any which our physical Ideas can disclose to us, there would

be, in such a belief, nothing at all inconsistent with the analogies

which our philosophy--the philosophy of our Ideas illustrated by the

whole progress of science--has impressed upon us. On the grounds of

this philosophy, we need find no difficulty in believing that as the

visible universe exhibits the operation of the Divine Ideas of Space,

Time, Cause, Substance, and the like, and discloses to us traces of

a Beginning of the present mode of operation, so the moral universe

exhibits to us the operation of the Divine Benevolence and Justice; and

that these Divine attributes wrought in a special and peculiar manner

in the Beginning; interposed in a peculiar and special manner in the

Middle; and will again act in a peculiar and special manner in the End

of the world. And thus the conditions of the physical universe, and the

Government of the Moral world, are both, though in different ways, a

part of the work which God is carrying on from the Beginning of things

to the End--_opus quod Deus operator a principio usque ad finem_.

17. We are led by such analogies as I have been adducing to believe

that the whole course of events in which the minds and souls of men

survive the present life, and are hereafter subjected to the Divine

government in such a way as to complete all that is here deficient in

the world's history, is a scheme of perfect Benevolence and Justice.

Now, can we discern in man's mind or soul itself any indication of a

destiny like this? Are there in us any powers and faculties which seem

as if they were destined to immortality? If there be, we have in such

faculties a strong confirmation of that belief in the future life of

man which has already been suggested to us as necessary to render the

Divine government conceivable.

18. According to our philosophy there are powers and faculties which

do thus seem fitted to endure, and not fitted to terminate and be

extinguished. The Ideas which we have in our minds--the physical

Ideas, as we have called them, according to which the universe is

constituted,--agree, as far as they go, with the Ideas of the Divine

Mind, seen in the constitution of the universe. But these Divine

Ideas are eternal and imperishable: we therefore naturally conclude

that the human mind which includes such elements, is also eternal and

imperishable. Since the mind can take hold of eternal truths, it must

be itself eternal. Since it is, to a certain extent, the image of God

in its faculties, it cannot ever cease to be the image of God. When it

has arrived at a stage in which it sees several aspects of the universe

in the same form in which they present themselves to the Divine Mind,

we cannot suppose that the Author of the human mind will allow it and

all its intellectual light to be extinguished.

19. And our conviction that this extinction of the human mind cannot

take place becomes stronger still, when we consider that the mind,

however imperfect and scanty its discernment of truth may be, is

still capable of a vast, and even of an unlimited progress in the

pursuit and apprehension of truth. The mind is capable of accepting

and appropriating, through the action of its own Ideas, every step in

science which has ever been made--every step which shall hereafter

be made. Can we suppose that this vast and boundless capacity exists

for a few years only, is unfolded only into a few of its simplest

consequences, and is then consigned to annihilation? Can we suppose

that the wonderful powers which carry man on, generation by generation,

from the contemplation of one great and striking truth to another, are

buried with each generation? May we not rather suppose that that mind,

which is capable of indefinite progression, is allowed to exist in an

infinite duration, during which such progression may take place?

20. I propose this argument as a ground of hope and satisfactory

reflexion to those who love to dwell on the natural arguments for the

Immortality of the Soul. I do not attempt to follow it into detail.

I know too well how little such a cause can gain by obstinate and

complicated argumentation, to attempt to urge the argument in that

manner: and probably different persons, among those who accept the

argument as valid, would give different answers to many questions of

detail, which naturally arise out of the acceptance of this argument.

I will not here attempt to solve, or even to propound these questions.

My main purpose in offering these views and this argument at all, is

to give some satisfaction to those who would think it a sad and blank

result of this long survey of the nature and progress of science in

which we have been so long engaged (through this series of works), that

it should in no way lead to a recognition of the Author of that world

about which our Science is, and to the high and consolatory hopes which

lift man beyond this world. No survey of the universe can be at all

satisfactory to thoughtful men, which has not a theological bearing;

nor can any view of man's powers and means of knowing be congenial to

such men, which does not recognize an infinite destination for the mind

which has an infinite capacity; an eternal being of the Faculty which

can take a steady hold of eternal being.

21. And as we may derive such a conviction from our physical Ideas, so

too may we no less from our moral Ideas. Our minds apprehend Space and

Time and Force and the like, as Ideas which are not dependent on the

body; and hence we believe that our minds shall not perish with our

bodies. And in the same manner our souls conceive pure Benevolence and

perfect Justice, which go beyond the conditions of this mortal life;

and hence we believe that our souls have to do with a life beyond this

mortal life.

It is more difficult to speak of man's indefinite moral progression

even than of his indefinite intellectual progression. Yet in every

path of moral speculation we have such a progression suggested to us.

We may begin, for instance, with the ordinary feelings and affections

of our daily nature:--Love, Hate, Scorn. But when we would elevate the

Soul in our imagination, we ascend above these ordinary affections, and

take the repulsive and hostile ones as fitted only to balance their own

influences. And thus the poet, speaking of a morally poetical nature,

describes it:

The Poet in a golden clime was born,

With golden stars above.

He felt the hate _of_ hate, the scorn _of_ scorn,

The love _of_ love.

But the loftier moralist can rise higher than this, and can, and will,

reject altogether Hate and Scorn from his view of man's better nature.

His description would rather be--

The good man in a loving clime was born,

With loving stars above.

He felt sorrow for hate, pity for scorn,

And love of love.

He would, in his conception of such a character, ascribe to it all

the virtues which result from the control and extinction of these

repulsive and hostile affections:--the virtues of magnanimity,

forgivingness, unselfishness, self-devotion, tenderness, sweetness. And

these we can conceive in a higher and higher degree, in proportion as

our own hearts become tender, forgiving, pure and unselfish. And though

in every human stage of such a moral proficiency, we must suppose

that there is still some struggle with the remaining vestiges of our

unkind, unjust, angry and selfish affections, we can see no limit to

the extent to which this struggle may be successful; no limit to the

degree in which these traces of the evil of our nature may be worn

out by an enduring practice and habit of our better nature. And when

we contemplate a human character which has, through a long course of

years, and through many trials and conflicts, made a large progress in

this career of melioration, and is still capable, if time be given,

of further progress towards moral perfection, is it not reasonable to

suppose that He who formed man capable of such progress, and who, as we

must needs believe, looks with approval on such progress where made,

will not allow the progress to stop when it has gone on to the end of

man's short earthly life? Is it not rather reasonable to suppose that

the pure and elevated and all-embracing affection, extinguishing all

vices and including all virtues, to which the good man thus tends,

shall continue to prevail in him as a permanent and ever-during

condition, in a life after this?

But can man raise himself to such a stage of moral progress, by his own

efforts? Such a progress is an approximation towards the perfection of

moral Ideas, and therefore an approximation towards the image of God,

in whom that perfection resides: is it not then reasonable to suppose

that man needs a Divine Influence to enable him to reach this kind of

moral completeness? And is it not also reasonable to suppose that,

as he needs such aid, in order that the Idea of his moral progress

may be realized, so he will receive such aid from the Divine Power

which realizes the Idea of Divine Love in the world; and to do so,

must realize it in those human souls which are most fitted for such a

purpose?

But these questions remind me how difficult, and indeed, how impossible

it is to follow such trains of reflexion by the light of philosophy

alone. To answer such questions, we need, not Religious Philosophy

only, but Religion: and as I do not here venture beyond the domain of

philosophy, I must, however abruptly, conclude.

THE END.

APPENDIX.

APPENDIX A.

OF THE PLATONIC THEORY OF IDEAS.

(_Cam. Phil. Soc._ Nov. 10, 1856.)

Though Plato has, in recent times, had many readers and admirers

among our English scholars, there has been an air of unreality and

inconsistency about the commendation which most of these professed

adherents have given to his doctrines. This appears to be no captious

criticism, for instance, when those who speak of him as immeasurably

superior in argument to his opponents, do not venture to produce

his arguments in a definite form as able to bear the tug of modern

controversy;--when they use his own Greek phrases as essential to the

exposition of his doctrines, and speak as if these phrases could not be

adequately rendered in English;--and when they assent to those among

the systems of philosophy of modern times which are the most clearly

opposed to the system of Plato. It seems not unreasonable to require,

on the contrary, that if Plato is to supply a philosophy for us, it

must be a philosophy which can be expressed in our own language;--that

his system, if we hold it to be well founded, shall compel us to deny

the opposite systems, modern as well as ancient;--and that, so far as

we hold Plato's doctrines to be satisfactorily established, we should

be able to produce the arguments for them, and to refute the arguments

against them. These seem reasonable requirements of the adherents of

_any_ philosophy, and therefore, of Plato's.

I regard it as a fortunate circumstance, that we have recently had

presented to us an exposition of Plato's philosophy which does conform

to those reasonable conditions; and we may discuss this exposition with

the less reserve, since its accomplished author, though belonging to

this generation, is no longer alive. I refer to the _Lectures_ on the

History of Ancient Philosophy, by the late Professor Butler of Dublin.

In these Lectures, we find an account of the Platonic Philosophy which

shows that the writer had considered it as, what it is, an attempt

to solve large problems, which in all ages force themselves upon the

notice of thoughtful men. In Lectures VIII. and X., of the Second

Series, especially, we have a statement of the Platonic Theory of

Ideas, which may be made a convenient starting point for such remarks

as I wish at present to make. I will transcribe this account; omitting,

as I do so, the expressions which Professor Butler uses, in order to

present the theory, not as a dogmatical assertion, but as a view, at

least not extravagant. For this purpose, he says, of the successive

portions of the theory, that one is "not too absurd to be maintained;"

that another is "not very extravagant either;" that a third is "surely

allowable;" that a fourth presents "no incredible account" of the

subject; that a fifth is "no preposterous notion in substance, and no

unwarrantable form of phrase." Divested of these modest formulæ, his

account is as follows: [Vol. II. p. 117.]

"Man's soul is made to contain not merely a consistent scheme of its

own notions, but a direct apprehension of _real and eternal laws beyond

it_. These real and eternal laws are things _intelligible_, and not

things sensible.

"These laws impressed upon creation by its Creator, and apprehended

by man, are something distinct equally from the Creator and from man,

and the whole mass of them may fairly be termed the World of Things

Intelligible.

"Further, there are qualities in the supreme and ultimate Cause of all,

which are manifested in His creation, and not merely manifested, but,

in a manner--after being brought out of his super-essential nature into

the stage of being [which is] below him, but next to him--are then by

the causative act of creation deposited in things, differencing them

one from the other, so that the things partake of them (μετέχουσι),

communicate with them (κοινωνοῦσι).

"The intelligence of man, excited to reflection by the impressions

of these objects thus (though themselves transitory) participant of

a divine quality, may rise to higher conceptions of the perfections

thus faintly exhibited; and inasmuch as these perfections are

unquestionably _real_ existences, and _known_ to be such in the very

act of contemplation,--this may be regarded as a direct intellectual

apperception of them,--a Union of the Reason with the Ideas in that

sphere of being which is common to both.

"Finally, the Reason, in proportion as it learns to contemplate the

Perfect and Eternal, _desires_ the enjoyment of such contemplations in

a more consummate degree, and cannot be fully satisfied, except in the

actual fruition of the Perfect itself.

"These suppositions, taken together, constitute the Theory of Ideas."

In remarking upon the theory thus presented, I shall abstain from any

discussion of the theological part of it, as a subject which would

probably be considered as unsuited to the meetings of this Society,

even in its most purely philosophical form. But I conceive that it will

not be inconvenient, if it be not wearisome, to discuss the Theory of

Ideas as an attempt to explain the existence of real knowledge; which

Prof. Butler very rightly considers as the necessary aim of this and

cognate systems of philosophy[321].

I conceive, then, that one of the primary objects of Plato's Theory

of Ideas is, to explain the existence of real knowledge, that is, of

demonstrated knowledge, such as the propositions of geometry offer

to us. In this view, the Theory of Ideas is one attempt to solve a

problem, much discussed in our times, What is the ground of geometrical

truth? I do not mean that this is the whole object of the Theory, or

the highest of its claims. As I have said, I omit its theological

bearings; and I am aware that there are passages in the Platonic

Dialogues, in which the Ideas which enter into the apprehension and

demonstration of geometrical truths are spoken of as subordinate to

Ideas which have a theological aspect. But I have no doubt that one

of the main motives to the construction of the Theory of Ideas was,

the desire of solving the Problem, "How is it possible that man should

apprehend necessary and eternal truths?" That the truths are necessary,

makes them eternal, for they do not depend on time; and that they are

eternal, gives them at once a theological bearing.

That Plato, in attempting to explain the nature and possibility of

real knowledge, had in his mind geometrical truths, as examples of

such knowledge is, I think, evident from the general purport of his

discourses on such subjects. The advance of Greek geometry into a

conspicuous position, at the time when the Heraclitean sect were

proving that nothing could be proved and nothing could be known,

naturally suggested mathematical truth as the refutation of the

skepticism of mere sensation. On the one side it was said, we can

know nothing except by our sensations; and that which we observe with

our senses is constantly changing; or at any rate, may change at any

moment. On the other hand it was said, we _do_ know geometrical truths,

and as truly as we know them, that they cannot change. Plato was quite

alive to the lesson, and to the importance of this kind of truths.

In the _Meno_ and in the _Phædo_ he refers to them, as illustrating

the nature of the human mind: in the _Republic_ and the _Timæus_ he

again speaks of truths which far transcend anything which the senses

can teach, or even adequately exemplify. The senses, he argues in the

_Theætetus_, cannot give us the knowledge which we have; the source

of it must therefore be in the mind itself; in the _Ideas_ which

it possesses. The impressions of sense are constantly varying, and

incapable of giving any certainty: but the Ideas on which real truth

depends are constant and invariable, and the certainty which arises

from these is firm and indestructible. Ideas are the permanent, perfect

objects, with which the mind deals when it contemplates necessary and

eternal truths. They belong to a region superior to the material world,

the world of sense. They are the objects which make up the furniture of

the Intelligible World; with which the Reason deals, as the Senses deal

each with its appropriate Sensation.

But, it will naturally be asked, what is the Relation of Ideas to the

Objects of Sense? Some connexion, or relation, it is plain, there

must be. The objects of sense can suggest, and can illustrate real

truths. Though these truths of geometry cannot be proved, cannot even

be exactly exemplified, by drawing diagrams, yet diagrams are of use

in helping ordinary minds to see the proof; and to all minds, may

represent and illustrate it. And though our conclusions with regard to

objects of sense may be insecure and imperfect, they have some show of

truth, and therefore some resemblance to truth. What does this arise

from? How is it explained, if there is no truth except concerning Ideas?

To this the Platonist replied, that the phenomena which present

themselves to the senses partake, in a certain manner, of Ideas, and

thus include so much of the nature of Ideas, that they include also

an element of Truth. The geometrical diagram of Triangles and Squares

which is drawn in the sand of the floor of the Gymnasium, partakes of

the nature of the true Ideal Triangles and Squares, so that it presents

an imitation and suggestion of the truths which are true of them. The

real triangles and squares are in the mind: they are, as we have said,

objects, not in the Visible, but in the Intelligible World. But the

Visible Triangles and Squares make us call to mind the Intelligible;

and thus the objects of sense suggest, and, in a way, exemplify the

eternal truths.

This I conceive to be the simplest and directest ground of two primary

parts of the Theory of Ideas;--The Eternal Ideas constituting an

Intelligible World; and the Participation in these Ideas ascribed to

the objects of the world of sense. And it is plain that so far, the

Theory meets what, I conceive, was its primary purpose; it answers the

questions, How can we have certain knowledge, though we cannot get it

from Sense? and, How can we have knowledge, at least apparent, though

imperfect, about the world of sense?

But is this the ground on which Plato himself rests the truth of his

Theory of Ideas? As I have said, I have no doubt that these were the

questions which suggested the Theory; and it is perpetually applied

in such a manner as to show that it was held by Plato in this sense.

But his applications of the Theory refer very often to another part

of it;--to the Ideas, not of Triangles and Squares, of space and its

affections; but to the Ideas of Relations--as the Relations of Like and

Unlike, Greater and Less; or to things quite different from the things

of which geometry treats, for instance, to Tables and Chairs, and other

matters, with regard to which no demonstration is possible, and no

general truth (still less necessary an eternal truth) capable of being

asserted.

I conceive that the Theory of Ideas, thus asserted and thus supported,

stands upon very much weaker ground than it does, when it is

asserted concerning the objects of thought about which necessary and

demonstrable truths are attainable. And in order to devise arguments

against _this_ part of the Theory, and to trace the contradictions to

which it leads, we have no occasion to task our own ingenuity. We find

it done to our hands, not only in Aristotle, the open opponent of the

Theory of Ideas, but in works which stand among the Platonic Dialogues

themselves. And I wish especially to point out some of the arguments

against the Ideal Theory, which are given in one of the most noted of

the Platonic Dialogues, the _Parmenides_.

The _Parmenides_ contains a narrative of a Dialogue held between

Parmenides and Zeno, the Eleatic Philosophers, on the one side, and

Socrates, along with several other persons, on the other. It may be

regarded as divided into two main portions; the first, in which the

Theory of Ideas is attacked by Parmenides, and defended by Socrates;

the second, in which Parmenides discusses, at length, the Eleatic

doctrine that _All things are One_. It is the former part, the

discussion of the Theory of Ideas, to which I especially wish to direct

attention at present: and in the first place, to that extension of

the Theory of Ideas, to things of which no general truth is possible;

such as I have mentioned, tables and chairs. Plato often speaks of

a Table, by way of example, as a thing of which there must be an

Idea, not taken from any special Table or assemblage of Tables; but

an Ideal Table, such that all Tables are Tables by participating in

the nature of this Idea. Now the question is, whether there is any

force, or indeed any sense, in this assumption; and this question is

discussed in the _Parmenides_. Socrates is there represented as very

confident in the existence of Ideas of the highest and largest kind,

the Just, the Fair, the Good, and the like. Parmenides asks him how

far he follows his theory. Is there, he asks, an Idea of Man, which is

distinct from us men? an Idea of Fire? of Water? "In truth," replies

Socrates, "I have often hesitated, Parmenides, about these, whether

we are to allow such Ideas." When Plato had proceeded to teach that

there is an Idea of a Table, of course he could not reject such Ideas

as Man, and Fire, and Water. Parmenides, proceeding in the same line,

pushes him further still. "Do you doubt," says he, "whether there

are Ideas of things apparently worthless and vile? Is there an Idea

of a Hair? of Mud? of Filth?" Socrates has not the courage to accept

such an extension of the theory. He says, "By no means. These are not

Ideas. These are nothing more than just what we see them. I have often

been perplexed what to think on this subject. But after standing to

this a while, I have fled the thought, for fear of falling into an

unfathomable abyss of absurdities." On this, Parmenides rebukes him for

his want of consistency. "Ah Socrates," he says, "you are yet young;

and philosophy has not yet taken possession of you as I think she will

one day do--when you will have learned to find nothing despicable in

any of these things. But now your youth inclines you to regard the

opinions of men." It is indeed plain, that if we are to assume an Idea

of a Chair or a Table, we can find no boundary line which will exclude

Ideas of everything for which we have a name, however worthless or

offensive. And this is an argument against the assumption of _such_

Ideas, which will convince most persons of the groundlessness of the

assumption:--the more so, as _for_ the assumption of such Ideas, it

does not appear that Plato offers any argument whatever; nor does

this assumption solve any problem, or remove any difficulty[322].

Parmenides, then, had reason to say that consistency required Socrates,

if he assumed any such Ideas, to assume all. And I conceive his reply

to be to this effect; and to be thus a _reductio ad absurdum_ of the

Theory of Ideas in this sense. According to the opinions of those

who see in the _Parmenides_ an exposition of Platonic doctrines, I

believe that Parmenides is conceived in this passage, to suggest to

Socrates what is necessary for the completion of the Theory of Ideas.

But upon either supposition, I wish especially to draw the attention

of my readers to the position of superiority in the Dialogue in which

Parmenides is here placed with regard to Socrates.

Parmenides then proceeds to propound to Socrates difficulties with

regard to the Ideal Theory, in another of its aspects;--namely, when it

assumes Ideas of Relations of things; and here also, I wish especially

to have it considered how far the answers of Socrates to these

objections are really satisfactory and conclusive.

"Tell me," says he (§ 10, Bekker), "You conceive that there are certain

Ideas, and that things partaking of these Ideas, are called by the

corresponding names;--an Idea of _Likeness_, things partaking of

which are called _Like_;--of _Greatness_, whence they are _Great_: of

_Beauty_, whence they are _Beautiful_?" Socrates assents, naturally:

this being the simple and universal statement of the Theory, in this

case. But then comes one of the real difficulties of the Theory. Since

the special things participate of the General Idea, has each got

the whole of the Idea, which is, of course, One; or has each a part

of the Idea? "For," says Parmenides, "can there be any other way of

participation than these two?" Socrates replies by a similitude: "The

Idea, though One, may be wholly in each object, as the Day, one and the

same, is wholly in each place." The physical illustration, Parmenides

damages by making it more physical still. "You are ingenious,

Socrates," he says, (§ 11) "in making the same thing be in many places

at the same time. If you had a number of persons wrapped up in a sail

or web, would you say that each of them had the whole of it? Is not the

case similar?" Socrates cannot deny that it is. "But in this case, each

person has only a part of the whole; and thus your Ideas are partible."

To this, Socrates is represented as assenting in the briefest possible

phrase; and thus, here again, as I conceive, Parmenides retains his

superiority over Socrates in the Dialogue.

There are many other arguments urged against the Ideal Theory by

Parmenides. The next is a consequence of this partibility of Ideas,

thus supposed to be proved, and is ingenious enough. It is this:

"If the Idea of Greatness be distributed among things that are Great,

so that each has a part of it, each separate thing will be Great in

virtue of a part of Greatness which is less than Greatness itself. Is

not this absurd?" Socrates submissively allows that it is.

And the same argument is applied in the case of the Idea of Equality.

"If each of several things have a part of the Idea of Equality, it

will be Equal to something, in virtue of something which is less than

Equality."

And in the same way with regard to the Idea of Smallness.

"If each thing be small by having a part of the Idea of Smallness,

Smallness itself will be greater than the small thing, since that is a

part of itself."

These ingenious results of the partibility of Ideas remind us of the

ingenuity shown in the Greek geometry, especially the Fifth Book of

Euclid. They are represented as not resisted by Socrates (§ 12): "In

what way, Socrates, can things participate in Ideas, if they cannot

do so either integrally or partibly?" "By my troth," says Socrates,

"it does not seem easy to tell." Parmenides, who completely takes the

conduct of the Dialogue, then turns to another part of the subject and

propounds other arguments. "What do you say to this?" he asks.

"There is an Ideal Greatness, and there are many things, separate from

it, and Great by virtue of it. But now if you look at Greatness and the

Great things together, since they are all Great, they must be Great in

virtue of some higher Idea of Greatness which includes both. And thus

you have a Second Idea of Greatness; and in like manner you will have a

third, and so on indefinitely."

This also, as an argument against the separate existence of Ideas,

Socrates is represented as unable to answer. He replies interrogatively:

"Why, Parmenides, is not each of these Ideas a Thought, which, by its

nature, cannot exist in anything except in the Mind? In that case your

consequences would not follow."

This is an answer which changes the course of the reasoning: but still,

not much to the advantage of the Ideal Theory. Parmenides is still

ready with very perplexing arguments. (§ 13.)

"The Ideas, then," he says, "are Thoughts. They must be Thoughts of

something. They are Thoughts of something, then, which exists in all

the special things; some one thing which the Thought perceives in all

the special things; and this one Thought thus involved in all, is the

_Idea_. But then, if the special things, as you say, participate in the

Idea, they participate in the Thought; and thus, all objects are made

up of Thoughts, and all things think; or else, there are thoughts in

things which do not think."

This argument drives Socrates from the position that Ideas are

Thoughts, and he moves to another, that they are Paradigms, Exemplars

of the qualities of things, to which the things themselves are like,

and their being thus like, is their participating in the Idea. But here

too, he has no better success. Parmenides argues thus:

"If the Object be like the Idea, the Idea must be like the Object.

And since the Object and the Idea are like, they must, according to

your doctrine, participate in the Idea of Likeness. And thus you have

one Idea participating in another Idea, and so on in infinitum."

Socrates is obliged to allow that this demolishes the notion of objects

partaking in their Ideas by likeness: and that he must seek some other

way. "You see then, O Socrates," says Parmenides, "what difficulties

follow, if any one asserts the independent existence of Ideas!"

Socrates allows that this is true. "And yet," says Parmenides, "you

do not half perceive the difficulties which follow from this doctrine

of Ideas." Socrates expresses a wish to know to what Parmenides

refers; and the aged sage replies by explaining that if Ideas exist

independently of us, we can never know anything about them: and that

even the Gods could not know anything about man. This argument, though

somewhat obscure, is evidently stated with perfect earnestness, and

Socrates is represented as giving his assent to it. "And yet," says

Parmenides (end of § 18), "if any one gives up entirely the doctrine of

Ideas, how is any reasoning possible?"

All the way through this discussion, Parmenides appears as vastly

superior to Socrates; as seeing completely the tendency of every line

of reasoning, while Socrates is driven blindly from one position to

another; and as kindly and graciously advising a young man respecting

the proper aims of his philosophical career; as well as clearly

pointing out the consequences of his assumptions. Nothing can be

more complete than the higher position assigned to Parmenides in the

Dialogue.

This has not been overlooked by the Editors and Commentators of Plato.

To take for example one of the latest; in Steinhart's Introduction to

Hieronymus Müller's translation of _Parmenides_ (Leipzig, 1852), p.

261, he says: "It strikes us, at first, as strange, that Plato here

seems to come forward as the assailant of his own doctrine of Ideas.

For the difficulties which he makes Parmenides propound against that

doctrine are by no means sophistical or superficial, but substantial

and to the point. Moreover there is among all these objections, which

are partly derived from the Megarics, scarce one which does not appear

again in the penetrating and comprehensive argumentations of Aristotle

against the Platonic Doctrine of Ideas."

Of course, both this writer and other commentators on Plato offer

something as a solution of this difficulty. But though these

explanations are subtle and ingenious, they appear to leave no

satisfactory or permanent impression on the mind. I must avow that, to

me, they appear insufficient and empty; and I cannot help believing

that the solution is of a more simple and direct kind. It may seem bold

to maintain an opinion different from that of so many eminent scholars;

but I think that the solution which I offer, will derive confirmation

from a consideration of the whole Dialogue; and therefore I shall

venture to propound it in a distinct and positive form. It is this:

I conceive that the _Parmenides_ is not a Platonic Dialogue at all;

but Antiplatonic, or more properly, _Eleatic_: written, not by Plato,

in order to explain and prove his Theory of Ideas, but by some one,

probably an admirer of Parmenides and Zeno, in order to show how strong

were his master's arguments against the Platonists and how weak their

objections to the Eleatic doctrine.

I conceive that this view throws an especial light on every part of the

Dialogue, as a brief survey of it will show. Parmenides and Zeno come

to Athens to the Panathenaic festival: Parmenides already an old man,

with a silver head, dignified and benevolent in his appearance, looking

five and sixty years old: Zeno about forty, tall and handsome. They are

the guests of Pythodorus, outside the Wall, in the Ceramicus; and there

they are visited by Socrates then young, and others who wish to hear

the written discourses of Zeno. These discourses are explanations of

the philosophy of Parmenides, which he had delivered in verse.

Socrates is represented as showing, from the first, a disposition to

criticize Zeno's dissertation very closely; and without any prelude or

preparation, he applies the Doctrine of Ideas to refute the Eleatic

Doctrine that All Things are One. (§ 3.) When he had heard to the

end, he begged to have the first Proposition of the First Book read

again. And then, "How is it, O Zeno, that you say, That if the Things

which exist are Many, and not One, they must be at the same time like

and unlike? Is this your argument? Or do I misunderstand you?" "No,"

says Zeno, "you understand quite rightly." Socrates then turns to

Parmenides, and says, somewhat rudely, as it seems, "Zeno is a great

friend of yours, Parmenides: he shows his friendship not only in

other ways, but also in what he writes. For he says the same things

which you say, though he pretends that he does not. You say, in your

poems, that All Things are One, and give striking proofs: he says that

existences are not many, and he gives many and good proofs. You seem

to soar above us, but you do not really differ." Zeno takes this sally

good-humouredly, and tells him that he pursues the scent with the

keenness of a Laconian hound. "But," says he (§ 6), "there really is

less of ostentation in my writing than you think. My Essay was merely

written as a defence of Parmenides long ago, when I was young; and is

not a piece of display composed now that I am older. And it was stolen

from me by some one; so that I had no choice about publishing it."

Here we have, as I conceive, Socrates already represented as placed

in a disadvantageous position, by his abruptness, rude allusions, and

readiness to put bad interpretations on what is done. For this, Zeno's

gentle pleasantry is a rebuke. Socrates, however, forthwith rushes into

the argument; arguing, as I have said, for his own Theory.

"Tell me," he says, "do you not think there is an Idea of Likeness, and

an Idea of Unlikeness? And that everything partakes of these Ideas? The

things which partake of Unlikeness are unlike. If all things partake of

both Ideas, they are both like and unlike; and where is the wonder? (§

7.) If you could show that Likeness itself was Unlikeness, it would be

a prodigy; but if things which partake of these opposites, have both

the opposite qualities, it appears to me, Zeno, to involve no absurdity.

"So if Oneness itself were to be shown to be Maniness" (I hope I may

use this word, rather than _multiplicity_) "I should be surprised; but

if any one say that _I_ am at the same time one and many, where is the

wonder? For I partake of maniness: my right side is different from my

left side, my upper from my under parts. But I also partake of Oneness,

for I am here One of us seven. So that both are true. And so if any one

say that stocks and stones, and the like, are both one and many,--not

saying that Oneness is Maniness, nor Maniness Oneness, he says nothing

wonderful: he says what all will allow. (§ 8.) If then, as I said

before, any one should take separately the Ideas or Essence of Things,

as Likeness and Unlikeness, Maniness and Oneness, Rest and Motion, and

the like, and then should show that these can mix and separate again,

I should be wonderfully surprised, O Zeno: for I reckon that I have

tolerably well made myself master of these subjects[323]. I should

be much more surprised if any one could show me this contradiction

involved in the Ideas themselves; in the object of the Reason, as well

as in Visible objects."

It may be remarked that Socrates delivers all this argumentation with

the repetitions which it involves, and the vehemence of its manner,

without waiting for a reply to any of his interrogations; instead

of making every step the result of a concession of his opponent, as

is the case in the Dialogues where he is represented as triumphant.

Every reader of Plato will recollect also that in those Dialogues,

the triumph of temper on the part of Socrates is represented as

still more remarkable than the triumph of argument. No vehemence or

rudeness on the part of his adversaries prevents his calmly following

his reasoning; and he parries coarseness by compliment. Now in this

Dialogue, it is remarkable that this kind of triumph is given to the

adversaries of Socrates. "When Socrates had thus delivered himself,"

says Pythodorus, the narrator of the conversation, "we thought that

Parmenides and Zeno would both be angry. But it was not so. They

bestowed entire attention upon him, and often looked at each other,

and smiled, as in admiration of Socrates. And when he had ended,

Parmenides said: 'O Socrates, what an admirable person you are, for the

earnestness with which you reason! Tell me then, Do you then believe

the doctrine to which you have been referring;--that there are certain

Ideas, existing independent of Things; and that there are, separate

from the Ideas, Things which partake of them? And do you think that

there is an Idea of Likeness besides the likeness which we have; and a

Oneness and a Maniness, and the like? And an Idea of the Right, and the

Good, and the Fair, and of other such qualities?'" Socrates says that

he does hold this; Parmenides then asks him, how far he carries this

doctrine of Ideas, and propounds to him the difficulties which I have

already stated; and when Socrates is unable to answer him, lets him off

in the kind but patronizing way which I have already described.

To me, comparing this with the intellectual and moral attitude of

Socrates in the most dramatic of the other Platonic Dialogues, it is

inconceivable, that this representation of Socrates should be Plato's.

It is just what Zeno would have written, if he had wished to bestow

upon his master Parmenides the calm dignity and irresistible argument

which Plato assigns to Socrates. And this character is kept up to the

end of the Dialogue. When Socrates (§ 19) has acknowledged that he is

at loss which way to turn for his philosophy, Parmenides undertakes,

though with kind words, to explain to him by what fundamental error in

the course of his speculative habits he has been misled. He says; "You

try to make a complete Theory of Ideas, before you have gone through

a proper intellectual discipline. The impulse which urges you to such

speculations is admirable--is divine. But you must exercise yourself in

reasoning which many think trifling, while you are yet young; if you

do not, the truth will elude your grasp." Socrates asks submissively

what is the course of such discipline: Parmenides replies, "The course

pointed out by Zeno, as you have heard." And then, gives him some

instructions in what manner he is to test any proposed Theory. Socrates

is frightened at the laboriousness and obscurity of the process. He

says, "You tell me, Parmenides, of an overwhelming course of study; and

I do not well comprehend it. Give me an example of such an examination

of a Theory." "It is too great a labour," says he, "for one so old

as I am." "Well then, you, Zeno," says Socrates, "will you not give

us such an example?" Zeno answers, smiling, that they had better get

it from Parmenides himself; and joins in the petition of Socrates to

him, that he will instruct them. All the company unite in the request.

Parmenides compares himself to an aged racehorse, brought to the course

after long disuse, and trembling at the risk; but finally consents.

And as an example of a Theory to be examined, takes his own Doctrine,

that All Things are One, carrying on the Dialogue thenceforth, not

with Socrates, but with Aristoteles (not the Stagirite, but afterwards

one of the Thirty), whom he chooses as a younger and more manageable

respondent.

The discussion of this Doctrine is of a very subtle kind, and it would

be difficult to make it intelligible to a modern reader. Nor is it

necessary for my purpose to attempt to do so. It is plain that the

discussion is intended seriously, as an example of true philosophy; and

each step of the process is represented as irresistible. The Respondent

has nothing to say but _Yes_; or _No_; _How so_? _Certainly_; _It does

appear_; _It does not appear_. The discussion is carried to a much

greater length than all the rest of the Dialogue; and the result of

the reasoning is summed up by Parmenides thus: "If One exist, it is

Nothing. Whether One exist or do not exist, both It and Other Things

both with regard to Themselves and to Each other, All and Everyway are

and are not, appear and appear not." And this also is fully assented

to; and so the Dialogue ends.

I shall not pretend to explain the Doctrines there examined that One

exists, or One does not exist, nor to trace their consequences. But

these were Formulæ, as familiar in the Eleatic school, as Ideas in the

Platonic; and were undoubtedly regarded by the Megaric contemporaries

of Plato as quite worthy of being discussed, after the Theory of Ideas

had been overthrown. This, accordingly, appears to be the purport of

the Dialogue; and it is pursued, as we see, without any bitterness

toward Socrates or his disciples; but with a persuasion that they were

poor philosophers, conceited talkers, and weak disputants.

The external circumstances of the Dialogue tend, I conceive, to confirm

this opinion, that it is not Plato's. The Dialogue begins, as the

_Republic_ begins, with the mention of a Cephalus, and two brothers,

Glaucon and Adimantus. But this Cephalus is not the old man of the

Piræus, of whom we have so charming a picture in the opening of the

_Republic_. He is from Clazomenæ, and tells us that his fellow-citizens

are great lovers of philosophy; a trait of their character which does

not appear elsewhere. Even the brothers Glaucon and Adimantus are not

the two brothers of Plato who conduct the Dialogue in the later books

of the _Republic_: so at least Ast argues, who holds the genuineness of

the Dialogue. This Glaucon and Adimantus are most wantonly introduced;

for the sole office they have, is to say that they have a half-brother

Antiphon, by a second marriage of their mother. No such half-brother of

Plato, and no such marriage of his mother, are noticed in other remains

of antiquity. Antiphon is represented as having been the friend of

Pythodorus, who was the host of Parmenides and Zeno, as we have seen.

And Antiphon, having often heard from Pythodorus the account of the

conversation of his guests with Socrates, retained it in his memory, or

in his tablets, so as to be able to give the full report of it which we

have in the Dialogue _Parmenides_[324]. To me, all this looks like a

clumsy imitation of the Introductions to the Platonic Dialogues.

I say nothing of the chronological difficulties which arise

from bringing Parmenides and Socrates together, though they are

considerable; for they have been explained more or less satisfactorily;

and certainly in the _Theætetus_, Socrates is represented as saying

that he when very young had seen Parmenides who was very old[325].

Athenæus, however[326], reckons this among Plato's fictions.

Schleiermacher gives up the identification and relation of the persons

mentioned in the Introduction as an unmanageable story.

I may add that I believe Cicero, who refers to so many of Plato's

Dialogues, nowhere refers to the _Parmenides_. Athenæus does refer to

it; and in doing so blames Plato for his coarse imputations on Zeno

and Parmenides. According to our view, these are hostile attempts to

ascribe rudeness to Socrates or to Plato. Stallbaum acknowledges that

Aristotle nowhere refers to this Dialogue.

FOOTNOTES:

[Footnote 321: P. 116. "No amount of human knowledge can be adequate

which does not solve the phenomena of these absolute certainties."]

[Footnote 322: Prof. Butler, Lect. ix. Second Series, p. 136, appears

to think that Plato had sufficient grounds (of a theological kind) for

the assumption of such Ideas; but I see no trace of them.]

[Footnote 323: I am aware that this translation is different from the

common translation. It appears to me to be consistent with the habit

of the Greek language. It slightly leans in favour of my view; but I

do not conceive that the argument would be perceptibly weaker, if the

common interpretation were adopted.]

[Footnote 324: In the _First Alcibiades_, Pythodorus is mentioned as

having paid 100 minæ to Zeno for his instructions (119 A).]

[Footnote 325: P. 183 e.]

[Footnote 326: _Deip._ xi. c. 15, p. 105.]

APPENDIX B.

ON PLATO'S SURVEY OF THE SCIENCES.

(_Cam. Phil. Soc._ APRIL 23, 1855.)

A survey by Plato of the state of the Sciences, as existing in his

time, may be regarded as hardly less interesting than Francis Bacon's

Review of the condition of the Sciences of _his_ time, contained in the

_Advancement of Learning_. Such a survey we have, in the seventh book

of Plato's _Republic_; and it will be instructive to examine what the

Sciences then were, and what Plato aspired to have them become; aiding

ourselves by the light afforded by the subsequent history of Science.

In the first place, it is interesting to note, in the two writers,

Plato and Bacon, the same deep conviction that the large and profound

philosophy which they recommended, had not, in their judgment, been

pursued in an adequate and worthy manner, by those who had pursued it

at all. The reader of Bacon will recollect the passage in the _Novum

Organon_ (Lib. I. Aphorism 80) where he speaks with indignation of

the way in which philosophy had been degraded and perverted, by being

applied as a mere instrument of utility or of early education: "So that

the great mother of the Sciences is thrust down with indignity to the

offices of a handmaid;--is made to minister to the labours of medicine

or mathematics; or again, to give the first preparatory tinge to the

immature minds of youth[327]."

In the like spirit, Plato says (_Rep._ VI. § 11, Bekker's ed.):

"Observe how boldly and fearlessly I set about my explanation of my

assertion that philosophers ought to rule the world. For I begin by

saying, that the State must begin to treat the study of philosophy in a

way opposite to that now practised. Now, those who meddle at all with

this study are put upon it when they are children, between the lessons

which they receive in the farm-yard and in the shop[328]; and as soon

as they have been introduced to the hardest part of the subject, are

taken off from it, even those who get the most of philosophy. By the

hardest part, I mean, the discussion of principles--Dialectic[329].

And in their succeeding years, if they are willing to listen to a

few lectures of those who make philosophy their business, they think

they have done great things, as if it were something foreign to the

business of life. And as they advance towards old age, with a very

few exceptions, philosophy in them is extinguished: extinguished far

more completely than the Heraclitean sun, for theirs is not lighted

up again, as that is every morning:" alluding to the opinion which

was propounded, by way of carrying the doctrine of the _unfixity_ of

sensible objects to an extreme; that the Sun is extinguished every

night and lighted again in the morning. In opposition to this practice,

Plato holds that philosophy should be the especial employment of men's

minds when their bodily strength fails.

What Plato means by _Dialectic_, which he, in the next Book, calls the

highest part of philosophy, and which is, I think, what he here means

by the hardest part of philosophy, I may hereafter consider: but at

present I wish to pass in review the Sciences which he speaks of, as

leading the way to that highest study. These Sciences are Arithmetic,

Plane Geometry, Solid Geometry, Astronomy and Harmonics.

The view in which Plato here regards the Sciences is, as the

instruments of that culture of the philosophical spirit which is

to make the philosopher the fit and natural ruler of the perfect

State--the Platonic Polity. It is held that to answer this purpose, the

mind must be instructed in something more stable than the knowledge

supplied by the senses;--a knowledge of objects which are constantly

changing, and which therefore can be no real permanent Knowledge, but

only Opinion. The real and permanent Knowledge which we thus require is

to be found in certain sciences, which deal with _truths necessary and

universal_, as we should now describe them: and which therefore are,

in Plato's language, a knowledge of that which really _is_[330].

This is the object of the Sciences of which Plato speaks. And hence,

when he introduces Arithmetic, as the first of the Sciences which are

to be employed in this mental discipline, he adds (VII. § 8) that

it must be not mere common Arithmetic, but a science which leads to

speculative truths[331], seen by Intuition[332]; not an Arithmetic

which is studied for the sake of buying and selling, as among tradesmen

and shopkeepers, but for the sake of pure and real Science[333].

I shall not dwell upon the details with which he illustrates this view,

but proceed to the other Sciences which he mentions.

Geometry is then spoken of, as obviously the next Science in order;

and it is asserted that it really does answer the required condition

of drawing the mind from visible, mutable phenomena to a permanent

reality. Geometers indeed speak of their visible diagrams, as if their

problems were certain practical processes; to erect a perpendicular; to

construct a square: and the like. But this language, though necessary,

is really absurd. The figures are mere aids to their reasonings.

Their knowledge is really a knowledge not of visible objects, but of

permanent realities: and thus, Geometry is one of the helps by which

the mind may be drawn to Truth; by which the philosophical spirit may

be formed, which looks upwards instead of downwards.

Astronomy is suggested as the Science next in order, but Socrates, the

leader of the dialogue, remarks that there is an intermediate Science

first to be considered. Geometry treats of plane figures; Astronomy

treats of solids in motion, that is, of spheres in motion; for the

astronomy of Plato's time was mainly the doctrine of the sphere. But

before treating of solids in motion, we must have a science which

treats of solids simply. After taking space of two dimensions, we must

take space of three dimensions, length, breadth and depth, as in cubes

and the like[334]. But such a Science, it is remarked, has not yet

been discovered. Plato "notes as deficient" this branch of knowledge;

to use the expression employed by Bacon on the like occasions in his

Review. Plato goes on to say, that the cultivators of such a science

have not received due encouragement; and that though scorned and

starved by the public, and not recommended by any obvious utility, it

has still made great progress, in virtue of its own attractiveness.

In fact, researches in Solid Geometry had been pursued with great zeal

by Plato and his friends, and with remarkable success. The five Regular

Solids, the Tetrahedron or Pyramid, Cube, Octahedron, Dodecahedron

and Icosahedron, had been discovered; and the curious theorem, that

of Regular Solids there can be just so many, these and no others,

was known. The doctrine of these Solids was already applied in a

way, fanciful and arbitrary, no doubt, but ingenious and lively, to

the theory of the Universe. In the _Timæus_, the elements have these

forms assigned to them respectively. Earth has the Cube: Fire has the

Pyramid: Water has the Octahedron: Air has the Icosahedron: and the

Dodecahedron is the plan of the Universe itself. This application of

the doctrine of the Regular Solids shows that the knowledge of those

figures was already established; and that Plato had a right to speak

of Solid Geometry as a real and interesting Science. And that this

subject was so recondite and profound,--that these five Regular Solids

had so little application in the geometry which has a bearing on man's

ordinary thoughts and actions,--made it all the more natural for Plato

to suppose that these solids had a bearing on the constitution of the

Universe; and we shall find that such a belief in later times found a

ready acceptance in the minds of mathematicians who followed in the

Platonic line of speculation.

Plato next proceeds to consider Astronomy; and here we have an amusing

touch of philosophical drama. Glaucon, the hearer and pupil in the

Dialogue, is desirous of showing that he has profited by what his

instructor had said about the real uses of Science. He says Astronomy

is a very good branch of education. It is such a very useful science

for seamen and husbandmen and the like. Socrates says, with a smile,

as we may suppose: "You are very amusing with your zeal for utility.

I suppose you are afraid of being condemned by the good people of

Athens for diffusing Useless Knowledge." A little afterwards Glaucon

tries to do better, but still with no great success. He says, "You

blamed me for praising Astronomy awkwardly: but now I will follow your

lead. Astronomy is one of the sciences which you require, because it

makes men's minds look upwards, and study things above. Any one can

see that." "Well," says Socrates, "perhaps any one can see it except

me--I cannot see it." Glaucon is surprised, but Socrates goes on: "Your

notice of 'the study of things above' is certainly a very magnificent

one. You seem to think that if a man bends his head back and looks at

the ceiling he 'looks upwards' with his mind as well as his eyes. You

may be right and I may be wrong: but I have no notion of any science

which makes the _mind_ look upwards, except a science which is about

the permanent and the invisible. It makes no difference, as to that

matter, whether a man gapes and looks up or shuts his mouth and looks

down. If a man merely look up and stare at sensible objects, his mind

does not look upwards, even if he were to pursue his studies swimming

on his back in the sea."

The Astronomy, then, which merely looks at phenomena does not satisfy

Plato. He wants something more. What is it? as Glaucon very naturally

asks.

Plato then describes Astronomy as a real science (§ 11). "The

variegated adornments which appear in the sky, the visible luminaries,

we must judge to be the most beautiful and the most perfect things of

their kind: but since they are mere visible figures, we must suppose

them to be far inferior to the true objects; namely, those spheres

which, with their real proportions of quickness and slowness, their

real number, their real figures, revolve and carry luminaries in their

revolutions. These objects are to be apprehended by reason and mental

conception, not by vision." And he then goes on to say that the varied

figures which the skies present to the eye are to be used as _diagrams_

to assist the study of that higher truth; just as if any one were to

study geometry by means of beautiful diagrams constructed by Dædalus or

any other consummate artist.

Here then, Plato points to a kind of astronomical science which goes

beyond the mere arrangement of phenomena: an astronomy which, it

would seem, did not exist at the time when he wrote. It is natural

to inquire, whether we can determine more precisely what kind of

astronomical science he meant, and whether such science has been

brought into existence since his time.

He gives us some further features of the philosophical astronomy which

he requires. "As you do not expect to find in the most exquisite

geometrical diagrams the true evidence of quantities being equal, or

double, or in any other relation: so the true astronomer will not think

that the proportion of the day to the month, or the month to the year,

and the like, are real and immutable things. He will seek a deeper

truth than these. We must treat Astronomy, like Geometry, as a series

of problems suggested by visible things. We must apply the intelligent

portion of our mind to the subject."

Here we really come in view of a class of problems which astronomical

speculators at certain periods have proposed to themselves. What is the

real ground of the proportion of the day to the month, and of the month

to the year, I do not know that any writer of great name has tried to

determine: but to ask the reason of these proportions, namely, that of

the revolution of the earth on its axis, of the moon in its orbit, and

of the earth in its orbit, are questions just of the same kind as to

ask the reason of the proportion of the revolutions of the planets in

their orbits, and of the proportion of the orbits themselves. Now who

has attempted to assign such reasons?

Of course we shall answer, Kepler: not so much in the Laws of the

Planetary motions which bear his name, as in the Law which at an

earlier period he thought he had discovered, determining the proportion

of the distances of the several Planets from the Sun. And, curiously

enough, this solution of a problem which we may conceive Plato to have

had in his mind, Kepler gave by means of the Five Regular Solids which

Plato had brought into notice, and had employed in his theory of the

Universe given in the _Timæus_.

Kepler's speculations on the subject just mentioned were given to the

world in the _Mysterium Cosmographicum_ published in 1596. In his

Preface, he says "In the beginning of the year 1595 I brooded with

the whole energy of my mind on the subject of the Copernican system.

There were three things in particular of which I pertinaciously sought

the causes; why they are not other than they are: the number, the

size, and the motion of the orbits." We see how strongly he had his

mind impressed with the same thought which Plato had so confidently

uttered: that there must be some reason for those proportions in the

scheme of the Universe which appear casual and vague. He was confident

at this period that he had solved two of the three questions which

haunted him;--that he could account for the number and the size of the

planetary orbits. His account was given in this way.--"The orbit of

the Earth is a circle; round the sphere to which this circle belongs

describe a dodecahedron; the sphere including this will give the orbit

of Mars. Round Mars inscribe a tetrahedron; the circle including this

will be the orbit of Jupiter. Describe a cube round Jupiter's orbit;

the circle including this will be the orbit of Saturn. Now inscribe in

the Earth's orbit an icosahedron: the circle inscribed in it will be

the orbit of Venus. Inscribe an octahedron in the orbit of Venus; the

circle inscribed in it will be Mercury's orbit. This is the reason of

the number of the planets;" and also of the magnitudes of their orbits.

These proportions were only approximations; and the Rule thus asserted

has been shown to be unfounded, by the discovery of new Planets. This

Law of Kepler has been repudiated by succeeding Astronomers. So far,

then, the Astronomy which Plato requires as a part of true philosophy

has not been brought into being. But are we thence to conclude

that the demand for such a kind of Astronomy was a mere Platonic

imagination?--was a mistake which more recent and sounder views have

corrected? We can hardly venture to say that. For the questions which

Kepler thus asked, and which he answered by the assertion of this

erroneous Law, are questions of exactly the same kind as those which

he asked and answered by means of the true Laws which still fasten his

name upon one of the epochs of astronomical history. If he was wrong

in assigning reasons for the number and size of the planetary orbits,

he was right in assigning a reason for the proportion of the motions.

This he did in the _Harmonice Mundi_, published in 1619: where he

established that the squares of the periodic times of the different

Planets are as the cubes of their mean distances from the central Sun.

Of this discovery he speaks with a natural exultation, which succeeding

astronomers have thought well founded. He says: "What I prophesied

two and twenty years ago as soon as I had discovered the five solids

among the heavenly bodies; what I firmly believed before I had seen

the _Harmonics_ of Ptolemy; what I promised my friends in the title of

this book (_On the perfect Harmony of the celestial motions_), which

I named before I was sure of my discovery; what sixteen years ago I

regarded as a thing to be sought; that for which I joined Tycho Brahe,

for which I settled in Prague, for which I devoted the best part of my

life to astronomical contemplations; at length I have brought to light,

and have recognized its truth beyond my most sanguine expectations."

(_Harm. Mundi_, Lib. V.)

Thus the Platonic notion, of an Astronomy which deals with doctrines

of a more exact and determinate kind than the obvious relations of

phænomena, may be found to tend either to error or to truth. Such

aspirations point equally to the five regular solids which Kepler

imagined as determining the planetary orbits, and to the Laws of

Kepler in which Newton detected the effect of universal gravitation.

The realities which Plato looked for, as something incomparably more

real than the visible luminaries, are found, when we find geometrical

figures, epicycles and eccentrics, laws of motion and laws of force,

which explain the appearances. His Realities are Theories which account

for the Phenomena, Ideas which connect the Facts.

But, is Plato right in holding that such Realities as these are _more

real_ than the Phenomena, and constitute an Astronomy of a higher kind

than that of mere Appearances? To this we shall, of course, reply

that Theories and Facts have each their reality, but that these are

realities of different kinds. Kepler's Laws are as real as day and

night; the force of gravity tending to the Sun is as real as the Sun;

but not more so. True Theories and Facts are equally real, for true

Theories _are_ Facts, and Facts are familiar Theories. Astronomy is, as

Plato says, a series of Problems suggested by visible Things; and the

Thoughts in our own minds which bring the solutions of these Problems,

have a reality in the Things which suggest them.

But if we try, as Plato does, to separate and oppose to each other the

Astronomy of Appearances and the Astronomy of Theories, we attempt that

which is impossible. There are no Phenomena which do not exhibit some

Law; no Law can be conceived without Phenomena. The heavens offer a

series of Problems; but however many of these Problems we solve, there

remain still innumerable of them unsolved; and these unsolved Problems

have solutions, and are not different in kind from those of which the

extant solution is most complete.

Nor can we justly distinguish, with Plato, Astronomy into transient

appearances and permanent truths. The theories of Astronomy are

permanent, and are manifested in a series of changes: but the change is

perpetual just _because_ the theory is permanent. The perpetual change

_is_ the permanent theory. The perpetual changes in the positions

and movements of the planets, for instance, manifest the permanent

machinery: the machinery of cycles and epicycles, as Plato would

have said, and as Copernicus would have agreed; while Kepler, with a

profound admiration for both, would have asserted that the motions

might be represented by ellipses, more exactly, if not more truly. The

cycles and epicycles, or the ellipses, are as real as space and time,

_in_ which the motions take place. But we cannot justly say that space

and time and motion are more real than the bodies which move in space

and time, or than the appearances which these bodies present.

Thus Plato, with his tendency to exalt Ideas above Facts,--to find a

Reality which is more real than Phenomena,--to take hold of a permanent

Truth which is more true than truths of observation,--attempts what

is impossible. He tries to separate the poles of the Fundamental

Antithesis, which, however antithetical, are inseparable.

At the same time, we must recollect that this tendency to find a

Reality which is something beyond appearance, a permanence which is

involved in the changes, is the genuine spring of scientific discovery.

Such a tendency has been the cause of all the astronomical science

which we possess. It appeared in Plato himself, in Hipparchus, in

Ptolemy, in Copernicus, and most eminently in Kepler; and in him

perhaps in a manner more accordant with Plato's aspirations when he

found the five Regular Solids in the Universe, than when he found there

the Conic Sections which determine the form of the planetary orbits.

The pursuit of this tendency has been the source of the mighty and

successful labours of succeeding astronomers: and the anticipations of

Plato on this head were more true than he himself could have conceived.

When the above view of the nature of true astronomy has been proposed,

Glaucon says:

"That would be a task much more laborious than the astronomy now

cultivated." Socrates replies: "I believe so: and such tasks must be

undertaken, if our researches are to be good for anything."

After Astronomy, there comes under review another Science, which is

treated in the same manner. It is presented as one of the Sciences

which deal with real abstract truth; and which are therefore suited to

that development of the philosophic insight into the highest truth,

which is here Plato's main object. This Science is _Harmonics_, the

doctrine of the mathematical relations of musical sounds. Perhaps

it may be more difficult to explain to a general audience, Plato's

views on this than on the previous subjects: for though Harmonics is

still acknowledged as a Science including the mathematical truths to

which Plato here refers, these truths are less generally known than

those of geometry or astronomy. Pythagoras is reported to have been

the discoverer of the cardinal proposition in this Mathematics of

Music:--namely, that the musical notes which the ear recognizes as

having that definite and harmonious relation which we call an _octave_,

a _fifth_, a _fourth_, a _third_, have also, in some way or other, the

numerical relation of 2 to 1, 3 to 2, 4 to 3, 5 to 4. I say "some way

or other," because the statements of ancient writers on this subject

are physically inexact, but are right in the essential point, that

those simple numerical ratios are characteristic of the most marked

harmonic relations. The numerical ratios really represent the rate of

vibration of the air when those harmonics are produced. This perhaps

Plato did not know: but he knew or assumed that those numerical ratios

were cardinal truths in harmony: and he conceived that the exactness

of the ratios rested on grounds deeper and more intellectual than any

testimony which the ear could give. This is the main point in his mode

of applying the subject, which will be best understood by translating

(with some abridgement) what he says. Socrates proceeds:

(§ 11 near the end.) "Motion appears in many aspects. It would take a

very wise man to enumerate them all: but there are two obvious kinds.

One which appears in astronomy, (the revolutions of the heavenly

bodies,) and another which is the echo of that[335]. As the eyes are

made for Astronomy, so are the ears made for the motion which produces

Harmony[336]: and thus we have two sister sciences, as the Pythagoreans

teach, and we assent.

(§ 12.) "To avoid unnecessary labour, let us first learn what _they_

can tell us, and see whether anything is to be added to it; retaining

our own view on such subjects: namely this:--that those whose education

we are to superintend--real philosophers--are never to learn any

imperfect truths:--anything which does not tend to that point (exact

and permanent truth) to which all our knowledge ought to tend, as we

said concerning astronomy. Now those who cultivate music take a very

different course from this. You may see them taking immense pains in

measuring musical notes and intervals by the ear, as the astronomers

measure the heavenly motions by the eye.

"Yes, says Glaucon, they apply their ears close to the instrument, as

if they could catch the note by getting near to it, and talk of some

kind of recurrences[337]. Some say they can distinguish an interval,

and that this is the smallest possible interval, by which others are to

be measured; while others say that the two notes are identical: both

parties alike judging by the ear, not by the intellect.

"You mean, says Socrates, those fine musicians who torture their

notes, and screw their pegs, and pinch their strings, and speak of the

resulting sounds in grand terms of art. We will leave them, and address

our inquiries to our other teachers, the Pythagoreans."

The expressions about the small interval in Glaucon's speech appear to

me to refer to a curious question, which we know was discussed among

the Greek mathematicians. If we take a keyed instrument, and ascend

from a key note by two _octaves_ and a _third_, (say from _A__{1} to

_C__{3}) we arrive at the _same nominal note_, as if we ascend four

times by a _fifth_ (_A__{1} to _E__{1}, _E__{1} to _B__{2}, _B__{2}

to _F__{2}, _F__{2} to _C__{3}). Hence one party might call this the

_same_ note. But if the Octaves, Fifths, and Third be perfectly true

intervals, the notes arrived at in the two ways will not be really

the same. (In the one case, the note is ½ × ½ × ⅘; in the other

⅔ × ⅔ × ⅔ × ⅔; which are ⅕ and 16/81, or in the ratio of

81 to 80). This small interval by which the two notes really differ,

the Greeks called a _Comma_, and it was the smallest musical interval

which they recognized. Plato disdains to see anything important in this

controversy; though the controversy itself is really a curious proof

of his doctrine, that there is a mathematical truth in Harmony, higher

than instrumental exactness can reach. He goes on to say:

"The musical teachers are defective in the same way as the

astronomical. They do indeed seek numbers in the harmonic notes, which

the ear perceives: but they do not ascend from them to the Problem,

What are harmonic numbers and what are not, and what is the reason of

each[338]?" "That", says Glaucon, "would be a sublime inquiry."

Have we in Harmonics, as in Astronomy, anything in the succeeding

History of the Science which illustrates the tendency of Plato's

thoughts, and the value of such a tendency?

It is plain that the tendency was of the same nature as that which

induced Kepler to call his work on Astronomy _Harmonice Mundi_; and

which led to many of the speculations of that work, in which harmonical

are mixed with geometrical doctrines. And if we are disposed to judge

severely of such speculations, as too fanciful for sound philosophy, we

may recollect that Newton himself seems to have been willing to find an

analogy between harmonic numbers and the different coloured spaces in

the spectrum.

But I will say frankly, that I do not believe there really exists any

harmonical relation in either of these cases. Nor can the problem

proposed by Plato be considered as having been solved since his

time, any further than the recurrence of vibrations, when their

ratios are so simple, may be easily conceived as affecting the ear

in a peculiar manner. The imperfection of musical scales, which the

_comma_ indicates, has not been removed; but we may say that, in the

case of this problem, as in the other ultimate Platonic problems,

the duplication of the cube and the quadrature of the circle, the

impossibility of a solution has been already established. The problem

of a perfect musical scale is impossible, because no power of 2 can

be equal to a power of 3; and if we further take the multiplier 5, of

course it also cannot bring about an exact equality. This impossibility

of a perfect scale being recognized, the practical problem is what is

the system of _temperament_ which will make the scale best suited for

musical purposes; and this problem has been very fully discussed by

modern writers.

FOOTNOTES:

[Footnote 327: Accedit et illud quod naturalis philosophia in iis ipsis

viris, qui ei incubuerunt, vacantem et integrum hominem, præsertim

his recentioribus temporibus, vix nacta sit; nisi forte quis monachi

alicujus in cellula, aut nobilis in villula lucubrantis, exemplum

adduxerit; sed facta est demum naturalis philosophia instar transitus

cujusdam et pontisternii ad alia. Atque magna ista scientiarum mater

ad officia ancillæ detrusa est; quæ medicinæ aut mathematicis operibus

ministrat, et rursus quæ adolescentium immatura ingenia lavat et imbuat

velut tinctura quadam prima, ut aliam postea felicius et commodius

excipiant.]

[Footnote 328: μεταξὺ οἰκονομίας καὶ χρεματισμοῦ, between house-keeping

and money-getting.]

[Footnote 329: τὸ περὶ τοὺς λόγους.]

[Footnote 330: The Sciences are to draw the mind from that which grows

and perishes to that which really is: μάθημα ψυχῆς ὁλκὸν ἀπὸ τοῦ

γιγνομένου ἐπι τὸ ὅν.]

[Footnote 331: ἐπὶ θέαν τῆς τῶν ἀριθμῶν φύσεως.]

[Footnote 332: τῇ νοηήσει αὐτῇ.]

[Footnote 333: He adds "and for the sake of war;" this point I have

passed by. Plato does not really ascribe much weight to this use of

Science, as we see in what he says of Geometry and Astronomy.]

[Footnote 334: ἀρθῶς ἕχει ἑξῆς μετὰ δευτέραν αὕξην τρίτην λαμβάνειν,

ἕστι δέ που τοῦτο περὶ τὴν τῶν κύβων αύξην καὶ τὸ βάθους μέτεχον.]

[Footnote 335: ἀντίστροφον αὐτοῦ.]

[Footnote 336: πρὸς ἐναρμόνιον φορὰν ὦτα παγῆναι.]

[Footnote 337: πυκνώματα ἄ ττα.]

[Footnote 338: τίνες ξύμφωνοι ἀριθμοὶ, &c.]