APPENDIX BB.

ON PLATO'S NOTION OF DIALECTIC.

(_Cam. Phil. Soc._ MAY 7, 1855.)

The survey of the sciences, arithmetic, plane geometry, solid geometry,

astronomy and harmonics--which is contained in the seventh Book of

the Republic (§ 6-12), and which has been discussed in the preceding

paper, represents them as instruments in an education, of which the

end is something much higher--as steps in a progression which is to go

further. "Do you not know," says Socrates (§ 12), "that all this is

merely a prelude to the strain which we have to learn?" And what that

strain is, he forthwith proceeds to indicate. "That these sciences

do not suffice, you must be aware: for--those who are masters of

such sciences--do they seem to you to be good in dialectic? δεινοὶ

διαλεκτικοὶ εἷναι;"

"In truth, says Glaucon, they are not, with very few exceptions, so far

as I have fallen in with them."

"And yet, said I, if persons cannot give and receive a reason, they

cannot attain that knowledge which, as we have said, men ought to have."

Here it is evident that "to give and to receive a reason," is a

phrase employed as coinciding, in a general way at least, with being

"good in dialectic;" and accordingly, this is soon after asserted in

another form, the verb being now used instead of the adjective. "It is

dialectic discussion τὸ διαλέγεσθαι, which executes the strain which we

have been preparing." It is further said that it is a progress to clear

intellectual light, which corresponds to the progress of bodily vision

in proceeding from the darkened cave described in the beginning of the

Book to the light of day. This progress, it is added, of course you

call _Dialectic_ διαλεκτικήν.

Plato further says, that other sciences cannot properly be called

sciences. They begin from certain assumptions, and give us only the

consequences which follow from reasoning on such assumptions. But these

assumptions they cannot prove. To do so is not in the province of

each science. It belongs to a higher science: to the science of Real

Existences. You call the man Dialectical, who requires a reason of the

essence of each thing[339].

And as Dialectic gives an account of other real existences, so does

it of that most important reality, the true guide of Life and of

Philosophy, the Real Good. He who cannot follow this through all the

windings of the battle of Life, knows nothing to any purpose. And

thus Dialectic is the pinnacle, the top stone of the edifice of the

sciences[340].

Dialectic is here defined or described by Plato according to the

_subject_ with which it treats, and the _object_ with which it is to

be pursued: but in other parts of the Platonic Dialogues, Dialectic

appears rather to imply a certain _method_ of investigation;--to

describe the _form_ rather than the _matter_ of discussion; and it will

perhaps be worth while to compare these different accounts of Dialectic.

(_Phædrus._) One of the cardinal passages on this Point is in the

Phædrus, and may be briefly quoted. Phædrus, in the Dialogue which

bears his name, appears at first as an admirer of Lysias, a celebrated

writer of orations, the contemporary of Plato. In order to expose this

writer's style of composition as frigid and shallow, a specimen of it

is given, and Socrates not only criticises this, but delivers, as rival

compositions, two discourses on the same subject. Of these discourses,

given as the inspiration of the moment, the first is animated and

vigorous; the second goes still further, and clothes its meaning in a

gorgeous dress of poetical and mythical images. Phædrus acknowledges

that his favourite is outshone; and Socrates then proceeds to point

out that the real superiority of his own discourse consists in its

having a dialectical structure, beneath its outward aspect of imagery

and enthusiasm. He says: (§ 109, Bekker. It is to be remembered that

the subject of all the discourses was _Love_, under certain supposed

conditions.)

"The rest of the performance may be taken as play: but there were, in

what was thus thrown out by a random impulse, two features, of which,

if any one could reduce the effect to an art, it would be a very

agreeable and useful task.

"What are they? Phædrus asks.

"In the first place, Socrates replies, the taking a connected view of

the scattered elements of a subject, so as to bring them into one

Idea; and thus to give a definition of the subject, so as to make it

clear what we are speaking of; as was then done in regard to _Love_.

A definition was given of it, what it is: whether the definition was

good or bad, at any rate there was a definition. And hence, in what

followed, we were able to say what was clear and consistent with itself.

"And what, Phædrus asks, was the other feature?

"The dividing the subject into kinds or elements, according to the

nature of the thing itself:--not breaking its natural members, like a

bad carver who cannot hit the joint. So the two discourses which we

have delivered, took the irrational part of the mind, as their common

subject; and as the body has two different sides, the right and the

left, with the same names for its parts; so the two discourses took

the irrational portion of man; and the one took the left-hand portion,

and divided this again, and again subdivided it, till, among the

subdivisions, it found a left-handed kind of Love, of which nothing

but ill was to be said. While the discourse that followed out the

right-hand side of phrenzy, (the irrational portion of man's nature,)

was led to something which bore the name of _Love_ like the other,

but which is divine, and was praised as the source of the greatest

blessing."

"Now I," Socrates goes on to say, "am a great admirer of these

processes of division and comprehension, by which I endeavour to speak

and to think correctly. And if I can find any one who is able to see

clearly what is by nature reducible to one and manifested in many

elements, I follow his footsteps as a divine guide. Those who can do

this, I call--whether rightly or not, God knows--but I have hitherto

been in the habit of calling them _dialectical_ men."

It is of no consequence to our present purpose whether either of the

discourses of Socrates in the Phædrus, or the two together, as is here

assumed, do contain a just division and subdivision of that part of the

human soul which is distinguishable from Reason, and do thus exhibit,

in its true relations, the affection of Love. It is evident that

division and subdivision of this kind is here presented as, in Plato's

opinion, a most valuable method; and those who could successfully

practise this method are those whom he admires as dialectical men. This

is here his _Dialectic_.

(_Sophistes._) We are naturally led to ask whether this method of

dividing a subject as the best way of examining it, be in any other

part of the Platonic Dialogues more fully explained than it is in the

Phædrus; or whether any rules are given for this kind of Dialectic.

To this we may reply, that in the Dialogue entitled _The Sophist_, a

method of dividing a subject, in order to examine it, is explained

and exemplified with extraordinary copiousness and ingenuity. The

object proposed in that Dialogue is, to define what a Sophist is;

and with that view, the principal speaker, (who is represented as an

Eleatic stranger,) begins by first exemplifying what is his method of

framing a definition, and by applying it to define an _Angler_. The

course followed, though it now reads like a burlesque of philosophical

methods, appears to have been at that time a _bona fide_ attempt to be

philosophical and methodical. It proceeds thus:

"We have to inquire concerning _Angling_. Is it an Art? It is. Now

what kind of art? All art is an art of making or an art of getting:

(_Poietic_ or _Ktetic_.) It is Ktetic. Now the art of getting, is

the art of getting by exchange or by capture: (_Metabletic_ or

_Chirotic_.) Getting by capture is by contest or by chase: (_Agonistic_

or _Thereutic_.) Getting by chase is a chase of lifeless or of living

things: (the first has no name, the second is _Zootheric_.) The chase

of living things is the chase of land animals or of water animals:

(_Pezotheric_ or _Enygrotheric_.) Chase of water animals is of birds

or of fish: (_Ornithothereutic_ and _Halieutic_.) Chase of fish is by

inclosing or by striking them: (_Hercotheric_ or _Plectic_.) We strike

them by day with pointed instruments, or by night, using torches:

(hence the division _Ankistreutic_ and _Pyreutic_.) Of Ankistreutic,

one kind consists in spearing the fish downwards from above, the other

in twitching them upwards from below: (these two arts are _Triodontic_

and _Aspalieutic_.) And thus we have, what we sought, the notion and

the description of angling: namely that it is a Ktetic, Chirotic,

Thereutic, Zootheric, Enygrotheric, Halieutic, Plectic, Ankistreutic,

Aspalieutic Art."

Several other examples are given of this ingenious mode of definition,

but they are all introduced with reference to the definition of the

Sophist. And it will further illustrate this method to show how,

according to it, the Sophist is related to the Angler.

The Sophistical Art is an art of getting, by capture, living things,

namely men. It is thus a Ktetic, Chirotic, Thereutic art, and so far

agrees with that of the Angler. But here the two arts diverge, since

that of the Sophist is Pezotheric, that of the Angler Enygrotheric.

To determine the Sophist still more exactly, observe that the chase

of land animals is either of tame animals (including man) or of

wild animals: (_Hemerotheric_ and _Agriotheric_.) The chase of tame

animals is either by violence, (as kidnapping, tyranny, and war in

general,) or by persuasion, (as by the arts of speech;) that is, it

is _Biaiotheric_ or _Pithanurgic_. The art of persuasion is a private

or a public proceeding: (_Idiothereutic_ or _Demosiothereutic_.)

The art of private persuasion is accompanied with the giving of

presents, (as lovers do,) or with the receiving of pay: (thus it is

_Dorophoric_ or _Mistharneutic_.) To receive pay as the result of

persuasion, is the course, either of those who merely earn their bread

by supplying pleasure, namely flatterers, whose art is _Hedyntic_;

or of those who profess for pay to teach virtue. And who are they?

Plainly the Sophists. And thus _Sophistic_ is that kind of Ktetic,

Chirotic, Thereutic, Zootheric, Pezotheric, Hemerotheric, Pithanurgic,

Idiothereutic, Mistharneutic art, which professes to teach virtue, and

takes money on that account.

The same process is pursued along several other lines of inquiry: and

at the end of each of them the Sophist is detected, involved in a

number of somewhat obnoxious characteristics. This process of division

it will be observed, is at every step bifurcate, or as it is called,

_dichotomous_. Applied as it is in these examples, it is rather the

vehicle of satire than of philosophy. Yet, I have no doubt that this

bifurcate method was admired by some of the philosophers of Plato's

time, as a clever and effective philosophical invention. We may the

more readily believe this, inasmuch as one of the most acute persons

of our own time, who has come nearer than any other to the ancient

heads of sects in the submission with which his followers have accepted

his doctrines, has taken up this Dichotomous Method, and praised it

as the only philosophical mode of dividing a subject. I refer to Mr.

Jeremy Bentham's _Chrestomathia_ (published originally in 1816), in

which this exhaustive bifurcate method, as he calls it, was applied

to classify sciences and arts, with a view to a scheme of education.

How exactly the method, as recommended by him, agrees with the method

illustrated in the _Sophist_, an examination of any of his examples

will show. Thus to take Mineralogy as an example: according to Bentham,

Ontology is Cœnoscopic or Idioscopic: the Idioscopic is Somatoscopic

or Pneumatoscopic; the Somatoscopic is Pososcopic or Poioscopic:

Poioscopic is Physiurgoscopic or Anthropurgoscopic: Physiurgoscopic is

Uranoscopic or Epigeoscopic: Epigeoscopic is Abioscopic or Embioscopic.

And thus Mineralogy is the Science Idioscopic, Somatoscopic,

Poioscopic, Physiurgoscopic, Epigeoscopic, Abioscopic: inasmuch as

it is the science which regards bodies, with reference to their

qualities,--bodies, namely, the works of nature, terrestrial, lifeless.

I conceive that this bifurcate method is not really philosophical or

valuable: but that is not our business here. What we have to consider

is whether this is what Plato meant by the term _Dialectic_.

The general description of Dialectic in the _Sophistes_ agrees very

closely with that quoted from the _Phædrus_, that it is the separation

of a subject according to its natural divisions.

Thus, see in the Sophist the passage § 83: "To divide a subject

according to the kinds of things, so as neither to make the same

kind different nor different kinds identical, is the office of the

Dialectical Science." And this is illustrated by observing that it is

the office of the science of Grammar to determine what letters may be

combined and what may not; it is the office of the science of Music to

determine what sounds differing as acute and grave, may be combined,

and what may not: and in like manner it is the office of the science of

Dialectic to determine what _kinds_ may be combined in one subject and

what may not. And the proof is still further explained.

In many of the Platonic Dialogues, the Dialectic which Socrates is thus

represented as approving, appears to include the form of Dialogue,

as well as the subdivision of the subject into its various branches.

Socrates is presented as attaching so much importance to this form,

that in the Protagoras (§ 65) he rises to depart, because his opponent

will not conform to this practice. And generally in Plato, Dialectic is

opposed to Rhetoric, as a string of short questions and answers to a

continuous dissertation.

Xenophon also seems to imply (_Mem._ IV. 5, 11) that Socrates included

in his notion of Dialectic the form of Dialogue as well as the division

of the subject.

But that the method of close Dialogue was not called _Dialectic_ by

the author of the _Sophist_, we have good evidence in the work itself.

Among other notions which are analysed by the bifurcate division here

exhibited, is that of getting by contest (_Agonistic_, previously given

as a division of _Ktetic_). Now getting by contest may be by peaceful

trial of superiority, or by fight: (_Hamilletic_ or _Machelic_). The

fight may be of body against body, or of words against words: these

may be called _Biastic_ and _Amphisbetic_. The fight of words about

right and wrong, may be by long discourses opposed to each other, as

in judicial cases; or by short questions and answers: the former may

be called _Dicanic_, the latter _Antilogic_. Of these colloquies,

about right and wrong, some are natural and spontaneous, others

artificial and studied: the former need no special name; the latter are

commonly called _Eristic_. Of Eristic colloquies, some are a source

of expense to those who hold them, some of gain: that is, they are

_Chrematophthoric_ or _Chrematistic_: the former, the occupation of

those who talk for pleasure's and for company's sake, is _Adoleschic_,

wasteful garrulity; the latter, that of those who talk for the sake

of gain, is _Sophistic_. And thus Sophistic is an art Eristic, which

is part of Antilogic, which is part of Amphisbetic, which is part of

Agonistic, which is part of Chirotic, which is a part of Ktetic. (§ 23.)

We may notice here an indication that satire rather than exact reason

directs these analyses; in that Sophistic, which was before a part of

the _thereutic_ branch of _chirotic_ and _ktetic_, is here a part of

the other branch, _agonistic_.

But the remark which I especially wish to make here is, that the art of

discussing points of right and wrong by short questions and answers,

being here brought into view, is not called _Dialectic_, which we

might have expected; but _Antilogic_. It would seem therefore that the

Author of the Sophist did not understand by _Dialectic_ such a process

as Socrates describes in Xenophon; (_Mem._ IV. 5, 11, 12;) where he

says it was called _Dialectic_, because it was followed by persons

_dividing things into their kinds in conversation_: (κοινῇ βουλεύεσθαι

διαλέγοντας:)or such as the Socrates of Plato insisted upon in the

Protagoras and the Gorgias. Of the two elements which the Dialectical

Process of Socrates implied, Division of the subject and Dialogue, the

author of the _Sophistes_ does not claim the name of _Dialectic_ for

either, and seems to reject it for the second.

But without insisting upon the name, are we to suppose that the

Dichotomous Method of the _Sophistes_ Dialogue, (I may add of the

_Politicus_, for the method is the same in this Dialogue also,) is the

method of division of a subject according to its natural members, of

which Plato speaks in the _Phædrus_?

If the _Sophistes_ be the work of Plato, the answer is difficult either

way. If this method be Plato's _Dialectic_, how came he to omit to say

so there? how came he even to seem to deny it? But on the other hand,

if this dichotomous division be a different process from the division

called _Dialectic_ in the Phædrus, had Plato two methods of division of

a subject? and yet has he never spoken of them as two, or marked their

distinction?

This difficulty would be removed if we were to adopt the opinion, to

which others, on other grounds, have been led, that the Sophistes,

though of Plato's time, is not Plato's work. The grounds of this

opinion are,--that the doctrines of the Sophistes are not Platonic:

(the doctrine of Ideas is strongly impugned and weakly defended:)

Socrates is not the principal speaker, but an Eleatic stranger: and

there is, in the Dialogue, none of the dramatic character which we

generally have in Plato. The Dialogue seems to be the work of some

Eleatic opponent of Plato, rather than his.

(_Rep._ B. VII.) But we can have no doubt that the _Phædrus_ contains

Plato's real view of the nature of Dialectic, as to its form; let us

see how this agrees with the view of Dialectic, as to its matter and

object, given in the seventh Book of the _Republic_.

According to Plato, Real Existences are the objects of the exact

sciences (as number and figure, of Arithmetic and Geometry). The things

which are the objects of sense transitory phenomena, which have no

reality, because no permanence. Dialectic deals with Realities in a

more general manner. This doctrine is everywhere inculcated by Plato,

and particularly in this part of the _Republic_. He does not tell us

how we are to obtain a view of the higher realities, which are the

objects of Dialectic: only he here assumes that it will result from

the education which he enjoins. He says (§ 13) that the Dialectic

Process (ἡ διαλεκτικὴ μέθοδος) alone leads to true science: it makes

no assumptions, but goes to First Principles, that its doctrines may

be firmly grounded: and thus it purges the eye of the soul, which was

immersed in barbaric mud, and turns it upward; using for this purpose

the aid of the sciences which have been mentioned. But when Glaucon

inquires about the details of this Dialectic, Socrates says he will not

then answer the inquiry. We may venture to say, that it does not appear

that he had any answer ready.

Let us consider for a moment what is said about a philosophy rendering

a reason for the First Principles of each Science, which the Science

itself cannot do. That there is room for such a branch of philosophy

in some sciences, we easily see. Geometry, for instance, proceeds

from Axioms, Definitions and Postulates; but by the very nature of

these terms, does not prove these First Principles. These--the Axioms,

Definitions and Postulates,--are, I conceive, what Plato here calls the

_Hypotheses_ upon which Geometry proceeds, and for which it is not the

business of Geometry to render a reason. According to him, it is the

business of "Dialectic" to give a just account of these "Hypotheses."

What then is _Dialectic?_

(_Aristotle._) It is, I think, well worthy of remark, that Aristotle,

giving an account in many respects different from that of Plato, of

the nature of Dialectic, is still led in the same manner to consider

Dialectic as the branch of philosophy which renders a reason for First

Principles. In the _Topics_, we have a distinction drawn between

reasoning demonstrative, and reasoning dialectical: and the distinction

is this:--(_Top_. I. 1) that demonstration is by syllogisms from true

first principles, or from true deductions from such principles; and

that the Dialectical Syllogism is that which syllogizes from probable

propositions (ἠξ ἠνδόξων). And he adds that probable propositions are

those which are accepted by all, or by the greatest part, or by the

wise. In the next chapter, he speaks of the uses of Dialectic, which,

he says, are three, mental discipline, debates, and philosophical

science. And he adds (_Top_. I. 2, 6) that it is also useful with

reference to the First Principles in each Science: for from the

appropriate Principles of each science we cannot deduce anything

concerning First Principles, since these principles are the beginning

of reasoning. But from the probable principles in each province of

science we must reason concerning First Principles: and this is either

the peculiar office of Dialectic, or the office most appropriate to it;

for it is a process of investigation, and must lead to the Principles

of all methods.

That a demonstrative science, as such, does not explain the origin

of its own First Principles, is undoubtedly true. Geometry does not

undertake to give a reason for the Axioms, Definitions, and Postulates.

This has been attempted, both in ancient and in modern times, by the

Metaphysicians. But the Metaphysics employed on such subjects has not

commonly been called Dialectic. The term has certainly been usually

employed rather as describing a Method, than as determining the subject

of investigation. Of the Faculty which apprehends First Principles,

both according to Plato and to Aristotle, I will hereafter say a few

words.

The object of the dichotomous process pursued in the Sophistes, and

its result in each case, is a Definition. Definition also was one of

the main features of the inquiries pursued by Socrates, Induction

being the other; and indeed in many cases Induction was a series of

steps which ended in Definition. And Aristotle also taught a peculiar

method, the object and result of which was the construction of

Definitions:--namely his _Categories_. This method is one of division,

but very different from the divisions of the Sophistes. His method

begins by dividing the whole subject of possible inquiry into ten heads

or _Categories_--Substance, Quantity, Quality, Relation, Place, Time,

Position, Habit, Action, Passion. These again are subdivided: thus

Quality is Habit or Disposition, Power, Affection, Form. And we have

an example of the application of this method to the construction of a

Definition in the Ethics; where he determines Virtue to be a Habit with

certain additional limitations.

Thus the Induction of Socrates, the Dichotomy of the Eleatics, the

Categories of Aristotle, may all be considered as methods by which we

proceed to the construction of Definitions. If, by any method, Plato

could proceed to the construction of a Definition, or rather of an

Idea, of the Absolute Realities on which First Principles depend,

such a method would correspond with the notion of Dialectic in the

_Republic_. And if it was a method of division like the Eleatic or

Aristotelic, it would correspond with the notion of Dialectic in the

_Phædrus_.

That Plato's notion, however, cannot have been exactly either of these

is, I think, plain. The colloquial method of stimulating and testing

the progress of the student in Dialectic is implied, in the sequel

of this discussion of the effect of scientific study. And the method

of Dialogue, as the instrument of instruction, being thus supposed,

the continuation of the account in the _Republic_, implies that Plato

expected persons to be made dialectical by the study of the exact

sciences in a comprehensive spirit. After insisting on Geometry and

other sciences, he says (_Rep._ VII. § 16): "The synoptical man is

dialectical; and he who is not the one, is not the other."

But, we may ask, does a knowledge of sciences lead naturally to a

knowledge of Ideas, as absolute realities from which First Principles

flow? And supposing this to be true, as the Platonic Philosophy

supposes, is the Idea of the Good, as the source of moral truths, to

be thus attained to? That it is, is the teaching of Plato, here and

elsewhere; but have the speculations of subsequent philosophers in the

same direction given any confirmation of this lofty assumption?

In reply to this inquiry, I should venture to say, that this assumption

appears to be a remnant of the Socratic doctrine from which Plato

began his speculations, that Virtue is a kind of knowledge; and that

all attempts to verify the assumption have failed. What Plato added to

the Socratic notion was, that the inquiry after The Good, the Supreme

Good, was to be aided by the analogy or suggestions of those sciences

which deal with necessary and eternal truths; the supreme good being

of the nature of those necessary and eternal truths. This notion is a

striking one, as a suggestion, but it has always failed, I think, in

the attempts to work it out. Those who in modern times, as Cudworth

and Samuel Clarke, have supposed an analogy between the necessary

truths of Geometry and the truths of Morality, though they have used

the like expressions concerning the one and the other class of truths,

have failed to convey clear doctrines and steady convictions to their

readers; and have now, I believe, few or no followers.

The result of our investigation appears to be, that though Plato added

much to the matter by means of which the mind was to be improved and

disciplined in its research after Principles and Definitions, he did

not establish any form of Method according to which the inquiry

must be conducted, and by which it might be aided. The most definite

notion of Dialectic still remained the same with the original informal

view which Socrates had taken of it, as Xenophon tells us, (_Mem._

IV. 5, 11) when he says: "He said that Dialectic (τὸ διαλέγεσθαι)

was so called because it is an inquiry pursued by persons who take

counsel together, separating the subjects considered according to

their kinds (διαλέγοντας). He held accordingly that men should try

to be well prepared for such a process, and should pursue it with

diligence: by this means, he thought, they would become good men,

fitted for responsible offices of command, and truly dialectical"

(διαλέκτικωτάτους). And this is, I conceive, the answer to Mr. Grote's

interrogatory exclamation (Vol. VIII. p. 577): "Surely the Etymology

here given by Xenophon or Socrates of the word (διαλέγεσθαι) cannot

be considered as satisfactory." The two notions, of investigatory

Dialogue, and Distribution of notions according to their kinds, which

are thus asserted to be connected in etymology, were, among the

followers of Socrates, connected in fact; the dialectic dialogue was

supposed to involve of course the dialectic division of the subject.

FOOTNOTES:

[Footnote 339: Η καὶ διαλεκτικὸν καλεῖς τὸν λόγον ἐκάστου λαμβάνοντα

τῆς οὐσίας; (§ 14).]

[Footnote 340: ὥσπερ θριγγὸς τοῖς μαθήμασιν ἡ διαλεκτικὴ ἦμιν ἐπάνω

κεῖσθαι. (§ 14).]

APPENDIX C.

OF THE INTELLECTUAL POWERS ACCORDING TO PLATO.

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

In the Seventh Book of Plato's _Republic_, we have certain sciences

described as the instruments of a philosophical and intellectual

education; and we have a certain other intellectual employment spoken

of, namely, Dialectic, as the means of carrying the mind beyond these

sciences, and of enabling it to see the sources of those truths which

the sciences assume as their first principles. These points have been

discussed in the two preceding papers. But this scheme of the highest

kind of philosophical education proceeds upon a certain view of the

nature and degrees of knowledge, and of the powers by which we know;

which view had been presented in a great measure in the Sixth Book;

this view I shall now attempt to illustrate.

To analyse the knowing powers of man is a task so difficult, that we

need not be surprised if there is much obscurity in this portion of

Plato's writings. But as a reason for examining what he has said, we

must recollect that if there be in it anything on this subject which

was true then, it is true still; and also, that if we know any truth on

that subject now, we shall find something corresponding to that truth

in the best speculations of sagacious ancient writers, like Plato.

It may therefore be worth while to discuss the Platonic doctrines on

this matter, and to inquire how they are to be expressed in modern

phraseology.

Plato's doctrine will perhaps be most clearly understood, if we begin

by considering the _diagram_ by which he illustrates the different

degrees of knowledge[341]. He sets out from the distinction of

_visible_ and _intelligible_ things. There are visible objects,

squares and triangles, for instance; but these are not the squares

and triangles about which the Geometer reasons. The exactness of

his reasoning does not depend on the exactness of his diagrams. He

reasons from certain mental squares and triangles, as he conceives and

understands them. "Thus there are visible and there are intelligible

things. There is a visible and an intelligible world[342]: and there

are two different regions about which our knowledge is concerned.

Now take a line divided into two unequal segments to represent these

two regions: and again, divide each segment in the same ratio. The

parts of each segment are to represent differences of clearness and

distinctness, and in the visible world these parts are _things_ and

_images_. By _images_ I mean shadows, and reflections in water, and in

polished bodies; and by _things_, I mean that of which these images

are the resemblances; as animals, plants, things made by man. This

difference corresponds to the difference of _Knowledge_ and mere

_Opinion_; and the _Opinable_ is to the _Knowable_ as the Image to the

Reality."

This analogy is assented to by Glaucon; and thus there is assumed a

ground for a further construction of the diagram.

"Now," he says, "we have to divide the segment which represents

Intelligible Things in the same way in which we have divided that which

represents Visible Things. The one part must represent the knowledge

which the mind gets by dealing as it were with images, and by reasoning

downwards _from_ Principles; the other that which it has by dealing

with the Ideas themselves, and going _to_ First Principles.

"The one part depends upon assumptions or hypotheses[343], the other is

unhypothetical or absolute truth.

"One kind of Intelligible Things, then, is Conceptions; for instance,

geometrical conceptions of figures, by means of which we reason

downwards, assuming certain First Principles.

"Now the other kind of Intelligible Things is this:--that which the

Reason includes in virtue of its power of reasoning, when it regards

the assumptions of the Sciences as, what they are, assumptions only;

and uses them as occasions and starting points, that from these it may

ascend to the _absolute_, (ἀνυπόθετον, unhypothetical,) which does

not depend upon assumption, but is the origin of scientific truth.

The Reason takes hold of this first principle of truth; and availing

itself of all the connections and relations of this principle, it

proceeds to the conclusion; using no sensible image in doing this, but

contemplating the Ideas alone; and with these Ideas the process begins,

goes on, and terminates."

This account of the matter will probably seem to require at least

further explanation; and that accordingly is acknowledged in the

Dialogue itself. Glaucon says:

"I apprehend your meaning in a certain degree, but not very clearly,

for the matter is somewhat abstruse. You wish to prove that the

knowledge which, by the Reason, we acquire, of Real Existence and

Intelligible Things, is of a higher degree of certainty than the

knowledge which belongs to what are commonly called Sciences. Such

sciences, you say, have certain assumptions for their bases; and these

assumptions are, by the students of such sciences, apprehended, not

by Sense (that is, the Bodily Senses), but by a Mental Operation,--by

Conception. But inasmuch as such students ascend no higher than the

assumptions, and do not go to the First Principles of Truth, they do

not seem to you to have true knowledge--intuitive insight--_Nous_--on

the subject of their reasonings, though the subjects are intelligible,

along with their principle. And you call this habit and practice of the

Geometers and others by the name _Conception_, not _Intuition_[344];

taking Conception to be something between Opinion on the one side, and

Intuitive Insight on the other."

"You have explained it well, said I. And now consider the four sections

(of the line) of which we have spoken, as corresponding to four

affections in the mind. Intuition, the highest; Conception, the next;

the third, Belief; and the fourth, Conjecture (from likenesses); and

arrange them in order, so that they may have more or less of certainty,

as their objects have more or less of truth[345].

"I understand, said he. I agree to what you say, and I arrange them as

you direct."

And so the Sixth Book ends: and the Seventh Book opens with the

celebrated image of the Cave, in which men are confined, and see all

external objects only by the shadows which they cast on the walls of

their prison. And this imperfect knowledge of things is to the true

vision of them, which is attained by those who ascend to the light of

day, as the ordinary knowledge of men is to the knowledge attainable by

those whose minds are purged and illuminated by a true philosophy.

Confining ourselves at present to the part of Plato's speculations

which we have mentioned, namely, the degrees of knowledge, and the

division of our knowing faculties, we may understand, and may in a

great degree accept, Plato's scheme. We have already (in the preceding

papers) seen that, by the knowledge of real things, he means, in the

first place, the knowledge of universal and necessary truths, such

as Geometry and the other exact sciences deal with. These _we_ call

sciences of Demonstration; and we are in the habit of contrasting the

knowledge which constitutes such sciences with the knowledge obtained

by the Senses, by Experience or mere Observation. This distinction of

Demonstrative and Empirical knowledge is a cardinal point in Plato's

scheme also; the former alone being allowed to deserve the name of

_Knowledge_, and the latter being only _Opinion_. The Objects with

which Demonstration deals may be termed _Conceptions_, and the objects

with which Observation or Sense has to do, however much speculation may

reduce them to mere Sensations, are commonly described as _Things_. Of

these Things, there may be Shadows or Images, as Plato says; and as we

may obtain a certain kind of knowledge, namely Opinion or Belief, by

seeing the Things themselves, we may obtain an inferior kind of Opinion

or Belief by seeing their Images, which kind of opinion we may for the

moment call _Conjecture_. Whether then we regard the distinctions of

knowledge itself or of the objects of it, we have three terms before us.

If we consider the kinds of knowledge, they are

Demonstration: Belief: Conjecture.

If the objects of this knowledge, they are

Conceptions: Things: Images.

But in each of these Series, the first term is evidently wanting: for

Demonstration supposes Principles to reason from. Conceptions suppose

some basis in the mind which gives them their evidence. What then is

the first term in each of these two Series?

The Principles of Demonstration must be seen by _Intuition_.

Conceptions derive their properties from certain powers or attributes

of the mind which we may term _Ideas_.

Therefore the two series are

Intuition: Demonstration: Belief: Conjecture.

Ideas: Conceptions: Things: Images.

Plato further teaches that the two former terms in each Series belong

to the Intelligible, the two latter to the Visible World: and he

supposes that the ratio of these two primary segments of the line is

the same as the ratio in which each segment is divided[346].

In using the term _Ideas_ to describe the mental sources from which

Conceptions derive their validity in demonstration, I am employing a

phraseology which I have already introduced in the _Philosophy of the

Inductive Sciences_. But independently altogether of this, I do not

see what other term could be employed to denote the mental objects,

attributes, or powers, whatever they be, from which Conceptions derive

their evidence, as Demonstrative Truths derive their evidence from

Intuitive Truths.

That the Scheme just presented is Plato's doctrine on this subject,

I do not conceive there can be any doubt. There is a little want of

precision in his phraseology, arising from his mixing together the two

series. In fact, his final series

_Noësis_: _Dianoia_: _Pistis_: _Eikasia_;

is made by putting in the second place, instead of _Demonstration_,

which is the _process_ pursued, or _Science_, which is the _knowledge_

obtained, _Conception_, which is the _object_ with which the mind

deals. Such deviations from exact symmetry and correlation in speaking

of the faculties of the mind, are almost unavoidable in every language.

And there is yet another source of such inaccuracies of language; for

we have to speak, not only of the process of acquiring knowledge, and

of the objects with which the mind deals, but of the Faculties of the

mind which are thus employed. Thus _Intuition_ is the Process; _Ideas_

are the Object, in the first term of our series. The Faculty also we

may call _Intuition_; but the Greek offers a distinction. _Noësis_ is

the _Process_ of Intuition; but the _Faculty_ is _Nous_. If we wish to

preserve this distinction in English, what must we call the Faculty?

I conceive we must call it _the Intuitive Reason_, a term well known

to our older philosophical writers[347]. Again: taking the second

term of the series, _Demonstration_ is the process, _Science_, the

result; and _Conceptions_ are the objects with which the mind deals.

But what is the _Faculty_ thus employed? What is the Faculty employed

in Demonstration? The same philosophical writers of whom I spoke would

have answered at once, _the Discursive Reason_; and I do not know

that, even now, we can suggest any better term. The Faculty employed

in acquiring the two lower kinds of knowledge, the Faculty which deals

with Things and their Images is, of course, _Sense_, or _Sensation_.

The assertion of a Faculty of the mind by which it apprehends Truth,

which Faculty is higher than the Discursive Reason, as the Truth

apprehended by it is higher than mere Demonstrative Truth, agrees (as

it will at once occur to several of my readers) with the doctrine

taught and insisted upon by the late Samuel Taylor Coleridge. And so

far as he was the means of inculcating this doctrine, which, as we

see, is the doctrine of Plato, and I might add, of Aristotle, and of

many other philosophers, let him have due honour. But in his desire

to impress the doctrine upon men's minds, he combined it with several

other tenets, which will not bear examination. He held that the two

Faculties by which these two kinds of truth are apprehended, and which,

as I have said, our philosophical writers call _the Intuitive Reason_

and _the Discursive Reason_, may be called, and ought to be called,

respectively, _The Reason_ and _The Understanding_; and that the second

of these is of the nature of the _Instinct_ of animals, so as to be

something intermediate between Reason and Instinct. These opinions,

I may venture to say, are altogether erroneous. The Intuitive Reason

and the Discursive Reason are not, by any English writers, called the

Reason and the Understanding; and accordingly, Coleridge has had to

alter all the passages, namely, those taken from Leighton, Harrington,

and Bacon, from which his exposition proceeds. The Understanding is so

far from being especially the Discursive or Reasoning Faculty, that

it is, in universal usage, and by our best writers, _opposed_ to the

Discursive or Reasoning Faculty. Thus this is expressly declared by Sir

John Davis in his poem _On the Immortality of the Soul_. He says, of

the soul,

When she _rates_ things, and moves from ground to ground,

The name of _Reason_ (_Ratio_) she acquires from this:

But when by reason she truth hath found,

And standeth fixt, she _Understanding_ is.

Instead of the Reason being fixed, and the Understanding discursive,

as Mr. Coleridge says, the Reason is distinctively discursive; that

is, it obtains conclusions by running from one point to another. This

is what is meant by _Discursus_; or, taking the full term, _Discursus

Rationis_, _Discourse of Reason_. Understanding is fixed, that is, it

dwells upon one view of a subject, and not upon the steps by which that

view is obtained. The verb _to reason_, implies the substantive, _the

Reason_, though it is not coextensive with it: for as I have said,

there is the Intuitive Reason as well as the Discursive Reason. But it

is by the Faculty of Reason that we are capable of reasoning; though

undoubtedly the practice or the pretence of reasoning may be carried so

far as to seem at variance with reason in the more familiar sense of

the term; as is the case also in French. Moliere's Crisale says (in the

_Femmes Savantes_),

Raisonner est l'emploi de toute ma maison,

Et le raisonnement en bannit la Raison.

If Mr. Coleridge's assertion were true, that the Understanding is the

discursive and the Reason the fixed faculty, we should be justified in

saying that _The Understanding is the faculty by which we reason, and

the Reason is the faculty by which we understand_. But this is not so.

Nor is the Understanding of the nature of Instinct, nor does it

approach nearer than the Reason to the nature of Instinct, but the

contrary. The Instincts of animals bear a very obscure resemblance

to any of man's speculative Faculties; but so far as there is any

such resemblance, Instinct is an obscure image of Reason, not of

Understanding. Animals are said to act as if they reasoned, rather than

as if they understood. The verb _understand_ is especially applied to

man as distinguished from animals. Mr. Coleridge tells a tale from

Huber, of certain bees which, to prevent a piece of honey from falling,

balanced it by their weight, while they built a pillar to support it.

They did this by Instinct, not _understanding_ what they did; men,

doing the same, would have _understood_ what they were doing. Our

Translation of the Scriptures, in making it the special distinction of

man and animals, that _he has Understanding_ and they have not, speaks

quite consistently with good philosophy and good English.

Mr. Coleridge's object in his speculations is nearly the same as

Plato's; namely, to declare that there is a truth of a higher kind than

can be obtained by mere reasoning; and also to claim, as portions of

this higher truth, certain fundamental doctrines of Morality. Among

these, Mr. Coleridge places the Authority of Conscience, and Plato, the

Supreme Good. Mr. Coleridge also holds, as Plato held, that the Reason

of man, in its highest and most comprehensive form, is a portion of a

Supreme and Universal Reason; and leads to Truth, not in virtue of its

special attributes in each person, but by its own nature.

Many of the opinions which are combined with these doctrines, both

in Plato and in Coleridge, are such as we should, I think, find it

impossible to accept, upon a careful philosophical examination of them;

but on these I shall not here dwell.

I will only further observe, that if any one were to doubt whether the

term Νοῦς is rightly rendered _Intuitive Reason_, we may find proof

of the propriety of such a rendering in the remarkable discussion

concerning the Intellectual Virtues, which we have in the Sixth Book

of the Nicomachean Ethics. It can hardly be questioned that Aristotle

had in his mind, in writing that passage, the doctrines of Plato, as

expounded in the passage just examined, and similar passages. Aristotle

there says that there are five Intellectual Virtues, or Faculties

by which the Mind aims at Truth in asserting or denying:--namely,

_Art_, _Science_, _Prudence_, _Wisdom_, _Nous_. In this enumeration,

passing over Art, Prudence, and Wisdom, as virtues which are mainly

concerned from practical life, we have, in the region of speculative

Truth, a distinction propounded between _Science_ and _Nous_: and this

distinction is further explained (c. 6) by the remarks that Science

reasons with Principles; and that these Principles cannot be given

_by_ Science, because Science reasons _from_ them; nor by Art, nor

Prudence, for these are conversant with matters contingent, not with

matters demonstrable; nor can the First Principles of the Reasonings

of Science be given by Wisdom, for Wisdom herself has often to reason

from Principles. Therefore the First Principles of Demonstrative

Reasoning must be given by a peculiar Faculty, _Nous_. As we have

said, _Intuitive Reason_ is the most appropriate English term for this

Faculty.

The view thus given of that higher kind of Knowledge which Plato and

Aristotle place above ordinary Science, as being the Knowledge of and

Faculty of learning First Principles, will enable us to explain some

expressions which might otherwise be misunderstood. Socrates, in the

concluding part of this Sixth Book of the _Republic_, says, that this

kind of knowledge is "that of which the Reason (λόγος) takes hold,

_in virtue of its power of reasoning_[348]." Here we are plainly not

to understand that we arrive at First Principles _by reasoning_: for

the very opposite is true, and is here taught;--namely, that First

Principles are not what we reason _to_, but what we reason _from_.

The meaning of this passage plainly is, that First Principles are

those of which the Reason takes hold _in virtue of its power of

reasoning_;--they are the conditions which must exist in order to make

any reasoning possible:--they are the propositions which the Reason

must involve implicitly, in order that we may reason explicitly;--they

are the intuitive roots of the dialectical power.

In accordance with the views now explained, Plato's Diagram may be

thus further expanded. The term ιδέα is not used in this part of the

_Republic_; but, as is well known, occurs in its peculiar Platonic

sense in the Tenth Book.

+---------+------------------------------------+-----------------------+

| | Intelligible World. νοήτον. | Visible World. ὁρατον.|

+---------+-----------------+------------------+-----------------------+

|_Object_ | Ideas | Conceptions | Things | Images |

| | ἰδέαι | διάνοια | ζῶα κ.τ.λ.| εἰκἰνες |

+---------+-----------------+------------------+-----------------------+

|_Process_| Intuition | Demonstration | Belief | Conjecture|

| | νἰησις | ἐπιστήμη | πίστις | είκασία |

+---------+-----------------+------------------+-----------------------+

|_Faculty_|Intuitive Reason | Discursive Reason| Sensation |

| | νοῦς | λόγος | αἴσθησις |

+---------+-----------------+------------------+-----------------------+

FOOTNOTES:

[Footnote 341: _Pol_. vi. § 19.]

[Footnote 342: He adds, "This _oraton_, this visible world, I will not

say has any connexion with _ouranon_, heaven, that I may not be accused

of playing upon words."]

[Footnote 343: It is plain that Plato, by _Hypotheses_, in this place,

means the usual foundations of Arithmetic and Geometry; namely,

Definitions and Postulates. He says that "the arithmeticians and

geometers take as hypotheses (hυποθεμενοι) odd and even, and the

three kinds of angles (right, acute, and obtuse); and figures, (as

a triangle, a square,) and the like." I say his "hypotheses" are

the Definitions and Postulates, not the Axioms: for the Axioms of

Arithmetic and Geometry belong to the Higher Faculty, which ascends

to First Principles. But this Faculty operates rather in using these

axioms than in enunciating them. It knows them implicitly rather than

expresses them explicitly.]

[Footnote 344: διάνοιαν άλλ' οὐ νοῦν.]

[Footnote 345: The Diagram, as here described, would be this:

+---------------------------+---------------------------+

| _Intelligible World._ | _Visible World._ |

|-------------+-------------+-------------+-------------+

| Intuition. | Conception. | Things. | Images. |

+-------------+-------------+-------------+-------------+

Plato supposes the whole, and each of the two parts, to be divided in

the same ratio, in order that the _analogy_ of the division in each

case may be represented.]

[Footnote 346: The four segments might be as 4: 2: 2: 1; or as 9: 6: 6:

4; or generally, as _a_: _ar_: _ar_: _ar_^2.]

[Footnote 347:

Hence the mind Reason receives

Intuitive or Discursive.

MILTON.]

[Footnote 348: τῇ τοῦ διαλέγεσθαι δυνόμει.]

APPENDIX D.

CRITICISM OF ARISTOTLE'S ACCOUNT OF INDUCTION.

(_Cam. Phil. Soc._ FEB. 11, 1850.)

The Cambridge Philosophical Society has willingly admitted among

its proceedings not only contributions to science, but also to the

philosophy of science; and it is to be presumed that this willingness

will not be less if the speculations concerning the philosophy of

science which are offered to the Society involve a reference to ancient

authors. Induction, the process by which general truths are collected

from particular examples, is one main point in such philosophy: and the

comparison of the views of Induction entertained by ancient and modern

writers has already attracted much notice. I do not intend now to go

into this subject at any length; but there is a cardinal passage on the

subject in Aristotle's _Analytics_, (_Analyt. Prior._ II. 25) which I

wish to explain and discuss. I will first translate it, making such

emendations as are requisite to render it intelligible and consistent,

of which I shall afterwards give an account.

I will number the sentences of this chapter of Aristotle in order that

I may afterwards be able to refer to them readily.

§ 1. "We must now proceed to observe that we have to examine not only

syllogisms according to the aforesaid _figures_,--syllogisms logical

and demonstrative,--but also rhetorical syllogisms,--and, speaking

generally, any kind of proof by which belief is influenced, following

any method.

§ 2. "All belief arises either from Syllogism or from Induction: [we

must now therefore treat of Induction.]

§ 3. "Induction, and the Inductive Syllogism, is when by means of one

extreme term we infer the other extreme term to be true of the middle

term.

§ 4. "Thus if _A_, _C_, be the extremes, and _B_ the mean, we have to

show, by means of _C_, that _A_ is true of _B_.

§ 5. "Thus let _A_ be _long-lived_; _B_, _that which has no

gall-bladder;_ and _C_, particular long-lived animals, as _elephant_,

_horse_, _mule_.

§ 6. "Then every _C_ is _A_, for all the animals above named are

long-lived.

§ 7. "Also every _C_ is _B_, for all those animals are destitute of

gall-bladder.

§ 8. "If then _B_ and _C_ are convertible, and the mean (_B_) does not

extend further than extreme (_C_), it necessarily follows that every

_B_ is _A_.

§ 9. "For it was shown before, that, if any two things be true of the

same, and if either of them be convertible with the extreme, the other

of the things predicated is true of the convertible (extreme).

§ 10. "But we must conceive that _C_ consists of a collection of all

the particular cases; for Induction is applied to all the cases.

§ 11. "But such a syllogism is an inference of a first truth and

immediate proposition.

§ 12. "For when there is a mean term, there is a demonstrative

syllogism through the mean; but when there is not a mean, there is

proof by Induction.

§ 13. "And in a certain way, Induction is contrary to Syllogism; for

Syllogism proves, by the middle term, that the extreme is true of the

third thing: but Induction proves, by means of the third thing, that

the extreme is true of the mean.

§ 14. "And Syllogism concluding by means of a middle term is prior

by nature and more usual to us; but the proof by Induction, is more

luminous."

I think that the chapter, thus interpreted, is quite coherent and

intelligible; although at first there seems to be some confusion, from

the author sometimes saying that Induction is a kind of Syllogism, and

at other times that it is not. The amount of the doctrine is this.

When we collect a general proposition by Induction from particular

cases, as for instance, that all animals destitute of gall-bladder

(_acholous_), are long-lived, (if this proposition were true, of which

hereafter,) we may express the process in the form of a Syllogism, if

we will agree to make a collection of particular cases our middle term,

and assume that the proposition in which the second extreme term occurs

is convertible. Thus the known propositions are

Elephant, horse, mule, &c., are long-lived.

Elephant, horse, mule, &c., are _acholous_.

But if we suppose that the latter proposition is convertible, we shall

have these propositions:

Elephant, horse, mule, &c., are long-lived.

All acholous animals are elephant, horse, mule, &c.,

from whence we infer, quite rigorously as to _form_,

All acholous animals are long-lived.

This mode of putting the Inductive inference shows both the strong and

the weak point of the illustration of Induction by means of Syllogism.

The strong point is this, that we make the inference perfect as to

form, by including an indefinite collection of particular cases,

elephant, horse, mule, &c., in a single term, _C_. The Syllogism then is

All _C_ are long-lived.

All acholous animals are _C_.

Therefore all acholous animals are long-lived.

The weak point of this illustration is, that, at least in some

instances, when the number of actual cases is necessarily indefinite,

the representation of them as a single thing involves an unauthorized

step. In order to give the reasoning which really passes in the mind,

we must say

Elephant, horse, &c., are long-lived.

All acholous animals are _as_ elephant, horse, &c.,

Therefore all acholous animals are long-lived.

This "_as_" must be introduced in order that the "all _C_" of the first

proposition may be justified by the "_C_" of the second.

This step is, I say, necessarily unauthorized, where the number of

particular cases is indefinite; as in the instance before us, the

species of acholous animals. We do not know how many such species

there are, yet we wish to be able to assert that _all_ acholous

animals are long-lived. In the proof of such a proposition, put in a

syllogistic form, there must necessarily be a logical defect; and the

above discussion shows that this defect is the substitution of the

proposition, "All acholous animals are _as_ elephant, &c.," for the

converse of the experimentally proved proposition, "elephant, &c., are

acholous."

In instances in which the number of particular cases is limited, the

necessary existence of a logical flaw in the syllogistic translation

of the process is not so evident. But in truth, such a flaw exists in

all cases of Induction _proper_: (for Induction by _mere enumeration_

can hardly be called _Induction_). I will, however, consider for a

moment the instance of a celebrated proposition which has often been

taken as an example of Induction, and in which the number of particular

cases is, or at least is at present supposed to be, limited. Kepler's

laws, for instance the law that the planets describe ellipses, may

be regarded as examples of Induction. The law was inferred, we will

suppose, from an examination of the orbits of Mars, Earth, Venus. And

the syllogistic illustration which Aristotle gives, will, with the

necessary addition to it, stand thus,

Mars, Earth, Venus describe ellipses.

Mars, Earth, Venus are planets.

Assuming the convertibility of this last proposition, _and its

universality_, (which is the necessary addition in order to make

Aristotle's syllogism valid) we say

All the planets are as Mars, Earth, Venus.

Whence it follows that all the planets describe ellipses.

If, instead of this assumed universality, the astronomer had made a

real enumeration, and had established the fact of each particular, he

would be able to say

Saturn, Jupiter, Mars, Earth, Venus, Mercury, describe ellipses.

Saturn, Jupiter, Mars, Earth, Venus, Mercury are all the planets.

And he would obviously be entitled to convert the second proposition,

and then to conclude that

All the planets describe ellipses.

But then, if this were given as an illustration of Induction by means

of syllogism, we should have to remark, in the first place, that the

conclusion that "all the planets describe ellipses," adds nothing to

the major proposition, that "S., J., M., E., V., m., do so." It is

merely the same proposition expressed in other words, so long as S.,

J., M., E., V., m., are supposed to be all the planets. And in the

next place we have to make a remark which is more important; that the

minor, in such an example, must generally be either a very precarious

truth, or, as appears in this case, a transitory error. For that the

planets known at any time are _all_ the planets, must always be a

doubtful assertion, liable to be overthrown to-night by an astronomical

observation. And the assertion, as received in Kepler's time, has been

overthrown. For Saturn, Jupiter, Mars, Earth, Venus, Mercury, are

not all the planets. Not only have several new ones been discovered

at intervals, as Uranus, Ceres, Juno, Pallas, Vesta, but we have new

ones discovered every day; and any conclusion depending upon this

premiss that _A_, _B_, _C_, _D_, _E_, _F_, _G_, _H_, to _Z_ are all the

planets, is likely to be falsified in a few years by the discovery of

_A´_, _B´_, _C´_, &c. If, therefore, this were the syllogistic analysis

of Induction, Kepler's discovery rested upon a false proposition;

and even if the analysis were now made conformable to our present

knowledge, that induction, analysed as above, would still involve a

proposition which to-morrow may show to be false. But yet no one, I

suppose, doubts that Kepler's discovery was really a discovery--the

establishment of a scientific truth on solid grounds; or, that it is

a scientific truth for us, notwithstanding that we are constantly

discovering new planets. Therefore the syllogistic analysis of it now

discussed (namely, that which introduces simple enumeration as a step)

is not the right analysis, and does not represent the grounds of the

Inductive Truth, that all the planets describe ellipses.

It may be said that all the planets discovered since Kepler's time

conform to his law, and thus confirm his discovery. This we grant:

but they only _confirm_ the discovery, they do not make it; they are

not its groundwork. It was a discovery before these new cases were

known; it was an inductive truth without them. Still, an objector might

urge, if any one of these new planets had contradicted the law, it

would have overturned the discovery. But this is too boldly said. A

discovery which is so precise, so complex (in the phenomena which it

explains), so supported by innumerable observations extending through

space and time, is not so easily overturned. If we find that Uranus,

or that Encke's comet, deviates from Kepler's and Newton's laws, we

do not infer that these laws must be false; we say that there must

be some disturbing cause in these cases. We seek, and we find these

disturbing causes: in the case of Uranus, a new planet; in the case

of Encke's comet, a resisting medium. Even in this case therefore,

though the number of particulars is limited, the Induction was not

made by a simple enumeration of all the particulars. It was made from

a few cases, and when the law was discerned to be true in these, it

was extended to all; the conversion and assumed universality of the

proposition that "these are planets," giving us the proposition which

we need for the syllogistic exhibition of Induction, "all the planets

are as these."

I venture to say further, that it is plain, that Aristotle did not

regard Induction as the result of simple enumeration. This is plain,

in the first place, from his example. Any proposition with regard to

a special class of animals, cannot be proved by simple enumeration:

for the number of particular cases, that is, of animal species in

the class, is indefinite at any period of zoological discovery, and

must be regarded as infinite. In the next place, Aristotle says (§

10 of the above extract), "We must conceive that _C_ consists of a

collection of all the particular cases; for induction is applied to

all the cases." We must _conceive_ (νοεῖν) that _C_ in the major,

consists of all the cases, in order that the conclusion may be true

of all the cases; but we cannot _observe_ all the cases. But the

evident proof that Aristotle does not contemplate in this chapter an

Induction by simple enumeration, is the contrast in which he places

Induction and Syllogism. For Induction by simple enumeration stands

in no contrast to Syllogism. The Syllogism of such Induction is quite

logical and conclusive. But Induction from a comparatively small

number of particular cases to a general law, does stand in opposition

to Syllogism. It gives us a truth,--a truth which, as Aristotle

says (§ 14), is more luminous than a truth proved syllogistically,

though Syllogism may be _more natural and usual_. It gives us (§ 11)

immediate propositions, obtained directly from observation, and not

by a chain of reasoning: "first truths," the principles from which

syllogistic reasonings may be deduced. The Syllogism proves by means of

a middle term (§ 13) that the extreme is true of a third thing: thus,

(_acholous_ being the middle term):

Acholous animals are long-lived:

All elephants are acholous animals:

Therefore all elephants are long-lived.

But Induction proves by means of a third thing (namely, particular

cases) that the extreme is true of the mean; thus (_acholous_, still

being the middle term)

Elephants are long-lived:

Elephants are acholous animals:

Therefore acholous animals are long-lived.

It may be objected, such reasoning as this is quite inconclusive:

and the answer is, that this is precisely what we, and as I believe,

Aristotle, are here pointing out. Induction _is_ inconclusive _as

reasoning_. It is not reasoning: it is another way of getting at

truth. As we have seen, no reasoning can prove such an inductive

truth as this, that all planets describe ellipses. It is _known_ from

observation, but it is not _demonstrated_. Nevertheless, no one doubts

its universal truth, (except, as aforesaid, when disturbing causes

intervene). And thence, Induction is, as Aristotle says, opposed to

syllogistic reasoning, and yet is a means of discovering truth: not

only so, but a means of discovering primary truths, immediately derived

from observation.

I have elsewhere taught that all Induction involves a _Conception_ of

the mind applied to facts. It may be asked whether this applies in

such a case as that given by Aristotle. And I reply, that Aristotle's

instance is a very instructive example of what I mean. The Conception

which is applied to the facts in order to make the induction possible

is the want of the gall-bladder;--and Aristotle supplies us with a

special term for this conception; _acholous_[349]. But, it may be

said, that the animals observed, the elephant, horse, mule, &c., are

acholous, is a mere fact of observation, not a Conception. I reply

that it is a _Selected_ Fact, a fact selected and compared in several

cases, which is what we mean by a _Conception_. That there is needed

for such selection and comparison a certain activity of the mind, is

evident; but this also may become more clear by dwelling a little

further on the subject. Suppose that Aristotle, having a desire to know

what class of animals are long-lived, had dissected for that purpose

many animals; elephants, horses, cows, sheep, goats, deer and the like.

How many resemblances, how many differences, must he have observed

in their anatomy! He was very likely long in fixing upon any one

resemblance which was common to all the long-lived. Probably he tried

several other characters, before he tried the presence and absence

of the gall-bladder:--perhaps, trying such characters, he found them

succeed for a few cases, and then fail in others, so that he had to

reject them as useless for his purpose. All the while, the absence of

the gall-bladder in the long-lived animals was a fact: but it was of

no use to him, because he had not selected it and drawn it forth from

the mass of other facts. He was looking for a mean term to connect his

first extreme, _long-lived_, with his second, the special cases. He

sought this middle term in the entrails of the many animals which he

used as extremes: it _was_ there, but he could not find it. The fact

existed, but it was of no use for the purpose of Induction, because

it did not become a special Conception in his mind. He considered the

animals in various points of view, it may be, as ruminant, as horned,

as hoofed, and the contrary; but not as _acholous_ and the contrary.

When he looked at animals in that point of view,--when he took up that

character as the ground of distinction, he forthwith imagined that he

found a separation of long-lived and short-lived animals. When that

Fact became a Conception, he obtained an inductive truth, or, at any

rate, an inductive proposition.

He obtained an inductive proposition by applying the Conception

_acholous_ to his observation of animals. This Conception divided

them into two classes; and these classes were, he fancied, long-lived

and short-lived respectively. That it was the Conception, and not

the Fact which enabled him to obtain his inductive proposition, is

further plain from this, that the supposed Fact is not a fact. Acholous

animals are not longer-lived than others. The presence or absence of

the gall-bladder is no character of longevity. It is true, that in one

familiar class of animals, the herbivorous kind, there is a sort of

first seeming of the truth of Aristotle's asserted rule: for the horse

and mule which have not the gall-bladder are longer-lived than the

cow, sheep, and goat, which have it. But if we pursue the investigation

further, the rule soon fails. The deer-tribe that want the gall-bladder

are not longer-lived than the other ruminating animals which have it.

And as a conspicuous evidence of the falsity of the rule, man and the

elephant are perhaps, for their size, the longest-lived animals, and

of these, man has, and the elephant has not, the organ in question.

The inductive proposition, then, is false; but what we have mainly

to consider is, where the fallacy enters, according to Aristotle's

analysis of Induction into Syllogism. For the two premisses are still

true; that elephants, &c., are long-lived; and that elephants, &c.,

are acholous. And it is plain that the fallacy comes in with that

conversion and generalization of the latter proposition, which we have

noted as necessary to Aristotle's illustration of Induction. When we

say "All acholous animals are as elephants, &c.," that is, as those

in their biological conditions, we say what is not true. Aristotle's

condition (§ 8) is not complied with, that the middle term shall not

extend beyond the extreme. For the character _acholous_ does extend

beyond the elephant and the animals biologically resembling it; it

extends to deer, &c., which are not like elephants and horses, in the

point in question. And thus, we see that the assumed conversion and

generalization of the minor proposition, is the seat of the fallacy of

false Inductions, as it is the seat of the peculiar logical character

of true Inductions.

As true Inductive Propositions cannot be logically demonstrated by

syllogistic rules, so they cannot be discovered by any rule. There

is no formula for the discovery of inductive truth. It is caught by

a peculiar sagacity, or power of divination, for which no precepts

can be given. But from what has been said, we see that this sagacity

shows itself in the discovery of propositions which are both _true_,

and _convertible_ in the sense above explained. Both these steps may

be difficult. The former is often very laborious: and when the labour

has been expended, and a true proposition obtained, it may turn out

useless, because the proposition is not convertible. It was a matter

of great labour to Kepler to prove (from calculation of observations)

that Mars moves elliptically. Before he proved this, he had tried

to prove many similar propositions:--that Mars moved according to

the "bisection of the eccentricity,"--according to the "vicarious

hypothesis,"--according to the "physical hypothesis,"--and the like;

but none of these was found to be exactly true. The proposition that

Mars moves elliptically was proved to be true. But still, there was

the question, Is it convertible? Do all the planets move as Mars

moves? This was proved, (suppose,) to be true, for the Earth and

Venus. But still the question remains, Do all the planets move as

Mars, Earth, Venus, do? The inductive generalizing impulse boldly

answers, Yes, to this question; though the rules of Syllogism do not

authorize the answer, and though there remain untried cases. The

inductive Philosopher tries the cases as fast as they occur, in order

to confirm his previous conviction; but if he had to wait for belief

and conviction till he had tried every case, he never could have belief

or conviction of such a proposition at all. He is prepared to modify or

add to his inductive truth according as new cases and new observations

instruct him; but he does not fear that new cases or new observations

will overturn an inductive proposition established by exact comparison

of many complex and various phenomena.

Aristotle's example offers somewhat similar reflections. He had to

establish a proposition concerning long-lived animals, which should

be true, and should be susceptible of generalized conversion. To

prove that the elephant, horse and mule are destitute of gall-bladder

required, at least, the labour of anatomizing those animals in the

seat of that organ. But this labour was not enough; for he would find

those animals to agree in many other things besides in being acholous.

He must have selected that character somewhat at a venture. And the

guess was wrong, as a little more labour would have shown him; if

for instance he had dissected deer: for they are acholous, and yet

short-lived. A trial of this kind would have shown him that the extreme

term, _acholous_, did extend beyond the mean, namely, animals such

as elephant, horse, mule; and therefore, that the conversion was not

allowable, and that the Induction was untenable. In truth, there is no

relation between bile and longevity[350], and this example given by

Aristotle of generalization from induction is an unfortunate one.

* * * * *

In discussing this passage of Aristotle, I have made two alterations in

the text, one of which is necessary on account of the fact; the other

on account of the sense. In the received text, the particular examples

of long-lived animals given are _man_, horse, and mule (ἐφ' ᾧ δὲ Γ, τὸ

καθέκαστον μακρόβιον, οἷον ἄνθρωπος, καὶ ἵππος, καὶ ἡμίονος). And it is

afterwards said that all these are _acholous_: (ἀλλὰ καὶ τὸ Β, τὸ μὴ

ἔχον χολὴν, παντὶ ὑπάρχει τῷ Γ). But man _has_ a gall-bladder: and the

fact was well known in Aristotle's time, for instance, to Hippocrates;

so that it is not likely that Aristotle would have made the mistake

which the text contains. But at any rate, it is a mistake; if not of

the transcriber, of Aristotle; and it is impossible to reason about the

passage, without correcting the mistake. The substitution of ἔλεφας

for ἄνθρωπος makes the reasoning coherent; but of course, any other

acholous long-lived animal would do so equally well.

The other emendation which I have made is in § 6. In the received text

§ 6 and 7 stand thus:

6. Then every _C_ is _A_, for _every acholous animal is long-lived_

(τῷ δὴ Γ ὅλω ὑπάρχει τὸ Α, πᾶν γὰρ τὸ ἄχολον μακρόβιον).

7. Also every _C_ is _B_, for all _C_ is destitute of bile.

Whence it may be inferred, says Aristotle, under certain conditions,

that every _B_ is _A_ (τὸ Α τῷ Β ὑπάρχειν) that is, that _every

acholous animal is long-lived_. But this conclusion is, according

to the common reading, identical with the major premiss; so that

the passage is manifestly corrupt. I correct it by substituting for

ἄχολον, Γ; and thus reading πᾶν γὰρ τὸ Γ μακρόβιον "for every _C_ is

long-lived:" just as in the parallel sentence, 7, we have ἀλλὰ καὶ τὸ

Β, τὸ μὴ ἔχον χολην, παντὶ ὑπάρχει τῷ Γ. In this way the reasoning

becomes quite clear. The corrupt substitution of ἄχολον for Γ may have

been made in various ways; which I need not suggest. As my business is

with the sense of the passage, and as it makes no sense without the

change, and very good sense with it, I cannot hesitate to make the

emendation. And these emendations being made, Aristotle's view of the

nature and force of Induction becomes, I think, perfectly clear and

very instructive.

* * * * *

ADDITIONAL NOTE.

I take the liberty of adding to this Memoir the following remarks, for

which I am indebted to Mr. Edleston, Fellow of Trinity College.

Several of the earlier editions of Aristotle have γ instead of ἄχολον

in the passage referred to in the above paper: ex. gr.

(1) The edition printed at Basle, 1539 (after Erasmus): "τὸ γ."

(2) Basil (Erasmus) 1550. "τὸ γ."

(3) Burana's Latin version, Venet. 1552, has "omne enim _C_ longævum."

(4) Sylburg, Francf. 1587 "τὸ γ" is printed in brackets thus: "[τὸ γ]

τὸ ἄχολον."

(5) So also in Casaubon's edition, 1590.

(6) Casaub. 1605 "τὸ γ," (though the Latin version has "vacans bile;")

not "[τὸ γ] τὸ ἄχολον," as the edition of 1590.

(7) In the edition printed Aurel. Allobr. 1607, "[τὸ γ] τὸ ἄχολον," as

in (4) and (5).

(8) Du Val's editions, Paris, 1619, 1629, 1654 "τὸ γ," though in

Pacius's translation in the adjacent column we find "vacans bile."

(9) In the critical notes to Waitz's edition of the _Organon_ (Lips.

1844) it is stated that "post ἄχολον del. γ. _n_," implying apparently,

that in the MS. marked _n_, the letter γ, which had been originally

written after ἄχολον, had been erased.

* * * * *

The following passages throw light upon the question whether ἄνθρωπος

ought or ought not to be retained in the passage discussed in the

Memoir.

(A) Aristot. _De Animalibus Histor._ II. 15, 9 (Bekk.), τῶν μὲν

ζωοτόκων καὶ τετραπόδων ἔλαφος οὐκ ἔχει [χολήν] οὐδὲ πρόξ, ἕτι δὲ

ἵππος, ὀρεύς, ὄνος, φώκη καὶ τῶν ὑῶν ἔνιοι.... Ἔχει δὲ καὶ ὁ ἐλέφας τὸ

ῆπαρ ἄχολον μέν, κ.τ.λ.

(B) Conf. Ib. I. 17, 10, 11. (In the beginning of Chap. 16, he says

that the external μορια of man are γνώριμα, "τὰ δ' ἐντὸς τοὐναντίον.

Ἄγνωστα γάρ ἐστι μάλιστα τὰ τῶν ἀνθρώπων, ὡστε δεῖ πρὸς τὰ τῶν ἄλλων μόρια

ζώων ἀνάγοντας σκοπεῖν," ...)

(C) Id _De Part. Animal._ IV. 2, 2. τὰ μὲν γὰρ ὅλως οὐκ ἕχει χολήν,

οἷον ἱππος και ὀρεύς καὶ ονος καὶ ἔλαφος καὶ πρόξ..... Ἐν δὲ τοῖς

γένεσι τοῖς αὐτοῖς τὰ μὲν ἔχειν φαίνεται, τὰ δ' οὐκ ἔχειν, οἷον ἐν

τῷ τῶν μυῶν. Τούτων δ' ἐστὶ καὶ ὁ ἄνθρωπος· ἔνιοι μὲν γὰρ φαίνονται

ἔχοντες χολὴν ἐπὶ του ἥπατος, ἔνιοι δ' οὐκ ἔχοντες. Διο καὶ γίνεται

ἀμφισβήτησις περὶ ὁλου τοῦ γένους· οἱ γὰρ ἐντυχόντες ὁποτερωσοῦν ἔχουσι

περὶ πάντων ὑπολαμβάνουσιν ὡς ἁπάντων ἐχόντων.....

(D) Ib. § 11. Διὸ καὶ χαριέστατα λέγουσι τῶν ῶρχαίων ὁι φάσκοντες

αἴτιον εῖναι τοῦ πλείω ζῆν χρόνον το μὴ ἔχειν χολήν, βλέψαντες ἐπὶ τὰ

μωνυχα και τὰς ελαφους· ταῦτα γὰρ ἄχολά τε καὶ ζῇ πολὺν χρόνον. Ἔτι

δὲ καὶ τὰ μὴ ἑωραμένα ὑπ' ἐκείνων ὁτι οὐκ ἔχει χολήν, οἷον δελφις καὶ

κάμηλος, καὶ ταῦτα τυγχάνει μακρόβια ὄντα. Εὔλογον γάρ, κ.τ.λ.

(E) The elephant and man are mentioned together as long-lived animals

(_De Long. et Brev. Vitæ_, IV. 2, and _De Generat. Animal._ IV. 10, 2.)

* * * * *

The following is the import of these passages:

(_A_) "Of viviparous quadrupeds, the deer, roe, horse, mule, ass, seal,

and some of the swine have not the gall-bladder....

The elephant also has the liver without gall-bladder, &c."

(_B_) "The external parts of man are well known: the internal parts are

far from being so. The parts of man are in a great measure unknown; so

that we must judge concerning them by reference to the analogy of other

animals...."

(_C_) "Some animals are altogether destitute of gall-bladder, as the

horse, the mule, the ass, the deer, the roe.... But in some kinds it

appears that some have it, and some have it not, as the mice kind. And

among these is man; for some men appear to have a gall-bladder on the

liver, and some not to have one. And thus there is a doubt as to the

species in general; for those who have happened to examine examples of

either kind, hold that all the cases are of that kind."

(_D_) Those of the ancients speak most plausibly, who say that the

absence of the gall-bladder is the cause of long life; looking at

animals with uncloven hoof, and deer: for these are destitute of

gall-bladder, and live a long time. And further, those animals in which

the ancients had not the opportunity of ascertaining that they have not

the gall-bladder, as the dolphin, and the camel, are also long-lived

animals."

It appears, from these passages, that Aristotle was aware that some

persons had asserted man to have a gall-bladder, but that he also

conceived this not to be universally true. He may have inclined to

the opinion, that the opposite case was the more usual, and may have

written ἄνθρωπος in the passage which I have been discussing. Another

mistake of his is the reckoning deer among long-lived animals.

It appears probable, from the context of the passages (_C_) and (_D_),

that the conjecture of a connexion between absence of the gall-bladder

and length of life was suggested by some such notion as this:--that

the gall, from its bitterness, is the cause of irritation, mental and

bodily, and that irritation is adverse to longevity. The opinion is

ascribed to "the ancients," not claimed by Aristotle as his own.

FOOTNOTES:

[Footnote 350: Mr. Owen, to whom I am indebted for the physiological

part of this criticism, tells me, "All mammalia have bile, the

carnivora in greater proportion than the herbivora: the gall-bladder

is a comparatively unimportant accessory to the biliary apparatus;

adjusting it to certain modifications of stomach and intestine: there

is no relation between natural longevity and bile. Neither has the

presence or absence of the gall-bladder any connexion with age. Man and

the elephant are perhaps for their size the longest lived animals, and

the latest at coming to maturity: one has the gall-bladder, and the

other not."]

APPENDIX E.

ON THE FUNDAMENTAL ANTITHESIS OF PHILOSOPHY.

(_Cam. Phil. Soc._ FEB. 5, 1844.)

1. All persons who have attended in any degree to the views generally

current of the nature of reasoning are familiar with the distinction

of _necessary_ truths and _truths of experience_; and few such

persons, or at least few students of mathematics, require to have this

distinction explained or enforced. All geometricians are satisfied that

the geometrical truths with which they are conversant are necessarily

true: they not only are true, but they must be true. The meaning of the

terms being understood, and the proof being gone through, the truth

of the proposition must be assented to. That parallelograms upon the

same base and between the same parallels are equal;--that angles in the

same segment are equal;--these are propositions which we learn to be

true by demonstrations deduced from definitions and axioms; and which,

when we have thus learnt them, we see could not be otherwise. On the

other hand, there are other truths which we learn from experience;

as for instance, that the stars revolve round the pole in one day;

and that the moon goes through her phases from full to full again in

thirty days. These truths we see to be true; but we know them only

by experience. Men never could have discovered them without looking

at the stars and the moon; and having so learnt them, still no one

will pretend to say that they are necessarily true. For aught we can

see, things might have been otherwise; and if we had been placed in

another part of the solar system, then, according to the opinions of

astronomers, experience would have presented them otherwise.

2. I take the astronomical truths of experience to contrast with the

geometrical necessary truths, as being both of a familiar definite

sort; we may easily find other examples of both kinds of truth. The

truths which regard numbers are necessary truths. It is a necessary

truth, that 27 and 38 are equal to 65; that half the sum of two

numbers added to half their difference is equal to the greater

number. On the other hand, that sugar will dissolve in water; that

plants cannot live without light; and in short, the whole body of our

knowledge in chemistry, physiology, and the other inductive sciences,

consists of truths of experience. If there be any science which offer

to us truths of an ambiguous kind, with regard to which we may for a

moment doubt whether they are necessary or experiential, we will defer

the consideration of them till we have marked the distinction of the

two kinds more clearly.

3. One mode in which we may express the difference of necessary truths

and truths of experience, is, that necessary truths are those _of

which we cannot distinctly conceive the contrary_. We can very readily

conceive the contrary of experiential truths. We can conceive the stars

moving about the pole or across the sky in any kind of curves with any

velocities; we can conceive the moon always appearing during the whole

month as a luminous disk, as she might do if her light were inherent

and not borrowed. But we cannot conceive one of the parallelograms on

the same base and between the same parallels larger than the other;

for we find that, if we attempt to do this, when we separate the

parallelograms into parts, we have to conceive one triangle larger

than another, both having all their parts equal; which we cannot

conceive at all, if we conceive the triangles distinctly. We make this

impossibility more clear by conceiving the triangles to be placed so

that two sides of the one coincide with two sides of the other; and it

is then seen, that in order to conceive the triangles unequal, we must

conceive the two bases which have the same extremities both ways, to

be different lines, though both straight lines. This it is impossible

to conceive: we assent to the impossibility as an axiom, when it is

expressed by saying, that two straight lines cannot inclose a space;

and thus we cannot distinctly conceive the contrary of the proposition

just mentioned respecting parallelograms.

4. But it is necessary, in applying this distinction, to bear in mind

the terms of it;--that we cannot _distinctly_ conceive the contrary

of a necessary truth. For in a certain loose, indistinct way, persons

conceive the contrary of necessary geometrical truths, when they

erroneously conceive false propositions to be true. Thus, Hobbes

erroneously held that he had discovered a means of geometrically

doubling the cube, as it is called, that is, finding two mean

proportionals between two given lines; a problem which cannot be solved

by plane geometry. Hobbes not only proposed a construction for this

purpose, but obstinately maintained that it was right, when it had

been proved to be wrong. But then, the discussion showed how indistinct

the geometrical conceptions of Hobbes were; for when his critics had

proved that one of the lines in his diagram would not meet the other

in the point which his reasoning supposed, but in another point near

to it; he maintained, in reply, that one of these points was large

enough to include the other, so that they might be considered as the

same point. Such a mode of conceiving the opposite of a geometrical

truth, forms no exception to the assertion, that this opposite cannot

be distinctly conceived.

5. In like manner, the indistinct conceptions of children and of rude

savages do not invalidate the distinction of necessary and experiential

truths. Children and savages make mistakes even with regard to numbers;

and might easily happen to assert that 27 and 38 are equal to 63 or

64. But such mistakes cannot make such arithmetical truths cease to be

necessary truths. When any person conceives these numbers and their

addition distinctly, by resolving them into parts, or in any other way,

he sees that their sum is necessarily 65. If, on the ground of the

possibility of children and savages conceiving something different, it

be held that this is not a necessary truth, it must be held on the same

ground, that it is not a necessary truth that 7 and 4 are equal to 11;

for children and savages might be found so unfamiliar with numbers as

not to reject the assertion that 7 and 4 are 10, or even that 4 and 3

are 6, or 8. But I suppose that no persons would on such grounds hold

that these arithmetical truths are truths known only by experience.

6. Necessary truths are established, as has already been said, by

demonstration, proceeding from definitions and axioms, according to

exact and rigorous inferences of reason. Truths of experience are

collected from what we see, also according to inferences of reason,

but proceeding in a less exact and rigorous mode of proof. The former

depend upon the relations of the ideas which we have in our minds:

the latter depend upon the appearances or phenomena, which present

themselves to our senses. Necessary truths are formed from our

thoughts, the elements of the world within us; experiential truths are

collected from things, the elements of the world without us. The truths

of experience, as they appear to us in the external world, we call

Facts; and when we are able to find among our ideas a train which will

conform themselves to the apparent facts, we call this a Theory.

7. This distinction and opposition, thus expressed in various forms;

as Necessary and Experiential Truth, Ideas and Senses, Thoughts and

Things, Theory and Fact, may be termed the _Fundamental Antithesis

of Philosophy_; for almost all the discussions of philosophers have

been employed in asserting or denying, explaining or obscuring this

antithesis. It may be expressed in many other ways; but is not

difficult, under all these different forms, to recognize the same

opposition: and the same remarks apply to it under its various forms,

with corresponding modifications. Thus, as we have already seen, the

antithesis agrees with that of Reasoning and Observation: again, it

is identical with the opposition of Reflection and Sensation: again,

sensation deals with Objects; facts involve Objects, and generally all

things without us are Objects:--Objects of sensation, of observation.

On the other hand, we ourselves who thus observe objects, and in whom

sensation is, may be called the Subjects of sensation and observation.

And this distinction of Subject and Object is one of the most general

ways of expressing the fundamental antithesis, although not yet perhaps

quite familiar in English. I shall not scruple however to speak of

the Subjective and Objective element of this antithesis, where the

expressions are convenient.

8. All these forms of antithesis, and the familiar references to them

which men make in all discussions, show the fundamental and necessary

character of the antithesis. We can have no knowledge without the

union, no philosophy without the separation, of the two elements. We

can have no knowledge, except we have both impressions on our senses

from the world without, and thoughts from our minds within:--except we

attend to things, and to our ideas;--except we are passive to receive

impressions, and active to compare, combine, and mould them. But on

the other hand, philosophy seeks to distinguish the impressions of our

senses from the thoughts of our minds;--to point out the difference of

ideas and things;--to separate the active from the passive faculties

of our being. The two elements, sensations and ideas, are both

requisite to the existence of our knowledge, as both matter and form

are requisite to the existence of a body. But philosophy considers the

matter and the form separately. The properties of the form are the

subject of geometry, the properties of the matter are the subject of

chemistry or mechanics.

9. But though philosophy considers these elements of knowledge

separately, they cannot really be separated, any more than can matter

and form. "We cannot exhibit matter without form, or form without

matter; and just as little can we exhibit sensations without ideas, or

ideas without sensations;--the passive or the active faculties of the

mind detached from each other.