CHAPTER VII
THE MEANING OF RISK AND UNCERTAINTY
Starting with the individual psychology of valuation andadding new factors step by step, we have now built up acompetitive industrial society involving valuation and distribution under the highly simplified conditions necessary

to perfect competition. The drastic assumptions madewere necessary to show the operation of the forces at work
free from all disturbing influences; and impossible as thepresuppositions have been, the principles involved havenot been falsified or changed, but merely exhibited inpurity and isolation. Chief among the simplifications ofreality prerequisite to the achievement of perfect competition is, as has been emphasized all along, the assumption of practical omniscience on the part of every memberof the competitive system. The task of the present chapter
isto inquire more fully into the meaning of this assump-tion.

We must take a brief excursion into the field of thetheory of knowledge and clarify our ideas as to its natureand limitations, and the relation between knowledge andbehavior.

On the basis of the insight thus gained, it will

be possible to illuminate that large group of economic
phenomena which are connected with the imperfection ofknowledge.

The problem may be set in view and its significancemade clear by recalling certain points already brought out
in the previous discussion. In chapter n it was pointed ©utthat the failure of competition and the emergence of profit

are connected with changes in economic conditions, butthat the connection is indirect. For profit arises from thefact that entrepreneurs contract for productive services inadvance at fixed rates, and realize upon their use by the

i

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RISK, UNCERTAINTY, AND PROFIT

sale of the product in the market after it is made.

j\,
'

f

Thus

the competition for productive services is based upon anticipations. The prices of the productive services being
the costs of production, changes in conditions give rise to'Iprofit by upsetting anticipations and producing a divergence

between costs and selling price, which would otherwise beequalized by competition. If all changes were to takeplace in accordance with invariable and universally known
laws, they could be foreseen for an indefinite period in advance of their occurrence, and would not upset the perfectapportionment of product values among the contributing
agencies, and profit (or loss) would not arise. Hence it is
our imperfect knowledge of the future, a consequence ofchange, not change as such, which is crucial for the understanding of our problem.
Again, in chapters in and iv, it was found necessary toassume static conditions in order to realize perfect competition.

But, as expressly stated, this assumption wasmade because it follows from it as a corollary that the
future will be foreknown, and not for the sake of the proposition itself. It is conceivable that all changes might takeplace in accordance with known laws,

and in fact very
do
occur
with
sufficientmany changes
regularity to bepractically predictable in large measure.

Hence the justi-

fication and the necessity for separating in our study theeffects of change from the effects of ignorance of the future.

And chapter v was devoted to a study of the effects ofchange as such with uncertainty absent. Here it was foundthat under such conditions distribution or the imputationof product values to production services will always be
perfect and exhaustive and profit absent.
Furthermore, as also argued in chapter n, it is unneces-sary to perfect, profitless imputation that particular occurrences be foreseeable, if only all the alternative possibilities
are known and the probability of the occurrence of eachcan be accurately ascertained. Even though the businessMEANING of RISK AND UNCERTAINTY

199

man could not know in advance the results of individual
ventures, lie could operate and base his competitive offers
upon accurate foreknowledge of the future if quantitativeknowledge of the probability of every possible outcome canbe had. For by figuring on the basis of a large number ofventures (whether in his own business alone or in that ofbusiness in general) the losses could be converted into fixed
costs.

Such special costs would, of course, have to be given

full weight, but they would be costs merely, like any othernecessary outlays, and would not give rise to profit, which
is a difference between cost and selling price. Such situations in more or less pure form are also common in every-

day life, and various devices for dealing with them form
an important phase of contemporary business organization.
Some of the more important of these devices will come up
for brief discussion later.

-.

At present we are concerned C~AV

only to emphasize the fact that knowledge is in a sense
variable in degree and that the practical problem mayfV

relate to the degree of knowledge rather than to its presenceJor absence in toto.

The facts of life in this regard are in a superficial sense-^
obtrusively obvious and are a matter of common observation.

It is a world of change in which we live, and a world

We live only by knowing something about
the future; while the problems of life, or of conduct atof uncertainty.

least, arise from the fact that we know so little.

This is astrue of business as of other spheres of activity.

The es-sence of the situation is action according to opinion, ofgreater or less foundation and value, neither entire ignorance nor complete and perfect information, but partial

knowledge. If we are to understand the workings of theeconomic system we must examine the meaning and significance of uncertainty; and to this end some inquiry into
the nature and function of knowledge itself is necessary. 1
1

The problem of uncertainty and risk in economics is, of course, notSome reference has already been made to the literature. It has

new.

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RISK, UNCERTAINTY, AND PROFIT

The first datum for the study of knowledge and behavior
the fact of consciousness itself. Apparently the higher
mental operations of reason are different only in degree,
isonly elaborations of what is inherent in the first spark of"awareness." The essence of mentality from a functional
standpoint seems to be its forward-looking character. Life

has been described as internal adaptations to external
coexistences and sequences. On the vegetable or unconscious plane, the internal changes are simultaneous withthe external. The fundamental difference in the case ofanimal or conscious life is that it can re Act to a situation
before that situation materializes; it can "see things com-

This is what the whole complicated mechanism of
the nervous system is "for," in the biological sense. The
ing."

readjustments by which the organism adapts itself to theenvironment require time, and the farther ahead the organism can "see," the more adequately it can adapt itself,
the more fully and competently it can live.
been recognized and discussed in three connections: (1) insurance; (2)speculation; and (3) entrepreneurship. For a full treatment of the lastnamed it is necessary to go to the German works cited in the historicalportion of this study. English economics has been too exclusively occupied with long-time tendencies or with "static" economics to giveadequate attention to this problem. For a very general discussion of uncertainty see, in addition to works already cited, Ross, Uncertainty as a
Factor in Production, Annals, American Academy, vol. viii, pp. 304 ff.
See also Leslie, T. E. Cliffe, "The Known and the Unknown in the
Economic World," Essays in Political Economy, pp. 221-42; Lavington,
F., "Uncertainty in its Relation to the Rate of Interest," in Economic
Journal, vol. xxn, pp. 398-409; and "The Social Interest in Speculation,"
ibid., vol. xxiii, pp. 36-52; Pigou, A. C, Wealth and Welfare, part v;
Haynes, John, "Risk as an Economic Factor," Quarterly Journal of
Economics, July, 1895.
In this superficial sketch of the theory of knowledge it has not seemed
important to give extended reference to philosophic literature. It will beevident that the doctrine expounded is a functional or pragmatic view,
with some reservations. By way of further "reservation" we should
point out that the tone of the discussion merely results from the factthat it is the function of consciousness and knowledge in relation to conduct that we are interested in, for present purposes, and the text must not

be taken as expressing any view whatever as to the ultimate nature of

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201

Just what consciousness as such has to do with it is a1mystery which will doubtless remain inscrutable. It is amere brute fact that wherever we find complicated adaptations we find consciousness, or at least are compelled to

Science can find no place for it, and no role for itto perform in the causal sequence. It is epiphenomenal. An
infer it.

explanation of the readjustment necessarily runs in terms ofstimulus and reaction, in this temporal order. Yet in ourown experience we know that we do not react to the past
stimulus, but to the "image" of a future state of affairs;

and for common sense, consciousness, the "image," is bothpresent and operative wherever adaptations are dissociatedfrom any immediate stimulus; i.e., are "spontaneous" andforward-looking. It is evident that all organic reactions
relate to future situations, farther in the future as the typeof life and activity is "higher."

However successful mech-

anistic science may be in explaining the reaction in termsof a past cause,itwill still

be irresistibly convenient forcommon sense to think of it as prompted by a future situation present to consciousness.

The role of consciousness is

to give the organism this "knowledge" of the future. Forall

we can see or for all that science can ever tell us, wemight just as well have been unconscious automata, but

we are not. At least the person speaking is not, and hecannot help attributing to other creatures similarly constituted and behaving in the same way with himself "insides," to use Descartes' picturesque term, like his own.
We perceive the world before we react to it, and we react
not to what we perceive, but always to what we infer.
The universal form of conscious behavior is thus action
designed to change a future situation inferred from a
reality or any other philosophic position. The writer is in fact a radical
empiricist in logic, which is to say, as far as theoretical reasoning is con-cerned, an agnostic on all questions beyond the fairly immediate facts ofexperience.
1
See the brilliant lectures of E. DuBois-Raymond,des Naturerkennens" and "Die sieben Weltratsel.""

Uber die Grenzen

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RISK, UNCERTAINTY, AND PROFIT

present one.

It

twofold inference.

involves

perception and, in addition,

We must infer what the future situation

would have been without our interference, and what change
will be wrought in it by our action.

Fortunately or unfor-

tunately, none of these processes is infallible, or indeed
ever accurate and complete. We do not perceive the present as it is and in its totality, nor do we infer the futurefrom the present with any high degree of dependability,
nor yet do we accurately know the consequences of our own
actions. In addition, there is a fourth source of error to
be taken into account, for we do not execute actions in
the precise form in which they are imaged and willed.

The presence of error in these processes is perhaps a phaseof the fundamental mystery of the processes themselves. It

seems to be an earnest of their non-mechanical character,for machines, generally speaking, do not make mistakes.

(Though it may not be legitimate to draw inferences fromthe crude machines of our own construction to the infinitely

more sensitive and intricate physico-chemical complexes
which make up organic systems.) In any case the fact ofliability to err is painfully familiar and is all that concerns
us here.

It is interesting to note that the perceptive

faculties seem often to be less acute and dependable in the

At least
weak in this respect in comparison

higher forms of life than in some of the lower.
civilized man is oftenwith primitive man and the higher animals. Higher powers
of inference may take the place of perceptive faculties to alarge extent, and we have undoubtedly developed reasoning
power and lost ground with respect to keenness of sense.
It must be recognized further that no sharp distinction
can be drawn between perception and reason. Our perceptive faculties are highly educated and sophisticated,

and what is present to consciousness in the simplest situation is more the product of inference, more an imaginative
construct than a direct communication from the nerve

terminal organs.

A rational animal differs from a merely

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203

conscious one in degree only; it is more conscious. It is im-material whether we say that it infers more or perceives
more. Scientifically we can analyze the mental content into
sense data and imagination data, but the difference hardly
exists for consciousness itself, at least in its practical as-

Even in "thought" in the narrow sense, when theofreflection is not present to sense at all, the expeobject
pects.

rience itself is substantially the same. The function of consciousness is to infer, and all consciousness is largely inferential, rational. By which, again, we mean that things
not present to sense are operative in directing behavior, thatreason, and all consciousness, is forward-looking; andanessential element in the phenomena is its lack of automaticmechanical accuracy, its liability to error.
The statement that a situation not in physical relations
with an organism, not even in existence, influences thatorganism, is of course in a sense figurative; the influence
operating through a situation with which theorganism is in contact at the moment. Hence, as alreadypointed out, it is always theoretically possible to ignore theform of the conscious relation, and interpret the reaction
as a mechanical effect of the cause actually present. But
it remains true that practically we must regard the situation present to consciousness, not the one physicallypresent, as the controlling cause. In spite of rash stateis indirect,

ments by over-ardent devotees of the new science of "behavior,"

itispreposterous to suppose thatitwill eversupersede psychology (which is something very different)or the theory of knowledge, in something like their historicfor £s.
It is evident that the possibility of a situation not pres-ent, operating through one which is present, is conditioned

upon some sort of dependable relation between the two.
This postulate of all knowledge and thought has beenvariously formulated as the "law" or "principle" of "causality," and "uniformity" or "regularity" of nature, etc.

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RISK, UNCERTAINTY, AND PROFIT

Remembering that we are speaking of the surface facts,
not metaphysical interpretations, we may say that allreasoning rests on the principle of analogy. We know theabsent from the present, the future from the now, by as-

suming that connections or associations among phenomena which have been valid will be so; we judge the futureby the past. Experience has taught us that certain timeand space relations subsist among phenomena in a degree
to be depended upon. This dogma of uniformity of coexistence and sequence among phenomena is a fairly satisfactory statement of the postulate of thought and forwardlooking action from the standpoint of the philosopher.
But from the more superficial standpoint of common
sense (and hence of an inquiry such as the present) theterm "phenomenon" is rather vague and elusive, and amore serviceable formulation seems possible. Common
sense works in terms of a world of objects or merely"things." Consequently the idea of things manifesting
constant modes of behavior seems to be a better "category"than that of uniformity of relation among phenomena.
This may be unsatisfactory to the philosopher, who willprotest at once that the thing is merely a sum of its modesof behavior, that no such separation is really possible. It is
the ancient riddle which so puzzled Locke, of the attributeand substratum, the substratum, of course, tending toevaporate under critical scrutiny. But this weakness may
prove rather a source of strength for the use which we intend to make of the notion, as will be argued.
We have, then, our dogma which is the presuppositionof knowledge, in this form; that the world is made up ofthings, which, under the same circumstances, always behavein the same way. The practical problem of inference or prediction in any particular situation centers around the firsttwo of these three factors what things are we dealing with,and what are the circumstances which condition their action? From knowledge of these two sets of facts it must be:

MEANING OF RISK AND UNCERTAINTY

205

possible to say what behavior is to be expected. The chief
logical problem, as already noticed, lies in the conception

For it is obvious that the "circumstances"which condition the behavior of any particular thing arecomposed of other things and their behavior. The assumption that under the same circumstances the samethings behave in the same ways thus raises the single question of how far and in what sense the universe is reallymade up of such "things" which preserve an unvarying
of a "thing."

identity(mode of behavior).

It is manifest that the or-

dinary objects of experience do not fit this description
closely, certainly not such "things" as men and animals
and probably not even rocks and planets in the strict
sense. Science has rested upon the further assumption that

this superficial divergence of fact from theory arises be-cause the "things" of everyday experience are not the"ultimate" things, but are complexes of things which really

And the progress of science has consisted
mostly in analyzing variable complexes into unvarying
constituents, until now we have with us the electron.
But workable knowledge of the world requires much morethan the assumption that the world is made up of units
which maintain an unvarying identity in time. There are
far too many objects to be dealt with by a finite intelligence, however unvarying they might be, if they were all
are unchanging.

different.

We require the further dogma of identical sim-

ilarity between large numbers of things. It must be possible not merely to assume that the same thing will always
behave in the same way, but that the same kind of thing
will do the same, and that there is in fact a finite, practi-

manageable number of kinds of things. Hence thefundamental role which classification has always played inthought and the theory of thought. For our limited intelligence to deal with the world, it must be possible toinfer from a perceived similarity in the behavior of objects
callyto a similarity in respects not open to immediate observa-

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206

That is, we must assume that the properties of things
are not shuffled and combined at random in nature, buttion.

that the number of groupings is limited or that there isconstancy of association. This is the dogma of the "realityof classes," familiar to students of logic.

But even this is not enough.

If the classification of ob-

jects be restricted to the grouping of things in all respects

similar or substantially identical, there would still be aquite impossible number of kinds of things for intelligence

Even in the sense of practical degrees of comof
pletenesssimilarity, identity to ordinary observation,
our groups would be far too small and too numerous. It is
to grasp.

questionable whether classification would be carried far
enough on this basis to be of substantial assistance in simplifying our problems to the point of manageability. It is
not that kind of a world. And even abstracting from meredifferences in degree such as size and the like, for which
intelligence readily makes allowance, the same would still
hold true. It is clear that to live intelligently in our world,— thatis, toadapt our conduct to future facts,— we must

use the principle that things similar in some respects will

behave similarly in certain other respects even when they
are very different in still other respects. We cannot makean exhaustive classification of things, but must take various
and shifting groupings according to the purpose or problem in view, assimilating things now on the basis of one
common property (mode of behavior) and now on the basisof another. The working assumption of practical inference
about the environment is thus a working number of properties or modes of resemblance between things, not a work-

number of kinds of things; this latter we do notThat is, the properties of things which influence
our reactions toward them must be sufficiently limited in
number and in modes of association for intelligence to
able

have.

grasp.

We may sum up these facts about the environment of

MEANING OF RISK AND UNCERTAINTY

207

our lives which are fundamental for conduct in the following propositions
1.

:

The world is made up of objects which are practically\
infinite in variety as aggregates of sensible qualities)

of behavior not immediately sensible. /And when we consider the number of objects which/and modes

function inany particular conduct situation, and /their possible variety, it is evident that only an ffi-(
intelligence co uld grasp all the possible~c om-

finitebinations.

£7 Finite intelligence is able to deal with the world be-

y/

cause
a.

The number of distinguishable properties an dmodes of behavior is li mited, the infinite variety
in nature being due to different combinations of

the attributes in objects.
b.

Because the properties of things rem ain fairly

consta nt; andSuch ch anges in them as take place occur infairly constant and ascer tainable ways.
d. The non-sensible properties and modes of bec.

havior of things are associated with sensible
properties in at least fairly uniform ways.
It is to be noted under (a) that differences in kind arereferred to rather than differences in degree, and we should

add that3.

The quantitative aspect of things and the power ofintelligence to deal with quantity is afundamental

element in the situation.
4. It is also fundamental that in regard to certain proper-

ties objects differ only in degree, that mass and spacial

magnitude axe universal qualities of things, which do
not exhibit differences in kind.
5.

Following out the same principle of (4 ) many of themost significant properties are common \p vpry largp
groups in respect to the qualities most important for;

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208

conduct, there are a very few kinds. The intelligi bility of the world is enormously in creas ed if notactually made possible by the_simplicity of the great
divisions into solid, liquid, and..ga,S i ntf> living andnot-living things, and the like. And there is a hierlarchy of attributes in order of generahty_down J;o^the slight peculiarities which probably distinguishin some mariner "and degree (other than mere situation) every nameable thing in the universe from every

other, giving it individuality.
6.

The postulates of intelligent behavior would be very
incomplete without formal insistence on the role"
played by the fact of consciousness inj;* objects outside ourselves, human beings and animals. The behaviorist notwithstanding, the inferences as to the
behavior to be anticipated which we draw from theconfiguration of the lines about the mouth, the gleamor "twinkle" of an eye or a shrill or "soft" vocal

sound, are not made from these physical features assuch or alone, but through "sympathetic introspec-tion" 2 into what is going on in the "mind" of the"object" contemplated, and would be impossible

without this mysterious capacity of interpretation.
It is always possible for the scientist to argue the con-trary, as it is for him to demonstrate that we are notreally conscious ourselves, but common sense properly

revolts against the one conclusion as against theother.

we must know ourselves
Hence we must list our sense of
our own powers of movement, etc.

7. It goes without saying that

as well as the world.

It is perhaps superfluous to speak here of the syllogism

and its place in logical theory. Empirical logicians such
1

Cf. Comte's Classification of the Sciences.

2

Professor

chap. i.

Cooley's descriptive phrase.

See Social Organization,

MEANING OF RISK AND UNCERTAINTY

209

as Mill and Venn have ventilated the subject sufficiently

and shown that no real inference is involved in the syllogisnritself, that the inference takes place in the formula-tion of the premises and consists in the recognition of aconstant factual connection between the predicates de-noted by the different terms.

We are rather concerned here with pointing out that thetheory of knowledge as it is worked out by logicians is
primarily a theory of exact knowledge, of rigorous demonIt has become somewhat the fashion, especiallystration.

since Bergson came into vogue, to be iirationalistic, andquestion the validity of logical processes. It seems to thewriter that there is much ground for this position, but thatits implications are very liable to be misunderstood.
is to

There

my mind no question of understanding the world by

any other method. There is, however, much question as tohow far the world is intelligible at all. This will be seen
to be a question of the facts as to the uniformity of behavior of natural objects and the similarities subsisting be-

tween them, on the ground of which inference is made from
one to another. In so far as there is "real change" in the
Bergsonian (i.e., Heracleitean) sense it seems clear thatreasoning is impossible. In addition we have to make themore questionable assumption that the situation elements or fundamental kinds of object properties uponwhich we fall back for simplicity (practically finitude) inview of the unmanageable number of kinds of objects as
wholes, are unvarying from one "combination" (i.e., onestill

object) to another. This assumption is doubtless valid insome connections. Thus weight, inertia, etc., are undoubt-

edly the same in a living as in a non-living object. Butthat the quality "living" is really the same in any two

kinds of living things is more open to doubt. In so far asthese general attributes are not uniform and cannot begiven a definite meaning which is the same for all the objects in the class which they designate, reasoning from one

RISK, UNCERTAINTY, AND PROFIT

210

member of the class to another is clearly invalid. That is,valid classification assumes identity in some respect. It is

not absolutely certain that the ground on which we ascribe similarity to things and class them together and reason from the behavior of one to that of the other is always

The power of one thing to suggest another is often quite mysterious, and may possibly not rest
upon the possession of any common real qualities whichof this character.

will support a valid inference. 1

The practical limitation of knowledge, however, rests
upon very different grounds. The universe may not be
ultimately knowable (we speak, of course, only of objective

phenomena, of behavior, not of problems which transcend
ordinary experience of fact) ; but it is certainly knowable toa degree so far beyond our actual powers of dealing with it
through knowledge that any limitations of knowledge due
to lack of real consistency in the cosmos may be ignored.
It probably occasions surprise to most persons the firsttime they consider seriously what a small portion of ourconduct makes any pretense to a foundation in accurate

and exhaustive knowledge of the things we are dealingwith.
It is only when our interest is restricted to a very narrow aspect of the behavior of an object, dependent uponits physical attributes of size, mass, strength, elasticity, or

the like, that exact determination is theoretically possible;

and only by refined laboratory technique that the determination can be actually made. The ordi nary decisions o flife aremade on t lie ba,si« of "^tfimntn" nf a midft nnd

superfici al character.

In general the future situation in

we act depends upon the behavior of
an indefinitely large number of objects, and is influenced
by so many factors that no real effort is made to take account of them all, much less estimate and summate theirrelation to which

separate significances. It is only in very special and crucial
1

See James, Psychology, chap, xxii, on "Association by Similarity."

MEANING OF RISK AND UNCERTAINTY

211

cases that anything like a mathematical (exhaustive andquantitative) study can be made.

The mental operations by which ordinary practical decisions are made are very obscure,and it is a matter forsurprise that neither logicians nor psychologists haveshown much interest in them. Perhaps (the writer is inclined to this view) it is because there is really very little
to say about the subject. Prophecy seems to be a gooddeal like memory itself, on which it is based.

When we wish

to think of some man's name, or recall a quotation which

has slipped our memory, we go to work to do it, and thewe are thinking
does not come, but indesired idea comes to mind, often whenabout something else

— orelse iteither case there is very little that we can tell about theoperation, very little "technique." So when we try to decide what to expect in a certain situation, and how to be-

have ourselves accordingly, we are likely to do a lot of irrelevant mental rambling, and the first thing we know wefind that we have made up our minds, that our course ofaction is settled. There seems to be very little meaning inwhat has gone on in our minds, and certainly little kinshipwith the formal processes of logic which the scientist uses
in an investigation. We contrast the two processes by recognizing that the former is not reasoned knowledge, but"judgment," "common sense," or "intuition." There isdoubtless some analysis of a crude type involved, but inthe main it seems that we "infer" largely from our experience of the past as a whole, somewhat in the same waythat we deal with intrinsically simple (unanalyzable) prob-

lems like estimating distances, weights, or other physicalmagnitudes, when measuring instruments are not at hand.

1

The foregoing discussion of reasoning relates to ideal orcomplete inference based on uniformity of association ofpredicates and which can be formulated in universal propo1
Marshall remarks that the business manager's decisions are guided by"trained instinct" rather than knowledge. (Principles, 6th ed., p. 406.)

RISK, UNCERTAINTY, AND PROFIT212

The theory of formal deductive logic has, ofcourse, always recognized also reasoning from what are"occaundescriptively called "particular" propositions

sitions.

——sional would be a better term
asserting that two pred"icates sometimes belong to the same subject, or thatclasses of objects overlap.

two

The goal of science is always to

get rid of this form of assertion, to "explain" the occurrence and non-occurrence of the quality by finding someother general fact in the past history of the object withwhich the association is universal. But there are large
classes of cases in which this cannot be done even scientifi-

and the rough operations of everyday unscientificthinking employ the form* quite commonly. In the crude
is F," such generalizations are very unform of "somecally,

X

satisfactory to the scientific mind and practically uselessexcept as a challenge and starting-point for further inquiry.

But when, as is so commonly the case, it is impossible or
impracticable to do better, the data can often be put in aform of a great deal of scientific utility. This is done byascertaining the numerical proportion of the cases in whichis associated with F, which yields the familiar probability

X

judgment.

If,

say, ninety per cent of

X

is

F,

that fraction of objects characterized by property
also property F,

—

i.e.,

if

X shows— the fact may obviously have much thesame significance for conduct as if the association were
universal. 1

Furthermore, even if the proportion is not approximately
one hundred per cent, even if it is only half or less, thesame fact may hold good. If, in a certain class o f cases a

XY

and are taken into
When variations in degree in the attributes
account, the problem must be dealt with by applying the statistical theoryof correlation, which is a further development of probability theory.
See especially the works of K. Pearson and F. Y. Edgeworth. An elementary discussion will be found in any treatise on statistics. A. L.
1

Bowley's Measurement of Groups and Series is particularly serviceable
A rough idea may be obtained from Elderton'sPrimer of Statistics. Pearson's Grammar of Science, chaps, iv and v, may
be consulted on the whole ground of the present chapter.

for the general reader.

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213

gi ven outcom e i s not certain, nor even extremely probable ,but only eontin gent. hnt if the nqmeriWI prpjfrflhilit.y of its
occurrence is known, conduct in relation to the situation inquestion may be ordered intelligently. Business operations,as already observed, illustrate the point perfectly. Thus, inthe example given by von Mangoldt, the bursting of bottles does not .introduce an uncertainty or hazard into the^Business of producing champagne; since in the operationsof any producer a practically constant and known proportion of the bottles burst, it does not especially matter even

whetheMhe proportion is large or small. The loss becomesa fixed cost in the indust ry and is passed on to the consumer, like the outlays for labor or materials or any other.

And even if a single producer does not deal with a sufficiently large number of cases of the contingency in question (in a sufficiently short period of time) to secure con-stancy in its effects, the same result may easily be realized,
through an organization taking in a large number of producers.

This, of course,isthe principle of insurance, asfamiliarly illustrated by the chance of fire loss.

No one cansay whether a particular building will burn, and most building owners do not operate on a sufficient scale to reduce theloss to constancy (though some do) .

But as i s well known the,effect of insurance is to extend this base to cover the opera-

tions of a large number of persons and convert, the eont i nt

jjency mto a fixed cost. It makes no difference in the principles whether the grouping of eases is effected through amutual organization of the persons directly aitected or
through an outside commercial agency.
It will be evident that the practical difficulties of order-

ing conduct intelligently are enormously increased where
the inference is contingent instead of being positive. The
difficulties of establishing an association between predicatesare great enough where the association is universal; sogreat, as we have already seen, that it is never done withany approach to accuracy except for critical cases of very

RISK, UNCERTAINTY, AND PROFIT

214

special importance justifying extensive study in laboratoryor "field." Where the connection is occasional, demonstra-tion of a dependable connection is vastly more difficult,and there is the added problem of ascertaining the precise
proportion of cases in which the connection occurs. In relation to everyday problems, where rigorous scientificprocedure is excluded, the difficulty and chance of error are,of course, multiplied in still greater degree We have to"estimate" not merely factors whose associates, implications, or effects are known, but in addition the degree of
dependability of the association between the (estimated)factors (the immediately perceptible attributes or modes of
behavior) and the inferred factors with relation to whichI

our action in the case is to be controlled.

Most of the realdecisions of life are based on "reasoning" (if such it may becalled) of this still more tenuous and uncertain character,and not even that which has already been described. We
have to estimate the given factors in a situation and also

estimate the probability that any particular consequence
will follow from any of them if present in the degree as^-sumed.
For logical accuracy and in order to understand thedifferent kinds of situations and modes of dealing withthem in practice, a further distinction must be drawn, adistinction of far-reaching consequences and much neghere arelected in the discussion of economic problems.

T

two fundamentally different ways of arriving at the probability judgment of the form that a givenbportion of X's are also Fs.
calculation,n umerical prp-

The first method is by a priori

and is applicable to and used in games ofThis is also the type of case usually assumed inlogical and mathematical treatments of probability. It
must be strongly contrasted with the very different type ofin which calculation is impossible and the result is
problem^-^i£chance.

method of applying statis tics to
As an illustration of the first type of)renohe.(\ by the empiricalactual instances.

MEANING OF RISK AND UNCERTAINTY

215

probability we may take throwing a perfect die. If the dieis really perfect and known to be so, it would be merely
ridiculous to undertake to throw it a few hundred thousand

times to ascertain the probability of its resting on one faceor another. And even if the experiment were performed,
the result of it would not be accepted as throwing any
lighton the actual probability. The mathematician caneasily calculate the probability that any proposed distribution of results will come out of any given number ofthrows, and no finite number would give certainty as to theprobable distribution. On the other hand, consider thecase already mentioned, the chance that a building will

burn. It would be as ridiculous to suggest calculating froma priori principles the proportion of buildings to be accidentally destroyed by fire in a given region and time as it

would to take statistics of the throws of dice.

The import of this distinction for present purposes isthat the first, ma thematical ova priori, type of probability
met with in business, while the second
It is difficult to think of a business"hazard" with regard to which it is in any degree possible to calculate in advance the proportion of distribution
among the different possible outcomes. 1 This must be
is practically neveris extremelycommon.

dealt with, if at all, by tabulating the results of experience.

The "if at all" is an important reservation, which will be
discussed presently. It is ev ident that a great many ha zards can be reduced t o a fair d egre e of certainty bvstatis-—

also that an equally imporfrfi.nf. ™.»pgnry
groupin gcannot. We should note, however, two other facts. First,

ti calthe statistical treatment never gives closely accuratequantitative results. Even in such simple cases as mechan-games of chance it would never be final, short of an
number of instances, as already observed. Furthermore, the fact that a priori methods are inapplicable is
ical

infinite

1

The calling of bonds by lot is an illustration. In Germany bond-holders often insure against this chance.

RISK, UNCERTAINTY, AND PROFIT

216

connected with a much greater complication in the data,
which again carries with it a difficulty, in fact impossibility, of securing the same degree of homogeneity in the instances classed together. This point will have to be gone

into more fully. The second fact mentioned in regard to
the two methods is that the hazards or probabilities met

with in business do admit of a certain small degree oftheoretical treatment, supplementing the application ofexperience data. Thus in the case of fire risk on buildings,

the fact that the cases are not really homogeneous may beoffset in part by the use of judgment,if

not calculation.

possible to tell with some accuracy whether the"real risk" in a particular case is higher or lower than thatIt

isof a group as a whole, and by how much. This procedure,

however, must be treated with caution. It is not clearthat there is an ultimate separation between the calculation of departures from a standard type and more minute

There is, however, a difference inandinsurance
form,
companies constantly follow bothclassification of types.

practices, that of defining groups as accurately as possible

and also that of modifying or adjusting the coefficient applied within a class according to special circumstances
which are practically always present.

We thus find that there are two logically different types
We shallof inference included in the probability judgment.

referfto these foT brevity under the names of the "a priori "and/xhe "statistical" respectively. The relations between
thetwo concepts as employed in the crude usage of com-

mon sense are much confused and the ideas themselves
blurred, so thatitisimportant to emphasize the con-

The precise meaning of "real probability" will haveto be examined more in detail presently, but we can see
trast.

that there is a difference in this respect in our feelings to-ward the two classes of cases. It seems clear that the probability of getting a six in throwing a die is "really" one insix,

no matter what actually happens in any particularMEANING OF RISK AND UNCERTAINTY

217

number of throws; but no one would assert confidently thatthe chance of a particular building burning on a particular
day is "really" of any definite assigned value. The firststatement has intuitive certainty with reference to a particular instance; in case of the second it is merely an empirical generalization with reference to a group.

Possibly
the difference is partly a matter of habit in our thinking
and to some extent illusory, but it is none the less real andfunctional in our thinking. There is, indeed, a sort oflogical paradox in the problem. If the probability in agame of chance is questioned, there is no test except that ofexperimental trial of a large number of cases, and undersome circumstances we should conclude that the die wasprobably "loaded." This would itself be a probability
judgment, to be sure, and would depend on the fact of ourignorance of the composition and manufacture of the die.
Given this ignorance, a mathematician could tell the probability that the die is false, indicated by any given number
and distribution of throws.

The pra ctical difference between a priori and statisti cal
probability seems t o depend upon the accuracy of clas sification of the instances grouped together.. In the case of

the die, the successive th rows are held to be "alike" in adegree and a sense which cannot be predicated of the dift'erent buildings exposed to hrejiazard. There is, of course,
a constant effort on the part of the actuary to make hisclassifications more exact, dividing groups into subgroups

to secure the greatest possible homogeneity. Yet we canhardly conceive this process being carried so far as to makeapplicable the idea of real probability in a particular instance.

There is a further (Jjffiq iltv. amounting to paradox, inth e idea of homo geneous groupin g.

Much is made of thispoint in treatises on statistics, the stude nt being warne dagainst drawing conclusions from distributions in non-homogeneous groups. Perhaps the most familiar example

j

(

218
is

RISK, UNCERTAINTY, AND PEG. IT

the age and sex distribution of population aggregates.

An illustration (used by Secrist) is the death rate of theAmerican soldiers in the Philippines, which was lower thanthat of the general population in the United States.

The

fallacy in the inference as to healthfulness of environmentis, of course, that the "general population" is not a ho-mogeneous group, but is made up of numerous age, sex,
race, and occupation classes, "naturally" subject to widelydifferent death rates. The para dox, which carries us atonce into the heart of the logical problem of probability is,that if we had ab solutely homogeneous groups we shouldhave uniformity and not probability in the result, or else

we must repudiate the dogma of the ultimate uniformity ofn ature, the persistence of identity in things If the idea of
natural law is valid at all, it would seem that men exactly.

alike and identically circumstanced would all die at once;

any particular interval either all or none would succumb, and the idea of probability becomes meaningless.
So even in the case of the dice; if we believe in the postulates
which make knowledge possible, then dice made alike andthrown alike will fall alike, and that is the end of it.
Yet practically there is no danger, figuratively speaking, that any of these phenomena will ever be amenable toprediction in the individual instance. T?he fundament alfact underlying probability reasoning is generally assumed
be ou r jgnorfl/nQp. If it were possible to measure withtoj
inabsolute accuracy all the determining circumstances in
the case it would seem that we should be able to predictthe result in the individual instance, but it is obtrusively
manifest that in many cases we cannot do this. It will certainly not be proposed in the typical insurance situations,the chance of death and of fire loss, probably not even in

The question arises whether
we should draw a distinction between necessary and only
factual ignorance of the data in a given case. Take thecase of balls in an urn. One man knows that there are
the case of gambling devices.

MEANING OF RIS5 AND UNCERTAINTY

219

red and black balls, but is ignorant of the numbers of each;another knows that the numbers are three of the former to"one of the latter. It may be argued that "to the first man
the probability of drawing a red ball is fifty-fifty, while tothe second it is seventy-five to twenty-five.

Or it may becontended that the probability is "really" in the latterratio, but that the first man simply does not know it. It
must be admitted that practically, if any decision as toconduct is involved, such as a wager, the first man would
have to act on the supposition that the chances are equal.
And if the real probability reasoning is followed out to its
conclusion, it seems that there is "really" no probability atall, but certainty, if knowledge is complete. The doctrineof real probability, if it is to be valid, must, iL seems, rest

upon inherent unknowability in the factors, naljnerely_the
And even then we must always consult
the empirical facts, for it will not do to assume out of handthat the unknown causes in a case will distribute themfact of ignorance.

selves according to the law of indifference among the different instances. We seem to be driven back to a logicalimpasse. The postulates of knowledge generally involvethe conclusion that it is really determined in the nature ofthings which house will burn, which man die, and whichface of the thrown die will come uppermost. The logic

which we actually use, however, assumes that the result
is really indeterminate, that the unknowable causes actually follow a law of indifference. The phenomenal constancy of distribution to which we are forced to appeal
justifies this reasoning on the whole, but clearly is not its
actual basis in our thinking. Wherever we find that there
not indifference, that the results show "bias," we assume some determinable cause at work; and the results ofisexperience on the whole justify this assumption also.
There is a further point of some interest in regard to ourprobability reasoning.

Examination of the mathematicaltheory of probability will show that the argument always

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RISK, UNCERTAINTY, AND PROFIT

proceeds on the assumption that there is no middle groundbetween complete determination and complete indifference.

That is, the elementary probabilities in any form of problem must always be equal. If the chance of any particular
result is more or less than one half, it is held to be axiomatic that there is a greater number of possible alternatives
which yield this result (or do not yield it) than of the otherkind; the alternatives themselves must be equally probable.
The whole mathematical theory of probability is obviously
a simple application of the principles of permutations andcombinations for finding out the number of alternatives.
Absolute indifference between the alternatives is taken for
granted. Wherever the results do not show complete indifference between alternatives it is assumed that these
are not simple, and further analysis is applied to reducethem to combinations of equally possible ones. And experience confirms these assumptions also.
Are we, then, to assume real indeterminateness, in thecosmos itself? This was the view of Cournot, and the mere

ignorance theory common among writers on probability
seems inadequate and untenable. There are, to be sure,cases which it seems to fit, like that referred to, where theprobability of drawing a red or black ball is even to one

who knows only that there are balls of the two colors in the1urn, but is ignorant of the numbers of each. But the case of
the man who does know the numbers of each seems to bedifferent. The dogmatic determinist can always maintainthat there are causes at work which decide the result, butcommon sense is not satisfied. How does it "happen"that experience justifies the calculation of probabilities
unless these unknown causes are really indifferent? When"e ver we find biflg" in the rpg]ilt,fi, p d ivergence from thean ticipations on the basis of probability theory, we assume
Professor Irving Fisher is particularly insistent upon the interpretation of probability as due to ignorance alone. See The Nature of Capital1

and Income, chap, xvi, sec. 1.

MEANING OF RISK AND UNCERTAINTY

221

the presence of some cause which is not indifferent, andthis procedure is also justified of its fruits.

When we can be

sure that we have eliminated every circumstance which

can be measured or which might act consistently, we feel
confident in assumin g th at in a large number ofjtriajs_theresults will come out in accordance with the assumptionthat the factors not subject to measure ment or eliminatio n
are in fact indifferent^ And not merely do we feel this way,

but "it works."
It is interesting to observe that the common applicationsof probability in games of chance relate to some action of

the human organism itself, the drawing of a card from a

deck or ball from an urn after random manipulations, theimpulse given to a wheel or coin or die, etc. The facts
suggest a connection with that other age-old bone of contention, the freedom of the will.

1

If there is real indeter-

minateness, andof the human (or perhaps organic) machine, there is in aif the ultimate seat of it is in the activities

sense an opening of the door to a conception of freedom in

conduct.

And when we consider the mystery of the role ofconsciousness in behavior and the repugnance which is felt

by common sense to the epiphenomenal theory, we feeljustified in further contending for at least the possibility

that "mind" may in some inscrutable way originate action.
Just how much or what sort of significance the admission

may have for practical ethics is another question, whichmust be passed over here. Of course we cannot prove thatthe exact distribution of all the coups of the roulette wheels
at Monte Carlo was not stowed away somewhere in theprimeval nebula; the final appeal must be to "intrinsic
reasonableness," the inveterate and necessary preference ofintelligence for the simplest formulation which conforms
to the facts. And about this, there may indeed be differencesof opinion, and from these there is apparently no appeal. 2
1

2

Cf. E. Borel, Le Hasard, pp. 196-97.
See Karl Pearson's essay on "The Scientific Aspects of Monte Carlo

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There

RISK, UNCERTAINTY, AND PROFIT

may be different brands of "common sense"(which some wag has averred is so called because so veryuncommon). In the writer's view the doctrine of ignorance or "insufficient reason" is untrue to the feelings ofunsophisticated intelligence.

We do not merely feel that

we know no reason why the coin shall fall heads or tail s;
we know in a positive sen se that there is no reason^smd only
under this condition do we make the probability judgment

And furthermore, as already argued,
appears that only on condition that there is no reason
would the results of experience confirm the judgment, aswith any confidence.

it

they do. Th e entire science of probability in the mathema tical sense is based on the dogmatic assumption that theulti mate alternatives are really equally vrobable. which
seems to the writer to mean real indeterminateness. 1
Professor Irving Fisher's view of probability as "always"
an estimate becomes conditionally valid, however, on two
interpretations. In the first place, it may be saved "theoretically" if the term "estimate" is construed broadly
enough. If there is no difference between our a priori
judgment of the absence of any cause which should lead a
Roulette," in The Chances of Death and Other Studies in Evolution. The
necessity of constant appeal to a dogmatic preference of simple to complicated hypotheses is brilliantly treated in Poincare's chapter on "Probabilities," in The Foundations of Science, Science and Hypothesis, chap,

See also Poincare's fascinating treatment of the relations between
small causes and large effects in the same volume, Science and Method,
chap. iv. Poincare bases the doctrine of equal probability on the mathematical principle that for small changes any continuous analytical function changes in the same ratio as the variable. The same unsatisfactory,
if not absurd, doctrine of "intrinsic reasonableness" (for how can one
xi.

thing be "intrinsically" more probable than another?) is developed froma different point of view in Balfour's Theism and Humanism, lecturevii, on "Probability, Calculable and Intuitive."1
For an excellent brief discussion of the issue, with references to theliterature, the reader is referred to Arne Fisher, The Mathematical Theoryof Probability, chap,i:"General Principles and Philosophic Aspects."

The writer's position is that taken by Fisher and designated the principleof "cogent reason" in opposition to the older view common among
mathematicians, of "insufficient reason." Compare also La Place,
Essay on the Philosophical Theory of Probability.

MEANING OF RISK AND UNCERTAINTY

223

coin or a die to fall on one face rather than another and an"estimate" of equal probability, then there is no opposition between the two views. This is, however, repugnant
to common sense (the present writer's brand).

We seemto experience an "apodeictic certainty" about the situa-tion of a game of chance, on a level with our confidence inthe axioms of mathematics, and quite different from an"estimate."

To illustrate, suppose we are allowed to look

into the urn containing a large number of black and redballs before making a wager, but are not allowed to countthe balls; this would give rise to an estimate of probability
it is something very different frommere consciousness or ignorance on which wein the correct sense;

either theact if we know only that there are balls of both colors
without any knowledge or opinion as to the numbers or

the exact knowledge of real probability attainedby anaccurate counting of the balls. In the second place, wemust admit that the actual basis of action in a large proportion of real cases is an estimate. Neither of these interpretations, however, justifies identifying probability withan estimate.

But the p robability^ which thestudent, of busin ess

risk is interested is an estimate, though in a sense different

from any of the propositions so far considered. To discuss
the question from this new point of view we must go backfor a moment to the general principles of the logic of conduct. We have emphasized above that the exact science ofinference has

little place in forming the opinions uponwhich -decisions of conduct are based, and that this is true
whether the implicit logic of the case is prediction on the
ground of exhaustive analysis or a probability judgment,a priori or statistical. We act upon estimates rath er thaninferences, upon "judgment" or "intuition," not reasoningJFor the most part. Now an estimate or intuitive judg-

ment is somewhat like a probability judgment, but very
di fferent

from either of the types of probability judg-(.

RISK, UNCERTAINTY, AND PROFIT

224

ment already described. The relations between the two
sorts" are in fact amazingly complex and as fraught withlogical paradox as the probability judgment itself. If theterm "probability" is to be applied to an estimate
andthe usage is so well established that there is no hope ofa third species under that genus
getting away from it
must be recognized. Such a third type of probability fits
very nicely in a scheme of classification with the two already discussed. We have insisted that there Jsjl fundamental difference between "a priori" probability, on the
one hand, and "statistical," on the other. In the formerthe "chances" can be computed on general principles,——while in the latter they can only be determined empirically.
This distinction is in opposition to the views of writers

such as Venn and Edgeworth, 1 who reduce the former
type to the latter on the basis of an empirical law of large

numbers and accept practically the assumption of realindeterminateness. We have already raised the questionof accuracy of classification in this connection, suggestingthat the "instances," "throws," or "coups" in a game ofchance form a homogeneous group in a higher sense thancan be predicated on life or fire hazards. This view and ourentire theory tend to be confirmed by the attempt tosecure complete homogeneity through more minute classification. The end result of this endeavor would be groupings in which only really indeterminate factors should
differ from one instance to another.
Taking, then, the classification point of view, we shallfind the following simple scheme for separating three differ-ent types of probability situation
1.

:

A pnon^rjiobability. Absolutely homogeneous classification of instances completely identical except for

really indeterminate facto rs. This judgment of probability is on the same logical plane as the propositionsof mathematics (which also may be viewed, and are
1"The Philosophy of Chance," Mind, vol. 9, 1884.

MEANING OF RISK AND UNCERTAINTY

225

viewed by the writer, as "ultimately" inductions
from experience).
2. Statistical probability.

Empirical evaluation of thefrequency of association between predicates, not analyzable into varying combinations of equally probable alternatives. It must be emphasized that any
high degree of confidence that the proportions foundin the past will hold in the future is still based on ana priori judgment of indeterminateness. Two complications are to be kept separate: firsts the impossibility of eliminating all factors not really indeter-

minate; andl feeconcLtne impossibility of enumerati ng
the equally probable alternatives involved anddetermining their mode of combination so as .toevaluate the probability by a priori calculation. The

main distinguishing characteristic of this type is thatit rests on an empirical classification of instances.
3.

Estimates.

The distinction here is that there is novalid basis of any kind for classifying instance s.

form"ofpSobability isThisinvolved in the greatest logicaldifficulties of all, and no very satisfactory discussionof it can be given, but its distinction from the othertypes must be emphasized and some of

its

com-

plicated relations indicated.

We know that estimates or judgments are "liable" toSometimes a rough determination of the magnitude of
In
the
value
determinationofofanestimate
general, anymust be merely empirical, secured by the tabulation oferr.

this "liability" is possible, but more generally it is not.

instances, thus reducing it to. a probability of the second or
statistical type. Indeed, since, as we have noticed, entirely

homogeneous classification of instances is practically neverpossible in dealing with statistical probability, it is clearthat the divergence from it of this third type where allclassification is excluded is a matter of degree only.

There

are all gradations from a perfectly homogeneous group of

RISK, UNCERTAINTY, AND PROFIT

226

life or fire hazards at one extreme to an absolutely unique

exercise of

judgment at the other.

All gradations,

weshould say, except the ideal extremes themselves; for as
we can never in practice secure completely homogeneousclasses in the one case, so in the other it probably never

happens that there is no basis of comparison for determining the probability of error in a judgment.
The theoretical difference between the probability
connected with an estimate and that involved in suchphenomena as are dealt with by insurance is, however, ofthe greatest importance, and is clearly discernible in nearly
any instance of the exercise of judgment. Take as an illustration any typical business decision.

A manufacturer isconsidering the advisability of making a large commitment in increasing the capacity of his works. He "figures'*more or less on the proposition, taking account as well as
possible of the various factors more or less susceptible ofmeasurement, but the final result is an "estimate" of theprobable outcome of any proposed course of action. Whatis the""probabilityof error (strictly, of any assigned de-gree of error) in the judgment? It is manifestly meaning-speak of either calculating such a probability aof determining it empirically by studying a large
or
prioriless tonumber of instances. The essential and outstanding fact
is that the "instance" in question is so entirely unique that

there are no others or not a sufficient number to make itpossible to tabulate enough like it to form a basis for any
inference of value about any real probability in the case weare interested in.

The same obviously applies to the mostof conduct and not to business decisions alone.

Yet it is true, and the fact can hardly be over-emphasized, that a judgment of probability is actually madein such cases. The business man himself not merely forms

the best estimate he can of the outcome of his actions, but
he is likely also to estimate the probability that his esti-"

mate is correct. The degree"of certainty or of confidence

MEANING OF RISK AND UNCERTAINTY<mfelt in the conclusion after it is reached cannot be ignored,

for it is of the greatest practical significance.

The action

which follows upon an opinion depends as much upon theamount of confidence in that opinion as it does upon thefavorableness of the opinion itself. The ultimate logic, or
psychology, of these deliberations is obscure, a part of thescientifically unfathomable mystery of life and mind.

"

We

"

must simply fall back upon a capacity in the intelligent
animal to form more or less correct judgments about things,
an intuitive sense of values. We are so built that what
seems to us reasonable is likely to be confirmed by experience, or we could not live in the world at all.

Fidelity to the actual psychology of the situation requires, we must insist, recognition of these two separate
exercises of judgment, the formation of an estimate and theestimation of its value. We must, therefore, disagree withProfessor Irving Fisher's contention 1 that there is only
one estimate, the subjective feeling of probability itself.
-

Moreover, it appears that the original estimate maybe aprobability judgment. A man may act upon an estimateof the chance that his estimate of the chance of an event isa correct estimate. To be sure, after the decision is madehe will be likely to sum all up in a certain degree of confidence that a certain outcome will be realized, and inpractice may go farther

and assume that the outcome

itself is a certainty.

Two sorts of difficulty tend to obscure the relation between our second and third types of probability, that which
rests upon an empirical classification of instances and thatwhich rests upon no classification, but is an estimate of an
estimate. In the first place, nothing in the universe ofexperience is absolutely unique any more than any twothings are absolutely alike. Consequently it is always possible to form classes if the bars are let down and a loose

enough interpretation of similarity is accepted. Thus, in1

See The Nature of Capital and Income, p. 266.

.

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RISK, UNCERTAINTY, AND PROFIT

the case above mentioned, it might or might not be
entirely meaningless to inquire as to the proportion of
successful factory extensions and the proportion of thosewhich are not. In this particular case it is hard to imagine
that any one would base conduct upon a judgment of theprobability of success arrived at in this way, but in othersituations the method could conceivably have more or lessvalidity. We must keep in mind that for conduct a probability judgment based on mere ignorance may be determining if it is the best that can be had. It would be aquestion, however, whether the person placed in the posi-tion of our business manager should regard the probability

for him of success as that indicated by statistics of "similar" instances or simply even chances each way based on

the fact of pure ignorance.

What does appear certain isthat his own estimate of the value of his own judgment

would be given far greater weight than either sort ofcomputation.

A still more interesting complication, and one of muchgreater practical significance, is the possibility of forming aclass of similar instances on entirely different grounds. Thatis, instead of taking the decisions of othermen in situations

more or less similar objectively, we may take decisions of
the same man in all sorts of situations. It is indisputablethat this procedure is followed in fact to a very large extent

and that an astounding number of decisions actually rest
upon such a probability judgment, though it cannot be
placed in the form of a definite statistical determination.
That is, men do form, on the basis of experience, more orless valid opinions as to their own capacity to form correct

judgments, and even of the capacities of other men in thisregard. To be sure, both bases of classification are more orless taken into account; the estimate (by A or any one else)of the probability that the outcome of a situation will bethat which A has predicted is not based on a perfectly general estimate of A's capacity to form judgments, but of his

MEANING OF RISK AND UNCERTAINTY

229

powers in a more or less defined field of prediction. It willat once occur to the reader that this capacity for forming
correct judgments (in a more or less extended or restricted
field) is the principal fact which makes a man serviceablein business;itisthe characteristic human activity, themost important endowment for which wages are received.
The stability and success of business enterprise in generalis largely dependent upon the possibility of estimating thepowers of men in this regard, both for assigning men to
their positions and for fixing the remunerations which they
are to receive for filling positions. The judgment or estimate as to the value of a man is a probability judgment of
a complex nature, indeed. More or less based on experience and observation of the outcome of his predictions,
it is doubtless principally after all simply an intuitive judgment or "unconscious induction," as one prefers.
It seems likely that a still further distinction may bezdrawn, leading to the recognition of another basis of classification of instances in order to reach a probability judg-ment.

We mean the subjective feeling of confidence of theperson making a prediction. I may have an intuitive feeling or "hunch" that a situation will eventuate in a certain way, and this feeling may inspire a more or less delib-

by its very strength and persistence.
The confidence in a prediction which is based on thestrength of an intuition may appear to be compounded toerative confidence

the point of nonsense, but in so far as there exist such feelings reached unconsciously or without deliberation and inso far as they may become the objects of deliberative con-templation, the situation is none the less real.

However,

we cannot extend our inquiry to cover all the grounds onwhich men, even educated men, actually make decisions,or it will degenerate into a catalogue of superstitions.

Let

us try, then, to sum up the conclusions, significant for
present purposes, to which the argument of the chapter
leads.

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RISK, UNCERTAINTY, AND PROFIT

The importance of uncertainty as a factor interferingwith the perfect workings of competition in accordancewith the laws of pure theory necessitated an examinationof foundations of knowledge and conduct.

The most im-

portant result of this survey is the emphatic contrast between knowledge as the scientist and the logician of science
uses the term and the convictions or opinions upon which

conduct is based outside of laboratory experiments. The
opinions upon which we act in everyday affairs and thosewhich govern the decisions of responsible business managers for the most part have little similarity with conclusions reached by exhaustive analysis and accurate measure-ment. The mental processes are entirely different in thetwo cases. In everyday life they are mostly subconscious.

We know as little why we expect certain things to happen
as we do the mechanism by which we recall a forgotten

name. There is doubtless some analogy between the subconscious processes of "intuition" and the structure of
logical deliberation, for the function of both is to anticipate

the future and the possibility of prediction seems to rest

upon the uniformity of nature. Hence there must be, in the
one case as in the other, some sort and amount of analysis
and synthesis; but the striking feature of the judging
faculty is its liability to error.
The real logic or psychology of ordinary conduct israther a neglected branch of inquiry, logicians having

devoted their attention more to the structure of demonstrative reasoning. This is in a way inevitable, since the processes of intuition or judgment, being unconscious, are in-

Such attention as has been given to
the problem of intuitive estimation has been connected
accessible to study.

with and largely vitiated by confusion with the logic of

A brief examination of the probability judg-

CLprobability.

J>

ment shows it to fall into two types, which we called thea priori and the statistical. In the latter type of situation,
we cannot, as we can in the former, calculate the true

MEANING OF RISK AND UNCERTAINTY
probabilit*

231

from external data, but must derive it from anA'inductive study of a large group of cases. This limitation
involves a serious logical weakness, since at best statistics

give but a probability as to what the true probability is.
In practice we are still further handicapped by the impossibility of attaining complete homogeneity in ourgroups of instances, in the sense in which the "coups" ina priori probability are homogeneous; that is, that thedivergences are practically indeterminate as well as undetermined.

The liability of opinion or estimate to error must be
radically distinguished from probability or chance of either
type, for there is no possibility of forming in any way

groups of instances of sufficient homogeneity to makepossible a quantitative determination of true probability.
Business decisions, for example, deal with situations which
are far too unique, generally speaking, for any sort ofstatistical tabulation to have any value for guidance. The

conception of an objectively measurable probability or
chance is simply inapplicable. The confusion arises fromthe fact that we do estimate the value or validity or dependability of our opinions and estimates, and such an
estimate has the same form as a probability judgment; itisa ratio, expressed by a proper fraction. But in fact it

appears to be meaningless and fatally misleading to speakof the probability, in an objective sense, that a judgment iscorrect.

As there is little hope of breaking away from well-established linguistic usage, even when vicious, we propose

to call the value of estimates a third type of probability

judgment, insisting on its differences from the other types
rather than its similarity to them.
It is this third type of probability or uncertainty which
has been neglected in economic theory, and which we pro-

As we have repeatedlyanwhich
can by any method
pointed out,
uncertainty
be reduced to an objective, quantitatively determinate
pose to put in its rightful place.

l/

2S2

RISK, UNCERTAINTY, AND PROFIT
J

probability, can be reduced to complete cei :ainty bygrouping cases. The business world has evolved several

organization devices for effectuating this consolidation,with the result that when the technique of business organization is fairly developed, measurable uncertainties

do not introduce into business any uncertainty whatever.
Later in our study we shall glance hurriedly at some ofthese organization expedients, which are the only economic
effect of uncertainty in the probability sense; but the pres-ent and more important task is to follow out the consequences of that higher form of uncertainty not susceptible to measurement and hence to elimination.

It is thistrue uncertainty which by preventing the theoretically perfect outworking of the tendencies of competition gives thecharacteristic form of "enterprise*' to economic organiza-tion as a whole and accounts for the peculiar income of theentrepreneur.