Let us not forget that, in assigning the actors then born to their

places, we are not narrating history, but studying a special phase of

evolution. It matters not for us that no university invited Leonardo to

its halls, and that his science was valued by his contemporaries only as

an adjunct to the art of engineering. The great fact still is that he

was the first of mankind to propound laws of motion. It is not for

anything in Luther's doctrines that he finds a place in our scheme. No

matter for us whether they were sound or not. What he did toward the

evolution of the scientific investigator was to show by his example that

a man might question the best-established and most venerable authority

and still live--still preserve his intellectual integrity--still command

a hearing from nations and their rulers. It matters not for us whether

Columbus ever knew that he had discovered a new continent. His work was

to teach that neither hydra, chimera, nor abyss--neither divine

injunction nor infernal machination--was in the way of men visiting

every part of the globe, and that the problem of conquering the world

reduced itself to one of sails and rigging, hull and compass. The better

part of Copernicus was to direct man to a viewpoint whence he should see

that the heavens were of like matter with the earth. All this done, the

acorn was planted from which the oak of our civilization should spring.

The mad quest for gold which followed the discovery of Columbus, the

questionings which absorbed the attention of the learned, the

indignation excited by the seeming vagaries of a Paracelsus, the fear

and trembling lest the strange doctrine of Copernicus should undermine

the faith of centuries, were all helps to the germination of the

seed--stimuli to thought which urged it on to explore the new fields

opened up to its occupation. This given, all that has since followed

came out in regular order of development, and need be here considered

only in those phases having a special relation to the purpose of our

present meeting.

So slow was the growth at first that the sixteenth century may scarcely

have recognized the inauguration of a new era. Torricelli and Benedetti

were of the third generation after Leonardo, and Galileo, the first to

make a substantial advance upon his theory, was born more than a century

after him. Only two or three men appeared in a generation who, working

alone, could make real progress in discovery, and even these could do

little in leavening the minds of their fellow men with the new ideas.

Up to the middle of the seventeenth century an agent which all

experience since that time shows to be necessary to the most productive

intellectual activity was wanting. This was the attraction of like

minds, making suggestions to each other, criticising, comparing, and

reasoning. This element was introduced by the organization of the Royal

Society of London and the Academy of Sciences of Paris.

The members of these two bodies seem like ingenious youth suddenly

thrown into a new world of interesting objects, the purposes and

relations of which they had to discover. The novelty of the situation is

strikingly shown in the questions which occupied the minds of the

incipient investigators. One natural result of British maritime

enterprise was that the aspirations of the Fellows of the Royal Society

were not confined to any continent or hemisphere. Inquiries were sent

all the way to Batavia to know "whether there be a hill in Sumatra which

burneth continually, and a fountain which runneth pure balsam." The

astronomical precision with which it seemed possible that physiological

operations might go on was evinced by the inquiry whether the Indians

can so prepare that stupefying herb Datura that "they make it lie

several days, months, years, according as they will, in a man's body

without doing him any harm, and at the end kill him without missing an

hour's time." Of this continent one of the inquiries was whether there

be a tree in Mexico that yields water, wine, vinegar, milk, honey, wax,

thread, and needles.

Among the problems before the Paris Academy of Sciences those of

physiology and biology took a prominent place. The distillation of

compounds had long been practiced, and the fact that the more spirituous

elements of certain substances were thus separated naturally led to the

question whether the essential essences of life might not be

discoverable in the same way. In order that all might participate in the

experiments, they were conducted in open session of the Academy, thus

guarding against the danger of any one member obtaining for his

exclusive personal use a possible elixir of life. A wide range of the

animal and vegetable kingdom, including cats, dogs, and birds of various

species, were thus analyzed. The practice of dissection was introduced

on a large scale. That of the cadaver of an elephant occupied several

sessions, and was of such interest that the monarch himself was a

spectator.

To the same epoch with the formation and first work of these two bodies

belongs the invention of a mathematical method which in its importance

to the advance of exact science may be classed with the invention of the

alphabet in its relation to the progress of society at large. The use of

algebraic symbols to represent quantities had its origin before the

commencement of the new era, and gradually grew into a highly developed

form during the first two centuries of that era. But this method could

represent quantities only as fixed. It is true that the elasticity

inherent in the use of such symbols permitted of their being applied to

any and every quantity; yet, in any one application, the quantity was

considered as fixed and definite. But most of the magnitudes of nature

are in a state of continual variation; indeed, since all motion is

variation, the latter is a universal characteristic of all phenomena. No

serious advance could be made in the application of algebraic language

to the expression of physical phenomena until it could be so extended as

to express variation in quantities, as well as the quantities

themselves. This extension, worked out independently by Newton and

Leibnitz, may be classed as the most fruitful of conceptions in exact

science. With it the way was opened for the unimpeded and continually

accelerated progress of the last two centuries.

The feature of this period which has the closest relation to the purpose

of our coming together is the seemingly unending subdivision of

knowledge into specialties, many of which are becoming so minute and so

isolated that they seem to have no interest for any but their few

pursuers. Happily science itself has afforded a corrective for its own

tendency in this direction. The careful thinker will see that in these

seemingly diverging branches common elements and common principles are

coming more and more to light. There is an increasing recognition of

methods of research, and of deduction, which are common to large

branches, or to the whole of science. We are more and more recognizing

the principle that progress in knowledge implies its reduction to more

exact forms, and the expression of its ideas in language more or less

mathematical. The problem before the organizers of this Congress was,

therefore, to bring the sciences together, and seek for the unity which

we believe underlies their infinite diversity.

The assembling of such a body as now fills this hall was scarcely

possible in any preceding generation, and is made possible now only

through the agency of science itself. It differs from all preceding

international meetings by the universality of its scope, which aims to

include the whole of knowledge. It is also unique in that none but

leaders have been sought out as members. It is unique in that so many

lands have delegated their choicest intellects to carry on its work.

They come from the country to which our republic is indebted for a third

of its territory, including the ground on which we stand; from the land

which has taught us that the most scholarly devotion to the languages

and learning of the cloistered past is compatible with leadership in the

practical application of modern science to the arts of life; from the

island whose language and literature have found a new field and a

vigorous growth in this region; from the last seat of the holy Roman

Empire; from the country which, remembering a monarch who made an

astronomical observation at the Greenwich Observatory, has enthroned

science in one of the highest places in its government; from the

peninsula so learned that we have invited one of its scholars to come

and tell us of our own language; from the land which gave birth to

Leonardo, Galileo, Torricelli, Columbus, Volta--what an array of

immortal names!--from the little republic of glorious history which,

breeding men rugged as its eternal snow-peaks, has yet been the seat of

scientific investigation since the day of the Bernoullis; from the land

whose heroic dwellers did not hesitate to use the ocean itself to

protect it against invaders, and which now makes us marvel at the amount

of erudition compressed within its little area; from the nation across

the Pacific, which, by half a century of unequaled progress in the arts

of life, has made an important contribution to evolutionary science

through demonstrating the falsity of the theory that the most ancient

races are doomed to be left in the rear of the advancing age--in a word,

from every great centre of intellectual activity on the globe I see

before me eminent representatives of that world-advance in knowledge

which we have met to celebrate. May we not confidently hope that the

discussions of such an assemblage will prove pregnant of a future for

science which shall outshine even its brilliant past?

Gentlemen and scholars all! You do not visit our shores to find great

collections in which centuries of humanity have given expression on

canvas and in marble to their hopes, fears, and aspirations. Nor do you

expect institutions and buildings hoary with age. But as you feel the

vigor latent in the fresh air of these expansive prairies, which has

collected the products of human genius by which we are here surrounded,

and, I may add, brought us together; as you study the institutions which

we have founded for the benefit, not only of our own people, but of

humanity at large; as you meet the men who, in the short space of one

century, have transformed this valley from a savage wilderness into what

it is to-day--then may you find compensation for the want of a past like

yours by seeing with prophetic eye a future world-power of which this

region shall be the seat. If such is to be the outcome of the

institutions which we are now building up, then may your present visit

be a blessing both to your posterity and ours by making that power one

for good to all mankind. Your deliberations will help to demonstrate to

us and to the world at large that the reign of law must supplant that of

brute force in the relations of the nations, just as it has supplanted

it in the relations of individuals. You will help to show that the war

which science is now waging against the sources of diseases, pain, and

misery offers an even nobler field for the exercise of heroic qualities

than can that of battle. We hope that when, after your all too fleeting

sojourn in our midst, you return to your own shores, you will long feel

the influence of the new air you have breathed in an infusion of

increased vigor in pursuing your varied labors. And if a new impetus is

thus given to the great intellectual movement of the past century,

resulting not only in promoting the unification of knowledge, but in

widening its field through new combinations of effort on the part of its

votaries, the projectors, organizers, and supporters of this Congress of

Arts and Science will be justified of their labors.

DIVISION A--NORMATIVE SCIENCE

DIVISION A--NORMATIVE SCIENCE

SPEAKER: PROFESSOR JOSIAH ROYCE, Harvard University

(_Hall 6, September 20, 10 a. m._)

THE SCIENCES OF THE IDEAL

BY JOSIAH ROYCE

[Josiah Royce, Professor of History of Philosophy, Harvard

University, since 1892. b. Grass Valley, Nevada County,

California, November 20, 1855. A.B. University of

California, 1875; Ph.D. Johns Hopkins 1878; LL.D. University

of Aberdeen, Scotland; LL.D. Johns Hopkins. Instructor in

English Literature and Logic, University of California,

1878-82. Instructor and Assistant Professor, Harvard

University, 1882-92. Author of _Religious Aspect of

Philosophy_; _History of California_; _The Feud of Oakfield

Creek_; _The Spirit of Modern Philosophy_; _Studies of Good

and Evil_; _The World and the Individual_; _Gifford

Lectures_; and numerous other works and memoirs.]

I shall not attempt, in this address, either to justify or to criticise

the name, normative science, under which the doctrines which constitute

this division are grouped. It is enough for my purpose to recognize at

the outset that I am required, by the plans of this Congress, to explain

what scientific interests seem to me to be common to the work of the

philosophers and of the mathematicians. The task is one which makes

severe demands upon the indulgence of the listener, and upon the

expository powers of the speaker, but it is a task for which the present

age has well prepared the way. The spirit which Descartes and Leibnitz

illustrated seems likely soon to become, in a new and higher sense,

prominent in science. The mathematicians are becoming more and more

philosophical. The philosophers, in the near future, will become, I

believe, more and more mathematical. It is my office to indicate, as

well as the brief time and my poor powers may permit, why this ought to

be so.

To this end I shall first point out what is that most general community

of interest which unites all the sciences that belong to our division.

Then I shall indicate what type of recent and special scientific work

most obviously bears upon the tasks of all of us alike. Thirdly, I shall

state some results and problems to which this type of scientific work

has given rise, and shall try to show what promise we have of an early

increase of insight regarding our common interests.

I

The most general community of interest which unites the various

scientific activities that belong to our division is this: We are all

concerned with what may be called ideal truth, as distinct from physical

truth. Some of us also have a strong interest in physical truth; but

none of us lack a notable and scientific concern for the realm of ideas,

viewed as ideas.

Let me explain what I mean by these terms. Whoever studies physical

truth (taking that term in its most general sense) seeks to observe, to

collate, and, in the end, to control, facts which he regards as external

to his own thought. But instead of thus looking mainly without, it is

possible for a man chiefly to take account, let us say, of the

consequences of his own hypothetical assumptions--assumptions which may

possess but a very remote relation to the physical world. Or again, it

is possible for such a student to be mainly devoted to reflecting upon

the formal validity of his own inferences, or upon the meaning of his

own presuppositions, or upon the value and the interrelation of human

ideals. Any such scientific work, reflective, considerate principally of

the thinker's own constructions and purposes, or of the constructions

and purposes of humanity in general, is a pursuit of ideal truth. The

searcher who is mainly devoted to the inquiry into what he regards as

external facts, is indeed active; but his activity is moulded by an

order of existence which he conceives as complete apart from his

activity. He is thoughtful; but a power not himself assigns to him the

problems about which he thinks. He is guided by ideals; but his

principal ideal takes the form of an acceptance of the world as it is,

independently of his ideals. His dealings are with nature. His aim is

the conquest of a foreign realm. But the student of what may be called,

in general terms, ideal truth, while he is devoted as his fellow, the

observer of outer nature, to the general purpose of being faithful to

the verity as he finds it, is still aware that his own way of finding,

or his own creative activity as an inventor of hypotheses, or his own

powers of inference, or his conscious ideals, constitute in the main the

object into which he is inquiring, and so form an essential aspect of

the sort of verity which he is endeavoring to discover. The guide, then,

of such a student is, in a peculiar sense, his own reason. His goal is

the comprehension of his own meaning, the conscious and thoughtful

conquest of himself. His great enemy is not the mystery of outer nature,

but the imperfection of his reflective powers. He is, indeed, as

unwilling as is any scientific worker to trust private caprices. He

feels as little as does the observer of outer facts, that he is merely

noting down, as they pass, the chance products of his arbitrary fantasy.

For him, as for any scientific student, truth is indeed objective; and

the standards to which he conforms are eternal. But his method is that

of an inner considerateness rather than of a curiosity about external

phenomena. His objective world is at the same time an essentially ideal

world, and the eternal verity in whose light he seeks to live has,

throughout his undertakings, a peculiarly intimate relation to the

purposes of his own constructive will.

One may then sum up the difference of attitude which is here in question

by saying that, while the student of outer nature is explicitly

conforming his plans of action, his ideas, his ideals, to an order of

truth which he takes to be foreign to himself--the student of the other

sort of truth, here especially in question, is attempting to understand

his own plans of action, that is, to develop his ideas, or to define his

ideals, or else to do both these things.

Now it is not hard to see that this search for some sort of ideal truth

is indeed characteristic of every one of the investigations which have

been grouped together in our division of the normative sciences. Pure

mathematics shares in common with philosophy this type of scientific

interest in ideal, as distinct from physical or phenomenal truth. There

is, to be sure, a marked contrast between the ways in which the

mathematician and the philosopher approach, select, and elaborate their

respective sorts of problems. But there is also a close relation between

the two types of investigation in question. Let us next consider both

the contrast and the analogy in some of their other most general

features.

Pure mathematics is concerned with the investigation of the logical

consequences of certain exactly stateable postulates or

hypotheses--such, for instance, as the postulates upon which arithmetic

and analysis are founded, or such as the postulates that lie at the

basis of any type of geometry. For the pure mathematician, the truth of

these hypotheses or postulates depends, not upon the fact that physical

nature contains phenomena answering to the postulates, but solely upon

the fact that the mathematician is able, with rational consistency, to

state these assumed first principles, and to develop their consequences.

Dedekind, in his famous essay, "Was Sind und Was Sollen die Zahlen,"

called the whole numbers "freie Schöpfungen des Menschlichen Geistes;"

and, in fact, we need not enter into any discussion of the psychology of

our number concept in order to be able to assert that, however we men

first came by our conception of the whole numbers, for the mathematician

the theory of numerical truth must appear simply as the logical

development of the consequences of a few fundamental first principles,

such as those which Dedekind himself, or Peano, or other recent writers

upon this topic, have, in various forms, stated. A similar formal

freedom marks the development of any other theory in the realm of pure

mathematics. Pure geometry, from the modern point of view, is neither a

doctrine forced upon the human mind by the constitution of any primal

form of intuition, nor yet a branch of physical science, limited to

describing the spatial arrangement of phenomena in the external world.

Pure geometry is the theory of the consequences of certain postulates

which the geometer is at liberty consistently to make; so that there are

as many types of geometry as there are consistent systems of postulates

of that generic type of which the geometer takes account. As is also now

well known, it has long been impossible to define pure mathematics as

the science of quantity, or to limit the range of the exactly stateable

hypotheses or postulates with which the mathematician deals to the world

of those objects which, ideally speaking, can be viewed as measurable.

For the ideally defined measurable objects are by no means the only ones

whose properties can be stated in the form of exact postulates or

hypotheses; and the possible range of pure mathematics, if taken in the

abstract, and viewed apart from any question as to the value of given

lines of research, appears to be identical with the whole realm of the

consequences of exactly stateable ideal hypotheses of every type.

One limitation must, however, be mentioned, to which the assertion just

made is, in practice, obviously subject. And this is, indeed, a

momentous limitation. The exactly stated ideal hypotheses whose

consequences the mathematician develops must possess, as is sometimes

said, sufficient intrinsic importance to be worthy of scientific

treatment. They must not be trivial hypotheses. The mathematician is

not, like the solver of chess problems, merely displaying his skill in

dealing with the arbitrary fictions of an ideal game. His truth is,

indeed, ideal; his world is, indeed, treated by his science as if this

world were the creation of his postulates a "freie Schöpfung." But he

does not thus create for mere sport. On the contrary, he reports a

significant order of truth. As a fact, the ideal systems of the pure

mathematician are customarily defined with an obvious, even though often

highly abstract and remote, relation to the structure of our ordinary

empirical world. Thus the various algebras which have been actually

developed have, in the main, definite relations to the structure of the

space world of our physical experience. The different systems of ideal

geometry, even in all their ideality, still cluster, so to speak, about

the suggestions which our daily experience of space and of matter give

us. Yet I suppose that no mathematician would be disposed, at the

present time, to accept any brief definition of the degree of closeness

or remoteness of relation to ordinary experience which shall serve to

distinguish a trivial from a genuinely significant branch of

mathematical theory. In general, a mathematician who is devoted to the

theory of functions, or to group theory, appears to spend little time in

attempting to show why the development of the consequences of his

postulates is a significant enterprise. The concrete mathematical

interest of his inquiry sustains him in his labors, and wins for him the

sympathy of his fellows. To the questions, "Why consider the ideal

structure of just this system of object at all?" "Why study various

sorts of numbers, or the properties of functions, or of groups, or the

system of points in projective geometry?"--the pure mathematician in

general, cares to reply only, that the topic of his special

investigation appears to him to possess sufficient mathematical

interest. The freedom of his science thus justifies his enterprise. Yet,

as I just pointed out, this freedom is never mere caprice. This ideal

interest is not without a general relation to the concerns even of

common sense. In brief, as it seems at once fair to say, the pure

mathematician is working under the influence of more or less clearly

conscious philosophical motives. He does not usually attempt to define

what distinguishes a significant from a trivial system of postulates, or

what constitutes a problem worth attacking from the point of view of

pure mathematics. But he practically recognizes such a distinction

between the trivial and the significant regions of the world of ideal

truth, and since philosophy is concerned with the significance of ideas,

this recognition brings the mathematician near in spirit to the

philosopher.

Such, then, is the position of the pure mathematician. What, by way of

contrast, is that of the philosopher? We may reply that to state the

formal consequences of exact assumptions is one thing; to reflect upon

the mutual relations, and the whole significance of such assumptions,

does indeed involve other interests; and these other interests are the

ones which directly carry us over to the realm of philosophy. If the

theory of numbers belongs to pure mathematics, the study of the place of

the number concept in the system of human ideas belongs to philosophy.

Like the mathematician, the philosopher deals directly with a realm of

ideal truth. But to unify our knowledge, to comprehend its sources, its

meaning, and its relations to the whole of human life, these aims

constitute the proper goal of the philosopher. In order, however, to

accomplish his aims, the philosopher must, indeed, take account of the

results of the special physical science; but he must also turn from the

world of outer phenomena to an ideal world. For the unity of things is

never, for us mortals, anything that we find given in our experience.

You cannot see the unity of knowledge; you cannot describe it as a

phenomenon. It is for us now, an ideal. And precisely so, the meaning of

things, the relation of knowledge to life, the significance of our

ideals, their bearing upon one another--these are never, for us men,

phenomenally present data. Hence the philosopher, however much he ought,

as indeed he ought, to take account of phenomena, and of the results of

the special physical sciences, is quite as deeply interested in his own

way, as the mathematician is interested in his way, in the consideration

of an ideal realm. Only, unlike the mathematician, the philosopher does

not first abstract from the empirical suggestions upon which his exact

ideas are actually based, and then content himself merely with

developing the logical consequences of these ideas. On the contrary, his

main interest is not in any idea or fact in so far as it is viewed by

itself, but rather in the interrelations, in the common significance, in

the unity, of all fundamental ideas, and in their relations both to the

phenomenal facts and to life! On the whole, he, therefore, neither

consents, like the student of a special science of experience, to seek

his freedom solely through conformity to the phenomena which are to be

described; nor is he content, like the pure mathematician, to win his

truth solely through the exact definition of the formal consequences of

his freely defined hypotheses. He is making an effort to discover the

sense and the unity of the business of his own life.

It is no part of my purpose to attempt to show here how this general

philosophical interest differentiates into the various interests of

metaphysics, of the philosophy of religion, of ethics, of æsthetics, of

logic. Enough--I have tried to illustrate how, while both the

philosopher and the mathematician have an interest in the meaning of

ideas rather than in the description of external facts, still there is a

contrast which does, indeed, keep their work in large measure asunder,

namely, the contrast due to the fact that the mathematician is directly

concerned with developing the consequences of certain freely assumed

systems of postulates or hypotheses; while the philosopher is interested

in the significance, in the unity, and in the relation to life, of all

the fundamental ideals and postulates of the human mind.

Yet not even thus do we sufficiently state how closely related the two

tasks are. For this very contrast, as we have also suggested, is, even

within its own limits, no final or perfectly sharp contrast. There is a

deep analogy between the two tasks. For the mathematician, as we have

just seen, is not evenly interested in developing the consequences of

any and every system of freely assumed postulates. He is no mere solver

of arbitrary ideal puzzles in general. His systems of postulates are so

chosen as to be not trivial, but significant. They are, therefore, in

fact, but abstractly defined aspects of the very system of eternal truth

whose expression is the universe. In this sense the mathematician is as

genuinely interested as is the philosopher in the significant use of his

scientific freedom. On the other hand, the philosopher, in reflecting

upon the significance and the unity of fundamental ideas, can only do so

with success in case he makes due inquiry into the logical consequences

of given ideas. And this he can accomplish only if, upon occasion, he

employs the exact methods of the mathematician, and develops his systems

of ideal truth with the precision of which only mathematical research is

capable. As a fact, then, the mathematician and the philosopher deal

with ideal truth in ways which are not only contrasted, but profoundly

interconnected. The mathematician, in so far as he consciously

distinguishes significant from trivial problems, and ideal systems, is a

philosopher. The philosopher, in so far as he seeks exactness of logical

method, in his reflection, must meanwhile aim to be, within his own

limits, a mathematician. He, indeed, will not in future, like Spinoza,

seek to reduce philosophy to the mere development, in mathematical form,

of the consequences of certain arbitrary hypotheses. He will distinguish

between a reflection upon the unity of the system of truth and an

abstract development of this or that selected aspect of the system. But

he will see more and more that, in so far as he undertakes to be exact,

he must aim to become, in his own way, and with due regard to his own

purposes, mathematical; and thus the union of mathematical and

philosophical inquiries, in the future, will tend to become closer and

closer.

II

So far, then, I have dwelt upon extremely general considerations

relating to the unity and the contrast of mathematical and philosophical

inquiries. I can well conceive, however, that the individual worker in

any one of the numerous branches of investigation which are represented

by the body of students whom I am privileged to address, may at this

point mentally interpose the objection that all these considerations

are, indeed, far too general to be of practical interest to any of us.

Of course, all we who study these so-called normative sciences are,

indeed, interested in ideas, for their own sakes--in ideas so distinct

from, although of course also somehow related to, phenomena. Of course,

some of us are rather devoted to the development of the consequences of

exactly stated ideal hypotheses, and others to reflecting as we can upon

what certain ideas and ideals are good for, and upon what the unity is

of all ideas and ideals. Of course, if we are wise enough to do so, we

have much to learn from one another. But, you will say, the assertion of

all these things is a commonplace. The expression of the desire for

further mutual coöperation is a pious wish. You will insist upon asking

further: "Is there just now any concrete instance in a modern type of

research which furnishes results such as are of interest to all of us?

Are we actually doing any productive work in common? Are the

philosophers contributing anything to human knowledge which has a

genuine bearing upon the interests of mathematical science? Are the

mathematicians contributing anything to philosophy?"

These questions are perfectly fair. Moreover, as it happens, they can be

distinctly answered in the affirmative. The present age is one of a

rapid advance in the actual unification of the fields of investigation

which are included within the scope of this present division. What

little time remains to me must be devoted to indicating, as well as I

can, in what sense this is true. I shall have still to deal in very

broad generalities. I shall try to make these generalities definite

enough to be not wholly unfruitful.

We have already emphasized one question which may be said to interest,

in a very direct way, both the mathematician and the philosopher. The

ideal postulates, whose consequences mathematical science undertakes to

develop, must be, we have said, significant postulates, involving ideas

whose exact definition and exposition repay the labor of scientific

scrutiny. Number, space, continuity, functional correspondence or

dependence, group-structure--these are examples of such significant

ideas; the postulates or ideal assumptions upon which the theory of such

ideas depends are significant postulates, and are not the mere

conventions of an arbitrary game. But now what constitutes the

significance of an idea, or of an abstract mathematical theory? What

gives an idea a worthy place in the whole scheme of human ideas? Is it

the possibility of finding a physical application for a mathematical

theory which for us decides what is the value of the theory? No, the

theory of functions, the theory of numbers, group theory, have a

significance which no mathematician would consent to measure in terms of

the present applicability or non-applicability of these theories in

physical science? In vain, then, does one attempt to use the test of

applied mathematics as the main criticism of the value of a theory of

pure mathematics. The value of an idea, for the sciences which

constitute our division, is dependent upon the place which this idea

occupies in the whole organized scheme or system of human ideas. The

idea of number, for instance, familiar as its applications are, does not

derive its main value from the fact that eggs and dollars and

star-clusters can be counted, but rather from the fact that the idea of

numbers has those relations to other fundamental ideas which recent

logical theory has made prominent--relations, for instance, to the

concept of order, to the theory of classes or collections of objects

viewed in general, and to the metaphysical concept of the self.

Relations of this sort, which the discussions of the number concept by

Dedekind, Cantor, Peano, and Russell have recently brought to

light--such relations, I say, constitute what truly justified Gauss in

calling the theory of numbers a "divine science." As against such deeper

relations, the countless applications of the number concept in ordinary

life, and in science, are, from the truly philosophical point of view,

of comparatively small moment. What we want, in the work of our division

of the sciences, is to bring to light the unity of truth, either, as in

mathematics, by developing systems of truth which are significant by

virtue of their actual relations to this unity, or, as in philosophy, by

explicitly seeking the central idea about which all the many ideas

cluster.

Now, an ancient and fundamental problem for the philosophers is that

which has been called the problem of the categories. This problem of the

categories is simply the more formal aspect of the whole philosophical

problem just defined. The philosopher aims to comprehend the unity of

the system of human ideas and ideals. Well, then, what are the primal

ideas? Upon what group of concepts do the other concepts of human

science logically depend? About what central interests is the system of

human ideals clustered? In ancient thought Aristotle already approached

this problem in one way. Kant, in the eighteenth century, dealt with it

in another. We students of philosophy are accustomed to regret what we

call the excessive formalism of Kant, to lament that Kant was so much

the slave of his own relatively superficial and accidental table of

categories, and that he made the treatment of every sort of

philosophical problem turn upon his own schematism. Yet we cannot doubt

that Kant was right in maintaining that philosophy needs, for the

successful development of every one of its departments, a well-devised

and substantially complete system of categories. Our objection to Kant's

over-confidence in the virtues of his own schematism is due to the fact

that we do not now accept his table of categories as an adequate view of

the fundamental concepts. The efforts of philosophers since Kant have

been repeatedly devoted to the task of replacing his scheme of

categories by a more adequate one. I am far from regarding these purely

philosophical efforts made since Kant as fruitless, but they have

remained, so far, very incomplete, and they have been held back from

their due fullness of success by the lack of a sufficiently careful

survey and analysis of the processes of thought as these have come to be

embodied in the living sciences. Such concepts as number, quantity,

space, time, cause, continuity, have been dealt with by the pure

philosophers far too summarily and superficially. A more thoroughgoing

analysis has been needed. But now, in comparatively recent times, there

has developed a region of inquiry which one may call by the general name

of modern logic. To the constitution of this new region of inquiry men

have principally contributed who began as mathematicians, but who, in

the course of their work, have been led to become more and more

philosophers. Of late, however, various philosophers, who were

originally in no sense mathematicians, becoming aware of the importance

of the new type of research, are in their turn attempting both to

assimilate and to supplement the undertakings which were begun from the

mathematical side. As a result, the logical problem of the categories

has to-day become almost equally a problem for the logicians of

mathematics and for those students of philosophy who take any serious

interest in exactness of method in their own branch of work. The result

of this actual coöperation of men from both sides is that, as I think,

we are to-day, for the first time, in sight of what is still, as I

freely admit, a somewhat distant goal, namely, the relatively complete

rational analysis and tabulation of the fundamental categories of human

thought. That the student of ethics is as much interested in such an

investigation as is the metaphysician, that the philosopher of religion

needs a well-completed table of categories quite as much as does the

pure logician, every competent student of such topics ought to admit.

And that the enterprise in question keenly interests the mathematicians

is shown by the prominent part which some of them have taken in the

researches in question. Here, then, is the type of recent scientific

work whose results most obviously bear upon the tasks of all of us

alike.

A catalogue of the names of the workers in this wide field of modern

logic would be out of place here. Yet one must, indeed, indicate what

lines of research are especially in question. From the purely

mathematical side, the investigations of the type to which I now refer

may be viewed (somewhat arbitrarily) as beginning with that famous

examination into one of the postulates of Euclid's geometry which gave

rise to the so-called non-Euclidean geometry. The question here

originally at issue was one of a comparatively limited scope, namely,

the question whether Euclid's parallel-line postulate was a logical

consequence of the other geometrical principles. But the investigation

rapidly develops into a general study of the foundations of geometry--a

study to which contributions are still almost constantly appearing.

Somewhat independently of this line of inquiry there grew up, during the

latter half of the nineteenth century, that reëxamination of the bases

of arithmetic and analysis which is associated with the names of

Dedekind, Weierstrass, and George Cantor. At the present time, the

labors of a number of other inquirers (amongst whom we may mention the

school of Peano and Pieri in Italy, and men such as Poincaré and

Couturat in France, Hilbert in Germany, Bertrand Russell and Whitehead

in England, and an energetic group of our American mathematicians--men

such as Professor Moore, Professor Halsted, Dr. Huntington, Dr. Veblen,

and a considerable number of others) have been added to the earlier

researches. The result is that we have recently come for the first time

to be able to see, with some completeness, what the assumed first

principles of pure mathematics actually are. As was to be expected,

these principles are capable of more than one formulation, according as

they are approached from one side or from another. As was also to be

expected, the entire edifice of pure mathematics, so far as it has yet

been erected, actually rests upon a very few fundamental concepts and

postulates, however you may formulate them. What was not observed,

however, by the earlier, and especially by the philosophical, students

of the categories, is the form which these postulates tend to assume

when they are rigidly analyzed.

This form depends upon the precise definition and classification of

certain types of relations. The whole of geometry, for instance,

including metrical geometry, can be developed from a set of postulates

which demand the existence of points that stand in certain ordinal

relationships. The ordinal relationships can be reduced, according as

the series of points considered is open or closed, either to the

well-known relationship in which three points stand when one is between

the other two upon a right line, or else to the ordinal relationship in

which four points stand when they are separated by pairs; and these two

ordinal relationships, by means of various logical devices, can be

regarded as variations of a single fundamental form. Cayley and Klein

founded the logical theory of geometry here in question. Russell, and in

another way Dr. Veblen, have given it its most recent expressions. In

the same way, the theory of whole numbers can be reduced to sets of

principles which demand the existence of certain ideal objects in

certain simple ordinal relations. Dedekind and Peano have worked out

such ordinal theories of the number concept. In another development of

the theory of the cardinal whole numbers, which Russell and Whitehead

have worked out, ordinal concepts are introduced only secondarily, and

the theory depends upon the fundamental relation of the equivalence or

nonequivalence of collections of objects. But here also a certain simple

type of relation determines the definitions and the development of the

whole theory.

Two results follow from such a fashion of logically analyzing the first

principles of mathematical science. In the first place, as just pointed

out, we learn _how few and simple are the conceptions and postulates_

upon which the actual edifice of exact science rests. Pure mathematics,

we have said, is free to assume what it chooses. Yet the assumptions

whose presence as the foundation principles of the actually existent

pure mathematics an exhaustive examination thus reveals, show by their

fewness that the ideal freedom of the mathematician to assume and to

construct what he pleases, is indeed, in practice, a very decidedly

limited freedom. The limitation is, as we have already seen, a

limitation which has to do with the essential significance of the

fundamental concepts in question. And so the result of this analysis of

the bases of the actually developed and significant branches of

mathematics, constitutes a sort of empirical revelation of what

categories the exact sciences have practically found to be of such

significance as to be worthy of exhaustive treatment. Thus the

instinctive sense for significant truth, which has all along been

guiding the development of mathematics, comes at least to a clear and

philosophical consciousness. And meanwhile the essential categories of

thought are seen in a new light.

The second result still more directly concerns a philosophical logic. It

is this: Since the few types of relations which this sort of analysis

reveals as the fundamental ones in exact science are of such importance,

the logic of the present day is especially required to face the

questions: _What is the nature of our concept of relations?_ What are

the various possible types of relations? Upon what does the variety of

these types depend? What unity lies beneath the variety?

As a fact, logic, in its modern forms, namely, first that symbolic logic

which Boole first formulated, which Mr. Charles S. Peirce and his pupils

have in this country already so highly developed, and which Schroeder in

Germany, Peano's school in Italy, and a number of recent English writers

have so effectively furthered--and secondly, the logic of scientific

method, which is now so actively pursued, in France, in Germany, and in

the English-speaking countries--this whole movement in modern logic, as

I hold, is rapidly approaching _new solutions of the problem of the

fundamental nature and the logic of relations_. The problem is one in

which we are all equally interested. To De Morgan in England, in an

earlier generation, and, in our time, to Charles Peirce in this country,

very important stages in the growth of these problems are due. Russell,

in his work on the _Principles of Mathematics_ has very lately

undertaken to sum up the results of the logic of relations, as thus far

developed, and to add his own interpretations. Yet I think that Russell

has failed to get as near to the foundations of the theory of relations

as the present state of the discussion permits. For Russell has failed

to take account of what I hold to be the most fundamentally important

generalization yet reached in the general theory of relations. This is

the generalization set forth as early as 1890, by Mr. A. B. Kempe, of

London, in a pair of wonderful but too much neglected, papers, entitled,

respectively, _The Theory of Mathematical Form_, and _The Analogy

between the Logical Theory of Classes and the Geometrical Theory of

Points_. A mere hint first as to the more precise formulation of the

problem at issue, and then later as to Kempe's special contribution to

that problem, may be in order here, despite the impossibility of any

adequate statement.

III

The two most obviously and universally important kinds of relations

known to the exact sciences, as these sciences at present exist, are:

(1) The relations of the type of equality or equivalence; and (2) the

relations of the type of before and after, or greater and less. The

first of these two classes of relations, namely, the class represented,

although by no means exhausted, by the various relations actually

called, in different branches of science by the one name equality, this

class I say, might well be named, as I myself have proposed, the

leveling relations. A collection of objects between any two of which

some one relation of this type holds, may be said to be a collection

whose members, in some defined sense or other, are on the same level.

The second of these two classes of relations, namely, those of the type

of before and after, or greater and less--this class of relations, I

say, consists of what are nowadays often called the serial relations.

And a collection of objects such that, if any pair of these objects be

chosen, a determinate one of this pair stands to the other one of the

same pair in some determinate relation of this second type, and in a

relation which remains constant for all the pairs that can be thus

formed out of the members of this collection--any such collection, I

say, constitutes a one-dimensional open series. Thus, in case of a file

of men, if you choose any pair of men belonging to the file, a

determinate one of them is, in the file, before the other. In the number

series, of any two numbers, a determinate one is greater than the other.

Wherever such a state of affairs exists, one has a series.

Now these two classes of relations, the leveling relations and the

serial relations, agree with one another, and differ from one another in

very momentous ways. They _agree_ with one another in that both the

leveling and the serial relations are what is technically called

_transitive_; that is, both classes conform to what Professor James has

called the law of "skipped intermediaries." Thus, if _A_ is equal to

_B_, and _B_ is equal to _C_, it follows that _A_ is equal to _C_. If

_A_ is before _B_, and _B_ is before _C_, then _A_ is before _C_. And

this property, which enables you in your reasonings about these

relations to skip middle terms, and so to perform some operation of

elimination, is the property which is meant when one calls relations of

this type transitive. But, on the other hand, these two classes of

relations _differ_ from each other in that the leveling relations are,

while the serial relations are not, _symmetrical_ or reciprocal. Thus,

if _A_ is equal to _B_, _B_ is equal to _A_. But if _X_ is greater than

_Y_, then _Y_ is not greater than _X_, but less than _X_. So the

leveling relations are symmetrical transitive relations. But the serial

relations are transitive relations which are not symmetrical.

All this is now well known. It is notable, however, that nearly all the

processes of our exact sciences, as at present developed, can be said to

be essentially such as lead either to the placing of sets or classes of

objects on the same level, by means of the use of symmetrical transitive

relations, or else to the arranging of objects in orderly rows or

series, by means of the use of transitive relations which are not

symmetrical. This holds also of all the applications of the exact

sciences. Whatever else you do in science (or, for that matter, in art),

you always lead, in the end, either to the arranging of objects, or of

ideas, or of acts, or of movements, in rows or series, or else to the

placing of objects or ideas of some sort on the same level, by virtue of

some equivalence, or of some invariant character. Thus numbers,

functions, lines in geometry, give you examples of serial relations.

Equations in mathematics are classic instances of leveling relations.

So, of course, are invariants. Thus, again, the whole modern theory of

energy consists of two parts, one of which has to do with levels of

energy, in so far as the quantity of energy of a closed system remains

invariant through all the transformations of the system, while the other

part has to do with the irreversible serial order of the transformations

of energy themselves, which follow a set of unsymmetrical relations, in

so far as energy tends to fall from higher to lower levels of intensity

within the same system.

The entire conceivable universe then, and all of our present exact

science, can be viewed, if you choose, as a collection of objects or of

ideas that, whatever other types of relations may exist, are at least

largely characterized either by the leveling relations, or by the serial

relations, or by complexes of both sorts of relations. Here, then, we

are plainly dealing with very fundamental categories. The "between"

relations of geometry can of course be defined, if you choose, in terms

of transitive relations that are not symmetrical. There are, to be sure,

some other relations present in exact science, but the two types, the

serial and leveling relations, are especially notable.

So far the modern logicians have for some time been in substantial

agreement. Russell's brilliant book is a development of the logic of

mathematics very largely in terms of the two types of relations which,

in my own way, I have just characterized; although Russell gives due

regard, of course, to certain other types of relations.

But hereupon the question arises, "Are these two types of relations what

Russell holds them to be, namely, ultimate and irreducible logical

facts, unanalyzable categories--mere data for the thinker?" Or can we

reduce them still further, and thus simplify yet again our view of the

categories?

Here is where Kempe's generalization begins to come into sight. These

two categories, in at least one very fundamental realm of exact thought,

can be reduced to one. There is, namely, a world of ideal objects which

especially interest the logician. It is the world of a _totality of

possible logical classes_, or again, it is the ideal world, equivalent

in formal structure to the foregoing, but composed of a _totality of

possible statements_, or thirdly, it is the world, equivalent once more,

in formal structure, to the foregoing, but consisting of a _totality of

possible acts of will_, of possible decisions. When we proceed to

consider the relational structure of such a world, taken merely in the

abstract as such a structure, a relation comes into sight which at once

appears to be peculiarly general in its nature. It is the so-called

illative relation, the relation which obtains between two classes when

one is subsumed under the other, or between two statements, or two

decisions, when one implies or entails the other. This relation is

transitive, but may be either symmetrical or not symmetrical; so that,

according as it is symmetrical or not, it may be used either to

establish levels or to generate series. In the order system of the

logician's world, the relational structure is thus, in any case, a

highly general and fundamental one.

But this is not all. In this the logician's world of classes, or of

statements, or of decisions, there is also another relation observable.

This is the relation of exclusion or mutual opposition. This is a purely

symmetrical or reciprocal relation. It has two forms--obverse or

contradictory opposition, that is, negation proper, and contrary

opposition. But both these forms are purely symmetrical. And by proper

devices each of them can be stated in terms of the other, or reduced to

the other. And further, as Kempe incidentally shows, and as Mrs. Ladd

Franklin has also substantially shown in her important theory of the

syllogism, _it is possible to state every proposition, or complex of

propositions involving the illative relation, in terms of this purely

symmetrical relation of opposition_. Hence, so far as mere relational

form is concerned, the illative relation itself may be wholly reduced to

the symmetrical relation of opposition. This is our first result as to

the relational structure of the realm of pure logic, that is, the realm

of classes, of statements, or of decisions.

It follows that, in describing the logician's world of possible classes

or of possible decisions, _all unsymmetrical, and so all serial,

relations can be stated solely in terms of symmetrical relations, and

can be entirely reduced to such relations_. Moreover, as Kempe has also

very prettily shown, the relation of opposition, in its two forms, just

mentioned, need not be interpreted as obtaining merely between pairs of

objects. It may and does obtain between triads, tetrads, _n_-ads of

logical entities; and so all that is true of the relations of logical

classes may consequently be stated merely by ascribing certain perfectly

symmetrical and homogeneous predicates to pairs, triads, tetrads, n-ads

of logical objects. The essential contrast between symmetrical and

unsymmetrical relations thus, in this ideal realm of the logician,

simply vanishes. The categories of the logician's world of classes, of

statements, or of decisions, are marvelously simple. All the relations

present may be viewed as variations of the mere conception of opposition

as distinct from non-opposition.

All this holds, of course, so far, merely for the logician's world of

classes or of decisions. There, at least, all serial order can actually

be derived from wholly symmetrical relations. But Kempe now very

beautifully shows (and here lies his great and original contribution to

our topic)--he shows, I say, that the ordinal relations of geometry, as

well as of the number system, can all be regarded as indistinguishable

from _mere variations of those relations which, in pure logic, one finds

to be the symmetrical relations obtaining within pairs or triads of

classes or of statements_. The formal identity of the geometrical

relation called "between" with a purely logical relation which one can

define as existing or as not existing amongst the members of a given

triad of logical classes, or of logical statements, is shown by Kempe in

a fashion that I cannot here attempt to expound. But Kempe's result thus

enables one, as I believe, to simplify the theory of relations far

beyond the point which Russell in his brilliant book has reached. For

Kempe's triadic relation in question can be stated, in what he calls its

obverse form, in perfectly symmetrical terms. And he proves very exactly

that the resulting logical relation is precisely identical, in all its

properties, with the fundamental ordinal relation of geometry.

Thus the order-systems of geometry and analysis appear simply as special

cases of the more general order-system of pure logic. The whole, both of

analysis and of geometry, can be regarded as a description of certain

selected groups of entities, which are chosen, according to special

rules, from a single ideal world. This general and inclusive ideal world

consists simply of _all the objects which can stand to one another in

those symmetrical relations wherein the pure logician finds various

statements, or various decisions inevitably standing_. "Let me," says in

substance Kempe, "choose from the logician's ideal world of classes or

decisions, what entities I will; and I will show you a collection of

objects that are in their relational structure, precisely identical with

the points of a geometer's space of _n_ dimensions." In other words, all

of the geometer's figures and relations can be precisely pictured by the

relational structure of a selected system of classes or of statements,

whose relations are wholly and explicitly logical relations, such as

opposition, and whose relations may all be regarded, accordingly, as

reducible to a single type of purely symmetrical relation.

Thus, for _all_ exact science, and not merely for the logician's special

realm, the contrast between symmetrical and unsymmetrical relations

proves to be, after all, superficial and derived. The purely logical

categories, such as opposition, and such as hold within the calculus of

statements, are, apparently, the basal categories of all the exact

science that has yet been developed. Series and levels are relational

structures that, sharply as they are contrasted, can be derived from a

single root.

I have restated Kempe's generalization in my own way. I think it the

most promising step towards new light as to the categories that we have

made for some generations.

In the field of modern logic, I say, then, work is doing which is

rapidly tending towards the unification of the tasks of our entire

division. For this problem of the categories, in all its abstractness,

is still a common problem for all of us. Do you ask, however, what such

researches can do to furnish more special aid to the workers in

metaphysics, in the philosophy of religion, in ethics, or in æsthetics,

beyond merely helping towards the formulation of a table of

categories--then I reply that we are already not without evidence that

such general researches, abstract though they may seem, are bearing

fruits which have much more than a merely special interest. Apart from

its most general problems, that analysis of mathematical concepts to

which I have referred has in any case revealed numerous unexpected

connections between departments of thought which had seemed to be very

widely sundered. One instance of such a connection I myself have

elsewhere discussed at length, in its general metaphysical bearings. I

refer to the logical identity which Dedekind first pointed out between

the mathematical concept of the ordinal number of series and the

philosophical concept of the formal structure of an ideally completed

self. I have maintained that this formal identity throws light upon

problems which have as genuine an interest for the student of the

philosophy of religion as for the logician of arithmetic. In the same

connection it may be remarked that, as Couturat and Russell, amongst

other writers, have very clearly and beautifully shown, the argument of

the Kantian mathematical antinomies needs to be explicitly and totally

revised in the light of Cantor's modern theory of infinite collections.

To pass at once to another, and a very different instance: The modern

mathematical conceptions of what is called group theory have already

received very wide and significant applications, and promise to bring

into unity regions of research which, until recently, appeared to have

little or nothing to do with one another. Quite lately, however, there

are signs that group theory will soon prove to be of importance for the

definition of some of the fundamental concepts of that most refractory

branch of philosophical inquiry, æsthetics. Dr. Emch, in an important

paper in the _Monist_, called attention, some time since, to the

symmetry groups to which certain æsthetically pleasing forms belong, and

endeavored to point out the empirical relations between these groups and

the æsthetic effects in question. The grounds for such a connection

between the groups in question and the observed æsthetic effects,

seemed, in the paper of Dr. Emch to be left largely in the dark. But

certain papers recently published in the country by Miss Ethel Puffer,

bearing upon the psychology of the beautiful (although the author has

approached the subject without being in the least consciously

influenced, as I understand, by the conceptions of the mathematical

group theory), still actually lead, if I correctly grasp the writer's

meaning, to the doctrine that the æsthetic object, viewed as a

psychological whole, must possess a structure closely, if not precisely,

equivalent to the ideal structure of what the mathematician calls a

group. I myself have no authority regarding æsthetic concepts, and speak

subject to correction. But the unexpected, and in case of Miss Puffer's

research, quite unintended, appearance of group theory in recent

æsthetic analysis is to me an impressive instance of the use of

relatively new mathematical conceptions in philosophical regions which

_seem_, at first sight, very remote from mathematics.

That both the group concept and the concept of the self just suggested

are sure to have also a wide application in the ethics of the future, I

am myself well convinced. In fact, no branch of philosophy is without

close relations to all such studies of fundamental categories.

These are but hints and examples. They suffice, I hope, to show that the

workers in this division have deep common interests, and will do well,

in future, to study the arts of coöperation, and to regard one another's

progress with a watchful and cordial sympathy. In a word: Our common

problem is the theory of the categories. That problem can be solved only

by the coöperation of the mathematicians and of the philosophers.

[Illustration: THE UNIVERSITY OF PARIS IN THE THIRTEENTH CENTURY

_Hand-painted Photogravure from a Painting by Otto Knille. Reproduced

from a Photograph of the Painting by permission of the Berlin Photograph

Co._

This famous painting is now in the University of Berlin. Thomas Aquinas,

one of the greatest of the scholastic philosophers, surnamed the

"Angelic Doctor," is delivering a learned discourse before King Louis

IX. To the right of the King stands Joinville, the French chronicler.

The Dominican monk with his hand to his face is Guillaume de Saint

Amour, and Vincent de Beauvais, and another Dominican are seated with

their backs to the platform desk from which Thomas Aquinas is making his

animated address. The picture is thoroughly characteristic of a

University disputation at the close of the Middle Ages.]

DEPARTMENT I--PHILOSOPHY

DEPARTMENT I--PHILOSOPHY

(_Hall 6, September 20, 11.15 a. m._)

CHAIRMAN: PROFESSOR BORDEN P. BOWNE, Boston University.

SPEAKERS: PROFESSOR GEORGE H. HOWISON, University of California.

PROFESSOR GEORGE T. LADD, Yale University.

In opening the Department of Philosophy, the Chairman, Professor Borden

P. Bowne, LL.D., of Boston University, made an interesting address on

the Philosophical Outlook. Professor Bowne said in part:--

I congratulate the members of the Philosophical Section on

the improved outlook in philosophy. In the generation just

passed, philosophy was somewhat at a discount. The great and

rapid development of physical science and invention,

together with the profound changes in biological thought,

produced for a time a kind of chaos. New facts were showered

upon us in great abundance, and we had no adequate

philosophical preparation for dealing with them. Such a

condition is always disturbing. The old mental equilibrium

is overthrown and readjustment is a slow process. Besides,

the shallow sense philosophy of that time readily lent

itself to mechanical and materialistic interpretations, and

for a while it seemed as if all the higher faiths of

humanity were permanently discredited. All this has passed

away. Philosophical criticism began its work and the naïve

dogmatism of materialistic naturalism was soon disposed of.

It quickly appeared that our trouble was not due to the new

facts, but to the superficial philosophy by which they had

been interpreted. Now that we have a better philosophy, we

have come to live in perfect peace with the facts once

thought disturbing, and even to welcome them as valuable

additions to knowledge....

The brief naturalistic episode was not without instruction

for us. It showed conclusively the great practical

importance of philosophy. Had we had thirty years ago the

current philosophical insight, the great development of the

physical and biological sciences would have made no

disturbance whatever. But being interpreted by a crude

scheme of thought, it produced somewhat of a storm.

Philosophy may not contribute much of positive value, but it

certainly has an important negative function in the way of

suppressing pretentious dogmatism and fictitious knowledge,

which often lead men astray. It is these things which

produce conflicts of science and religion or which find in

evolution the solvent of all mysteries and the source of all

knowledge.

Concerning the partition of territory between science and

philosophy, there are two distinct questions respecting the

facts of experience. First, we need to know the facts in

their temporal and spatial order, and the way they hang

together in a system of law. To get this knowledge is the

function of science, and in this work science has

inalienable rights and a most important practical function.

This work cannot be done by speculation nor interfered with

by authority of any kind. It is not surprising, then, that

scientists in their sense of contact with reality should be

indignant with, or feel contempt for, any who seek to limit

or proscribe their research. But supposing this work all

done, there remains another question respecting the

causality and interpretation of the facts. This question

belongs to philosophy. Science describes and registers the

facts with their temporal and spatial laws; philosophy

studies their causality and significance. And while the

scientist justly ignores the philosopher who interferes with

his inquiries, so the philosopher may justly reproach the

scientist who fails to see that the scientific question does

not touch the philosophic one....

In the field of metaphysics proper I note a strong tendency

toward personal idealism, or as it might be called,

Personalism; that is, the doctrine that substantial reality

can be conceived only under the personal form and that all

else is phenomenal. This is quite distinct from the

traditional idealisms of mere conceptionism. It holds the

essential fact to be a community of persons with a Supreme

Person at their head while the phenomenal world is only

expression and means of communication. And to this view we

are led by the failure of philosophizing on the impersonal

plane, which is sure to lose itself in contradiction and

impossibility. Under the form of mechanical naturalism, with

its tendencies to materialism and atheism, impersonalism has

once more been judged and found wanting. We are not likely

to have a recurrence of this view unless there be a return

to philosophical barbarism. But impersonalism at the

opposite pole in the form of abstract categories of being,

causality, unity, identity, continuity, sufficient reason,

etc., is equally untenable. Criticism shows that these

categories when abstractly and impersonally taken cancel

themselves. On the impersonal plane we can never reach unity

from plurality, or plurality from unity; and we can never

find change in identity, or identity in change. Continuity

in time becomes mere succession without the notion of

potentiality, and this in turn is empty. Existence itself is

dispersed into nothingness through the infinite divisibility

of space and time, while the law of the sufficient reason

loses itself in barren tautology and the infinite regress.

The necessary logical equivalence of cause and effect in any

impersonal scheme makes all real explanation and progress

impossible, and shuts us up to an unintelligible oscillation

between potentiality and actuality, to which there is no

corresponding thought....

Philosophy is still militant and has much work before it,

but the omens are auspicious, the problems are better

understood, and we are coming to a synthesis of the results

of past generations of thinking which will be a very

distinct progress. Philosophy has already done good service,

and never better than in recent times, by destroying

pretended knowledge and making room for the higher faiths of

humanity. It has also done good service in helping these

faiths to better rational form, and thus securing them

against the defilements of superstition and the cavilings of

hostile critics. With all its aberrations and shortcomings,

philosophy deserves well of humanity.

PHILOSOPHY: ITS FUNDAMENTAL CONCEPTIONS AND ITS METHODS

BY GEORGE HOLMES HOWISON

[George Holmes Howison, Mills Professor of Intellectual and

Moral Philosophy and Civil Polity, University of California.

b. Montgomery County, Maryland, 1834. A.B. Marietta College,

1852; M.A. 1855; LL.D. _ibid._ 1883. Post-graduate, Lane

Theological Seminary, University of Berlin, and Oxford.

Headmaster High School, Salem, Mass., 1862-64; Assistant

Professor of Mathematics, Washington University, St. Louis,

1864-66; Tileston Professor of Political Economy, _ibid._

1866-69; Professor of Logic and the Philosophy of Science,

Massachusetts Institute of Technology, 1871-79; Lecturer on

Ethics, Harvard University, 1879-80; Lecturer on Logic and

Speculative Philosophy, University of Michigan, 1883-84.

Member and vice-president St. Louis Philosophical Society;

member California Historical Society; American Historical

Association; American Association for the Advancement of

Science; National Geographic Society, etc. Author of

_Treatise on Analytic Geometry_, 1869; _The Limits of

Evolution_, 1901, 2d edition, 1904; joint author and editor

of _The Conception of God_, 1897, etc. Editor Philosophical

Publications of University of California; American Editorial

Representative _Hibbert Journal_, London.]

The duty has been assigned me, honored colleagues, of addressing you on

the Fundamental Conceptions and the Methods of our common

pursuit--philosophy. In endeavoring to deal with the subject in a way

not unworthy of its depth and its extent, I have found it impossible to

bring the essential material within less compass than would occupy, in

reading, at least four times the period granted by our programme. I have

therefore complied with the rule of the Congress which directs that, if

a more extended writing be left with the authorities for publication,

the reading must be restricted to such a portion of it as will not

exceed the allotted time. I will accordingly read to you, first, a brief

summary of my entire discussion, by way of introduction, and then an

excerpt from the larger document, which may serve for a _specimen_, as

our scholastic predecessors used to say, of the whole inquiry I have

carried out. The impression will, of course, be fragmentary, and I must

ask beforehand for your most benevolent allowances, to prevent a

judgment too unfavorable.

The discussion naturally falls into two main parts: the first dealing

with the Fundamental Conceptions; and the second, with the Methods.

In the former, after presenting the conception of philosophy itself, as

_the consideration of things in the light of the whole_, I take up the

involved Fundamental Concepts in the following order:--

I. Whole and Part;

II. Subject and Object (Knowing and Being, Mind and Matter; Dualism,

Materialism, Idealism);

III. Reality and Appearance (Noumenon and Phenomenon);

IV. Cause and Effect (Ground and Consequence; Causal System);

V. One and Many (Number System; Monism and Pluralism);

VI. Time and Space (their relation to Number; their Origin and

Real Meaning);

VII. Unconditioned and Conditioned (Soul, World, God; their

Reinterpretation in terms of Pluralism);

VIII. The True, the Beautiful, the Good (their relation to the

question between Monism and Pluralism).

These are successively dealt with as they rise one out of the other in

the process of interpreting them and applying them in the actual

creation of philosophy, as this goes on in the historic schools. The

theoretic progress of philosophy is in this way explained by them, in

its movement from natural dualism, or realism, through the successive

forms of monism, materialistic, agnostic, and idealistic, until it

reaches the issue, now coming so strongly forward within the school of

idealism, between the adherents of monism and those of pluralism.

The importance of the Fundamental Concepts is shown to increase as we

pass along the list, till on reaching Cause and Effect, and entering

upon its full interpretation into the complete System of Causes, we

arrive at the very significant conception of the RECIPROCITY OF FIRST

CAUSES, and through it come to the PRIMACY OF FINAL CAUSE, and the

derivative position of the other forms of cause, Material, Formal,

Efficient. The philosophic strength of idealism, but especially of

idealistic pluralism, comes into clear light as the result of this stage

of the inquiry. But it appears yet more decidedly when One and Many,

Time and Space, and their interrelations, are subjected to analysis. So

the discussion next passes to the higher conceptions, Soul, World, God,

by the pathway of the correlation Unconditioned and Conditioned, and its

kindred contrasts Absolute and Relative, Necessary and Contingent,

Infinite and Finite, corroborating and reinforcing the import of

idealism, and, still more decidedly, that of its plural form. Finally,

the strong and favorable bearing of this last on the dissolution of

agnosticism and the habilitation of the ideals, the True, the Beautiful,

and the Good, in a heightened meaning, is brought out.

This carries the inquiry to the second part of it, that of the

Philosophical Methods. Here I recount these in a series of six: the

Dogmatic, the Skeptical, the Critical, the Pragmatic, the Genetic, the

Dialectic. These, I show, in spite of the tendency of the earlier

members in the series to over-emphasis, all have their place and

function in the development of a complete philosophy, and in fact form

an ascending series in methodic effectiveness, all that precede the last

being taken up into the comprehensive Critical Rationalism of the last.

Methodology thus passes upward, over the ascending and widening roadways

of (1) Intuition and Deduction; (2) Experience and Induction; (3)

Intuition and Experience adjusted by Critical Limits; (4) Skepticism

reinforced and made _quasi_-affirmative by Desire and Will; (5)

Empiricism enlarged by substitution of cosmic and psychic history for

subjective consciousness; (6) Enlightened return to a Rationalism

critically established by the inclusion of the preceding elements, and

by the sifting and the grading of the Fundamental Concepts through their

behavior when tested by the effort to make them universal. In this way,

the methods fall into a System, the organic principle of which is this

principle of Dialectic, which proves itself alone able to establish

_necessary_ truths; that is, _truths indeed_,--judgments that are seen

to exclude their opposites, because, in the attempt to substitute the

opposite, the place of it is still filled by the judgment which it aims

to dislodge.

And now, with your favoring leave, I will read the excerpt from my

larger text.

The task to which, in an especial sense, the cultivators of philosophy

are summoned by the plans of the present Congress of Arts and Science,

is certainly such as to stir an ambition to achieve it. At the same

time, it tempers eagerness by its vast difficulty, and the apprehension

lest this may prove insuperable. The task, the officers of the Congress

tell us, is no less than to promote the unification of all human

knowledge. It requires, then, the reduction of the enormous detail in

our present miscellany of sciences and arts, which to a general glance,

or even to a more intimate view, presents a confusion of differences

that seems overwhelming, to a system nevertheless clearly

harmonious,--founded, that is to say, upon universal principles which

control all differences by explaining them, and which therefore, in the

last resort, themselves flow lucidly from a single supreme principle.

Simply to state this meaning of the task set us, is enough to awaken the

doubt of its practicability.

This doubt, we are bound to confess, has more and more impressed itself

upon the general mind, the farther this has advanced in the experience

of scientific discovery. The very increase in the multiplicity and

complexity of facts and their causal groupings increases the feeling

that at the root of things there is "a final inexplicability"--total

reality seems, more and more, too vast, too profound, for us to grasp or

to fathom. And yet, strangely enough, this increasing sense of

mysterious vastness has not in the least prevented the modern mind from

more and more asserting, with a steadily increasing insistence, the

essential and unchangeable unity of that whole of things which to our

ordinary experience, and even to all our sciences, appears such an

endless and impenetrable complex of differences,--yes, of

contradictions. In fact, this assertion of the unity of all things,

under the favorite name of the Unity of Nature, is the pet dogma of

modern science; or, rather, to speak with right accuracy, it is the

stock-in-trade of a _philosophy_ of science, current among many of the

leaders of modern science; for every such assertion, covering, as it

tacitly and unavoidably does, a view about the absolute whole, is an

assertion belonging to the province of philosophy, before whose tribunal

it must come for the assessment of its value. The presuppositions of all

the special sciences, and, above all, this presupposition of the Unity

and Uniformity of Nature, common to all of them, must thus come back for

justification and requisite definition to philosophy--that uppermost and

all-inclusive form of cognition which addresses itself to the whole as

whole. In their common assertion of the Unity of Nature, the exponents

of modern science come unawares out of their own province into quite

another and a higher; and in doing so they show how unawares they come,

by presenting in most instances the curious spectacle of proclaiming at

once their increasing belief in the unity of things, and their

increasing disbelief in its penetrability by our intelligence:--

_In's Innere der Natur,

Dringt kein erschaffner Geist,_

is their chosen poet's expression of their philosophic mood. Curious we

have the right to call this state of the scientific mind, because it is

to critical reflection so certainly self-contradictory. How can there be

a real unity belonging to what is inscrutable?--what evidence of unity

can there be, except in intelligible and explanatory continuity?

But, at all events, this very mood of agnostic self-contradiction, into

which the development of the sciences casts such a multitude of minds,

brings them,--brings all of us,--as already indicated, into that court

of philosophy where alone such issues lawfully belong, and where alone

they can be adjudicated. If the unification of the sciences can be made

out to be real by making out its sole sufficient condition, namely, that

there is a genuine, and not a merely nominal, unity in the whole of

reality itself,--a unity that explains because it is itself, not simply

intelligible, but the only completely intelligible of things,--this

desirable result must be the work of philosophy. However difficult the

task may be, it is rightly put upon us who belong to the Department

listed first among the twenty-four in the programme of this

representative Congress.

I cannot but express my own satisfaction, as a member of this

Department, nor fail to extend my congratulations to you who are my

colleagues in it, that the Congress, in its programme, takes openly the

affirmative on this question of the possible unification of knowledge.

The Congress has thus declared beforehand for the practicability of the

task it sets. It has even declared for its not distant accomplishment;

indeed, not impossibly, its accomplishment through the transactions of

the Congress itself; and it indicates, by no uncertain signs, the

leading, the determining part that philosophy must have in the

achievement. In fact, the authorities of the Congress themselves suggest

a solution of their own for their problem. In their programme we see a

renewed Hierarchy of the Sciences, and at the summit of this appears now

again, after so long a period of humiliating obscuration, the figure of

Philosophy, raised anew to that supremacy, as Queen of the Sciences,

which had been hers from the days of Plato to those of Copernicus, but

which she began to lose when modern physical and historical research

entered upon its course of sudden development, and which, until

recently, she has continued more and more to lose as the sciences have

advanced in their career of discoveries,--ever more unexpected, more

astonishing, yet more convincing and more helpful to the welfare of

mankind. May this sign of her recovered empire not fail! If we rejoice

at the token, the Congress has made it our part to see that the title is

vindicated. It is ours to show this normative function of philosophy,

this power to reign as the unifying discipline in the entire realm of

our possible knowledge; to show it by showing that the very nature of

philosophy--its elemental concepts and its directing ideals, its methods

taken in their systematic succession--is such as must result in a view

of universal reality that will supply the principle at once giving rise

to all the sciences and connecting them all into one harmonious whole.

Such, and so grave, my honored colleagues, is the duty assigned to this

hour. Sincerely can I say, Would it had fallen to stronger hands than

mine! But since to mine it has been committed, I will undertake it in no

disheartened spirit; rather, in that temper of animated hope in which

the whole Congress has been conceived and planned. And I draw

encouragement from the place, and its associations, where we are

assembled--from its historic connections not only with the external

expansion of our country, but with its growth in culture, and especially

with its growth in the cultivation of philosophy. For your speaker, at

least, can never forget that here in St. Louis, the metropolis of the

region by which our national domain was in the Louisiana Purchase so

enlarged,--here was the centre of a movement in philosophic study that

has proved to be of national import. It is fitting that we all, here

to-day, near to the scene itself, commemorate the public service done by

our present National Commissioner of Education and his group of

enthusiastic associates, in beginning here, in the middle years of the

preceding century, those studies of Kant and his great idealistic

successors that unexpectedly became the nucleus of a wider and more

penetrating study of philosophy in all parts of our country. It is with

quickened memories belonging to the spot where, more than

five-and-thirty years ago, it was my happy fortune to take some part

with Dr. Harris and his companions, that I begin the task assigned me.

The undertaking seems less hopeless when I can here recall the names and

the congenial labors of Harris, of Davidson, of Brockmeyer, of Snider,

of Watters, of Jones,--half of them now gone from life. They "builded

better than they knew;" and, humbly as they may themselves have

estimated their ingenuous efforts to gain acquaintance with the greatest

thoughts, history will not fail to take note of what they did, as

marking one of the turning-points in the culture of our nation. The

publication of the _Journal of Speculative Philosophy_, granting all the

subtractions claimed by its critics on the score of defects (of which

its conductors were perhaps only too sensible), was an influence that

told in all our circles of philosophical study, and thence in the whole

of our social as well as our academic life.

* * * * *

[Here I enter upon the discussion of the subject proper, beginning, as

above indicated, with the Fundamental Conceptions. Having followed these

through the contrasts Whole and Part, Subject and Object, Reality and

Appearance (or Noumenon and Phenomenon), and developed the bearing of

these on the procedure of thought from the dualism of natural realism to

materialism and thence to idealism, with the issue now coming on, in

this last, between monism and pluralism, I strike into the contrast

Cause and Effect, and, noting its unfolding into the more comprehensive

form of Ground and Consequence, go on thence as follows:]

* * * * *

It is plain that the contrast Ground and Consequence will enable us to

state the new issue with closer precision and pertinence than Reality

and Appearance, Noumenon and Phenomenon, can supply; while, at the same

time, Ground and Consequence exhibits Cause and Effect as presenting a

contrast that only fulfills what Noumenon and Phenomenon foretold and

strove towards; in fact, what was more remotely, but not less surely,

also indicated by Whole and Part, Knowing and Being, Subject and Object.

For in penetrating to the coherent meaning of these conceptions, the

philosophic movement, as we saw, advanced steadily to the fuller and

fuller translating of each of them into the reality that unifies _by

explanation_, instead of pretending to explain by merely unifying; and

this, of course, will now be put forward explicitly, in the clarified

category of Cause and Effect, transfigured from a physical into a purely

logical relation. What idealism now says, in terms of this, is that the

Cause (or, as we now read it, the Ground) of all that exists is the

Subject; is Mind, the intelligently Self-conscious; and that all things

else, the mere objects, material things, are its Consequence, its

Outcome,--in that sense its Effect. And what the new pluralistic

idealism says, is that the _assemblage of individual minds_--intelligence

being essentially personal and individual, and never merely universal

and collective--is the true total Cause of all, and that every mind thus

belongs to the order of First Causes; nevertheless, that part, and the

most significant part, of the nature of every mind, essential to its

personality and its reason, is _its recognition of other minds in the

very act of its own self-definition_. That is to say, a mind by its

spontaneous nature as intelligence, by its intrinsic rational or logical

genius, puts itself as member of a _system_ of minds; all minds are put

by each other as Ends--completely standard and sacred Objects, as much

parts of the system of true Causes as each is, in its capacity of

Subject; and we have a noumenal Reality that is properly to be described

as the eternal Federal Republic of Spirits.

Consequently, the relation of Cause and Effect now expands and heightens

into a system of the RECIPROCITY OF FIRST CAUSES; causes, that is,

which, while all coefficients in the existence and explanation of that

natural world of experience which forms their passive effect, their

objects of mere perception, are themselves related only in the higher

way of Final Causes--that is, Defining-Bases and Ends--of each other,

making them the logical Complements, and the Objects of conduct, all for

each, and each for all. Hence, the system of causation undergoes a

signal transformation, and proves to be organized by Final Cause as its

basis and root, instead of by Efficient Cause, or Originating Ground, as

the earlier stages of thinking had always assumed.

The causal relation between the absolute or primary realities being

purely Final, or Defining and Purposive; that is to say, the uncoercive

influence of recognition and ideality; all the other forms of cause, as

grouped by Aristotle,--Material, Formal, and Efficient,--are seen to be

the derivatives of Final Cause, as being supplied by the action of the

minds that, as absolute or underived realities, exist only in the

relation of mutual Complements and Ends. Accordingly, Efficient Cause

operates only from minds, as noumena, to matter, as their phenomenon,

their presented contents of experience; or, in a secondary and

derivative sense, from one phenomenon to another, or from one group of

phenomena to another group, these playing the part of transmitters, or

(as some logicians would say) Instrumental Causes, or Means. Cause, as

Material, is hence defined as the elementary phenomenon, and the

combinations of this; and therefore, strictly taken, is merely Effect

(or Outcome) of the self-active consciousness, whose spontaneous forms

of conception and perception become the Formal Cause that organizes the

sum of phenomena into cosmic harmony or unity.

Here, accordingly, comes into view the further and in some respects

deeper conceptual pair, Many and One. The history of philosophic thought

proves that this antithesis is darkly obscure and deeply ambiguous; for

about it have centred a large part of the conflicts of doctrine. This

pair has already been used, implicitly, in exhibiting the development of

the preceding group, Cause and Effect; and in so using it we have

supplied ourselves with a partial clarification of it, and with one

possible solution of its ambiguity. We have seen, namely, how our strong

natural persuasion that philosophy guided by the fundamental concept

Cause must become the search for the One amid the wilderness of the

Many, and that this search cannot be satisfied and ended except in an

all-inclusive Unit, in which the Many is embraced as the integral and

originated parts, completely determined, subjected, and controlled, may

give way to another and less oppressive conception of unity; a

conception of it as the harmony among many free and independent primary

realities, a harmony founded on their intelligent and reasonable mutual

recognition. This conception casts at least _some_ clearing light upon

the long and dreary disputes over the Many and the One; for it exposes,

plainly, the main source of them. They have arisen out of two chief

ambiguities,--the ambiguity of the concept One, and the ambiguity of the

concept Cause in its supreme meaning. The normal contrast between the

One and the Many is a clear and simple contrast: the One is the single

unit, and the Many is the repetition of the unit, or is the collection

of the several units. But if we go on to suppose that there is a

collection or sum of all possible units, and call this the Whole, then,

since there can be no second such, we call it also "one" (or the One, by

way of preëminence), overlooking the fact that it differs from the

simple one, or unit, _in genere_; that it is in fact not a unit at all,

not an elementary member of a series, but the annulment of all series;

that our name "one" has profoundly changed its meaning, and now stands

for the Sole, the Only. Thus, by our forgetfulness of differences, we

fall into deep water, and, with the confused illusions of the drowning,

dream of the One and All as the single _punctum originationis_ of all

things, the Source and Begetter of the very units of which it is in

reality only the resultant and the derivative. Or, from another point of

view, and in another mood, we rightly enough take the One to mean the

coherent, the intelligible, the consistent, the harmonious; and putting

the Many, on the misleading hint of its contrast to the unit, in

antithesis to this One of harmony, we fall into the belief that the Many

cannot be harmonious, is intrinsically a cluster of repulsions or of

collisions, incapable of giving rise to accord; indeed, essentially

hostile to it. So, as accord is the aim and the essence of our reason,

we are caught in the snare of monism, pluralism having apparently become

the equivalent of chaos, and thus the _bête noir_ of rational

metaphysics. Nay, in the opposed camp itself, some of the most ardent

adherents of pluralism, the liveliest of wit, the most exuberant in

literary resources, are the abjectest believers in the hopeless

disjunction and capriciousness of the plural, and hold there is a rift

in the texture of reality that no intelligence, "even though you dub it

'the Absolute,'" can mend or reach across. Yet surely there is nothing

in the Many, as a sum of units, the least at war with the One as a

system of harmony. On the contrary, even in the pure form of the Number

Series, the Many is impossible except on the principle of harmony,--the

units can be collected and summed (that is, constitute the Many), only

if they cohere in a community of intrinsic kindred. Consequently the

whole question of the chaotic or the harmonic nature of a plural world

turns on the nature of the genus which we find characteristic of the

absolutely (_i. e._, the unreservedly) real, and which is to be taken as

the common denomination enabling us to count them and to sum them. When

minds are seen to be necessarily the primary realities, but _also

necessarily federal_ as well as individual, the illusion about the

essential disjunction and non-coherence of the plurally real dissolves

away, and a primordial world of manifold persons is seen to involve no

fundamental or hopeless anarchy of individualism, irreducible in

caprice, but an indwelling principle of harmony, rather, that from the

springs of individual being intends the control and composure of all the

disorders that mark the world of experiential appearance, and so must

tend perpetually to effect this.

The other main source of our confusions over the Many and the One is the

variety of meaning hidden in the concept Cause, and our propensity to

take its most obvious but least significant sense for its supreme

intent. Closest at hand, in experience, is our productive causation of

changes in our sense-world, and hence most obvious is that reading of

Cause which takes it as the producer of changes and, with a deeper

comprehension of it, of the inalterable linkage between changes, whereby

one follows regularly and surely upon another. Thus what we have in

philosophy agreed to call Efficient Cause comes to be mistaken for the

profoundest and the supreme form of cause, and all the other modes of

cause, the Material (or Stuff), the Form (or Conception), and the End

(or Purpose), its consequent and derivative auxiliaries. Under the

influence of this strong impression, we either assume total reality to

be One Whole, all-embracing and all-producing of its manifold modes, or

else view it as a duality, consisting of One Creator and his manifold

creatures. So it has come about that metaphysics has hitherto been

chiefly a contention between pantheism and monotheism, or, as the latter

should for greater accuracy be called, monarchotheism; and, it must be

acknowledged, this struggle has been attended by a continued (though not

continual) decline of this later dualistic theory before the steadfast

front and unyielding advance of the older monism. Thus persistent has

been the assumption that harmony can only be assured by the unity given

in some single productive causation: the only serious uncertainty has

been about the most rational way of conceiving the operation of this

Sole Cause; and this doubt has thus far, on the whole, declined in favor

of the Elder Oriental or monistic conception, as against the Hebraic

conception of extraneous creation by fiat. The frankly confessed mystery

of the latter, its open appeal to miracle, places it at a fatal

disadvantage with the Elder Orientalism, when the appeal is to reason

and intelligibility. It is therefore no occasion for wonder that,

especially since the rise of the scientific doctrine of Evolution, with

its postulate of a universal unity, self-varying yet self-fulfilling,

even the leaders of theology are more and more falling into the monistic

line and swelling the ever-growing ranks of pantheism. If it be asked

here, _And why not?_--_where is the harm of it?_--_is not the whole

question simply of what is true_? the answer is, _The mortal harm of the

destruction of personality, which lives or dies with the preservation or

destruction of individual responsibility; while the completer truth is,

that there are other and profounder (or, if you please, higher) truths

than this of explanation by Efficient Cause_. In fact, there is a higher

conception of Cause itself than this of production, or efficiency; for,

of course, as we well might say, that alone can be the supreme

conception of Cause which can subsist between absolute or unreserved

realities, and such must exclude their production or their necessitating

control by others. So that we ought long since to have realized that

Final Cause, the recognized presence to each other as unconditioned

realities, or Defining Auxiliaries and Ends, is the sole causal relation

that can hold among primary realities; though among such it _can_ hold,

and in fact must.

For the absolute reality of personal intelligences, at once individual

and universally recognizant of others, is called for by other

conceptions fundamental to philosophy. These other fundamental concepts

can no more be counted out or ignored than those we have hitherto

considered; and when we take them up, we shall see how vastly more

significant they are. They alone will prove supreme, truly organizing,

normative; they alone can introduce gradation in truths, for they alone

introduce the judgment of worth, of valuation; they alone can give us

counsels of perfection, for they alone rise from those elements in our

being which deal with ideals and with veritable Ideas. So let us proceed

to them.

* * * * *

Our path into their presence, however, is through another pair, not so

plainly antithetic as those we have thus far considered. This pair that

I now mean is Time and Space, which, though not obviously antinomic, yet

owes its existence, as can now be shown, to that profoundest of

concept-contrasts which we earlier considered under the head of Subject

and Object, when the Object takes on its only adequate form of Other

Subject. But in passing from the contrast One and Many towards its

rational transformation into the moral society of Mind and Companion

Minds, we break into this pair of Time and Space, and must make our way

through it by taking in its full meaning.

Time and Space play an enormous part in all our empirical thinking, our

actual use of thought in our sense-perceptive life. And no wonder; for,

in coöperation, they form the postulate and condition of all our

possible sensuous consciousness. Only on them as backgrounds can thought

take on the peculiar clearness of an image or a picture; only on the

screens which they supply can we literally _depict_ an object. And this

clarity of outline and boundary is so dear to our ordinary

consciousness, that we are prone to say there is no sufficient, no real

clearness, unless we can clarify by the bounds either of place or of

date, or of both. In this mood, we are led to deny the reality and

validity of thought altogether, when it cannot be defined in the metes

and bounds afforded by Time or by Space: that which has no date nor

place, we say,--no extent and no duration,--cannot be real; it is but a

pseudo-thought, a pretense and a delusion. Here is the extremely

plausible foundation of the philosophy known as sensationism, the

refined or second-thought form of materialism, in which it begins its

euthanasia into idealism.

Without delaying here to criticise this, let us notice the part that

Time and Space play in reference to the conceptual pair we last

considered, the One and the Many; for not otherwise shall we find our

way beyond them to the still more fundamental conceptions which we are

now aiming to reach. Indeed, it is through our surface-apprehension of

the pair One and Many, as this illumines experience, that we most

naturally come at the pair Time and Space; so that these are at first

taken for mere generalizations and abstractions, the purely nominal

representatives of the actual distinctions between the members of the

Many by our sense perception of this from that, of here from there, of

now from then. It is not till our reflective attention is fixed on the

fact that _there_ and _here_, _now_ and _then_, are _peculiar_

distinctions, wholly different from other contrasts of this with

that,--which may be made in all sorts of ways, by difference of quality,

or of quantity, or of relations quite other than place and date,--it is

not till we realize this _peculiar_ character of the Time-contrast and

the Space-contrast, that we see these singular differential _qualia_

cannot be derived from others, not even from the contrast One and Many,

but are independent, are themselves underived and spontaneous utterances

of our intelligent, our percipient nature. But when Kant first helped

mankind to the realization of this spontaneous (or _a priori_) character

of this pair of perceptive conditions, or Sense-Forms, he fell into the

persuasion, and led the philosophic world into it, that though Time and

Space are not derivatives of the One and the Many read as the numerical

aspect of our perceptive experiences, yet there _is_ between the two

pairs a connection of dependence as intimate as that first supposed, but

in exactly the opposite sense; namely, that the One and the Many are

conditioned by Time and Space, or, when it comes to the last resort, are

at any rate completely dependent upon Time. By a series of units, this

view means, we really understand a set of items discriminated and

related either as points or as instants: in the last analysis, as

instants: that is, it is impossible to apprehend a unit, or to count and

sum units, unless the unit is taken as an instant, and the units as so

many instants. Numbers, Kant holds, are no doubt pure (or quite

unsensuous) percepts,--discerned particulars,--therefore spontaneous

products of the mind _a priori_, but made possible only by the primary

pure percept Time, or, again, through the mediation of this, by the

conjoined pure percept Space; so that the numbers, in their own pure

character, are simply the instants in their series. As the instants, and

therefore the numbers, are pure percepts,--particulars discerned without

the help of sense,--so pure percepts, in a primal and comprehensive

sense, argues Kant, must their conditioning postulates Time and Space

be, to supply the "element," or "medium," that will render such pure

percepts possible.

This doctrine of Kant's is certainly plausible; indeed, it is

impressively so; and it has taken a vast hold in the world of science,

and has reinforced the popular belief in the unreality of thought apart

from Time and Space; an unreality which it is an essential part of

Kant's system to establish critically. But as a graver result, it has

certainly tended to discredit the belief in personal identity as an

abiding and immutable reality, enthroned over the mutations of things in

Time and Space; since all that is in these is numbered and is mutable,

and is rather many than one, yet nothing is believed real except as it

falls under them, at any rate under Time. And with this decline of the

belief in a changeless self, has declined, almost as rapidly and

extensively, the belief in immortality. Or, rather, the permanence and

the identity of the person has faded into a question regarded as

unanswerable; though none the less does this agnostic state of belief

tend to take personality, in any responsible sense of the word, out of

the region of practical concern. With what is unknowable, even if

existing, we can have no active traffic; 't is for our conduct as if it

were not.

So it behooves us to search if this prevalent view about the relation of

One and Many to Time and Space is trustworthy and exact. What place and

function in philosophy must Space and Time be given?--for they certainly

have a place and function; they certainly are among the inexpugnable

conceptions with which thought has to concern itself when it undertakes

to gain a view of the whole. But it may be easy to give them a larger

place and function than belong to them by right. Is it true, then, that

the One and the Many--that the system of Numbers, in short--are

unthinkable except as in Space and Time, or, at any rate, in Time? Or,

to put the question more exactly, as well as more gravely and more

pertinently, Are Space and Time the true _principia individui_, and is

Time preëminently the ultimate _principium individuationis_? Is there

accordingly no individuality, and no society, no associative assemblage,

except in the fleeting world of phenomena, dated and placed? Simply to

ask the question, and thus bring out the full drift of this Kantian

doctrine, is almost to expose the absurdity of it. Such a doctrine,

though it may be wisely refusing to confound personality, true

individuality, with the mere logical singular; nay, worse, with a

limited and special illustration of the singular, the one _here_ or the

one _there_, the one _now_ or the one _then_; nevertheless, by confining

numerability to things material and sensible, makes personal identity

something unmeaning or impossible, and destroys part of the foundation

for the relations of moral responsibility. Though the vital trait of the

person, his genuine individuality, doubtless lies, not in his being

exactly numerable, but in his being aboriginal and originative; in a

word, in his self-activity, in his being a centre of autonomous social

recognition; yet exactly numerable he indeed is, and must be, not

confusable with any other, else his professed autonomy, his claim of

rights and his sense of duty, can have no significance, must vanish in

the universal confusion belonging to the indefinite. Nor, on the other

hand, is it at all true that a number has to be a point or an instant,

nor that things when numbered and counted are implicitly pinned upon

points or, at all events, upon instants. It may well enough be the fact

that in our empirical use of number we have to employ Time, or even

Space, but it is a gaping _non sequitur_ to conclude that we therefore

can count nothing but the placed and the dated. Certainly we count

whenever we _distinguish_,--by whatever means, on whatever ground. To

think is, in general, at least to "distinguish the things that differ;"

but this will not avail except we keep account of the differences; hence

the One and the Many lie in the very bosom of intelligence, and this

fundamental and spontaneous contrast can not only rive Time and Space

into expressions of it, in instants and in points, but travels with

thought from its start to its goal, and as organic factor in

mathematical science does indeed, as Plato in the _Republic_ said, deal

with absolute being, if yet dreamwise; so that One and Many, and Many as

the sum of the ones, makes part of the measure of that primally real

world which the world of minds alone can be. If the contrast One and

Many can pass the bounds of the merely phenomenal, by passing the

temporal and the spatial; if it applies to universal being, to the

noumenal as well as to the phenomenal; then the absolutely real world,

so far as concerns this essential condition, can be a world of genuine

individuals, identifiable, free, abiding, responsible, and there can be

a real moral order; if not, then there can be no such moral world, and

the deeper thought-conceptions to which we now approach must be

regarded, at the best, as fair illusions, bare ideals, which the serious

devotee of truth must shun, except in such moments of vacancy and

leisure as he may venture to surrender, at intervals, to purely hedonic

uses. But if the One and the Many are not dependent on Time and Space,

their universal validity is possible; and it has already been shown that

they are not so dependent, are not thus restricted.

And now it remains to show their actual universality, by exhibiting

their place in the structure of the absolutely real; since nobody calls

in question their pertinence to the world of phenomena. But their

noumenal applicability follows from their essential implication with all

and every difference: no difference, no distinction, that does not carry

counting; and this is quite as true as that there can be no counting

without difference. The One and the Many thus root in Identity and

Difference, pass up into fuller expression in Universal and Particular,

hold forward into Cause and Effect, attain their commanding presentation

in the Reciprocity of First Causes, and so keep record of the contrast

between Necessity and Contingency. In short, they are founded in, and in

their turn help (indispensably) to express, _all_ the categories,--Quality,

Quantity, Relation, Modality. Nor do they suffer arrest there; they hold

in the ideals, the True, the Beautiful, the Good, and in the primary

Ideas, the Self, the World, and God. For all of these differ, however

close their logical linkage may be; and in so far as they differ, each

of them is a counted unit, and so they are many. And, most profoundly of

all, One and Many take footing in absolute reality so soon as we realize

that nothing short of intelligent being can be primordially real,

underived, and truly causal, and that intelligence is, by its idea, at

once an _I_-thinking and a universal recognizant outlook upon others

that think _I_.