III

§ 18. Such an examination will speedily establish that the mental

attitude of the discoverer is, and must be, quite different from that

of the prover.

In the first place, the discoverer is not in possession of the

knowledge he covets. It is for him a desire, an aspiration, an aim to

be attained. Proof, on the other hand, presupposes knowledge. Not only

must the demonstrator _know_ the assured truths he uses as premisses,

not only must he have a supply of absolutely certain truths if his

proof is not to remain hypothetical (§ 9), but he must already _know_

the conclusion he exhibits. He cannot be ignorant, like the discoverer,

of the result he is to arrive at. He is not engaged in _discovering_

new truth, he is only showing how it _follows from_ old truths. His

retrospective contemplation has merely to retrace the history of its

attainment, or rather to rearrange it in the more pleasing order

which he calls ‘logical’. This order is not that in which it _was_

discovered, nor even that in which it _could be_ discovered. For

there are such things as necessary errors, indispensable artifices,

and indefensible fictions, and the way to a truth often lies through

them. Thus from time immemorial mathematicians have represented the

continuous by the discrete, quantities by numbers, knowing full

well what fictions their practice involved. Again, mathematical

calculation of shapes, areas, and motions necessarily presupposes the

fictions that bodies have the ideal and regular forms to which they

‘approximate’, and that their ‘mass’ is concentrated at their (ideal)

‘centre of gravity’. It is more than doubtful whether the notion of

an ‘evolution’ of species could ever have been reached, except by

starting from the false notion of the fixity of species, or whether

the true nature of the mobility and development of meanings could have

been understood except by correcting the Platonic theory of immutable

and eternal ‘universals’. To ‘proof’ all these incidents and accidents

of the history of discovery are irrelevant; all that has to be done

is to show that the new truth can be deduced from the old, and that a

‘logical connexion’ exists between them.

§ 19. Not only is this much easier to do than to make the discovery,

but it is very much easier to follow. Any one can see the connexion

once the data have been arranged in logical order. Hence the assumption

that this order somehow represents the actual process in a perfected

form is natural enough. But it leads to contempt for the procedure

of discovery. The discovery is made to look so easy that it becomes

impossible to appreciate its difficulty and its merit, and it seems

astonishing that no one made it long before. For did not the ‘facts’

all but force it upon the dullest mind? Who could have failed to see

that fossils must be (at least) as old as the rocks in which they are

embedded, that obviously worked flints, similarly, attest the antiquity

of man, that northern Europe is scratched all over with the marks of

a gigantic glaciation? It is forgotten that these ‘facts’ were _not_

there until there came a mind prepared to notice them. Hence none of

these discoveries were in fact easy to make, and they were preceded by

a long struggle of the human mind with false preconceptions and the

illusory ‘facts’ which they had engendered.

Nor are discoveries easy to get recognized when they have been made.

The persecutions to which discoverers of new truth are subjected

always and everywhere (more or less) form as discreditable a chapter

of human history as the persecution of moral reformers. Those may

count themselves fortunate who are simply ignored. Hence everything

has to be ‘discovered’ over and over again. Nothing new ever enters

the world, just as nothing old ever passes away, without infinite

pains and after a protracted struggle. One curious result of this

inertia which deserves to rank among the great fundamental ‘laws’ of

nature, is that when a discovery has finally won tardy recognition, it

is usually found to have been anticipated, often with cogent reasons

and in great detail. Darwinism, e.g., may be traced back through the

ages to Heraclitus and Anaximander. Thus it is true that there is

‘nothing new under the sun’; but only because when a new truth first

appears it does not prevail: when after a hundred repetitions it is at

length recognized, it is no longer strictly _new_. Accordingly, the

‘discovery’ of a truth is only the beginning of its career, the first

step by which it makes its way in the world, and still very distant

from the crowning ‘proof’ with which logic complacently adorns it _ex

post facto_, when it has ‘arrived’. The slowness and difficulty, then,

with which the human race makes discoveries, and its blindness to the

most obvious facts, if it happens to be unprepared or unwilling to see

them, should suffice to show that there is something gravely wrong

about the logician’s account of discovery.

§ 20. Quite apart from the difficulties which the psychological

constitution and social organization of man put in the way of

innovators, the making of a new truth which formulates a new ‘fact’

is also intrinsically anxious work. It is not merely that its maker

can have no assurance that his enterprise will succeed, that he cannot

start with a feeling of certainty from established truths, and be

wafted by an irresistible wave of logical necessity to the safe haven

of a predestined conclusion. He _must_ start with a consciousness of

ignorance and an all-pervading feeling of doubt about every step of his

inquiry. This doubt he should not, moreover, endeavour to disregard

or to suppress; for it is the best guarantee that no way to the truth

will be passed by in his explorations. Doubt, therefore, should be

recognized on principle, and equipped with a technique of testing and

experimentation: the inquirer should be proud that he has to feel his

way in fear and trembling to the very end.

Yet his condition will not contravene Aristotle’s dictum that all

inquiry and research proceed from knowledge previously acquired.[394]

In a sense he will still start from what he knows, or thinks he knows.

For it is psychologically impossible to do anything else. The knowledge

he believes himself to have cannot but affect all his ideas, and he

cannot get away from it. His boldest speculations, his most hazardous

hypotheses, will have _some_ relation, however subtle and recondite,

to the knowledge at his disposal. It will influence all his thoughts

and guide his guesses. As he cannot divest himself of his knowledge

and the ideas it has rendered familiar to him, he has to accept its

limitations. His only problem is to use it as effectively as possible.

But it is clear that he cannot regard his knowledge with the same

sort and amount of confidence as the believer in demonstrative proof.

He must conceive himself as an explorer, and his attitude must be

tentative throughout. Knowing that his premisses are questionable and

only doubtfully true, he will recognize that his inferences are only

probable, and stand in need of confirmation. As a rule he can, no

doubt, find accepted truths to argue from; but these being relative to

the existing state of knowledge are known to be subject to correction.

Even where he has started with premisses of the most superior kind,

which are generally deemed absolutely self-evident and certain in

themselves, he will still be conscious of a doubt whether they will

prove to be the right premisses _for his purpose_. If they are not,

their truth is irrelevant and will lead him astray. In no case,

therefore, can he escape the responsibility of _choosing the right

ones_ from his limited stock of known truths and familiar ideas, as he

contemplates the infinite expanse of possible discovery. In whatever

direction he moves, the unknown lies before him; he may come upon

surprises or be stopped by unsuspected obstacles. In short, there is

nothing of the irresistible about his progress; it has not the faintest

resemblance to the majestic march from inevitable premisses to a

predestined conclusion which so fascinates us in the theory of proof.

§ 21. But, it may be said, all this is not enough. The differences in

the attitudes assumed by the reasoner in discovery and in proof may

be only psychological. They do not prove any real logical difference

between them; the logician’s account may still be what the discoverer

would acknowledge to have been his best course, if he could have seen

it. It has, therefore, to be shown that the differences in question

arise out of, and develop into, differences which are indisputably

logical.

Thus, the ignorance which the inquirer feels is doubtless a

psychological fact, but the lack of knowledge which engenders it is

surely a logical fact of some importance. In general, the feelings of

doubt, expectancy, and perplexity which beset the mind of the inquirer,

and contrast so distinctly with the feelings of confidence, knowledge,

certainty, and necessity which accompany a ‘proof’, originate in a

logical fact. Every inquiry starts from a _problem_, of which the

solution is not yet known. An _inquiry_ is, as the name implies, a

_question_, put, not to nature at large and at random, but to some

_part_ of it, which is taken to be relevant and to contain a possible

answer to the inquirer’s question. Now this dependence of inquiry

upon problems springs no doubt from the psychological fact that until

there is something put before it the mind cannot get to work upon it;

but it is surely a fact of the utmost logical significance, and it is

astounding that the logical tradition should have slurred it over so

completely.

Especially as in the very beginnings of logic some of the Greeks

distinctly caught a glimpse of it. For, having started their reflection

upon reasoning from a desire to regulate debate and to argue a case

at law, they naturally noticed that there are two sides (at least)

to every question. Accordingly, Protagoras appears to have taught

systematically that there were always two reasonings (λόγοι) to be

considered,[395] Socrates, treated scientific inquiry as an extension

of the art of cross-examination, and Plato conceived the search for

ideal truth as a ‘dialectical’ process, as a sort of dialogue of the

soul with itself. Now this whole doctrine is equally good as logic

and as psychology. It is profoundly true of the inquirer’s mind; he

must be keenly alive, not only to the evidence _for_, but also to

that _against_ his working theory. But it is also true of the logical

nature of inquiry that it is a process of determining _which_ of the

alleged ‘facts’ and of the theories to interpret them are real and

true. Inquiry logically ‘presupposes’ a conflict between the data, and

a dispute about them.

Unfortunately, however, the conception of scientific research as

an inquiry lapses from the logical consciousness in consequence

of Aristotle’s work. His discovery of the forms and formulas of

demonstration overshadowed it, and restored the reign of dogma which is

so congenial to the authorities everywhere.[396] The true conception of

inquiry does not revive again until our days, when Mr. Alfred Sidgwick

and Professor John Dewey have endeavoured, not with the success

they deserved, to reopen the eyes of logicians to the facts of the

scientific situation.

§ 22. To conceive an inquiry as a question then is, we see, implicitly

to conceive it as having a plurality of answers, all of which have

to be examined. All these answers are initially hypotheses, and a

choice has to be made between them. This renders the recognition of

alternatives a paramount necessity for a logic of discovery, which

can no longer dismiss them with a jejune chapter on ‘disjunctive

propositions’. Their existence is no longer to be treated as an

annoying complication which delays the progress of science, but must be

taken to inhere in the logical nature of problems, and to be essential

to their proper elucidation.

Logic, therefore, should regard it as its duty to inquire (1) how the

inquirer is furnished with an adequate supply of theories for analysing

and testing the apparent facts of his subject, (2) what methods are

used to sift hypotheses and to select the more valuable, and (3) if it

can, to add some hints as to how theories and methods _ought_ to be

handled.

(1) To the first question there is no exhaustive answer. No logic can

guarantee that _all_ the possible theories which concern the facts

under inquiry will be available. They may not yet have occurred to any

human mind, and may never do so. This alone ought to be considered a

fatal objection to all methods which presuppose exhaustiveness, and are

pressed by the logician upon the man of science. It ought to dispose of

methods which demand that _all_ the facts should be assembled before

theorizing is begun, or that _all_ the alternatives should be stated

and the true one extracted by the successive elimination of the false

ones, or that define a ‘cause’ as reciprocating with its ‘effect’, and

assume that the true cause has been discovered when no other has been

thought of, or that if a theory works we may take it that it alone will

do so and is (absolutely) true. All these notions demand an impossible

exhaustion of the alternatives, and try to convert a (psychological)

failure to think of any more into a logical proof that there are no

more. And they all regard the plurality of alternatives as a hindrance

to be got rid of, and not as a safeguard and a help to proper inquiry.

Hence the real difficulty was not perceived, viz. that there is no

formal guarantee that the supply of hypotheses for use upon the facts

in any inquiry will be adequate. It may well be that for lack of a

good working theory to go upon, all the theorizing on a subject proves

vain and sterile. In the beginnings of all the sciences this sort of

condition always exists and often lasts for centuries, and it is a main

reason why some sciences make little progress even now.

Nevertheless, the difficulty is not in practice as fatal as it looks

on paper. It is probable that the inquirer will in fact usually have

a supply of alternatives to start from. For (_a_) he will naturally

select a subject in which there are disputed points. And (_b_), what

is even more important, human minds are naturally various: they put,

therefore, different interpretations on the same facts and value them

differently. Some are attracted by novelty, others by orthodoxy; some

incline to one type of theory and method of inquiry, others to another.

Hence in any inquiry upon which a number of minds are actively engaged,

there will always be differences of opinion, and these will be most

marked in the rapidly growing regions of every progressive science,

which, like the growing cells in the trunk of a tree, are always on the

outskirts. There will always be a conservative and a liberal party,

even in science, and the clash between their views will always provide

alternative solutions of problems, the comparative merits of which the

inquirer can examine. But the sciences owe their progress largely to

the man who raises new questions, and should provide for him in their

organization.

§ 23. It should be noted further that if this feature in discovery

were properly recognized and emphasized, it would have important

educational and ethical effects. At present the study of logic can

hardly be said to liberalize and broaden the mind or to improve the

temper. So long as its chief interest is in a theory of absolute proof

and complete certainty, it will tend to breed pedants and bigots. The

effect would be very different if an adequate logic of discovery had

imbued the mind with an ever-present thought that every subject may and

must be considered from several points of view, and that an inquirer

should beware of letting his predilections and preconceptions blind

him to possible alternatives. The logical attitude of inquiry, when

fully understood, demands a tolerant and open mind, and excludes the

narrow-mindedness and dogmatism which the theory of proof has fostered

by its pretence of showing that there was but one truth and one

inevitable way of reaching it. Moreover, the necessity of continually

choosing between a number of alternatives should cultivate a judicial

temper, conducing to fair-mindedness and consideration towards the

views of others. For a mind which is in the habit of choosing between

alternatives must be impressed by the facts that there is something to

be said for the views it does not accept, that the view accepted is

often not so very much superior to those rejected, and that new facts

and new knowledge may always revive views which were supposed to be

defunct.

Of course our natural dogmatism will take alarm at the flabby

toleration of ideas which this attitude seems to imply. It will be

objected that no one who can see the good and truth in beliefs he

does not accept, can really be strenuous in upholding those he does.

The full answer to this bigots’ argument can only be appreciated when

the attitude of progressive science is fully understood (cf. § 33),

but in general it may be pointed out that a power of first weighing

alternatives, choosing the best and acting upon it strenuously, is

precisely what life demands of us at every step. It should not,

therefore, be impossible to compass it in science.

§ 24. (2) To the second question of § 22, viz. what are the methods

used by the inquirer in sifting the alternative hypotheses in the

field, and picking out the most valuable, the answer is comparatively

easy. It is substantially the answer given by the pragmatist analysis

of knowledge. That theory is preferred, and tends to be accepted as

true, which for the time being _works_ best. The formula looks simple,

but needs more thinking out than its critics usually bestow upon it.

(_a_) It implies, of course, that _all_ the alternatives (before the

mind) ‘work’ more or less. They must be (or appear) scientifically

plausible, and proffer a more or less satisfactory explanation of some

or all of the admitted ‘facts’. This is why agencies like the Devil,

who could once be extensively alleged to explain anything unusual, have

dropped out of the purview of science.

(_b_) ‘Working’ must be conceived somewhat widely. Its _primary_

appeal is to the accepted principles and recognized interests of the

science; practically to ‘work’ means to conduce to the development of

the science on the recognized lines, and the proper judges of what

‘working’ counts are the experts who cultivate each science.

(_c_) But there will often be complications due to certain disputable

workings, of which the relevance is not yet established, and about

these there will legitimately be differences of opinion. These should

not be suppressed, but candidly argued out.

(_d_) Moreover, every _new_ departure will be _pro tanto_ disputable,

because it will conflict more or less with the vested interests of the

established doctrines. One great factor in the ‘working’ of a new truth

is the extent to which it upsets, or is thought to upset, the old, and

demands a reconstruction of beliefs, a correction of authorities, a

revision of text-books, a renewal of plant, &c. Hence what works best

in the abstract may not do so under the actual conditions. It may ‘pay’

a professor better to be ‘orthodox’ than to be an innovator, and he

is usually quite alive to this, though it does not render him a good

investment scientifically for the institution that appoints him. If

then we looked at this side of the matter alone, the verdict would

always go against the novelty. For very few new truths are fortunate

enough to find the field free and unoccupied. Usually they have to

spring up in a soil densely overgrown with a rank growth of prejudices,

dogmas, and superstitions, to which the world is accustomed and even

devoted. So they have to fight for an opening in which they can take

root and grow up.

(_e_) The ‘working’, however, need not amount to a claim to represent

‘the’ truth. A discoverer may know that by reason of his deliberate use

of fictions, his results have forfeited their claims to be strictly

true; yet they may ‘work’ better than anything else in sight. The

typical example here is, of course, mathematics. When physical objects

are treated mathematically, they are identified by a fiction with the

objects of pure mathematics, and it is only on this assumption that

their behaviour can be calculated. They are, of course, vastly _more_

than mathematical objects, but their surplus meaning becomes irrelevant

wherever objects admit of mathematical treatment. And apart from the

restriction of the claim to truth necessitated by the use of fictions,

it should, of course, be recognized also that there are sound logical

reasons for denying that truths which rest on their ‘workings’ can ever

be ‘absolute’ (§ 26 _s.f._). Their truth is pragmatic, and is _optimi

iuris_ only if pragmatism establishes that no other and no better truth

exists.

(_f_) More specifically a very important form of working is the

prediction of events. Knowledge of the future is an almost universal

object of human desire, which men have sought to compass by fair means

and foul, and the calculation of the future is the avowed aim of many

scientific inquiries. Hence there is nothing more potent to dispose

the mind to accept a theory than the success of the predictions it

has led to. Yet here again this form of ‘working’ differs generically

from ‘proof’. It is clear that prediction is not strictly proof. For

predictions may be made with considerable accuracy by the aid of

hypotheses which turn out to be false or impossible. Thus eclipses

and other celestial events were predicted for centuries by means of

the Ptolemaic astronomy, and they cannot be predicted even now with

absolute accuracy. Indeed, physically speaking, absolute accuracy is

unthinkable. No instrument and no organ of observation can be conceived

to measure to more than a finite degree of accuracy, and the _best

value_ for any physical ‘fact’ will always be the mean of a number of

good observations after all the accessible sources of error have been

allowed for.

At no point, then, does the test of ‘working’ conduct to the notion

that absolute truth is discoverable. But the right inference may be,

not that the test is worthless, but that absolute truth is a chimera.

§ 25. (3) It cannot then be seriously disputed either that alternative

hypotheses are always (more or less consciously) present to the mind

of the inquirer, or that the working of a theory is in fact used, in

all the sciences, to test its claim to be true. But does it follow that

logic should bow to scientific fact and recognize these practices?

Should it set itself to devise a _technique_ for regulating the

formation of hypotheses and the establishment of their truth by their

working? It is here that the traditional logic demurs, and disputes

begin. Nevertheless, strong reasons may be advanced for answering both

questions in the affirmative.

(_a_) An abundance of hypotheses is a guarantee of great logical

value that all the important facts will be properly observed. For it

is evident that every theory will produce a certain _bias_ in the

observer. It will direct his attention upon those facts and those

features which are _relevant_ to his theory, and, more particularly,

which _support_ it. This is usually an advantage, because it helps him

to select what is relevant to his inquiry from the chaos of events; but

it will _pari passu_ blind him to whatever does not seem to be related

to, and to fit into, his theory. He will, therefore, fail to observe

and to appreciate what will seem to him to have little or no scientific

interest. And in so thinking he may be quite wrong.

The old theory of ‘induction,’ thought to get over this difficulty by

saying, ‘Well, of course, _all_ the facts must be observed’. It did

not observe the fact that in practice this is impossible, and is never

done. Nothing is observed but what the knowledge and preconceptions

of the time make visible to the scientific eye. Of what is visible at

any time only a small part seems worthy of the scientific microscope.

Complete observation, therefore, of literally all the facts is

scientifically impracticable.

As a logical ideal also this notion of all-inclusiveness is absurd. If

no inquiry could ever begin until _all_ the facts had been assembled,

how could anything be discovered until omniscience had been achieved,

i.e. when there was nothing left to discover? For how are we to know

that our assembly of ‘facts’ really is complete? And if literally all

the facts have to be used as data in any inquiry, shall we not speedily

find that every fact ramifies into infinity, and drags in the totality

of reality, and a knowledge of all things present, past, and future?

This ‘logical ideal’, therefore, renders inquiry impossible.

In point of fact the data of any inquiry are always a _selection_. They

are such of the recognized facts as are thought to be _relevant_, i.e.

to be truly ‘facts’ for the purpose in hand. But being a selection they

involve us in the risk that we may have selected wrongly, and omitted

what is important while admitting what is not. _From this risk there

is no escape._ For we cannot effect a compromise by including merely

so much of the facts as we can lay hold of. Not only does this yield

no guarantee that everything that is needed has been included, but it

may be a positive hindrance to try to include too much. For if our data

grow into an unwieldy mass, they will not seem susceptible of any order

or principle, and even the most penetrating inquirer will lose his way.

It is better, therefore, to give up altogether the idea of securing

formal validity by postulating an all-inclusive exhaustiveness. The

obvious alternative is to operate simultaneously with a plurality

of theories, each of which means a certain ordering of the ‘facts’

relatively to what seems a relevant and promising point of view. Each

will involve a selection and induce a bias; but with any luck they will

neutralize each other’s bias, and so will increase the probability that

no really relevant fact has escaped notice. This will not satisfy the

logical ‘ideal’, but in practice it means a good deal, and is enough

for scientific progress. Of course it must be understood that the

hypotheses employed are in a general way relevant to the problems and

the condition of the sciences, and not random guesses. This proviso

will cut down their exuberance even more than the limitations of the

human imagination, which seems to be psychologically incapable of

really departing very far from the suggestions of experience.

§ 26. When logic has recognized the use and value of ‘working’ as

the test of truth, it must, however, make it clear to itself and to

others both what precisely this test is, and what it can, and cannot,

accomplish.

In the first place, it must be made clear that it is _not_ a logical

implication of the test that ‘whatever works is true’, and the reasons

for disputing this dictum must be set forth. The fact is that we

all have a strong psychological tendency to believe in the truth of

what is found to work, without much criticism of the sort and extent

of the ‘working’. But the logician should carefully investigate the

various sorts of working that occur, and take special note of those

which either do not themselves lay claim to full truth, or do not

(ordinarily) have their claim conceded.

For example, ‘_fictions_’ are not supposed to be strictly true; but

they may ‘work’ and be ‘as good as true’, or ‘pragmatically true’, or

‘sufficiently true for the purpose in hand’. They work, in fact, within

limits; but these limits are _known_, and so they are not confused with

full-fledged truths, to the applicability of which there are no known

limits.

The case of ‘_methodological assumptions_’ is more difficult and

instructive, and is usually misconceived. In their case the existence

of limits to their ‘working’ is either not known or not relevant,

because they owe their adoption to their use and convenience in

analysing and organizing a subject of inquiry. Thus the principle of

Causation, the assumption that every event has a cause which determines

it fully, is properly to be regarded as methodological. It declares

merely that if we desire to calculate the course of events, it is

scientifically convenient to treat events as if they had ‘causes’,

from which their occurrence could be predicted, whether or not they

have them in fact. This assumption may be purely methodological; it

need not, and should not, be turned into a dogmatic, metaphysical

denial that there may be indeterminate happenings. There may even

be good reasons to suspect their occurrence, and indeterminism may

be ultimately true, and yet scientific method may rightly ignore

this possibility, because it would render the calculation of events

impossible.[397] Even an indeterminist then is fully entitled to

reason _as if_ events were determined, and to search for ‘causes’, for

the purely methodological reason that this enables him to calculate

events, and that after all they may be calculable. So long as they

work for scientific purposes it is not, in the case of methodological

principles, necessary to raise the question of their metaphysical truth.

The ‘lie’ again is a curious case of ‘working’. A lie, works, as a

rule, only so long as it passes for truth, and is believed to have

the meaning and value its author claims for it; when it is ‘found

out’, it ceases to work. Hence it can both work and fail to work at

the same time, according as it is, or is not, known to be a ‘lie’.

Clearly nothing can be made of the lie logically, until this double

aspect inherent in its nature is recognized; if the logician refuses to

distinguish between the _persons_ concerned in its making, acceptance,

and rejection, it remains (like ‘error’ to Plato) an insoluble

‘contradiction’. It is, however, a mere prejudice to refuse to make

these distinctions.

The ‘working’ of hypotheses is by no means simple and unambiguous.

It admits of infinite gradations in amount and kind, and the ‘truth’

which is implicated in ‘working’ is nothing essentially but an index

of its logical value, and may vary in quantity between values which

cannot be _psychologically_ discriminated from zero and from 100% or

1 (= ‘absolute’ certainty). It is crude, therefore, to confront a

scientific hypothesis with the rigid alternative ‘either (absolutely)

true, or (utterly) false’; its ‘truth’ really rests on its greater

value, as compared with its competitors. Its value, then, is a question

of more or less. The more extensively, conveniently, and economically

a hypothesis works, the more value has it, i.e. the more likely is

it to be called ‘true’, and to be supposed true absolutely: the more

continuously and successfully the test of working has been applied to

a doctrine, the greater the confidence and affection with which it is

regarded, and the greater the presumption that it will continue to

approve itself as true.

But, as we anticipated in § 24 (_s.f._), it is vain to expect to

establish any absolute truth by this method. It provides truth with

ever-growing probability, but never with absolute certainty. For,

however well a theory works, the thought that one may hereafter be

found to work better can never logically be excluded. Even if every

one alive were perfectly satisfied, and no one could imagine any

improvement in an accepted truth--and these conditions are by no

means often realized--such psychological considerations would not

disprove the logical possibility that the best known was not the best

absolutely, and logic would continue to distinguish between a truth

that was absolute, and one liable to one billionth chance of error. The

latter chance could be disregarded for all practical and scientific

purposes, and would not have the slightest psychological effect on

the confidence with which the truth was regarded; but logically it

would still be there. Science, therefore, has to resign itself to the

conclusion that its method cannot conceivably attain to absolute truth,

and to make the best of it.

§ 27. Curiously enough this conclusion is fully confirmed by Formal

Logic. It prides itself on pointing out that there is a formal

fallacy involved in establishing truth by ‘working’. The essence of

this method is to argue that if a theory is found to work (after the

proper precautions have been taken), it is true. If e.g. the events

anticipated by a theory occur, and nothing occurs that could not be

anticipated, it grows more and more probable until it convinces every

one. But ought it logically to have done this? The logician declares

emphatically, it ought not. For the argument suffers from an incurable

flaw, which has been recorded as a ‘fallacy’ for over 2,000 years. It

is a flagrant ‘affirmation of the consequent’; symbolically, it argues

that _if A is, B is, but B is, ∴ A is_. Now this is not ‘cogent’ or

‘valid’. That _A is_ can be proved only from the premiss ‘_only_ if A

is, B is’, i.e. if A is the _only_ theory which will account for the

observed consequences. But this the fallacious method did not assert,

and indeed could not assert. For that the best known is the best

absolutely never can be proved (cf. § 26); and even if they happened to

be identical, and we had somehow stumbled upon an absolute truth, we

should never know that this was so.

§ 28. To the logician this fact only seems to prove the superiority

of his conception of ‘proof’. He infers, consistently enough, that no

inductive reasoning from ‘facts’, no verification of hypotheses by

events, can possibly amount to proof. What he seeks to impress upon

his pupils is that _verification is not proof and can never lead to it_.

He considers himself entitled to look down upon science accordingly,

its evidence, its methods, and its reasonings, and to contrast them

with the absoluteness of his own ideal of demonstration. He upholds

its validity in spite of all the failures of the sciences to realize

it. As a rule he seems willing to grant that some mathematical proofs

amount to logical demonstration;[398] but if pressed he would confess

that scientific truth was only probable, whereas certain metaphysical

truths, such as the law of contradiction, alone were absolutely certain.

The scientist, of course, is not in a position to deny that the nature

of his truth is such as has been stated: but he should not attempt to

do so. He should content himself with scientific truth, and contend

that at its best it is good enough for any one. And he can carry the

war into Africa by a vigorous counter-attack.

(1) He can deny--for the reasons stated in § 13--that the logician’s

formal ‘proof’ is as cogent and formally valid as the latter supposes,

and show that after a conclusion has been ‘_proved_’ true, it has still

to _come true_ before it can be trusted to be ‘true’.

(2) He can point out that there is a serious _lacuna_ in the logician’s

plea for his notion of ‘proof’. The logician has assumed that the

only alternative to his belief in absolutely certain premisses is

complete scepticism, arguing that it must be possible to start from

certainty, because otherwise no knowledge would be possible at all.

He then urged ‘but there clearly _is_ knowledge--the sciences attest

it’, and consistently inferred that absolutely certain premisses must

be obtainable. The more or less obvious failure of his attempts to

explain their genesis by ‘self-evidence’, ‘intuition’, ‘necessities of

thought’, &c. (§ 15), could not deter him from clinging to his belief,

because the principles themselves seemed to him to be inevitable and to

admit of no alternative.

In fact, however, there _is_ a _via media_ between scepticism and

absolutism, and science safely pursues it, though logic has overlooked

it. It is _not_ necessary to start with absolutely certain premisses,

because it is possible to adopt premisses hypothetically, to take

them as true for the argument’s sake and for the purposes of the

inquiry, to experiment with them, and to revise them in the light of

the results of such experiments. Thus _their_ value may be judged and

established, _after_ their adoption, by the experimental results,

and they may come to depend logically upon these, and not upon the

processes (analogies, suggestions, guesses, fancies, &c.) which led

to their adoption. If they show themselves capable of advancing the

science and solving its problems, confidence in their ‘truth’ increases

progressively, and their initial assumption is justified. They _cease_

to be ‘hypotheses’ and become ‘facts’, and even ‘principles’ beyond

dispute. If they fail to ‘work’, they may be discarded in favour of

others which are tried in their turn and similarly tested. Hence it

is not true that what is uncertain to begin with must always remain

so, nor is it hard to understand that hypothesis, willingness to

believe, and belief may be the psychological forerunners of logical

proof, which, nevertheless, rests not upon them, but upon the solid

value of the results subsequently reached by their means. The

certainty of scientific premisses then admits of indefinite growth,

which at some point or other will overpower even the most obstinately

sceptical temper. This point naturally lies at a greater distance from

the starting-point for some minds than for others, but when it is

reached, and when the last doubts and scruples have been overcome, the

triumphant truth will _feel_ absolutely certain, and to all intents

and purposes will function as such. But the ‘practical certainty’ thus

achieved will still be distinguishable in thought from the absolute

certainty which logical theory mistakenly demanded. And logicians,

from Plato downwards,[399] will be convicted of having failed to allow

for the possibility that the certainty of premisses and principles may

be a fruit of continuous experience and experiment, and to perceive

that this is the method the sciences have actually employed. In short,

necessary (needed) ‘truths’ need _not_ be regarded as ‘_a priori_’, if

it is seen how hypotheses are consolidated by experience.

(3) The scientist can deny that the ideal case, contemplated with so

much satisfaction by the logician, can ever occur in actual knowing.

He can point out that if the logical apparatus of demonstration is

to work, it must be supplied with premisses that are absolutely

true. But whence is the logician to obtain them? The ‘self-evident’

principles and ‘necessary’ axioms, for which so much has been claimed,

have been shown (§ 15) to be highly disputable, and are themselves

in need of support and verification. The truths which the sciences

supply abundantly are all products of the method to which he takes

exception. There are no scientific truths which have not to be, and

have not been, verified, and if verification is logically vicious,

and cannot amount to proof, they are not absolutely true. But if the

premisses of a demonstration are not absolutely true, neither can its

conclusion be. What then becomes first of the value, and ultimately of

the ‘validity’, of an ideal of proof which can never be exemplified by

actual reasoning, and serves only to condemn it?

(4) The ideal of absolute certainty may be repudiated altogether, even

as an ideal, for sound scientific reasons. It may be shown that if it

were possible it would be scientifically undesirable. For it would mean

the creation of absolute bars to scientific progress. If truths existed

which were absolutely certain, this would mean that nothing more could

be learnt about them, and nothing could be done to strengthen their

position. No experience, no inquiry, no experiment, could any longer

affect them, and add to or detract from their value. They could not,

therefore, form avenues to further knowledge. They would simply be

stops which would arrest scientific inquiry. But how could such things

form an ideal of scientific knowledge? How could it be in the spirit,

and to the interest, of science to recognize them? They would merely

be for science brute facts which it was forbidden to investigate. And

must not science on principle hold out for the right to inquire into

everything, to test every belief, however true it may seem? How, then,

can it be the ideal of science to adopt an ideal which would stop

inquiry?

Nor will it suffice in reply to point to the fact that the sciences

continually assume the truth of the premisses they argue from. For

though this is often a convenient assumption for the purpose in hand,

it is one thing to assume the truth of premisses for the purposes of

an inquiry, and quite another to assume it absolutely. For in the

former case our assumption may be, and should be, accompanied by a

consciousness that upon another and fitting occasion the premisses now

assumed to be true may themselves be inquired into: to regard them,

therefore, as absolute is to misinterpret their logical condition.

There are no good reasons, then, why the sciences should surrender to

the arbitrary demands of the traditional logic, and sacrifice their

practices which have been sanctified by the successes of 2,000 years to

theories which sprang from a misunderstanding of scientific procedure,

and have since lost all contact with it. The original mistake was

pardonable, but it ought not to be regarded as an insult to logic to

require it to understand the procedure by which the sciences actually

progress.

§ 29. The scientist then should not be terrified by the charge that his

‘truths’ are ‘only probable’. For it is better to be satisfied with

probabilities than to demand impossibilities and starve. Moreover, a

high degree of probability means ‘practical certainty’, i.e. confidence

enough to move to action. Such certainty so convinces and satisfies

the mind that it cannot feel more certain about anything; the logical

gap between it and absolute certainty is psychologically negligible.

We are sacrificing, therefore, nothing but a superstition, nothing

that has any value for us, by renouncing the demand for absolute truth

and demonstrative ‘proof’, and we gain in return a charter of liberty.

For to admit the essential progressiveness of scientific truth and

its indefinite capacity for improvement means unlimited freedom to

research into truths which are infinitely perfectible, because they are

never ‘absolute’. The ideal of the infinite perfectibility of truth,

and the infinite progressiveness of science, is more than an adequate

substitute for the ‘logical ideal’ which is abandoned. For not only is

it an ideal which works, but it really embodies a nobler aspiration

than that which represented science as ‘resting’ in absolute perfection

on fixed ‘foundations’ of ‘eternal’ truth. The sentiment which inspires

this group of metaphors is given away by the word ‘rest’. A science

that desires to _rest_ is one that is unwilling to _move_ and unable

to _advance_. Fixed ‘foundations’ are needed only for standing firm

and standing still, and it turns out that what is strictly meant

by ‘eternal’ is not that truths last for ever, but that they are

not related to ‘time’ at all, and so have really no application to

‘events’.[400]

On the other hand, a science which sincerely desires to progress

needs fixed foundations as little as fixed ideas, and firm ground as

little as assurances to ‘rest’ on. It needs only a starting-point,

or jumping-off place, whence it can plunge into the unharvested

seas of the unknown. Now the essence of a starting-point is to be a

place you want to get away from, and its excellence lies in being

such as to prompt you to leave it as easily and eagerly as possible.

If, therefore, scientific ‘principles’ (ἀρχαί) are really to be

starting-points, they need not, and must not, be so comfortable and so

deceptively similar to ‘absolute’ truths as to tempt the scientific

spirit to repose. They should be tentative assumptions which are gladly

abandoned in the hope of reaching something better, stepping-stones to

farther and higher things, which are valued for their consequences,

and logically dependent on the conclusions to which they formed

the premisses. The logic of science, therefore, has no reason to

postulate stability or solidity for its initial principles: the most

indispensable of them are only principles of method, and even of the

tried and tested principles it arrives at the ‘validity’ (= strength)

demanded is merely that they should be able to float the accumulated

wealth of knowledge down the stream of time.