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CHAPTER

VII

THE MEANING OF RISK AND UNCERTAINTY
Starting with the individual psychology of valuation and
adding new factors step by step, we have now built up a
competitive industrial society involving valuation and distribution under the highly simplified conditions necessary
to perfect competition. The drastic assumptions made

were necessary to show the operation of the forces at work
free from all disturbing influences; and impossible as the
presuppositions have been, the principles involved have
not been falsified or changed, but merely exhibited in
purity and isolation. Chief among the simplifications of
reality prerequisite to the achievement of perfect competition is, as has been emphasized all along, the assumption of practical omniscience on the part of every member
of the competitive system. The task of the present chapter
is to inquire more fully into the meaning of this assumption.

We must

take a brief excursion into the

field of

the

theory of knowledge and clarify our ideas as to its nature
and limitations, and the relation between knowledge and
behavior.

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 of
knowledge.

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

are connected with changes in economic conditions, but

that the connection

is

indirect.

For

profit arises

from the

fact that entrepreneurs contract for productive services in
advance at fixed rates, and realize upon their use by the

i

RISK,

198

j\,
'

f

'

I

UNCERTAINTY, AND PROFIT

sale of the product in the market after
the competition for productive services

it is

made. Thus

based upon anticipations. The prices of the productive services being
the costs of production, changes in conditions give rise to
profit by upsetting anticipations and producing a divergence
between costs and selling price, which would otherwise be
is

equalized by competition. If all changes were to take
place 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 perfect

apportionment 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 of
change, not change as such, which is crucial for the understanding of our problem.
Again, in chapters in and iv, it was found necessary to
assume static conditions in order to realize perfect comBut, as expressly stated, this assumption was
it follows from it as a corollary that the
future will be foreknown, and not for the sake of the proppetition.

made because

might take
with known laws, and in fact very
many changes do occur with sufficient regularity to be
practically predictable in large measure. Hence the justification and the necessity for separating in our study the
osition itself. It

is

conceivable that all changes

place in accordance

change from the effects of ignorance of the future.
chapter v was devoted to a study of the effects of
change as such with uncertainty absent. Here it was found
that under such conditions distribution or the imputation
of product values to production services will always be
effects of

And

perfect

and exhaustive and

profit absent.

Furthermore, as also argued in chapter n, it is unnecessary to perfect, profitless imputation that particular occurrences be foreseeable, if only all the alternative possibilities
are known and the probability of the occurrence of each

can be accurately ascertained. Even though the business

MEANING of RISK AND UNCERTAINTY
man

could not

know

199

advance the results of individual

in

could operate and base his competitive offers
accurate foreknowledge of the future if quantitative
upon
knowledge of the probability of every possible outcome can
be had. For by figuring on the basis of a large number of
ventures,

lie

ventures (whether in his

own

business alone or in that of

business 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 other
necessary outlays, and would not give rise to profit, which
is a difference between cost and selling price. Such situa-

more or less pure form are also common in everyday 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~A
tions in

V

only to emphasize the fact that knowledge is in a sense
variable in degree and that the practical problem may
relate to the degree of knowledge rather than to its presence
or absence in

f

V

J

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

We

live,

and a world

only by knowing something about
the future; while the problems of life, or of conduct at
least, arise from the fact that we know so little. This is as
of uncertainty.

live

true of business as of other spheres of activity. The essence of the situation is action according to opinion, of
greater or less foundation and value, neither entire ignorance nor complete and perfect information, but partial
knowledge. If we are to understand the workings of the
economic system we must examine the meaning and significance of uncertainty;

and to

this

end some inquiry into

the nature and function of knowledge
1

itself is

necessary.

1

The problem of uncertainty and risk in economics is, of course, not
Some reference has already been made to the literature. It has

new.

200

RISK,

UNCERTAINTY, AND PROFIT

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,

The

is

only 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 with
the external. The fundamental difference in the case of
animal or conscious life is that it can re Act to a situation
before that situation materializes; it can "see things comThis is what the whole complicated mechanism of

ing."

the nervous system is "for," in the biological sense. The
readjustments by which the organism adapts itself to the
environment 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 historical
portion of this study. English economics has been too exclusively occupied with long-time tendencies or with "static" economics to give
adequate 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 be
evident 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 fact
that 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

MEANING OF RISK AND UNCERTAINTY

201

Just what consciousness as such has to do with it is a
1
mystery which will doubtless remain inscrutable. It is a
mere brute fact that wherever we find complicated adapta-

we

tions
infer

it.

find consciousness, or at least are compelled to
Science can find no place for it, and no role for it

to perform in the causal sequence. It is epiphenomenal. An
explanation of the readjustment necessarily runs in terms of
stimulus and reaction, in this temporal order. Yet in our

own experience we know that we do not react to the past
stimulus, but to the "image" of a future state of affairs;
for common sense, consciousness, the "image," is both
present and operative wherever adaptations are dissociated
from any immediate stimulus; i.e., are "spontaneous" and
forward-looking. It is evident that all organic reactions

and

relate to future situations, farther in the future as the type

of

life

and

activity

is

"higher."

However

successful

mech-

may be in explaining the reaction in terms
of a past cause, it will still be irresistibly convenient for
common sense to think of it as prompted by a future situaanistic science

tion present to consciousness. The role of consciousness is
to give the organism this "knowledge" of the future. For
all

we can

see or for all that science

can ever

tell us,

we

might just as well have been unconscious automata, but
we are not. At least the person speaking is not, and he
cannot 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
any other philosophic position. The writer is in fact a radical
empiricist in logic, which is to say, as far as theoretical reasoning is concerned, an agnostic on all questions beyond the fairly immediate facts of
reality or

experience.

1
See the brilliant lectures of E. DuBois-Raymond, " Uber die Grenzen
des Naturerkennens" and "Die sieben Weltratsel."

202

UNCERTAINTY, AND PROFIT

RISK,

present one.

involves

It

twofold inference.

perception and, in addition,

We must infer what the future situation

interference, and what change
be wrought in it by our action. Fortunately or unfortunately, 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 future
from 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.

would have been without our
will

The

presence of error in these processes is perhaps a phase
mystery of the processes themselves. It

of the fundamental

seems to be an earnest of their non-mechanical character,
do not make mistakes.
it may not be legitimate to draw inferences from
(Though
the crude machines of our own construction to the infinitely

for machines, generally speaking,

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

It is interesting to note that the perceptive
less acute and dependable in the

seem often to be
forms of life than
higher
faculties

civilized

man

is

often

in

weak

some

of the lower.

in this respect in

At

least

comparison

man and the higher animals. Higher powers
may take the place of perceptive faculties to a

with primitive
of inference

and we have undoubtedly developed reasoning
and lost ground with respect to keenness of sense.
power
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
large extent,

construct than a direct communication from the nerve

terminal organs.

A

rational animal differs

from a merely

MEANING OF RISK AND UNCERTAINTY

203

conscious one in degree only; it is more conscious. It is immaterial whether we say that it infers more or perceives

more. Scientifically we can analyze the mental content into
and imagination data, but the difference hardly

sense data

exists for consciousness itself, at least in its practical aspects. Even in "thought" in the narrow sense, when the

object of reflection is not present to sense at all, the experience itself is substantially the same. The function of consciousness

is

to infer,

and

all

consciousness

is

largely in-

we mean

that things
By which, again,
not present to sense are operative in directing behavior, that
reason, and all consciousness, is forward-looking; and an
essential element in the phenomena is its lack of automatic
ferential, rational.

mechanical accuracy, its liability to error.
The statement that a situation not in physical relations
with an organism, not even in existence, influences that
organism,

of course in a sense figurative; the influence
operating through a situation with which the

is

is indirect,

organism is in contact at the moment. Hence, as already
pointed out, it is always theoretically possible to ignore the
form 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 physically
present, as the controlling cause. In spite of rash statements by over-ardent devotees of the new science of "be-

havior,"

it

is

preposterous to suppose that

it

will ever

supersede psychology (which is something very different)
or the theory of knowledge, in something like their historic
for £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 been
variously formulated as the "law" or "principle" of "causality,"

and "uniformity" or "regularity" of nature,

etc.

204

RISK,

UNCERTAINTY, AND PROFIT

Remembering that we

are speaking of the surface facts,
not metaphysical interpretations, we may say that all
reasoning rests on the principle of analogy. We know the
absent 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 future
by the past. Experience has taught us that certain time
and 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) the
term "phenomenon" is rather vague and elusive, and a
more 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.

may be unsatisfactory to the philosopher, who will
protest at once that the thing is merely a sum of its modes
of behavior, that no such separation is really possible. It is
the ancient riddle which so puzzled Locke, of the attribute
This

and substratum, the substratum,

of course, tending to
evaporate 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 presupposition

of knowledge, in this form; that the world
things, which,

is

made up

of

under the same circumstances, always behave

in the same way. The practical problem of inference or prediction in any particular situation centers around the first

two 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
what behavior

possible to say

is

to be expected.

The

205
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 are
composed of other things and their behavior. The assumption that under the same circumstances the same
things behave in the same ways thus raises the single question of how far and in what sense the universe is really
made 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 because the "things" of everyday experience are not the

"ultimate" things, but are complexes of things which really
And the progress of science has consisted

are unchanging.

mostly in analyzing variable complexes into unvarying
constituents, until now we have with us the electron.
But workable knowledge of the world requires much more
than 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
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 the
fundamental role which classification has always played in
thought and the theory of thought. For our limited intelligence to deal with the world, it must be possible to
infer from a perceived similarity in the behavior of objects
cally

to a similarity in respects not open to immediate observa-

RISK,

206
tion.

UNCERTAINTY, AND PROFIT

we must assume that the properties of things
random in nature, but
the number of groupings is limited or that there is
That

is,

are not shuffled and combined at

that

constancy of association. This

is the dogma of the "reality
of classes," familiar to students of logic.
But even this is not enough. If the classification of ob-

be restricted to the grouping of things in all respects
similar or substantially identical, there would still be a
quite impossible number of kinds of things for intelligence
jects

Even in the sense of practical degrees of comof similarity, identity to ordinary observation,
pleteness
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 mere

and the like, for which
makes allowance, the same would still

differences in degree such as size
intelligence readily

hold true. It

is clear that to live intelligently in our world,
to adapt our conduct to future facts,
we must
is,
use the principle that things similar in some respects will

— that

—

behave similarly in certain other respects even when they
are very different in still other respects. We cannot make
an exhaustive classification of things, but must take various

and
lem

shifting groupings according to the purpose or probin view, assimilating things now on the basis of one

common property (mode of behavior) and now on the basis
of 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 not
That 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
our

lives

which are fundamental for conduct in the follow-

ing propositions
1.

207

:

The world is made up

of objects

which are practically\

infinite in variety as aggregates of sensible qualities

)

of behavior not immediately sensible. /
we consider the number of objects which/

and modes

And when

function in

any

particular conduct situation, and /
it is evident that only an
ffi-(

their possible variety,

intelligence co uld grasp all the possible~c om-

finite

binations

£7 Finite

.

intelligence is able to deal with the

world be-

y/

cause
a.

The number
modes

of distinguishable properties

of behavior

is

li

an d

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; and
c.

Such ch anges

in

them

as take place occur in

and ascer tainable ways.
The non-sensible properties and modes
fairly constant

d.

of be-

havior of things are associated with sensible
It

is

properties in at least fairly uniform ways.
to be noted under (a) that differences in kind are

referred to rather than differences in degree,

and we should

add that
3.

The

quantitative aspect of things and the power of

intelligence to deal with quantity
element in the situation.

is

a fundamental

fundamental that in regard to certain properthat mass and spacial
magnitude axe universal qualities of things, which do

4. It is also

ties objects differ only in degree,

not exhibit differences in kind.
5.

Following out the same principle of

most

significant properties are

(4 )

common

many

of the

\p vpry largp

groups in respect to the qualities most important for
;

208

RISK,

UNCERTAINTY, AND PROFIT

conduct, there are a very few kinds. The intelligi bility of the world is enormously in creas ed if not
actually made possible by the_simplicity of the great
divisions into solid, liquid, and..ga,S i ntf> living and
not-living things, and the like. And there is a hierl
archy of attributes in order of generahty_down J;o^

the slight peculiarities which probably distinguish
in some mariner "and degree (other than mere situation) every

nameable thing

other, giving

in the universe

from every

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

out-

human

beings and animals. The behaviorist notwithstanding, the inferences as to the
side ourselves,

behavior to be anticipated which we draw from the
configuration of the lines about the mouth, the gleam
or "twinkle" of an eye or a shrill or "soft" vocal
sound, are not made from these physical features as
such or alone, but through "sympathetic introspec-

what is going on in the "mind" of the
contemplated, and would be impossible
"object"
without this mysterious capacity of interpretation.
It is always possible for the scientist to argue the contion"

2

into

trary, as

it is

for

him

to demonstrate that

we

are not

really conscious ourselves, but common sense properly
revolts against the one conclusion as against the

other.

goes without saying that
as well as the world. Hence

7. It

our
its

Cf.

2

Professor
i.

movement,

place in logical theory.

1

chap.

of

etc.

perhaps superfluous to speak here of the syllogism

It is

and

own powers

we must know ourselves
we must list our sense of

Comte's

Empirical logicians such

Classification of the Sciences.

Cooley's descriptive phrase.

See Social Organization,

MEANING OF RISK AND UNCERTAINTY

209

and Venn have ventilated the subject sufficiently
and shown that no real inference is involved in the sylloas Mill

gisnritself, that the inference takes place in the formula-

tion of the premises and consists in the recognition of a
constant factual connection between the predicates de-

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

stration.

came into vogue, to be iirationalistic, and
question the validity of logical processes. It seems to the
writer that there is much ground for this position, but that

since Bergson

implications are very liable to be misunderstood. There
to my mind no question of understanding the world by
any other method. There is, however, much question as to
its

is

how

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 between them, on the ground of which inference is made from

one to another. In so far as there
Bergsonian
reasoning

is

is

"real change" in the

Heracleitean) sense it seems clear that
impossible. In addition we have to make the

(i.e.,

more questionable assumption that the situation elements or fundamental kinds of object properties upon

still

which we fall back for simplicity (practically finitude) in
view of the unmanageable number of kinds of objects as
wholes, are unvarying from one "combination" (i.e., one
object) to another. This assumption is doubtless valid in
some connections. Thus weight, inertia, etc., are undoubtedly the same in a living as in a non-living object. But
that the quality "living" is really the same in any two
kinds of living things is more open to doubt. In so far as
these general attributes are not uniform and cannot be
given a definite meaning which is the same for all the objects in the class

which they designate, reasoning from one

210

RISK,

UNCERTAINTY, AND PROFIT

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 as-

cribe 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 anoften quite mysterious, and may possibly not rest
the possession of any common real qualities which

of this character.

other

upon
will

is

1
support a valid inference.

The

practical limitation of knowledge, however, rests
different grounds. The universe may not be

upon very

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 to
a 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 first
time they consider seriously what a small portion of our
conduct makes any pretense to a foundation in accurate

and exhaustive knowledge

of the things

we

are dealing

with.
It is only

row aspect

when our

interest

of the behavior of

is restricted to a very naran object, dependent upon

physical attributes of size, mass, strength, elasticity, or
the like, that exact determination is theoretically possible;
its

and only by

refined laboratory technique that the determination can be actually made. The ordi nary decisions o f
life are made on t lie ba,si« of "^tfimntn" nf a midft nnd
superfici al character. In general the future situation in
relation to

an

by

which we act depends upon the behavior of
and is influenced

indefinitely large number of objects,
so many factors that no real effort is

count of them

all,

much

separate significances. It
1

less
is

made to take acsummate their

estimate and

only in very special and crucial

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

MEANING OF RISK AND UNCERTAINTY
cases that anything like a mathematical (exhaustive

211

and

quantitative) study can be made.
The mental operations by which ordinary practical decisions are made are very obscure, and it is a matter for
surprise that neither logicians nor psychologists have
shown 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 good
deal 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 the
desired idea comes to mind, often when we are thinking
or else it does not come, but in
about something else
either case there is very little that we can tell about the
operation, very little "technique." So when we try to decide what to expect in a certain situation, and how to behave ourselves accordingly, we are likely to do a lot of irrelevant mental rambling, and the first thing we know we
find that we have made up our minds, that our course of
action is settled. There seems to be very little meaning in
what has gone on in our minds, and certainly little kinship
with 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 is
doubtless some analysis of a crude type involved, but in
the main it seems that we "infer" largely from our experience of the past as a whole, somewhat in the same way
that we deal with intrinsically simple (unanalyzable) problems like estimating distances, weights, or other physical
1
magnitudes, when measuring instruments are not at hand.

—

The

foregoing discussion of reasoning relates to ideal or
complete inference based on uniformity of association of
predicates

and which can be formulated

in universal propo-

1
Marshall remarks that the business manager's decisions are guided by
"trained instinct" rather than knowledge. (Principles, 6th ed., p. 406.)

UNCERTAINTY, AND PROFIT

212

RISK,

sitions.

The theory

of formal

deductive logic has, of

course, always recognized also reasoning from
undescriptively called "particular" propositions
sional

"

would be a better term

icates sometimes belong to the

what are

— "occa-

— asserting that two predsame

subject, or that

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 some
classes of objects overlap.

other general fact in the past history of the object with

which 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 unscientific
thinking employ the form* quite commonly. In the crude
is F," such generalizations are very unform of "some
cally,

X

satisfactory to the scientific mind and practically useless
except 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 a
form of a great deal of scientific utility. This is done by

ascertaining the numerical proportion of the cases in which
is associated with F, which yields the familiar probability

X

judgment.

If,

say, ninety per cent of

X

is

F,

—

i.e.,

if

X

shows
that fraction of objects characterized by property
the fact may obviously have much the
also property F,

—

same

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, the
same fact may hold good. If, in a certain class o f cases a

X

Y

and are taken into
When variations in degree in the attributes
account, the problem must be dealt with by applying the statistical theory
of 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's
Primer 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.

MEANING OF RISK AND UNCERTAINTY

213

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 in
question may be ordered intelligently. Business operations,
gi ven

,

as already observed, illustrate the point perfectly. Thus, in
the example given by von Mangoldt, the bursting of bottles does not .introduce an uncertainty or hazard into the

champagne; since in the operations
and known proportion of the bottles burst, it does not especially matter even
whetheMhe proportion is large or small. The loss becomes
a fixed cost in the indust ry and is passed on to the con-

^Business of producing

of

any producer a

practically constant

sumer, like the outlays for labor or materials or any other.
if a single producer does not deal with a suffi-

And even

ciently large number of cases of the contingency in question (in a sufficiently short period of time) to secure conits effects, the same result may easily be realized,
through an organization taking in a large number of pro-

stancy in
ducers.

This, of course,

familiarly illustrated

is

the principle of insurance, as

by the chance

of fire loss.

No one can

say whether a particular building will burn, and most building owners do not operate on a sufficient scale to reduce the
loss to constancy (though some do) But as i s well known the
.

,

extend this base to cover the operaof a large number of persons and convert, the eont ntions
jjency mto a fixed cost. It makes no difference in the principles whether the grouping of eases is effected through a
effect of insurance is to

i

t

mutual organization of the persons directly aitected or
through an outside commercial agency.
It will be evident that the practical difficulties of ordering conduct intelligently are enormously increased where
the inference

is

contingent instead of being positive.

difficulties of establishing

The

an association between predicates

are great enough where the association is universal; so
great, as we have already seen, that it is never done with
any approach to accuracy except for critical cases of very

214

RISK,

UNCERTAINTY, AND PROFIT

special importance justifying extensive study in laboratory
or "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 scientific

procedure

is

excluded, the difficulty and chance of error are,
still greater degree
have to

of course, multiplied in

I

We

"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 which

our action in the case

is

to be controlled.

Most

of the real

are based on "reasoning" (if such it may be
called) of this still more tenuous and uncertain character,
and not even that which has already been described.
decisions of

life

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 the
different kinds of situations and modes of dealing with
them in practice, a further distinction must be drawn, a
distinction of far-reaching consequences and much neglected in the discussion of economic problems. There are

two fundamentally different ways of arriving at the probability judgment of the form that a given n umerical prpportion of X's are also Fs. The first method is by a priori
calculation, and is applicable to and used in games of
chance This is also the type of case usually assumed in
logical and mathematical treatments of probability. It
must be strongly contrasted with the very different type of
problem in which calculation is impossible and the result is
^-^
i
)renohe.(\ by the empirical method of applying statis tics to
actual instances. As an illustration of the first type of

b
£

.

MEANING OF RISK AND UNCERTAINTY

215

we may take throwing a perfect die. If the die
perfect and known to be so, it would be merely

probability
is

really
ridiculous to undertake to

throw

it

a few hundred thousand

times to ascertain the probability of its resting on one face
or another. And even if the experiment were performed,
the result of it would not be accepted as throwing any

on the actual probability. The mathematician can
easily calculate the probability that any proposed distribution of results will come out of any given number of
throws, and no finite number would give certainty as to the
light

probable distribution. On the other hand, consider the
case already mentioned, the chance that a building will
burn. It would be as ridiculous to suggest calculating from
a priori principles the proportion of buildings to be accidentally destroyed

would to take

The import
that the
is

first,

fire in

by

statistics of

a given region and time as
the throws of dice.

it

of this distinction for present purposes is

mathematical ova priori, type of probability

practically never

met with

in business, while the

second

extremely common. 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
is

the different possible outcomes. 1 This must be
dealt with, if at all, by tabulating the results of experience.

among
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 g
cannot. We should note, however, two other facts. First,
the statistical treatment never gives closely accurate

ti cal

Even in such simple cases as mechangames of chance it would never be final, short of an
infinite number of instances, as already observed. Furthermore, the fact that a priori methods are inapplicable is
quantitative results.
ical

1

The

calling of

bonds by

lot is

an

illustration.

holders often insure against this chance.

In Germany bond-

216

RISK,

UNCERTAINTY, AND PROFIT

connected with a

which again

much

carries with

greater complication in the data,
it a difficulty, in fact impossibil-

ity, 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 of
theoretical treatment, supplementing the application of
experience data. Thus in the case of fire risk on buildings,

the fact that the cases are not really homogeneous may be
offset in part by the use of judgment, if not calculation.
is possible to tell with some
accuracy whether the
"real risk" in a particular case is higher or lower than that
of a group as a whole, and by how much. This procedure,

It

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

There is, however, a difference in
and insurance companies constantly follow both
form,
classification of types.

practices, that of defining groups as accurately as possible
and also that of modifying or adjusting the coefficient ap-

plied within a class according to special circumstances
which are practically always present.
thus find that there are two logically different type s

We

We

of inference included in the probability judgment.
shall
referfto these foT brevity under the names of the "a priori "
and/xhe "statistical" respectively. The relations between

thetwo concepts

mon

sense are

blurred, so that
trast.

as employed in the crude usage of comconfused and the ideas themselves

much
it

is

important to emphasize the con-

The precise meaning of

to be examined

"real probability" will have

more

in detail presently, but we can see
that there is a difference in this respect in our feelings toward the two classes of cases. It seems clear that the probability of getting

six,

a

six in

throwing a die

no matter what actually happens

is

in

"really" one in

any

particular

MEANING OF RISK AND UNCERTAINTY

217

number of throws; but no one would assert confidently that
the chance of a particular building burning on a particular
is "really" of any definite assigned value. The first
statement 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

day

the difference

is

partly a matter of habit in our thinking
illusory, but it is none the less real and

and to some extent

functional in our thinking. There is, indeed, a sort of
logical paradox in the problem. If the probability in a
game of chance is questioned, there is no test except that of

experimental trial of a large number of cases, and under
some circumstances we should conclude that the die was
probably "loaded." This would itself be a probability
judgment, to be sure, and would depend on the fact of our
ignorance 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 a
degree and a sense which cannot be predicated of the dift'er-

ent buildings exposed to hrejiazard. There is, of course,
a constant effort on the part of the actuary to make his

more exact, dividing groups into subgroups
to secure the greatest possible homogeneity. Yet we can
hardly conceive this process being carried so far as to make
applicable the idea of real probability in a particular inclassifications

stance.

There

is

th e idea of

a further (Jjffiq iltv. amounting to paradox, in
homo geneous groupin g. Much is made of this

point in treatises on statistics, the stude nt being warne d
against drawing conclusions from distributions in non-

homogeneous groups. Perhaps the most familiar example

j

(

218

RISK,

UNCERTAINTY, AND PEG. IT

the age and sex distribution of population aggregates.
illustration (used by Secrist) is the death rate of the
American soldiers in the Philippines, which was lower than
is

An

that of the general population in the United States.

The

fallacy in the inference as to healthfulness of environment
is, of course, that the "general population" is not a homogeneous group, but is made up of numerous age, sex,

and occupation classes, "naturally" subject to widely
The paradox, which carries us at
once into the heart of the logical problem of probability is
that if we had ab solutely homogeneous groups we should
have uniformity and not probability in the result, or else
we must repudiate the dogma of the ultimate uniformity of
n 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;
in 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 and
thrown 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 to
prediction in the individual instance. T?he fundament al
fact underlying probability reasoning is generally assumed
be ou r jgnorfl/nQp. If it were possible to measure with
toj
race,

different death rates.

,

.

absolute accuracy all the determining circumstances in
the case it would seem that we should be able to predict

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

MEANING OF RIS5 AND UNCERTAINTY

219

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 to

red and black

the second

it is

seventy-five to twenty-five.

Or

it

may be

contended that the probability is "really" in the latter
ratio, but that the first man simply does not know it. It
must be admitted that practically, if any decision as to
conduct 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 at
all, but certainty, if knowledge is complete. The doctrine
of real probability, if it is to be valid, must, iL seems, rest

upon inherent unknowability
fact of ignorance.

in the factors, naljnerely_the

And even

then we must always consult
will not do to assume out of hand

the empirical facts, for it
that the unknown causes in a case will distribute them-

selves according to the law of indifference among the different instances. We seem to be driven back to a logical

impasse. The postulates of knowledge generally involve
the conclusion that it is really determined in the nature of
things which house will burn, which man die,
face of the thrown die will come uppermost.

which we actually

and which

The

logic

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
is

use, however,

not indifference, that the results show "bias," we asat work; and the results of

sume some determinable cause

experience on the whole justify this assumption also.
There is a further point of some interest in regard to our
probability reasoning.

Examination of the mathematical

theory of probability will

show that the argument always

220

RISK,

UNCERTAINTY, AND PROFIT

proceeds on the assumption that there is no middle ground
between 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
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 other
kind; the alternatives themselves must be equally probable.
The whole mathematical theory of probability is obviously

result

a simple application of the principles of permutations and
combinations 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 reduce
them to combinations of equally possible ones. And experience confirms these assumptions also.

Are we, then, to assume real indeterminateness, in the
cosmos 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 the
probability of drawing a red or black ball is even to one
who knows only that there are balls of the two colors in the
1
urn, but is ignorant of the numbers of each. But the case of
the man who does know the numbers of each seems to be
different. The dogmatic determinist can always maintain
that there are causes at work which decide the result, but

common

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 the

an ticipations on the

basis of probability theory,

we assume

1
Professor Irving Fisher is particularly insistent upon the interpretation of probability as due to ignorance alone. See The Nature of Capital
and Income, chap, xvi, sec. 1.

MEANING OF RISK AND UNCERTAINTY

221

the presence of some cause which is not indifferent, and
procedure is also justified of its fruits. When we can be
sure that we have eliminated every circumstance which
this

can be measured or which might act consistently, we
confident in assumin g th at in a large

come out

results will

in

number

feel

ofjtriajs_the

accordance with the assumption

that 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 applications
of 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, the
impulse 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-

it is in the activities
minateness, and
of the human (or perhaps organic) machine, there is in a
sense an opening of the door to a conception of freedom in
if

conduct.

the ultimate seat of

And when we

consider the mystery of the role of
and the repugnance which is felt

consciousness in behavior

by common sense to the epiphenomenal

theory,

we

feel

justified in further contending for at least the possibility
that "mind" may in some inscrutable way originate action.

Just

how much

may

have

must

or what sort of significance the admission
for practical ethics is another question, which
be passed over here. Of course we cannot prove that

the exact distribution of
at

Monte Carlo was

all

the coups of the roulette wheels
away somewhere in the

not stowed

primeval nebula; the final appeal must be to "intrinsic
reasonableness," the inveterate and necessary preference of
intelligence for the simplest formulation which conforms
to the facts. And about this, there may indeed be differences
of opinion,
1

2

and from these there

is

2
apparently no appeal.

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

Monte Carlo

222

RISK,

There

may

(which some

uncommon).

UNCERTAINTY, AND PROFIT

be different brands of

wag has averred

"common

sense"

so called because so veryIn the writer's view the doctrine of igno-

rance or "insufficient reason"
unsophisticated intelligence.

we know no reason why the

is

is

untrue to the feelings of
do not merely feel that

We

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
with any confidence. And furthermore, as already argued,
it

appears that only on condition that there is no reason
results of experience confirm the judgment, as

would the
they do.
ical

The entire science of probability in the mathemat-

sense

ulti mate

is

based on the dogmatic assumption that the

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
alternatives are really equally vrobable.

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 from
a different point of view in Balfour's Theism and Humanism, lecture
vii, on "Probability, Calculable and Intuitive."
1
For an excellent brief discussion of the issue, with references to the
literature, the reader is referred to Arne Fisher, The Mathematical Theory
of Probability, chap,

i:

"General Principles and Philosophic Aspects."

The

writer's position is that taken by Fisher and designated the principle
of "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

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

coin or a die to

We

seem
common sense (the present writer's brand).
to experience an "apodeictic certainty" about the situation of a game of chance, on a level with our confidence in

to

the 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 red

making a wager, but are not allowed to count
the balls; this would give rise to an estimate of probability
in the correct sense; it is something very different from
either the mere consciousness or ignorance on which we
balls before

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 attained by an
accurate counting of the balls. In the second place, we

act

must admit that the actual basis of action in a large prois an estimate. Neither of these inter-

portion of real cases

pretations, however, justifies identifying probability with
an estimate.

But the p robability
risk

is

interested is

^

which the student, of busin ess
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 back
for a moment to the general principles of the logic of conduct. We have emphasized above that the exact science of
inference has

little place in forming the opinions upon
which -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 than
inferences, upon "judgment" or "intuition," not reasoningJFor the most part. Now an estimate or intuitive judg-

ment

is

di fferent

somewhat

like a probability judgment, but very
from either of the types of probability judg-

(.

224

RISK,

ment already

UNCERTAINTY, AND PROFIT
The

between the two
and as fraught with
amazingly complex
logical paradox as the probability judgment itself. If the
term "probability" is to be applied to an estimate
and
the usage is so well established that there is no hope of
a 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 former
the "chances" can be computed on general principles,
described.

relations

sorts" are in fact

—

—

while in the latter they can only be determined empirically.
is in opposition to the views of writers

This distinction

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 real
indeterminateness.

We

have already raised the question

of accuracy of classification in this connection, suggesting
that the "instances," "throws," or "coups" in a game of

chance form a homogeneous group in a higher sense than
can be predicated on life or fire hazards. This view and our
entire theory tend to be confirmed by the attempt to
secure 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 shall
find the following simple scheme for separating three different types of probability situation
1.

A

pnon^rjiobability.

:

Absolutely homogeneous clas-

completely identical except for
indeterminate facto rs. This judgment of probreally
ability is on the same logical plane as the propositions
of mathematics (which also may be viewed, and are
1
"The Philosophy of Chance," Mind, vol. 9, 1884.
sification of instances

MEANING OF RISK AND UNCERTAINTY

225

viewed by the writer, as "ultimately" inductions
from experience).
Empirical evaluation of the
frequency of association between predicates, not analyzable into varying combinations of equally probable alternatives. It must be emphasized that any

2. Statistical probability.

high degree of confidence that the proportions found
in the past will hold in the future is still based on an
a 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 and

determining their mode of combination so as .to
evaluate the probability by a priori calculation. The
main distinguishing characteristic of this type is that
it

3.

rests

on an empirical

Estimates.

The

valid basis of

any kind

form"ofpSobability
difficulties of all,

classification of instances.

distinction here

is

is

that there

for classifying instance s.

no
This

is

involved in the greatest logical

and no very

satisfactory discussion

can be given, but its distinction from the other
types must be emphasized and some of its com-

of

it

plicated relations indicated.
that estimates or judgments are "liable" to

We know

Sometimes a rough determination of the magnitude of
is possible, but more generally it is not. In
determination of the value of an estimate
general, any
must be merely empirical, secured by the tabulation of

err.

this "liability"

instances, thus reducing

it to.

a probability of the second or

statistical type. Indeed, since, as

we have noticed,

entirely
practically never
possible in dealing with statistical probability, it is clear
that the divergence from it of this third type where all

homogeneous

classification of instances

excluded is a matter of degree only. There
gradations from a perfectly homogeneous group of

classification is

are

all

is

RISK, UNCERTAINTY,

226
life

AND PROFIT

or fire hazards at one extreme to an absolutely unique
judgment at the other. All gradations, we

exercise of

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

happens that there

is

no basis of comparison for determin-

ing the probability of error in a judgment.
The theoretical difference between the

probability

connected with an estimate and that involved in such
phenomena as are dealt with by insurance is, however, of
the 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

is

considering 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 of
measurement, but the final result is an "estimate" of the

probable outcome of any proposed course of action. What
"
"
the probability of error (strictly, of any assigned degree of error) in the judgment? It is manifestly meaningis

speak of either calculating such a probability a
it empirically by studying a large
number 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 it
possible to tabulate enough like it to form a basis for any
less to

priori or of determining

inference of value about

are interested
of conduct

Yet

it

in.

any real probability in the case we
obviously applies to the most

The same

and not to business decisions alone.
true, and the fact can hardly be over-em-

is

phasized, that a judgment of probability is actually made
in such cases. The business man himself not merely forms

the best estimate he can of the outcome of his actions, but
is likely also to estimate the probability that his esti"
"
mate is correct. The degree of certainty or of confidence

he

MEANING OF RISK AND UNCERTAINTY
felt in

for

<m

it is reached cannot be ignored,
of the greatest practical significance. The action
follows upon an opinion depends as much upon the

the conclusion after

it is

which

amount

of confidence in that opinion as it does upon the
favorableness of the opinion itself. The ultimate logic, or
psychology, of these deliberations is obscure, a part of the

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
scientifically

seems to us reasonable
rience, or

we could not

is

likely to

live in

be confirmed by expe-

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 the
its value. We must, therefore, disagree with
Professor Irving Fisher's contention 1 that there is only
one estimate, the subjective feeling of probability itself.

estimation of

-

Moreover,

it

appears that the original estimate

maybe a

probability judgment. A man may act upon an estimate
of the chance that his estimate of the chance of an event is

a correct estimate. To be sure, after the decision is made
he will be likely to sum all up in a certain degree of confidence that a certain outcome will be realized, and in
practice 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 that
which rests upon no classification, but is an estimate of an
estimate. In the first place, nothing in the universe of
experience is absolutely unique any more than any two
things are absolutely alike. Consequently it is always possible to form classes if the bars are let down and a loose

enough interpretation of similarity
1

is

accepted.

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

Thus, in

.

228

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 those
which are not. In this particular case it is hard to imagine
that any one would base conduct upon a judgment of the
probability of success arrived at in this way, but in other
situations the
validity.

method could conceivably have more or

less

We must keep in mind that for conduct a proba-

bility judgment based on mere ignorance may be determining if it is the best that can be had. It would be a
question, 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 is
that his own estimate of the value of his own judgment

would be given

far greater weight

than either sort of

computation.

A

still more interesting complication, and one of much
greater practical significance, is the possibility of forming a
class of similar instances on entirely different grounds. That
is,

instead of taking the decisions of other

men in situations

more or less similar objectively, we may take decisions of
the same man in all sorts of situations. It is indisputable
that 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 or
less valid

opinions as to their

own

capacity to form correct

judgments, and even of the capacities of other men in this
regard. To be sure, both bases of classification are more or
less taken into account; the estimate (by A or any one else)
of the probability that the outcome of a situation will be
that 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 will
at 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 serviceable
in business;

it

the characteristic

is

human

activity, the

most important endowment for which wages are received.
The stability and success of business enterprise in general
is largely dependent upon the possibility of estimating the
powers of men in this regard, both for assigning men to
their positions and for fixing the remunerations which they

are to receive for

mate

filling positions.

as to the value of a

man

a complex nature, indeed.

is

The judgment

or esti-

a probability judgment of

More

or less based on experi-

ence and observation of the outcome of his predictions,
it is doubtless principally after all simply an intuitive judg-

ment

z

or "unconscious induction," as one prefers.
seems likely that a still further distinction may be
drawn, leading to the recognition of another basis of classification of instances in order to reach a probability judgment. We mean the subjective feeling of confidence of the
person 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 delibIt

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

erative confidence

The

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

we cannot extend our

inquiry to cover all the grounds on
which 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.

230

RISK, UNCERTAINTY,

AND PROFIT

The importance of uncertainty as a factor interfering
with the perfect workings of competition in accordance
with the laws of pure theory necessitated an examination
of foundations of knowledge and conduct. The most important 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 those
which 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 the
cases. In everyday life they are mostly subconscious.

two

We know as little why we expect certain things to happen
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
as

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
in the other, some sort and amount of analysis
synthesis; but the striking feature of the judging
faculty is its liability to error.

one case as

and

The real logic or psychology of ordinary conduct is
rather 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 inaccessible to study. Such attention as has been given to

the problem of intuitive estimation has been connected
with and largely vitiated by confusion with the logic of

A

CL

probability.

J>

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

brief

examination of the probability judg-

MEANING OF RISK AND UNCERTAINTY
probabilit

*

from external data, but must derive

it

231

from an

A
'

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 im-

homogeneity in our
which the "coups" in
a priori probability are homogeneous; that is, that the
divergences are practically indeterminate as well as unpossibility of attaining complete
groups of instances, in the sense in

determined.

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 make

possible a quantitative determination of true probability.
Business decisions, for example, deal with situations which

are far too unique, generally speaking, for any sort of
statistical tabulation to have any value for guidance. The

conception of an objectively measurable probability or
chance is simply inapplicable. The confusion arises from
the fact that

we do

estimate the value or validity or de-

pendability of our opinions and estimates, and such an
estimate has the same form as a probability judgment; it
is a ratio, expressed by a proper fraction. But in fact it

appears to be meaningless and fatally misleading to speak
of the probability, in an objective sense, that a judgment is
correct.

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
similarity to them.
type of probability or uncertainty which
has been neglected in economic theory, and which we pro-

rather than

its

It is this third

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

l/

2S2

RISK,

UNCERTAINTY, AND PROFIT
J

probability, can be reduced to complete cei :ainty by
grouping 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 of
these 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 this
which by preventing the theoretically per-

true uncertainty

outworking of the tendencies of competition gives the
form of "enterprise*' to economic organization as a whole and accounts for the peculiar income of the

fect

characteristic

entrepreneur.