The assertion that mathematics is a "pure" science is often taken to

mean that it is in no way dependent on experience in the construction of

its basal concepts. The space with which geometry deals may be Euclidean

or not, as we please; it may be the real space of experience or not; the

properties of it and the conclusions reached about it may hold in the

real world or they may not; for the mind is free to construct its

conception and definition of space in accordance with its own aims.

Whether geometry is to be ultimately a science of this type must be

left, I suppose, for the mathematicians to decide. A logician may

suggest, however, that the propriety of calling all these conceptions

"space" is not as clear as it ought to be. Still further, there seems to

underlie all arbitrary spaces, as their foundation, a good deal of the

solid material of empirical knowledge, gained by human beings through

contact with an environing world, the environing character of which

seems to be quite independent of the freedom of their thought. However

that may be, it is evident, I think, that the generalization of the

principle involved in this idea of the freedom of thought in framing its

conception of space, would, if extended to logic, give us a science of

knowledge which would have no necessary relation to the real things of

experience, although these are the things with which all concrete

knowledge is most evidently concerned. It would inform us about the

conclusions which necessarily follow from accepted conceptions, but it

could not inform us in any way about the real truth of these

conclusions. It would, thus, always leave a gap between our knowledge

and its objects which logic itself would be quite impotent to close.

Truth would thus become an entirely extra-logical matter. So far as the

science of knowledge is concerned, it would be an accident if knowledge

fitted the world to which it refers. Such a conception of the science of

knowledge is not the property of a few mathematicians exclusively,

although they have, perhaps, done more than others to give it its

present revived vitality. It is the classic doctrine that logic is the

science of thought as thought, meaning thereby thought in independence

of any specific object whatever.

In regard to this doctrine, I would not even admit that such a science

of knowledge is possible. You cannot, by a process of generalization or

free construction, rid thought of connection with objects; and there is

no such thing as a general content or as content-in-general.

Generalization simply reduces the richness of content and, consequently,

of implication. It deals with concrete subject-matter as much and as

directly as if the content were individual and specialized. "Things

equal to the same thing are equal to each other," is a truth, not about

thought, but about things. The conclusions about a fourth dimension

follow, not from the fact that we have thought of one, but from the

conception about it which we have framed. Neither generalization nor

free construction can reveal the operations of thought in transcendental

independence.

It may be urged, however, that nothing of this sort was ever claimed.

The bondage of thought to content must be admitted, but generalization

and free construction, just because they give us the power to vary

conditions as we please, give us thinking in a relative independence of

content, and thus show us how thought operates irrespective of, although

not independent of, its content. The binomial theorem operates

irrespective of the values substituted for its symbols. But I can find

no gain in this restatement of the position. It is true, in a sense,

that we may determine the way thought operates irrespective of any

specific content by the processes of generalization and free

construction; but it is important to know in what sense. Can we claim

that such irrespective operation means that we have discovered certain

logical constants, which now stand out as the distinctive tools of

thought? Or does it rather mean that this process of varying the content

of thought as we please reveals certain real constants, certain ultimate

characters of reality, which no amount of generalization or free

construction can possibly alter? The second alternative seems to me to

be the correct one. Whether it is or not may be left here undecided.

What I wish to emphasize is the fact that the decision is one of the

things of vital interest for logic, and properly belongs in that

science. Clearly, we can never know the significance of ultimate

constants for our thinking until we know what their real character is.

To determine that character we must most certainly pass out of the realm

of generalization and free construction; logic must become other than

simply mathematical or symbolic.

There is another sense in which the determination of the operations of

thought irrespective of its specific content is interpreted in

connection with the exaltation of generalization and free construction.

Knowledge, it is said, is solely a matter of implication, and logic,

therefore, is the science of implication simply. If this is so, it would

appear possible to develop the whole doctrine of implication by the use

of symbols, and thus free the doctrine from dependence on the question

as to how far these symbols are themselves related to the real things of

the world. If, for instance, _a_ implies _b_, then, if _a_ is true, _b_

is true, and this quite irrespective of the real truth of _a_ or _b_. It

is to be urged, however, in opposition to this view, that knowledge is

concerned ultimately only with the real truth of _a_ and _b_, and that

the implication is of no significance whatever apart from this truth.

There is no virtue in the mere implication. Still further, the

supposition that there can be a doctrine of implication, simply, seems

to be based on a misconception. For even so-called formal implication

gets its significance only on the supposed truth of the terms with which

it deals. We suppose that _a_ _does_ imply _b_, and that _a_ _is_ true.

In other words, we can state this law of implication only as we first

have valid instances of it given in specific, concrete cases. The law is

a generalization and nothing more. The formal statement gives only an

apparent freedom from experience. Moreover, there is no reason for

saying that _a_ implies _b_ unless it does so either really or by

supposition. If _a_ really implies _b_, then the implication is clearly

not a matter of thinking it; and to suppose the implication is to feign

a reality, the implications of which are equally free from the processes

by which they are thought. Ultimately, therefore, logic must take

account of real implications. We cannot avoid this through the use of a

symbolism which virtually implies them. Implication can have a logical

character only because it has first a metaphysical one.

The supposition underlying the conception of logic I have been examining

is, itself, open to doubt and seriously questioned. That supposition was

the so-called freedom of thought. The argument has already shown that

there is certainly a very definite limit to this freedom, even when

logic is conceived in a very abstract and formal way. The processes of

knowledge are bound up with their contents, and have their character

largely determined thereby. When, moreover, we view knowledge in its

genesis, when we take into consideration the contributions which

psychology and biology have made to our general view of what knowledge

is, we seem forced to conclude that the conceptions which we frame are

very far from being our own free creations. They have, on the contrary,

been laboriously worked out through the same processes of successful

adaptation which have resulted in other products. Knowledge has grown up

in connection with the unfolding processes of reality, and has, by no

means, freely played over its surface. That is why even the most

abstract of all mathematics is yet grounded in the evolution of human

experience.

In the remaining parts of this paper, I shall discuss further the claims

of psychology and biology. The conclusion I would draw here is that the

field of logic cannot be restricted to a realm where the operations of

thought are supposed to move freely, independent or irrespective of

their contents and the objects of a real world; and that mathematics,

instead of giving us any support for the supposition that it can,

carries us, by the processes of symbolization and formal implication, to

recognize that logic must ultimately find its field where implications

are real, independent of the processes by which they are thought, and

irrespective of the conceptions we choose to frame.

II

The processes involved in the acquisition and systematization of

knowledge may, undoubtedly, be regarded as mental processes and fall

thus within the province of psychology. It may be claimed, therefore,

that every logical process is also a psychological one. The important

question is, however, is it nothing more? Do its logical and

psychological characters simply coincide? Or, to put the question in

still another form, as a psychological process simply, does it also

serve as a logical one? The answers to these questions can be determined

only by first noting what psychology can say about it as a mental

process.

In the first place, psychology can analyze it, and so determine its

elements and their connections. It can thus distinguish it from all

other mental processes by pointing out its unique elements or their

unique and characteristic connection. No one will deny that a judgment

is different from an emotion, or that an act of reasoning is different

from a volition; and no one will claim that these differences are

entirely beyond the psychologist's power to ascertain accurately and

precisely. Still further, it appears possible for him to determine with

the same accuracy and precision the distinction in content and

connection between processes which are true and those which are false.

For, as mental processes, it is natural to suppose that they contain

distinct differences of character which are ascertainable. The states of

mind called belief, certainty, conviction, correctness, truth, are thus,

doubtless, all distinguishable as mental states. It may be admitted,

therefore, that there can be a thoroughgoing psychology of logical

processes.

Yet it is quite evident to me that the characterization of a mental

process as logical is not a psychological characterization. In fact, I

think it may be claimed that the characterization of any mental process

in a specific way, say as an emotion, is extra-psychological. Judgments

and inferences are, in short, not judgments and inferences because they

admit of psychological analysis and explanation, any more than space is

space because the perception of it can be worked out by genetic

psychology. In other words, knowledge is first _knowledge_, and only

later a set of processes for psychological analysis. That is why, as it

seems to me, all psychological logicians, from Locke to our own day,

have signally failed in dealing with the problem of knowledge. The

attempt to construct knowledge out of mental states, the relations

between ideas, and the relation of ideas to things, has been, as I read

the history, decidedly without profit. Confusion and divergent opinion

have resulted instead of agreement and confidence. On precisely the same

psychological foundation, we have such divergent views of knowledge as

idealism, phenomenalism, and agnosticism, with many other strange

mixtures of logic, psychology, and metaphysics. The lesson of these

perplexing theories seems to be that logic, as logic, must be divorced

from psychology.

It is also of importance to note, in this connection, that the

determination of a process as mental and as thus falling within the

domain of psychology strictly, has by no means been worked out to the

general satisfaction of psychologists themselves. Recent literature

abounds in elaborate discussion of the distinction between what is a

mental fact and what not, with a prevailing tendency to draw the

remarkable conclusion that all facts are somehow mental or experienced

facts. The situation would be worse for psychology than it is, if that

vigorous science had not learned from other sciences the valuable knack

of isolating concrete problems and attacking them directly, without the

burden of previous logical or metaphysical speculation. Thus knowledge,

which is the peculiar province of logic, is increased, while we wait for

the acceptable definition of a mental fact. But definitions, be it

remembered, are themselves logical matters. Indeed, some psychologists

have gone so far as to claim that the distinction of a fact as mental is

a purely logical distinction. This is significant as indicating that the

time has not yet come for the identification of logic and psychology.

In refreshingly sharp contrast to the vagueness and uncertainty which

beset the definition of a mental fact are the palpable concreteness and

definiteness of knowledge itself. Every science, even history and

philosophy, are instances of it. What constitutes a knowledge ought to

be as definite and precise a question as could be asked. That logic has

made no more progress than it has in the answer to it appears to be due

to the fact that it has not sufficiently grasped the significance of its

own simplicity. Knowledge has been the important business of thinking

man, and he ought to be able to tell what he does in order to know, as

readily as he tells what he does in order to build a house. And that is

why the Aristotelian logic has held its own so long. In that logic, "the

master of them that know" simply rehearsed the way he had systematized

his own stores of knowledge. Naturally we, so far as we have followed

his methods, have had practically nothing to add. In our efforts to

improve on him, we have too often left the right way and followed the

impossible method inaugurated by Locke. Had we examined with greater

persistence our own methods of making science, we should have profited

more. The introduction of psychology, instead of helping the situation,

only confuses it.

Let it be granted, however, in spite of the vagueness of what is meant

by a mental fact, that logical processes are also mental processes. This

fact has, as I have already suggested, an important bearing on their

genesis, and sets very definite limits to the freedom of thought in

creating. It is not, however, as mental processes that they have the

value of knowledge. A mental process which is knowledge purports to be

connected with something other than itself, something which may not be a

mental process at all. This connection should be investigated, but the

investigation of it belongs, not to psychology, but to logic.

I am well aware that this conclusion runs counter to some metaphysical

doctrines, and especially to idealism in all its forms, with the

epistemologies based thereon. It is, of course, impossible here to

defend my position by an elaborate analysis of these metaphysical

systems. But I will say this. I am in entire agreement with idealism in

its claim that questions of knowledge and of the nature of reality

cannot ultimately be separated, because we can know reality only as we

know it. But the general question as to how we know reality can still be

raised. By this I do not mean the question, how is it possible for us to

have knowledge at all, or how it is possible for reality to be known at

all, but how, as a matter of fact, we actually do know it? That we

really do know it, I would most emphatically claim. Still further, I

would claim that what we know about it is determined, not by the fact

that we can know in general, but by the way reality, as distinct from

our knowledge, has determined. These ways appear to me to be

ascertainable, and form, thus, undoubtedly, a section of metaphysics.

But the metaphysics will naturally be realistic rather than idealistic.

III

Just as logical processes may be regarded as, at the same time,

psychological processes, so they may be regarded, with equal right, as

vital processes, coming thus under the categories of evolution. The

tendency so to regard them is very marked at the present day, especially

in France and in this country. In France, the movement has perhaps

received the clearer definition. In America the union of logic and

biology is complicated--and at times even lost sight of--by emphasis on

the idea of evolution generally. It is not my intention to trace the

history of this movement, but I should like to call attention to its

historic motive in order to get it in a clear light.

That the theory of evolution, even Darwinism itself, has radically

transformed our historical, scientific, and philosophical methods, is

quite evident. Add to this the influence of the Hegelian philosophy,

with its own doctrine of development, and one finds the causes of the

rather striking unanimity which is discoverable in many ways between

Hegelian idealists, on the one hand, and philosophers of evolution of

Spencer's type, on the other. Although two men would, perhaps, not

appear more radically different at first sight than Hegel and Spencer, I

am inclined to believe that we shall come to recognize more and more in

them an identity of philosophical conception. The pragmatism of the day

is a striking confirmation of this opinion, for it is often the

expression of Hegelian ideas in Darwinian and Spencerian terminology.

The claims of idealism and of evolutionary science and philosophy have

thus sought reconciliation. Logic has been, naturally, the last of the

sciences to yield to evolutionary and genetic treatment. It could not

escape long, especially when the idea of evolution had been so

successful in its handling of ethics. If morality can be brought under

the categories of evolution, why not thinking also? In answer to that

question we have the theory that thinking is an adaptation, judgment is

instrumental. But I would not leave the impression that this is true of

pragmatism alone, or that it has been developed only through pragmatic

tendencies. It is naturally the result also of the extension of

biological philosophy. In the biological conception of logic, we have,

then, an interesting coincidence in the results of tendencies differing

widely in their genesis.

It would be hazardous to deny, without any qualifications, the

importance of genetic considerations. Indeed, the fact that evolution in

the hands of a thinker like Huxley, for instance, should make

consciousness and thinking apparently useless epiphenomena, in a

developing world, has seemed like a most contradictory evolutionary

philosophy. It was difficult to make consciousness a real function in

development so long as it was regarded as only cognitive in character.

Evolutionary philosophy, coupled with physics, had built up a sort of

closed system with which consciousness could not interfere, but which it

could know, and know with all the assurance of a traditional logic. If,

however, we were to be consistent evolutionists, we could not abide by

such a remarkable result. The whole process of thinking must be brought

within evolution, so that knowledge, even the knowledge of the

evolutionary hypothesis itself, must appear as an instance of

adaptation. In order to do this, however, consciousness must not be

conceived as only cognitive. Judgment, the core of logical processes,

must be regarded as an instrument and as a mode of adaptation.

The desire for completeness and consistency in an evolutionary

philosophy is not the only thing which makes the denial of genetic

considerations hazardous. Strictly biological considerations furnish

reasons of equal weight for caution. For instance, one will hardly deny

that the whole sensory apparatus is a striking instance of adaptation.

Our perceptions of the world would thus appear to be determined by this

adaptation, to be instances of adjustment. They might conceivably have

been different, and in the case of many other creatures, the perceptions

of the world are undoubtedly different. All our logical processes,

referring ultimately as they do to our perceptions, would thus appear

finally to depend on the adaptation exhibited in the development of our

sensory apparatus. So-called laws of thought would seem to be but

abstract statements or formulations of the results of this adjustment.

It would be absurd to suppose that a man thinks in a sense radically

different from that in which he digests, or a flower blossoms, or that

two and two are four in a sense radically different from that in which a

flower has a given number of petals. Thinking, like digesting and

blossoming, is an effect, a product, possibly a structure.

I am not at all interested in denying the force of these considerations.

They have, to my mind, the greatest importance, and due weight has, as

yet, not been given to them. To one at all committed to a unitary and

evolutionary view of the world, it must indeed seem strange if thinking

itself should not be the result of evolution, or that, in thinking,

parts of the world had not become adjusted in a new way. But while I am

ready to admit this, I am by no means ready to admit some of the

conclusions for logic and metaphysics which are often drawn from the

admission. Just because thought, as a product of evolution, is

functional and judgment instrumental, it by no means follows that logic

is but a branch of biology, or that knowledge of the world is but a

temporary adjustment, which, as knowledge, might have been radically

different. In these conclusions, often drawn with Protagorean assurance,

two considerations of crucial importance seem to be overlooked, first,

that adaptation is itself metaphysical in character, and secondly, that

while knowledge may be functional and judgment instrumental, the

character of the functioning has the character of knowledge, which sets

it off sharply from all other functions.

It seems strange to me that the admission that knowledge is a matter of

adaptation, and thus a relative matter, should, in these days, be

regarded as in any way destroying the claims of knowledge to

metaphysical certainty. Yet, somehow, the opinion widely prevails that

the doctrine of relativity necessarily involves the surrender of

anything like absolute truth. "All our knowledge is relative, and,

therefore, only partial, incomplete, and but practically trustworthy,"

is a statement repeatedly made. The fact that, if our development had

been different, our knowledge would have been different, is taken to

involve the conclusion that our knowledge cannot possibly disclose the

real constitution of things, that it is essentially conditional, that it

is only a mental device for getting results, that any other system of

knowledge which would get results equally well would be equally true; in

short, that there can be no such thing as metaphysical or

epistemological truth. These conclusions do indeed seem strange, and

especially strange on the basis of evolution. For while the evolutionary

process might, conceivably, have been different, its results are, in any

case, the results of the process. They are not arbitrary. We might have

digested without stomachs, but the fact that we use stomachs in this

important process ought not to free us from metaphysical respect for the

organ. As M. Rey suggests, in the _Revue Philosophique_ for June, 1904,

a creature without the sense of smell would have no geometry, but that

does not make geometry essentially hypothetical, a mere mental

construction; for we have geometry because of the working out of

nature's laws. Indeed, instead of issuing in a relativistic metaphysics

of knowledge, the doctrine of relativity should issue in the recognition

of the finality of knowledge in every case of ascertainably complete

adaptation. In other words, adaptation is itself metaphysical in

character. Adjustment is always adjustment between things, and yields

only what it does yield. The things or elements get into the state which

is their adjustment, and this adjustment purports to be their actual and

unequivocal ordering in relation to one another. Different conditions

might have produced a different ordering, but, again, this ordering

would be equally actual and unequivocal, equally the _one_ ordering to

issue from them. To suppose or admit that the course of events might

have been and might be different is not at all to suppose or admit that

it was or is different; it is, rather, to suppose and admit that we have

real knowledge of what that course really was and is. This seems to be

very obvious.

Yet the evolutionist often thinks that he is not a metaphysician, even

when he brings all his conceptions systematically under the conception

of evolution. This must be due to some temporary lack of clearness. If

evolution is not a metaphysical doctrine when extended to apply to all

science, all morality, all logic, in short, all things, then it is quite

meaningless for evolutionists to pronounce a metaphysical sentence on

logical processes. But if evolution is a metaphysics, then its sentence

is metaphysical, and in every case of adjustment or adaptation we have a

revelation of the nature of reality in a definite and unequivocal form.

This conclusion applies to logical processes as well as to others. The

recognition that they are vital processes can, therefore, have little

significance for these processes in their distinctive character as

logical. They are like all other vital processes in that they are vital

and subject to evolution. They are unlike all others in that thought is

unlike digestion or breathing. To regard logical processes as vital

processes does not in any way, therefore, invalidate them as logical

processes or make it superfluous to consider their claim to give us real

knowledge of a real world. Indeed, it makes such a consideration more

necessary and important.

A second consideration overlooked by the Protagorean tendencies of the

day is that judgment, even if it is instrumental, purports to give us

knowledge, that is, it claims to reveal what is independent of the

judging process. Perhaps I ought not to say that this consideration is

overlooked, but rather that it is denied significance. It is even denied

to be essential to judgment. It is claimed that, instead of revealing

anything independent of the judging process, judgment is just the

adjustment and no more. It is a reorganization of experience, an attempt

at control. All this looks to me like a misstatement of the facts.

Judgment _claims_ to be no such thing. It does not function as such a

thing. When I make any judgment, even the simplest, I may make it as the

result of tension, because of a demand for reorganization, in order to

secure control of experience; but the judgment _means_ for me something

quite different. It means decidedly and unequivocally that in reality,

apart from the judging process, things exist and operate just as the

judgment declares. If it is claimed that this meaning is illusory, I

eagerly desire to know on what solid ground its illusoriness can be

established. When the conclusion was reached that gravitation varies

directly as the mass and inversely as the square of the distance, it was

doubtless reached in an evolutionary and pragmatic way; but it claimed

to disclose a fact which prevailed before the conclusion was reached,

and in spite of the conclusion. Knowledge has been born of the travail

of living, but it has been born as knowledge.

When the knowledge character of judgment is insisted on, it seems almost

incredible that any one would think of denying or overlooking it.

Indeed, current discussions are far from clear on the subject.

Pragmatists are constantly denying that they hold the conclusions that

their critics almost unanimously draw. There is, therefore, a good deal

of confusion of thought yet to be dispelled. Yet there seems to be

current a pronounced determination to banish the epistemological problem

from logic. This is, to my mind, suspicious, even when epistemology is

defined in a way which most epistemologists would not approve. It is

suspicious just because we must always ask eventually that most

epistemological and metaphysical question: "Is knowledge true?" To

answer, it is true when it functions in a way to satisfy the needs which

generated its activity, is, no doubt, correct, but it is by no means

adequate. The same answer can be made to the inquiry after the

efficiency of any vital process whatever, and is, therefore, not

distinctive. We have still to inquire into the specific character of the

needs which originate judgments and of the consequent satisfaction. Just

here is where the uniqueness of the logical problem is disclosed. With

conscious beings, the success of the things they do has become

increasingly dependent on their ability to discover what takes place in

independence of the knowing process. That is the need which generates

judgment. The satisfaction is, of course, the attainment of the

discovery. Now to make the judgment itself and not the consequent action

the instrumental factor seems to me to misstate the facts of the case.

Nothing is clearer than that there is no necessity for knowledge to

issue in adjustment. And it is clear to me that increased control of

experience, while resulting from knowledge, does not give to it its

character. Omniscience could idly view the transformations of reality

and yet remain omniscient. Knowledge works, but it is not, therefore,

knowledge.

These considerations have peculiar force when applied to that branch of

knowledge which is knowledge itself. Is the biological account of

knowledge correct? That question we must evidently ask, especially when

we are urged to accept the account. Can we, to put the question in its

most general form, accept as an adequate account of the logical process

a theory which is bound up with some other specific department of human

knowledge? It seems to me that we cannot. Here we must be

epistemologists and metaphysicians, or give up the problem entirely.

This by no means involves the attempt to conceive pure thought set over

against pure reality--the kind of epistemology and metaphysics justly

ridiculed by the pragmatist--for knowledge, as already stated, is given

to us in concrete instances. How knowledge in general is possible is,

therefore, as useless and meaningless a question as how reality in

general is possible. The knowledge is given as a fact of life, and what

we have to determine is not its non-logical antecedents or its practical

consequences, but its constitution as knowledge and its validity. It may

be admitted that the question of validity is settled pragmatically. No

knowledge is true unless it yields results which can be verified, unless

it _can_ issue in increased control of experience. But I insist again

that that fact is not sufficient for an account of what knowledge claims

to be. It claims to issue in control because it is true in independence

of the control. And it is just this assurance that is needed to

distinguish knowledge from what is not knowledge. It is the necessity of

exhibiting this assurance which makes it impossible to subordinate

logical problems, and forces us at last to questions of epistemology and

metaphysics.

As I am interested here primarily in determining the field of logic, it

is somewhat outside my province to consider the details of logical

theory. Yet the point just raised is of so much importance in connection

with the main question that I venture the following general

considerations. This is, perhaps, the more necessary because the

pragmatic doctrine finds in the concession made regarding the test of

validity one of its strongest defenses.

Of course a judgment is not true simply because it is a judgment. It may

be false. The only way to settle its validity is to discover whether

experience actually provides what the judgment promises, that is,

whether the conclusions drawn from it really enable us to control

experience. No mere speculation will yield the desired result, no matter

with how much formal validity the conclusions may be drawn. That merely

formal validity is not the essential thing, I have pointed out in

discussing the relation of logic to mathematics. The test of truth is

pragmatic. It is apparent, therefore, that the formal validity does not

determine the actual validity. What is this but the statement that the

process of judgment is not itself the determining factor in its real

validity? It is, in short, only valid judgments that can really give us

control of experience. The implications taken up in the judgment must,

therefore, be real implications which, as such, have nothing to do with

the judging process, and which, most certainly, are not brought about by

it. And what is this but the claim that judgment as such is never

instrumental? In other words, a judgment which effected its own content

would only by the merest accident function as valid knowledge. We have

valid knowledge, then, only when the implications of the judgment are

found to be independent of the judging process. We have knowledge only

at the risk of error. The pragmatic test of validity, instead of proving

the instrumental character of judgment, would thus appear to prove just

the reverse.

Valid knowledge has, therefore, for its content a system of real, not

judged or hypothetical implications. The central problem of logic which

results from this fact is not how a knowledge of real implications is

then possible, but what are the ascertainable types of real

implications. But, it may be urged, we need some criterion to determine

what a real implication is. I venture to reply that we need none, if by

such is meant anything else than the facts with which we are dealing. I

need no other criterion than the circle to determine whether its

diameters are really equal. And, in general, I need no other criterion

than the facts dealt with to determine whether they really imply what I

judge them to imply. Logic appears to me to be really as simple as this.

Yet there can be profound problems involved in the working out of this

simple procedure. There is the problem already stated of the most

general types of real implication, or, in other words, the time-honored

doctrine of categories. Whether there are categories or basal types of

existence seems to me to be ascertainable. When ascertained, it is also

possible to discover the types of inference or implication which they

afford. This is by no means the whole of logic, but it appears to me to

be its central problem.

These considerations will, I hope, throw light on the statement that

while knowledge works, it is not therefore knowledge. It works because

its content existed before its discovery by the knowledge process, and

because its content was not effected or brought about by that process.

Judgment was the instrument of its discovery, not the instrument which

fashioned it. While, therefore, willing to admit that logical processes

are vital processes, I am not willing to admit that the problem of logic

is radically changed thereby in its formulation or solution, for the

vital processes in question have the unique character of knowledge, the

content of which is what it claims to be, a system of real implications

which existed prior to its discovery.

In the psychological and biological tendencies in logic, there is,

however, I think, a distinct gain for logical theory. The insistence

that logical processes are both mental and vital has done much to take

them out of the transcendental aloofness from reality in which they have

often been placed, especially since Kant. So long as thought and object

were so separated that they could never be brought together, and so long

as logical processes were conceived wholly in terms of ideas set over

against objects, there was no hope of escape from the realm of pure

hypothesis and conjecture. Locke's axiom that "the mind, in all its

thoughts and reasonings, hath no other immediate object but its own

ideas," an axiom which Kant did so much to sanctify, and which has been

the basal principle of the greater part of modern logic and metaphysics,

is most certainly subversive of logical theory. The transition from

ideas to anything else is rendered impossible by it. Now it is just this

axiom which the biological tendencies in logic have done so much to

destroy. They have insisted, with the greatest right, that logical

processes are not set over against their content as idea against object,

as appearance against reality, but are processes of reality itself. Just

as reality can and does function in a physical or a physiological way,

so also it functions in a logical way. The state we call knowledge

becomes, thus, as much a part of the system of things as the state we

call chemical combination. The problem how thought can know anything

becomes, therefore, as irrelevant as the problem how elements can

combine at all. The recognition of this is a great gain, and the promise

of it most fruitful for both logic and metaphysics.

But, as I have tried to point out, all this surrendering of pure thought

as opposed to pure reality, does not at all necessitate our regarding

judgment as a process which makes reality different from what it was

before. Of course there is one difference, namely, the logical one; for

reality prior to logical processes is unknown. As a result of these

processes it becomes known. These processes are, therefore, responsible

for a known as distinct from an unknown reality. But what is the

transformation which reality undergoes in becoming known? When it

becomes known that water seeks its own level, what change has taken

place in the water? It would appear that we must answer, none. The water

which seeks its own level has not been transformed into ideas or even

into a human experience. It appears to remain, as water, precisely what

it was before. The transformation which takes place, takes place in the

one who knows, a transformation from ignorance to knowledge. Psychology

and biology can afford us the natural history of this transformation,

but they cannot inform us in the least as to why it should have its

specific character. That is given and not deduced. The attempts to

deduce it have, without exception, been futile. That is why we are

forced to take it as ultimate in the same way we take as ultimate the

specific character of any definite transformation. To my mind, there is

needed a fuller and more cordial recognition of this fact. The

conditions under which we, as individuals, know are certainly

discoverable, just as much as the conditions under which we breathe or

digest. And what happens to things when we know them is also as

discoverable as what happens to them when we breathe them or digest

them.

But here the idealist may interpose that we can never know what happens

to things when we know them, because we can never know them before they

become known. I suppose I ought to wrestle with this objection. It is an

obvious one, but, to my mind, it is without force. The objection, if

pursued, can carry us only in a circle. The problem of knowledge is

still on our hands, and every logician of whatever school, the offerer

of this objection also, has, nevertheless, attempted to show what the

transformation is that thought works, for all admit that it works some.

Are we, therefore, engaged in a hopeless task? Or have we failed to

grasp the significance of our problem? I think the latter. We fail to

recognize that, in one way or other, we do solve the problem, and that

our attempts to solve it show quite clearly that the objection under

consideration is without force. Take, for instance, any concrete case of

knowledge, the water seeking its own level, again. Follow the process of

knowledge to the fullest extent, we never find a single problem which is

not solvable by reference to the concrete things with which we are

dealing, nor a single solution which is not forced upon us by these

things rather than by the fact that we deal with them. The

transformation wrought is thus discovered, in the progress of knowledge

itself, to be wrought solely in the inquiring individual, and wrought by

repeated contact with the things with which he deals. In other words,

all knowledge discloses the fact that its content is not created by

itself, but by the things with which it is concerned.

It is quite possible, therefore, that knowledge should be what we call

transcendent and yet not involve us in a transcendental logic. That we

should be able to know without altering the things we know is no more

and no less remarkable and mysterious than that we should be able to

digest by altering the things we digest. In other words, the fact that

digestion alters the things is no reason that knowledge should alter

them, even if we admit that logical processes are vital and subject to

evolution. Indeed, if evolution teaches us anything on this point, it is

that knowledge processes are real just as they exist, as real as growth

and digestion, and must have their character described in accordance

with what they are. The recognition that knowledge can be transcendent

and yet its processes vital seems to throw light on the difficulty

evolution has encountered in accounting for consciousness and knowledge.

All the reactions of the individual seem to be expressible in terms of

chemistry and physics without calling in consciousness as an operating

factor. What is this but the recognition of its transcendence,

especially when the conditions of conscious activity are quite likely

expressible in chemical and physical terms? While, therefore, biological

considerations result in the great gain of giving concrete reality to

the processes of knowledge, the gain is lost, if knowledge itself is

denied the transcendence which it so evidently discloses.

IV

The argument advanced in this discussion has had the aim of emphasizing

the fact that in knowledge we have actually given, as content, reality

as it is in independence of the act of knowing, that the real world is

self-existent, independent of the judgments we make about it. This fact

has been emphasized in order to confine the field of logic to the field

of knowledge as thus understood. In the course of the argument, I have

occasionally indicated what some of the resulting problems of logic are.

These I wish now to state in a somewhat more systematic way.

The basal problem of logic becomes, undoubtedly, the metaphysics of

knowledge, the determination of the nature of knowledge and its relation

to reality. It is quite evident that this is just the problem which the

current tendencies criticised have sought, not to solve, but to avoid or

set aside. Their motives for so doing have been mainly the difficulties

which have arisen from the Kantian philosophy in its development into

transcendentalism, and the desire to extend the category of evolution to

embrace the whole of reality, knowledge included. I confess to feeling

the force of these motives as strongly as any advocate of the criticised

opinions. But I do not see my way clear to satisfying them by denying or

explaining away the evident character of knowledge itself. It appears

far better to admit that a metaphysics of knowledge is as yet hopeless,

rather than so to transform knowledge as to get rid of the problem; for

we must ultimately ask after the truth of the transformation. But I am

far from believing that a metaphysics of knowledge is hopeless. The

biological tendencies themselves seem to furnish us with much material

for at least the beginnings of one. Reality known is to be set over

against reality unknown or independent of knowledge, not as image to

original, idea to thing, phenomena to noumena, appearance to reality;

but reality as known is a new stage in the development of reality

itself. It is not an external mind which knows reality by means of its

own ideas, but reality itself becomes known through its own expanding

and readjusting processes. So far I am in entire agreement with the

tendencies I have criticised. But what change is effected by this

expansion and readjustment? I can find no other answer than this simple

one: the change to knowledge. And by this I mean to assert unequivocally

that the addition of knowledge to a reality hitherto without it is

simply an addition to it and not a transformation of it. Such a view may

appear to make knowledge a wholly useless addition, but I see no

inherent necessity in such a conclusion. Nor do I see any inherent

necessity of supposing that knowledge must be a useful addition. Yet I

would not be so foolish as to deny the usefulness of knowledge. We have,

of course, the most palpable evidences of its use. As we examine them, I

think we find, without exception, that knowledge is useful just in

proportion as we find that reality is not transformed by being known. If

it really were transformed in that process, could anything else than

confusion result from the multitude of knowing individuals?

To me, therefore, the metaphysics of the situation resolves itself into

the realistic position that a developing reality develops, under

ascertainable conditions, into a known reality without undergoing any

other transformation, and that this new stage marks an advance in the

efficiency of reality in its adaptations. My confidence steadily grows

that this whole process can be scientifically worked out. It is

impossible here to justify my confidence in detail, and I must leave the

matter with the following suggestion. The point from which knowledge

starts and to which it ultimately returns is always some portion of

reality where there is consciousness, the things, namely, which, we are

wont to say, are in consciousness. These things are not ideas

representing other things outside of consciousness, but real things,

which, by being in consciousness, have the capacity of representing

_each other_, of standing for or implying each other. Knowledge is not

the creation of these implications, but their successful

systematization. It will be found, I think, that this general statement

is true of every concrete case of knowledge which we possess. Its

detailed working out would be a metaphysics of knowledge, an

epistemology.

Since knowledge is the successful systematization of the implications

which are disclosed in things by virtue of consciousness, a second

logical problem of fundamental importance is the determination of the

most general types of implication with the categories which underlie

them. The execution of this problem would naturally involve, as

subsidiary, the greater part of formal and symbolic logic. Indeed, vital

doctrines of the syllogism, of definition, of formal inference, of the

calculus of classes and propositions, of the logic of relations, appear

to be bound up ultimately with a doctrine of categories; for it is only

a recognition of basal types of existence with their implications that

can save these doctrines from mere formalism. These types of existence

or categories are not to be regarded as free creations or as the

contributions of the mind to experience. There is no deduction of them

possible. They must be discovered in the actual progress of knowledge

itself, and I see no reason to suppose that their number is necessarily

fixed, or that we should necessarily be in possession of all of them. It

is requisite, however, that in every case categories should be incapable

of reduction to each other.

A doctrine of categories seems to me to be of the greatest importance in

the systematization of knowledge, for no problem of relation is even

stateable correctly before the type of existence to which its terms

belong has been first determined. I submit one illustration to reinforce

this general statement, namely, the relation of mind to body. If mind

and body belong to the same type of existence, we have one set of

problems on our hands; but if they do not, we have an entirely different

set. Yet volumes of discussion written on this subject have abounded in

confusion, simply because they have regarded mind and body as belonging

to radically different types of existence and yet related in terms of

the type to which one of them belongs. The doctrine of parallelism is,

perhaps, the epitome of this confusion.

The doctrine of categories will involve not only the greater part of

formal and symbolic logic, but will undoubtedly carry the logician into

the doctrine of method. Here it is to be hoped that recent tendencies

will result in effectively breaking down the artificial distinctions

which have prevailed between deduction and induction. Differences in

method do not result from differences in points of departure, or between

the universal and the particular, but from the categories, again, which

give the method direction and aim, and result in different types of

synthesis. In this direction, the logician may hope for an approximately

correct classification of the various departments of knowledge. Such a

classification is, perhaps, the ideal of logical theory.

SECTION D--METHODOLOGY OF SCIENCE

SECTION D--METHODOLOGY OF SCIENCE

(_Hall 6, September 22, 3 p. m._)

CHAIRMAN: PROFESSOR JAMES E. CREIGHTON, Cornell University.

SPEAKERS: PROFESSOR WILHELM OSTWALD, University of Leipzig.

PROFESSOR BENNO ERDMANN, University of Bonn.

SECRETARY: DR. R. B. PERRY, Harvard University.

ON THE THEORY OF SCIENCE

BY WILHELM OSTWALD

(_Translated from the German by Dr. R. M. Yerkes, Harvard University_)

[Wilhelm Ostwald, Professor of Physical Chemistry,

University of Leipzig, since 1887. b. September 2, 1853,

Riga, Russia. Grad. Candidate Chemistry, 1877; Master

Chemistry, 1878; Doctor Chemistry, Dorpat. Dr. Hon. Halle

and Cambridge; Privy Councilor; Assistant, Dorpat, 1875-81;

Regular Professor, Riga 1881-87. Member various learned and

scientific societies. Author of _Manual of General

Chemistry_; _Electro Chemistry_; _Foundation of Inorganic

Chemistry_; _Lectures on Philosophy of Nature_; _Artist's

Letters_; _Essays and Lectures_; and many other noted works

and papers on Chemistry and Philosophy.]

One of the few points on which the philosophy of to-day is united is the

knowledge that the only thing completely certain and undoubted for each

one is the content of his own consciousness; and here the certainty is

to be ascribed not to the content of consciousness in general, but only

to the momentary content.

This momentary content we divide into two large groups, which we refer

to the inner and outer world. If we call any kind of content of

consciousness an experience, then we ascribe to the outer world such

experiences as arise without the activity of our will and cannot be

called forth by its activity alone. Such experiences never arise without

the activity of certain parts of our body, which we call sense organs.

In other words, the outer world is that which reaches our consciousness

through the senses.

On the other hand, we ascribe to our inner world all experiences which

arise without the immediate assistance of a sense organ. Here, first of

all, belong all experiences which we call remembering and thinking. An

exact and complete differentiation of the two territories is not

intended here, for our purpose does not demand that this task be

undertaken. For this purpose the general orientation in which every one

recognizes familiar facts of his consciousness is sufficient.

Each experience has the characteristic of uniqueness. None of us doubts

that the expression of the poet "Everything is only repeated in life" is

really just the opposite of the truth, and that in fact nothing is

repeated in life. But to express such a judgment we must be in position

to compare different experiences with each other, and this possibility

rests upon a fundamental phenomenon of our consciousness, memory. Memory

alone enables us to put various experiences in relation to each other,

so that the question as to their likeness or difference can be asked.

We find the simpler relations here in the inner experiences. A certain

thought, such as twice two is four, I can bring up in my consciousness

as often as I wish, and in addition to the content of the thought I

experience the further consciousness that I have already had this

thought before, that it is familiar to me.

A similar but somewhat more complex phenomenon appears in the

experiences in which the outer world takes part. After I have eaten an

apple, I can repeat the experience in two ways. First, as an inner

experience, I can remember that I have eaten the apple and by an effort

of my will I can re-create in myself, although with diminished strength

and intensity, a part of the former experience--the part which belonged

to my inner world. Another part, the sense impression which belonged to

that experience, I cannot re-create by an effort of my will, but I must

again eat an apple in order to have a similar experience of this sort.

This is a complete repetition of the experience to which the external

world also contributes. Such a repetition does not depend altogether on

my own powers, for it is necessary that I have an apple, that is, that

certain conditions which are independent of me and belong to the outer

world be fulfilled.

Whether the outer world takes part in the repetition of an experience or

not has no influence upon the possibility of the content of

consciousness which we call memory. From this it follows that this

content depends upon the inner experience alone, and that we remember an

external event only by means of its inner constituents. The mere

repetition of corresponding sense impressions is not sufficient for

this, for we can see the same person repeatedly without recognizing him,

if the inner accompanying phenomena were so insignificant, as a result

of lack of interest, that their repetition does not produce the content

of consciousness known as memory. If we see him quite frequently, the

frequent repetition of the external impression finally causes the memory

of the corresponding inner experience.

From this it results that for the "memory"-reaction a certain intensity

of the inner experience is necessary. This threshold can be attained

either at once or by continued repetition. The repetitions are the more

effective the more rapidly they follow each other. From this we may

conclude that the memory-value of an experience, or its capacity for

calling forth the "memory"-reaction by repetition, decreases with the

lapse of time. Further, we must consider the fact mentioned above, that

an experience is never exactly repeated, and that therefore the

"memory"-reaction occurs even where there is only resemblance or partial

agreement in place of complete agreement. Here, too, there are different

degrees; memory takes place more easily the more perfectly the two

experiences agree, and _vice versa_.

If we look at these phenomena from the physiological side, we may say we

have two kinds of apparatus or organs, one of which does not depend upon

our will, whereas the other does. The former are the sense organs. The

latter constitutes the organ of thought. Only the activities of the

latter constitute our experiences or the content of our consciousness.

The activities of the former may call forth the corresponding processes

of the latter, but this is not always necessary. Our sense organs can be

influenced without our "noticing" it, that is, without the thinking

apparatus being involved. An especially important reaction of the

thinking apparatus is memory, that is, the consciousness that an

experience which we have just had possesses more or less agreement with

former experiences. With reference to the organ of thought, it is the

expression of the general physiological fact that every process

influences the organ in such a way that it has a different relation to

the repetition of this process, from the first time, and moreover that

the repetition is rendered easier. This influence decreases with time.

It is chiefly upon these phenomena that experience rests. Experience

results from the fact that all events consist of a complete series of

simultaneous and successive components. When a connection between some

of those parts has become familiar to us by the repetition of similar

occurrences (for instance, the succession of day and night), we do not

feel such an occurrence as something completely new, but as something

partially familiar, and the single parts or phases of it do not surprise

us, but rather we anticipate their coming or expect them. From

expectation to prediction is only a short step, and so experience

enables us to prophesy the future from the past and present.

Now this is also the road to science: for science is nothing but

systematized experience, that is, experience reduced to its simplest and

clearest forms. Its purposes to predict from a part of a phenomenon

which is known another part which is not yet known. Here it may be a

question of spatial as well as of temporal phenomena. Thus the

scientific zoölogist knows how to "determine," that is, to tell, from

the skull of an animal, the nature of the other parts of the animal to

which the skull belongs; likewise the astronomer is able to indicate the

future, situation of a planet from a few observations of its present

situation; and the more exact the first observations were, the more

distant the future for which he can predict. All such scientific

predictions are limited, therefore, with reference to their number and

their accuracy. If the skull shown to the zoölogist is that of a

chicken, then he will probably be able to indicate the general

characteristics of chickens, and also perhaps whether the chicken had a

top-knot or not; but not its color, and only uncertainly its age and its

size. Both facts, the possibility of prediction and its limitation in

content and amount, are an expression for the two fundamental facts,

that among our experiences there is similarity, but not complete

agreement.

The foregoing considerations deserve to be discussed and extended in

several directions. First, the objection will be made that a chicken or

a planet is not an experience; we call them rather by the most general

name of thing. But our knowledge of the chicken begins with the

experiencing of certain visual impressions, to which are added, perhaps,

certain impressions of hearing and touch. The sight impressions (to

discuss these first) by no means completely agree. We see the chicken

large or small, according to the distance; and according to its position

and movement its outline is very different. As we have seen, however,

these differences are continually grading into one other and do not

reach beyond certain limits; we neglect to observe them and rest

contented with the fact that certain other peculiarities (legs, wings,

eyes, bill, comb, etc.) remain and do not change. The constant

properties we group together as a thing, and the changing ones we call

the states of this thing. Among the changing properties, we distinguish

further those which depend upon us (for example, the distance) and those

upon which we have no immediate influence (for instance, the position or

motion): the first is called the subjective changeable part of our

experience, while the second is called the objective mutability of the

thing.

This omission of both the subjectively and objectively changeable

portion of the experience in connection with the retention of the

constant portion and the gathering together of the latter into a unity

is one of the most important operations which we perform with our

experiences. We call it the process of abstraction, and its product, the

permanent unity, we call a concept. Plainly this procedure contains

arbitrary as well as necessary factors. Arbitrary or accidental is the

circumstance that quite different phases of a given experience come to

consciousness according to our attention, the amount of practice we have

had, indeed according to our whole intellectual nature. We may overlook

constant factors and attend to changeable ones. The objective factors,

however, become necessary as soon as we have noticed them; after we have

seen that the chicken is black, it is not in our power to see it red.

Accordingly, in general, our knowledge of that which agrees must be less

than it actually could be, since we have not been able to observe every

agreement, and our concept is always poorer in constituents at any given

time than it might be. To seek out such elements of concepts as have

been overlooked, and to prove that they are necessary factors of the

corresponding experiences, is one of the never-ending tasks of science.

The other case, namely, that elements have been received in the concept

which do not prove to be constant, also happens, and leads to another

task. One can then leave that element out of the concept, if further

experiences show that the other elements are found in them, or one can

form a new concept which contains the former elements, leaving out those

that have been recognized as unessential. For a long time the white

color belonged to the concept swan. When the Dutch black swans became

known, it was possible either to drop the element white from the concept

swan (as actually happened), or to make a new concept for the bird which

is similar to the swan but black. Which choice is made in a given case

is largely arbitrary, and is determined by considerations of expediency.

Into the formation of concepts, therefore, two factors are operative, an

objective empirical factor, and a subjective or purposive factor. The

fitness of a concept is seen in relation to its purpose, which we shall

now consider.

The purpose of a concept is its use for prediction. The old logic set up

the syllogism as the type of thought-activity, and its simplest example

is the well-known

All men are mortal,

Caius is a man,

Therefore Caius is mortal.

In general, the scheme runs

To the concept M belongs the element B,

C belongs under the concept M,

Therefore the element B is found in C.

One can say that this method of reasoning is in regular use even to this

day. It must be added, however, that this use is of a quite different

nature from that of the ancients. Whereas formerly the setting up of the

first proposition or the major premise was considered the most important

thing, and the establishment of the second proposition or minor premise

was thought to be a rather trifling matter, now the relation is

reversed. The major premise contains the description of a concept, the

minor makes the assertion that a certain thing belongs under this

concept. What right exists for such an assertion? The most palpable

reply would be, since all the elements of the concept M (including B)

are found in C, C belongs under the concept M. Such a conclusion would

indeed be binding, but at the same time quite worthless, for it only

repeats the minor premise. Actually the method of reasoning is

essentially different, for the minor premise is not obtained by showing

that all the elements of the concept M are found in C, but only some of

them. The conclusion is not necessary, but only probable, and the whole

process of reasoning runs: Certain elements are frequently found

together, therefore they are united in the concept M. Certain of these

elements are recognized in the thing C, therefore probably the other

elements of the concept M will be found in C.

The old logic, also, was familiar with this kind of conclusion. It was

branded, however, as the worst of all, by the name of incomplete

induction, since the absolute certainty demanded of the syllogism did

not belong to its results. One must admit, however, that the whole of

modern science makes use of no other form of reasoning than incomplete

induction, for it alone admits of a prediction, that is, an indication

of relations which have not been immediately observed.

How does science get along with the defective certainty of this process

of reasoning? The answer is, that the probability of the conclusion can

run through all degrees from mere conjecture to the maximum probability,

which is practically indistinguishable from certainty. The probability

is the greater the more frequently an incomplete induction of this kind

has proven correct in later experience. Accordingly we have at our

command a number of expressions which in their simplest and most general

form have the appearance: If an element A is met within a thing, then

the element B is also found in it (in spatial or temporal relationship).

If the relation is temporal, this general statement is known by some

such name as the law of causality. If it is spatial, one talks of the

idea (in the Platonic sense), or the type of the thing, of substance,

etc.

From the considerations here presented we get an easy answer to many

questions which are frequently discussed in very different senses.

First, the question concerning the general validity of the law of

causality. All attempts to prove such a validity have failed, and there

has remained only the indication that without this law we should feel an

unbearable uncertainty in reference to the world. From this, however, we

see very plainly that here it is merely a question of expediency. From

the continuous flux of our experiences we hunt out those groups which

can always be found again, in order to be able to conclude that if the

element A is given, the element B will be present. We do not find this

relationship as "given," but we put it into our experiences, in that we

consider the parts which correspond to the relationship as belonging

together.

The very same thing may be said of spatial complexes. Such factors as

are always, or at any rate often, found together are taken by us as

"belonging together," and out of them a concept is formed which embraces

these factors. A question as to the why has here, as with the temporal

complexes, no definite meaning. There are countless things that happen

together once to which we pay no attention because they happen only once

or but seldom. The knowledge of the fact that such a single concurrence

exists amounts to nothing, since from the presence of one factor it does

not lead to a conclusion as to the presence of another, and therefore

does not make possible prediction. Of all the possible, and even actual

combinations, only those interest us which are repeated, and this

arbitrary but expedient selection produces the impression that the world

consists only of combinations that can be repeated; that, in other

words, the law of causality or of the type is a general one. However

general or limited application those laws have, is more a question of

our skill in finding the constant combinations among those that are

present than a question of objective natural fact.

Thus we see the development and pursuit of all sciences going on in such

a way that on the one hand more and more constant combinations are

discovered, and on the other hand more inclusive relations of this kind

are found out, by means of which elements are united with each other

which before no one had even tried to bring together. So sciences are

increasing both in the sense of an increasing complication and in an

increasing unification.

If we consider from this standpoint the development and procedure of the

various sciences, we find a rational division of the sum total of

science in the question as to the scope and multiplicity of the

combinations or groups treated of in them. These two properties are in a

certain sense antithetical. The simpler a complex is, that is, the fewer

elements brought together in it, the more frequently it is met with, and

_vice versa_. One can therefore arrange all the sciences in such a way

that one begins with the least multiplicity and the greatest scope, and

ends with the greatest multiplicity and the least scope. The first

science will be the most general, and will therefore contain the most

general and therefore the most barren concepts; the last will contain

the most specific and therefore the richest.

What are these limiting concepts? The most general is the concept of

_thing_, that is, any piece of experience, seized arbitrarily from the

flux of our experiences, which can be repeated. The most specific and

richest is the concept of _human intercourse_. Between the science of

things and the science of human intercourse, all the other sciences are

found arranged in regular gradation. If one follows out the scheme the

following outline results:

1. Theory of order. }

2. Theory of numbers, or arithmetic. } Mathematics.

3. Theory of time. }

4. Theory of space, or geometry. }

5. Mechanics. }

6. Physics. } Energetics.

7. Chemistry. }

8. Physiology. }

9. Psychology. } Biology.

10. Sociology. }

This table is arbitrary in so far as the grades assumed can be increased

or diminished according to need. For example, mechanics and physics

could be taken together; or between physics and chemistry, physical

chemistry could be inserted. Likewise between physiology and psychology,

anthropology might find a place; or the first five sciences might be

united under mathematics. How one makes these divisions is entirely a

practical question, which will be answered at any time in accordance

with the purposes of division; and dispute concerning the matter is

almost useless.

I should like, however, to call attention to the three great groups of

mathematics, energetics, and biology (in the wider sense). They

represent the decisive regulative thought which humanity has evolved,

contributed up to this time, toward the scientific mastery of its

experiences. Arrangement is the fundamental thought of mathematics. From

mechanics to chemistry the concept of energy is the most important; and

for the last three sciences it is the concept of life. Mathematics,

energetics, and biology, therefore, embrace the totality of the

sciences.

Before we enter upon the closer consideration of these sciences, it will

be well to anticipate another objection which can be raised on the basis

of the following fact. Besides the sciences named (and those which lie

between them) there are many others, as geology, history, medicine,

philology, which we find difficulty in arranging in the above scheme,

which must, however, be taken into consideration in some way or other.

They are often characterized by the fact that they stand in relation

with several of the sciences named, but even more by the following

circumstance. Their task is not, as is true of the pure sciences above

named, the discovery of general relationships, but they relate rather to

existing complex objects whose origin, scope, extent, etc., in short,

whose temporal and spatial relationships they have to discover or to

"explain." For this purpose they make use of relations which are placed

at their disposal by the first-named pure sciences. These sciences,

therefore, had better be called applied sciences. However, in this

connection we should not think only or even chiefly of technical

applications; rather the expression is used to indicate that the

reciprocal relations of the parts of an object are to be called to mind

by the application of the general rules found in pure science.

While in such a task the abstraction process of pure science is not

applicable (for the omission of certain parts and the concentration upon

others which is characteristic of these is excluded by the nature of the

task), yet in a given case usually the necessity of bringing in various

pure sciences for the purpose of explanation is evident.

Astronomy is one of these applied sciences. Primarily it rests upon

mechanics, and in its instrumental portion, upon optics; in its present

development on the spectroscopic side, however, it borrows considerably

of chemistry. In like manner history is applied sociology and

psychology. Medicine makes use of all the sciences before mentioned, up

to psychology, etc.

It is important to get clearly in mind the nature of these sciences,

since, on account of their compound nature, they resist arrangement

amongst the pure sciences, while, on account of their practical

significance, they still demand consideration. The latter fact gives

them also a sort of arbitrary or accidental character, since their

development is largely conditioned by the special needs of the time.

Their number, speaking in general, is very large, since each pure

science may be turned into an applied science in various ways; and since

in addition we have combinations of two, three, or more sciences.

Moreover, the method of procedure in the applied sciences is

fundamentally different from that in the pure sciences. In the first it

is a question of the greatest possible analysis of a single given

complex into its scientifically comprehensible parts; while pure

science, on the other hand, considers many complexes together in order

to separate out from them their common element, but expressly disclaims

the complete analysis of a single complex.

In scientific work, as it appears in practice, pure and applied science

are by no means sharply separated. On the one hand the auxiliaries of

investigations, such as apparatus, books, etc., demand of the pure

investigator knowledge and application in applied science; and, on the

other hand, the applied scientist is frequently unable to accomplish his

task unless he himself becomes for the time being a pure investigator

and ascertains or discovers the missing general relationships which he

needs for his task. A separation and differentiation of the two forms of

science was necessary, however, since the method and the aim of each

present essential differences.

In order to consider the method of procedure of pure science more

carefully, let us turn back to the table on pages 339, 340, and attend

to the single sciences separately. The theory of arrangement was

mentioned first, although this place is usually assigned to mathematics.

However, mathematics has to do with the concepts of number and magnitude

as fundamentals, while the theory of arrangement does not make use of

these. Here the fundamental concept is rather the thing or object of

which nothing more is demanded or considered than that it is a fragment

of our experience which can be isolated and will remain so. It must not

be an arbitrary combination; such a thing would have only momentary

duration, and the task of science, to learn the unknown from the given,

could not find application. Rather must this element have such a nature

that it can be characterized and recognized again, that is, it must

already have a conceptual nature. Therefore only parts of our experience

which can be repeated (which alone can be objects of science) can be

characterized as things or objects. But in saying this we have said all

that was demanded of them. In other respects they may be just as

different as is conceivable.

If the question is asked, What can be said scientifically about

indefinite things of this sort? it is especially the relations of

arrangement and association which yield an answer. If we call any

definite combination of such things a group, we can arrange such a group

in different ways, that is, we can determine for each thing the relation

in which it is to stand to the neighboring thing. From every such

arrangement result not only the relationships indicated, but a great

number of new ones, and it appears that when the first relationships are

given the others always follow in like manner. This, however, is the

type of the scientific proposition or natural law (page 335). From the

presence of certain relations of arrangement we can deduce the presence

of others which we have not yet demonstrated.

To illustrate this fact by an example, let us think of the things

arranged in a simple row, while we choose one thing as a first member

and associate another with it as following it; with the latter another

is associated, etc. Thereby the position of each thing in the row is

determined only in relation to the immediately preceding thing.

Nevertheless, the position of every member in the whole row, and

therefore its relation to every other member, is determined by this.

This is seen in a number of special laws. If we differentiate former and

latter members we can formulate the proposition, among others, if B is a

later member with reference to A, and C with reference to B, then C is

also a later member with reference to A.

The correctness and validity of this proposition seems to us beyond all

doubt. But this is only a result of the fact that we are able to

demonstrate it very easily in countless single cases, and have so

demonstrated it. We know only cases which correspond to the proposition,

and have never experienced a contradictory case. To call such a

proposition, however, a necessity of thinking, does not appear to me

correct. For the expression necessity of thinking can only rest upon the

fact that every time the proposition is thought, that is, every time one

remembers its demonstration, its confirmation always arises. But every

sort of false proposition is also thinkable. An undeniable proof of this

is the fact that so much which is false is actually thought. But to base

the proof for the correctness of a proposition upon the impossibility of

thinking its opposite is an impossible undertaking, because every sort

of nonsense can be thought: where the proof was thought to have been

given, there has always been a confusion of thought and intuition, proof

or inspection.

With this one proposition of course the theory of order is not

exhausted, for here it is not a question of the development of this

theory, but of an example of the nature of the problems of science. Of

the further questions we shall briefly discuss the problem of

association.

If we have two groups A and B given, one can associate with every member

of A one of B; that is, we determine that certain operations which can

be carried on with the members of A are also to be carried on with those

of B. Now we can begin by simply carrying out the association, member

for member. Then we shall have one of three results: A will be exhausted

while there are still members of B left, or B will be exhausted first,

or finally A and B will be exhausted at the same time. In the first case

we call A poorer than B; in the second B poorer than A; in the third

both quantities are alike.

Here for the first time we come upon the scientific concept of equality,

which calls for discussion. There can be no question of a complete

identity of the two groups which have been denominated equal, for we

have made the assumption that the members of both groups can be of any

nature whatever. They can then be as different as possible, considered

singly, but they are alike as groups. However I may arrange the members

of A, I can make a similar arrangement of the members of B, since every

member of A has one of B associated with it; and with reference to the

property of arrangement there is no difference to be observed between A

and B. If, however, A is poorer or richer than B, this possibility

ceases, for then one of the groups has members to which none of the

members in the other group corresponds; so that the operations carried

out with these members cannot be carried out with those of the other

group.

Equality in the scientific sense, therefore, means equivalence, or the

possibility of substitution in quite definite operations or for quite

definite relations. Beyond this the things which are called like may

show any differences whatever. The general scientific process of

abstraction is again easily seen in this special case.

On the basis of the definitions just given, we can establish further

propositions. If group A equals B, and B equals C, then A also equals C.

The proof of this is that we can relate every member of A to a

corresponding member of B and by hypothesis no member will be left. Then

C is arranged with reference to B, and here also no member is left. By

this process every member of A, through the connecting link of a member

of B, is associated with a member of C, and this association is

preserved even if we cut out the group B. Therefore A and C are equal.

The same process of reasoning can be carried out for any number of

groups.

Likewise it can be demonstrated that if A is poorer than B and B poorer

than C, then A is also poorer than C. For in the association of B with A

some members of B are left over by hypothesis, and likewise some members

of C are left over if one associates C with B. Therefore in the

association of C with A, not only those members are left over which

could not be associated with B, but also those members of C which extend

beyond B. This proposition can be extended to any number of groups, and

permits the arrangement of a number of different groups in a simple

series by beginning with the poorest and choosing each following so that

it is richer than the preceding but poorer than the following. From the

proposition just established, it follows that every group is so arranged

with reference to all other groups that it is richer than all the

preceding and poorer than all the following.[3]

[Footnote 3: Equal groups cannot be distinguished here, and

therefore represent only a group.]

In this derivation of scientific proposition or laws of the simplest

kinds, the process of derivation and the nature of the result becomes

particularly clear. We arrive at such a proposition by performing an

operation and expressing the result of it. This expression enables us to

avoid the repetition of the operation in the future, since in accordance

with the law we can indicate the result immediately. Thus an

abbreviation and therefore, a facilitation of the problem is attained

which is the more considerable the larger the number of operations

saved.

If we have a number of equal groups, we know by the process of

association that all of the operations with reference to arrangement

which we can perform with one of them can be performed with all the

others. It is sufficient, therefore, to determine the properties of

arrangement of one of these groups in order to know forthwith the

properties of all the others. This is an extremely important

proposition, which is continually employed for the most various

purposes. All speaking, writing, and reading rests upon the association

of thoughts with sounds and symbols, and by arranging the signs in

accordance with our thoughts we bring it to pass that our hearers or

readers think like thoughts in like order. In a similar fashion we make

use of various systems of formulæ in the different sciences, especially

in the simpler sciences; and these formulæ we correlate with phenomena

and use in place of the phenomena themselves, and can therefore derive

from them certain characteristics of phenomena without being compelled

to use the latter. The force of this process appears very strikingly in

astronomy where, by the use of definite formulæ associated with the

different heavenly bodies, we can foretell the future positions of these

bodies with a high degree of approximation.

From the theory of order we come to the theory of number or arithmetic

by the systematic arrangement or development of an operation just

indicated (page 343). We can arrange any number of groups in such a way

that a richer always follows a poorer. But the complex obtained in this

manner is always accidental with reference to the number and the

richness of its members. A regular and complete structure of all

possible groups is evidently obtained only if we start from a group of

one member or from a simple thing, and by the addition of one member at

a time make further groups out of those that we have. Thus we obtain

different groups arranged according to an increasing richness, and since

we have advanced one member at a time, that is, made the smallest step

which is possible, we are certain that we have left out no possible

group which is poorer than the richest to which the operation has been

carried.

This whole process is familiar; it gives the series of the positive

whole numbers, that is, the cardinal numbers. It is to be noted that the

concept of quantity has not yet been considered; what we have gained is

the concept of number. The single things or members in this number are

quite arbitrary, and especially they do not need to be alike in any

manner. Every number forms a group-type, and arithmetic or the science

of numbers has the task of investigating the properties of these

different types with reference to their division and combination. If

this is done in general form, without attention to the special amount of

the number, the corresponding science is called algebra. On the other

hand, by the application of formal rules of formation, the number system

has had one extension after another beyond the territory of its original

validity. Thus counting backward led to zero and to the negative

numbers; the inversion of involution to the imaginary numbers. For the

group-type of the positive whole numbers is the simplest but by no means

the only possible one, and for the purpose of representing other

manifolds than those which are met with in experience, these new types

have proved themselves very useful.

At the same time the number series gives us an extremely useful type of

arrangement. In the process of arising it is already ordered, and we

make use of it for the purpose of arranging other groups. Thus, we are

accustomed to furnish the pages in a book, the seats in a theatre, and

countless other groups which we wish to make use of in any kind of order

with the signs of the number series, and thereby we make the tacit

assumption that the use of that corresponding group shall take place in

the same order as the natural numbers follow each other. The ordinal

numbers arising therefrom do not represent quantities, nor do they

represent the only possible type of arrangement, but they are again the

simplest of all. We come to the concept of magnitude only in the theory

of time and space. The theory of time has not been developed as a

special science; on the contrary, what we have to say about time first

appears in mechanics. Meantime we can present the fundamental concepts,

which arise in this connection, with reference to such well-known

characteristics of time that the lack of a special science of time is no

disadvantage.

The first and most important characteristic of time (and of space, too)

is that it is a continuous manifold; that is, every portion of time

chosen can be divided at any place whatever. In the number series this

is not the case; it can be divided only between the single numbers. The

series one to ten has only nine places of division and no more. A

minute, or a second, on the other hand, has an unlimited number of

places of division. In other words, there is nothing in the lapse of any

time which hinders us from separating or distinguishing in thought at

any given instant the time which has elapsed till then from the

following time. It is just the same with space, except that time is a

simple manifold and space a threefold, continuous manifold.

Nevertheless, when we measure them, we are accustomed to indicate times

and spaces with numbers. If we first examine, for example, the process

of measuring a length, it consists in our applying to the distance to be

measured a length conceived as unchangeable, the unit of measure, until

we have passed over the distance. The number of these applications gives

us the measure or magnitude of the distance. The result is that by the

indication of arbitrarily chosen points upon the continuous distance, we

place upon it an artificial discontinuity which enables us to associate

it with the discontinuous number series.

A still further assumption, however, belongs to the concept of

measuring, namely, that the parts of the distance cut off by the unit

used as a measure be equal, and it is taken for granted that this

requirement will be fulfilled to whatever place the unit of measure is

shifted. As may be seen, this is a definition of equality carried

further than the former, for one cannot actually replace a part of the

distance by another in order to convince one's self that it has not

changed. Just as little can one assert or prove that the unit of measure

in changing its place in space remains of the same length; we can only

say that such distances as are determined by the unit of measure in

different places are declared or defined as equal. Actually, for our

eye, the unit of measure becomes smaller in perspective the farther away

from it we find ourselves.

From this example we see again the great contribution which

arbitrariness or free choice has made to all our structure of science.

We could develop a geometry in which distances which seem subjectively

equal to our eye are called equal, and upon this assumption we would be

able to develop a self-consistent system or science. Such a geometry,

however, would have an extremely complex and impractical structure for

objective purposes (as, for example, land measurement), and so we strive

to develop a science as free as possible from subjective factors.

Historically, we have before us a process of this sort in the astronomy

of Ptolemy and that of Copernicus. The former corresponded to the

subjective appearances in the assumption that all heavenly bodies

revolved around the earth, but proved to be very complicated when

confronted with the task of mastering these movements with figures. The

latter gave up the subjective standpoint of the observer, who looked

upon himself as the centre, and attained a tremendous simplification by

placing the centre of revolution in the sun.

A few words are to be said here about the application of arithmetic and

algebra to geometry. It is well known that under definite assumptions

(coördinates), geometrical figures can be represented by means of

algebraic formulæ, so that the geometrical properties of the figure can

be deduced from the arithmetical properties of the formulæ, and _vice

versa_. The question must be asked how such a close and univocal

relationship is possible between things of such different nature. The

answer is, that here is an especially clear case of association. The

manifold of numbers is much greater than that of surface or space, for

while the latter are determined by two or three independent

measurements, one can have any number of independent number series

working together. Therefore the manifold of numbers is arbitrarily

limited to two or three independent series, and in so far determines

their mutual relations (by means of the laws of cosine) that there

results a manifold, corresponding to the spatial, which can be

completely associated with the spatial manifold. Then we have two

manifolds of the same manifold character, and all characteristics of

arrangement and size of the one find their likeness in the other.

This again characterizes an extremely important scientific procedure

which consists, namely, in constructing a formal manifold for the

content of experience of a certain field, to which one attributes the

same manifold character which the former possesses. Every science

reaches by this means a sort of formal language of corresponding

completeness, which depends upon how accurately the manifold character

of the object is recognized and how judiciously the formulæ have been

chosen. While in arithmetic and algebra this task has been performed

fairly well (though by no means absolutely perfectly), the chemical

formulæ, for instance, express only a relatively small part of the

manifold to be represented; and in biology as far as sociology, scarcely

the first attempts have been made in the accomplishment of this task.

Language especially serves as such a universal manifold to represent the

manifolds of experience. As a result of its development from a time of

less culture, it has by no means sufficient regularity and completeness

to accomplish its purpose adequately and conveniently. Rather, it is

just as unsystematic as the events in the lives of single peoples have

been, and the necessity of expressing the endlessly different

particulars of daily life has only allowed it to develop so that the

correspondence between word and concept is kept rather indefinite and

changeable, according to need within somewhat wide limits. Thus all work

in those sciences which must make vital use of these means, as

especially psychology and sociology, or philosophy in general, is made

extremely difficult by the ceaseless struggle with the indefiniteness

and ambiguity of language. An improvement of this condition can be

effected only by introducing signs in place of words for the

representation of concepts, as the progress of science allows it, and

equipping these signs with the manifold which from experience belongs to

the concept.

An intermediate position in this respect is taken by the sciences which

were indicated above as parts of energetics. In this realm there is

added to the concepts order, number, size, space, and time, a new

concept, that of energy, which finds application to every single

phenomenon in this whole field, just as do those more general concepts.

This is due to the fact that a certain quantity, which is known to us

most familiarly as mechanical work, on account of its qualitative

transformability and quantitative constancy, can be shown to be a

constituent of every physical phenomenon, that is, every phenomenon

which belongs to the field of mechanics, physics, and chemistry. In

other words, one can perfectly characterize every physical event by

indicating what amounts and kinds of energy have been present in it and

into what energies they have been transformed. Accordingly, it is

logical to designate the so-called physical phenomena as energetical.

That such a conception is possible is now generally admitted. On the

other hand, its expediency is frequently questioned, and there is at

present so much the more reason for this because a thorough presentation

of the physical sciences in the energetical sense has not yet been made.

If one applies to this question the criterion of the scientific system

given above, the completeness of the correspondence between the

representing manifold and that to be represented, there is no doubt that

all previous systematizations in the form of hypotheses which have been

tried in these sciences are defective in this respect. Formerly, for the

purpose of representing experiences, manifolds whose character

corresponded to the character of the manifold to be represented only in

certain salient points without consideration of any rigid agreement,

indeed, even without definite question as to such an agreement, have

been employed.

The energetical conception admits of that definiteness of representation

which the condition of science demands and renders possible. For each

special manifold character of the field a special kind of energy

presents itself: science has long distinguished mechanical, electric,

thermal, chemical, etc., energies. All of these different kinds hold

together by the law of transformation with the maintenance of the

quantitative amount, and in so far are united. On the other hand, it has

been possible to fix upon the corresponding energetical expression for

every empirically discovered manifold. As a future system of united

energetics, we have then a table of possible manifolds of which energy

is capable. In this we must keep in mind the fact that, in accordance

with the law of the conservation, energy is a necessarily positive

quantity which also is furnished with the property of unlimited

possibility of addition; therefore, every particular kind of energy must

have this character.

The very small manifold which seems to lack this condition is much

widened by the fact that every kind of energy can be separated into two

factors, which are only subject to the limitation that their product,

the energy, fulfills the conditions mentioned while they themselves are

much freer. For example, one factor of a kind of enemy can become

negative as well as positive; it is only necessary that at the same time

the other factor should become negative, viz., positive.

Thus it seems possible to make a table of all possible forms of energy,

by attributing all thinkable manifold characteristics to the factors of

the energy and then combining them by pairs and cutting out those

products which do not fulfill the above-mentioned conditions. For a

number of years I have tried from time to time to carry out this

programme, but I have not yet got far enough to justify publication of

the results obtained.

If we turn to the biological sciences, in them the phenomenon of life

appears to us as new. If we stick to the observed facts, keeping

ourselves free from all hypotheses, we observe as the general

characteristics of the phenomena of life the continuous stream of energy

which courses through a relatively constant structure. Change of

substance is only a part, although a very important part, of this

stream. Especially in plants we can observe at first hand the great

importance of energy in its most incorporeal form, the sun's rays. Along

with this, self-preservation and development and reproduction, the

begetting of offspring of like nature, are characteristic. All of these

properties must be present in order that an organism may come into

existence; they must also be present if the reflecting man is to be able

by repeated experience to form a concept of any definite organism,

whether of a lion or of a mushroom. Other organisms are met with which

do not fulfill these conditions; on account of their rarity, however,

they do not lead to a species concept, but are excluded from scientific

consideration (except for special purposes) as deformities or monsters.

While organisms usually work with kinds of energy which we know well

from the inorganic world, organs are found in the higher forms which

without doubt cause or assist transfers of energy, but we cannot yet say

definitely what particular kind of energy is active in them. These

organs are called nerves, and their function is regularly that, after

certain forms of energy have acted upon one end of them, they should act

at the other end and release the energies stored up there which then act

in their special manner. That energetical transformations also take

place in the nerve during the process of nervous transmission can be

looked upon as demonstrated. We shall thus be justified in speaking of a

nerve energy, while leaving it undecided whether there is here an energy

of a particular kind, or perhaps chemical energy, or finally a

combination of several energies.

While these processes can be shown objectively by the stimulation of the

nerve and its corresponding releasing reaction in the end apparatus (for

instance, a muscle), we find in ourselves, connected with certain

nervous processes, a phenomenon of a new sort which we call

self-consciousness. From the agreement of our reactions with those of

other people we conclude with scientific probability that they also have

self-consciousness; and we are justified in making the same conclusion

with regard to some higher animals. How far down something similar to

this is present cannot be determined by the means at hand, since the

analogy of organization and of behavior diminishes very quickly; but the

line is probably not very long, in view of the great leap from man to

animal. Moreover, there are many reasons for the view that the gray

cortical substance in the brain, with its characteristic pyramidal cell,

is the anatomical substratum of this kind of nervous activity.

The study of the processes of self-consciousness constitutes the chief

task of psychology. To this science belong those fields which are

generally allotted to philosophy, especially logic and epistemology,

while æsthetics, and still more ethics, are to be reckoned with the

social sciences.

The latter have to do with living beings in so far as they can be united

in groups with common functions. Here in place of the individual mind

appears a collective mind, which owing to the adjustment of the

differences of the members of society shows simpler conditions than

that. From this comes especially the task of the historical sciences.

The happenings in the world accessible to us are conditioned partly by

physical, partly by psychological factors, and both show a temporal

mutability in one direction. Thus arises on the one hand a history of

heaven and earth, on the other hand a history of organisms up to man.

All history has primarily the task of fixing past events through the

effects which have remained from them. Where such are not accessible,

only analogy is left, a very doubtful means for gaining a conception of

those events. But it must be kept in mind that an event which has left

no evident traces has no sort of interest for us, for our interest is

directly proportional to the amount of change which that event has

caused in what we have before us. The task of historical science is just

as little exhausted, however, with the fixing of former events as, for

instance, the task of physics with the establishment of a single fact,

as the temperature of a given place at a given time. Rather the

individual facts must serve to bring out the general characteristics of

the collective mind, and the much discussed historical laws are laws of

collective psychology. Just as physical and chemical laws are deduced in

order with their help to predict the course of future physical events

(to be called forth either experimentally or technically), so should the

historical laws contribute to the formation and control of social and

political development. We see that the great statesmen of all time have

eagerly studied history for this purpose, and from that we derive the

assurance that there are historical laws in spite of the objections of

numerous scholars.

After this brief survey, if we look back over the road we have come, we

observe the following general facts. In every case the development of a

science consists in the formation of concepts by certain abstractions

from experience, and setting of these concepts in relation with each

other so that a systematical control of certain sides of our experience

is made possible. These relations, according to their generality and

reliability, are called rules or laws. A law is the more important the

more it definitely expresses concerning the greatest possible number of

things, and the more accurately, therefore, it enables us to predict the

future. Every law rests upon an incomplete induction, and is therefore

subject to modification by experience. From this there results a double

process in the development of science.

First, the actual conditions are investigated to find out whether,

besides those already known, new rules or laws, that is, constant

relations between individual peculiarities, cannot be discovered between

them. This is the inductive process, and the induction is always an

incomplete one on account of the limitlessness of all possible

experience.

Immediately the relationship found inductively is applied to cases which

have not yet been investigated. Especially such cases are investigated

as result from a combination of several inductive laws. If these are

perfectly certain, and the combination is also properly made, the result

has claim to unconditional validity. This is the limit which all

sciences are striving to reach. It has almost been reached in the

simpler sciences: in mathematics and in certain parts of mechanics. This

is called the deductive process.

In the actual working of every science the two methods of investigation

are continually changing. The best means of finding new successful

inductions is in the making of a deduction on a very insufficient basis,

perhaps, and subsequently testing it in experience. Sometimes the

elements of his deductions do not come into the investigator's

consciousness; in such cases we speak of scientific instinct. On the

other hand we have much evidence from great mathematicians that they

were accustomed to find their general laws by the method of induction,

by trying and considering single cases; and that the deductive

derivation from other known laws is an independent operation which

sometimes does not succeed until much later. Indeed there is to-day a

number of mathematical propositions which have not yet reached the

second stage and therefore have at present a purely inductive empirical

character. The proportion of such laws in science increases very quickly

with the rise in the scale (page 339).

Another peculiarity which may be mentioned here is that in the scale all

previous sciences have the character of applied sciences (page 341) with

reference to those which follow, since they are everywhere necessary in

the technique of the latter, yet do not serve to increase their own

field but are merely auxiliaries to the latter.

If we ask finally what influence upon the shaping of the future such

investigations as those which have been sketched in outline above can

have, the following can be said. Up till now it has been considered a

completely uncontrollable event whether and where a great and

influential man of science has developed. It is obvious that such a man

is among the most costly treasures which a people (and, indeed,

humanity) can possess. The conscious and regular breeding of such

rarities has not been considered possible. While this is still the case

for the very exceptional genius, we see in the countries of the older

civilization, especially in Germany at present, a system of education in

vogue in the universities by which a regular harvest of young scientific

men is gained who not only have a mastery of knowledge handed down, but

also of the technique of discovery. Thereby the growth of science is

made certain and regular, and its pursuit is raised to a higher plane.

These results were formerly attained chiefly by empirically and

oftentimes by accidental processes. It is a task of scientific theory to

make this activity also regular and systematic, so that success is no

more dependent solely upon a special capacity for the founding of a

"school" but can also be attained by less original minds. By the mastery

of methods the way to considerably higher performances than he could

otherwise attain will be open for the exceptionally gifted.

THE CONTENT AND VALIDITY OF THE CAUSAL LAW

BY BENNO ERDMANN

(_Translated from the German by Professor Walter T. Marvin, Western

Reserve University_)

[Benno Erdmann, Professor of Philosophy, University of Bonn,

since 1898. b. October 5, 1851, Glogau in Schlesien,

Germany. Ph.D.; Privy Councilor. Academical Lecturer,

Berlin, 1876- ; Special Professor, Kiel, 1878-79; Regular

Professor, _ibid._ 1879-84; _ibid._ Breslau, 1884-90;

_ibid._ Halle, 1890-98. Member various scientific and

learned societies. Author of _The Axioms of Geometry_;

_Kant's Criticism_; _Logic_; _Psychological Researches on

Reading_ (together with Prof. Ramon Dodge); _The Psychology

of the Child and the School_; _Historical Researches an

Kant's Prolegomena_, and many other works and papers in

Philosophy.]

We have learned to regard the real, which we endeavor to apprehend

scientifically in universally valid judgments, as a whole that is

connected continuously in time and in space and by causation, and that

is accordingly continuously self-evolving. This continuity of connection

has the following result, namely, every attempt to classify the sum

total of the sciences on the basis of the difference of their objects

leads merely to representative types, that is, to species which glide

into one another. We find no gaps by means of which we can separate

sharply physics and chemistry, botany and zoölogy, political and

economic history and the histories of art and religion, or, again,

history, philology, and the study of the prehistoric.

As are the objects, so also are the methods of science. They are

separable one from another only through a division into representative

types; for the variety of these methods is dependent upon the variety of

the objects of our knowledge, and is, at the same time, determined by

the difference between the manifold forms of our thought, itself a part

of the real, with its elements also gliding into One another.[4]

[Footnote 4: Cf. the author's "Theorie der

Typeneinteilungen," _Philosophische Monatshefte_, vol. xxx,

Berlin, 1894.]

The threads which join the general methodology of scientific thought

with neighboring fields of knowledge run in two main directions. In the

one direction they make up a closely packed cable, whereas in the other

their course diverges into all the dimensions of scientific thought.

That is to say, first, methodology has its roots in logic, in the

narrower sense, namely, in the science of the elementary forms of our

thought which enter into the make-up of all scientific methods.

Secondly, methodology has its source in the methods themselves which

actually, and therefore technically, develop in the various fields of

our knowledge out of the problems peculiar to those fields.

It is the office of scientific thought to interpret validly the objects

that are presented to us in outer and inner perception, and that can be

derived from both these sources. We accomplish this interpretation

entirely through judgments and combinations of judgments of manifold

sorts. The concepts, which the older logic regarded as the true

elementary forms of our thinking, are only certain selected types of

judgment, such stereotyped judgments as those which make up definitions

and classifications, and which appear independent and fundamental

because their subject-matter, that is, their intension or extension, is

connected through the act of naming with certain words. Scientific

methods, then, are the ways and means by which our thought can

accomplish and set forth, in accordance with its ideal, this universally

valid interpretation.