II

What kind of Physics would be developed by a man alone on an island?

We are assuming, of course, that this favourite figure of speculative

writers enjoys the properties usually attributed to him; he is

remarkably intelligent, and can create by a word any scientific

apparatus he requires. The point is that he has no need to take into

account the judgments of other people. Let us choose an experiment

designed to make clear the consequences of his isolated state.

Suppose our islander, after looking at a red patch, glances at a

white ceiling. He sees a green patch. Now suppose that he heats a

copper wire in the flame of a Bunsen burner. The flame turns green.

Will our islander proceed to construct a physics which shall embrace

both these observations? Before we can answer this question we must

consider why our own physics distinguishes so sharply between them.

In the first place, it may be said that all observers, except the man

who contemplated a patch of red, agree that the colour of the ceiling

is unchanged, whereas, in the case of the copper wire, all observers

agree that the flame has turned green. In the first case, therefore,

we say that there has occurred a change in the observer, and in the

second case a change in the flame. We invoke the criterion of universal

assent. But it can readily be shown that we have not, in fact, invoked

this criterion, for in saying that the flame has turned green, we have

left out the testimony of colour-blind persons. Not everybody would

agree that the flame has turned green, and on what principle are we to

decide between the conflicting opinions of different observers? Mr.

Campbell’s examination of this question appears to take us to the root

of the matter. Universal assent is involved, but also something more,

and it is the something more which will probably enable our islander

to form a physics like our own. Let us first consider the way in which

universal assent is involved in science.

We must obviously leave out judgments of colour; similarly, science

does not now measure electrical quantities in the manner of Cavendish,

by comparing the intensities of electric shocks experienced by the

observer. Science makes a choice of the judgments it shall consider;

it does not even embrace all judgments for which universal assent may

be obtained. The judgments on which science is based, and for which

universal agreement may be obtained, are divided by Mr. Campbell into

three groups: (1) Judgments of simultaneity, consecutiveness and

“betweenness” in time;[1] (2) Judgments of coincidence and betweenness

in space; (3) Judgments of number, such as, The number of the group

A is equal to, greater than or less than, the number of the group

B. Now it is judgments of this kind that are involved in physical

observations: the deflection of a spot of light on a scale, the reading

of a stop-watch, and so on. These judgments are fundamental to science

and are such that universal assent may be obtained for them. Let us

now consider the case of the copper wire in the Bunsen flame. We have

said that not all people will agree that the flame has turned green.

But the light from the Bunsen has other properties than its colour;

it has a measurable refrangibility and a measurable wave-length. The

important point for physics is that all observers, both “normal”

and colour-blind, would agree on these measurements, since they are

connected with the fundamental judgments mentioned above. The fact that

different observers associate these same measurements with different

colours is a fact of no importance for physics; “colour” is not a

notion essential to physics at all; when phrases containing such words

as “red” or “yellow” occur in physics they may always be replaced by

words depending for their meaning solely on fundamental time, space and

number judgments. It is for this reason, then, that science builds on

perfectly sure foundations; its foundations can only be denied by an

imposter, that is, by one whose actions show that he actually believes

what he says he denies. Now, how does this apply to our islander?

We may assume that he can measure refrangibility and wave-length.

He finds that, in these particulars, the light from the ceiling is

unaltered, while the light from the Bunsen flame is altered. But these

observations have no greater support than his colour judgments. On both

occasions the only testimony is his own. But he would notice a great

difference directly he began to establish the laws connecting these

phenomena. The laws derived from the second set of observations would

be much more satisfactory than those derived from the first set. He

would undoubtedly prefer them and would unhesitatingly adopt them. When

it is put in this way, there certainly seems something arbitrary about

the process by which science selects its fundamental judgments. They

are selected because they fall neatly and satisfactorily into laws. Mr.

Campbell further suggests that the laws used in science are selected

from amongst other possible laws because the selected laws fit into

theories, “the form of which is dictated chiefly by preconceived ideas

of what a theory should be.” It may be stated at once that Mr. Campbell

admits the presence of an arbitrary element in science, but it is

precisely his case that this arbitrary element gives to science its

value.

We cannot here summarise his exposition, because it would be

unintelligible except to readers with a scientific training, since Mr.

Campbell has adopted the very sound method of analysing the actual

laws and theories current in physics. We may indicate, however, the

general lines of his investigation. He attempts to analyse the kind of

relation involved in a scientific “law.” It has been generally assumed

by philosophers that this relation is the “causal” relation, but, in

fact, it is very doubtful whether this relation is ever used in the

statement of laws. It is a very special kind of relation, and its

supposed importance to science seems to rest on a confusion between the

psychological process in an observer performing an experiment and the

relation stated to exist between his observations. Thus, in Ohm’s Law,

does the potential difference enter as cause or effect of the current?

The question is sufficient to show that the causal relation is not

concerned. Mr. Campbell admits that he has not succeeded in making a

final analysis of the propositions called laws, but we think that he

has certainly established several points of great value. It is more to

our present purpose, however, that this analysis shows more clearly

how an arbitrary element enters into scientific laws. A law does

not simply relate concepts in a manner consistent with observation;

it would be perfectly possible, for instance, to replace Ohm’s Law,

expressing simple proportionality between current and potential

difference, by a much more complicated expression which should agree

equally well with observation. There are always several laws which will

satisfy the observations; the one that is chosen is chosen for its

simplicity, i.e., because of the mental satisfaction it affords. The

fact that it does fit the observations gives it what Mr. Campbell calls

its “truth,” and the fact that it affords intellectual satisfaction

gives it what he calls its “meaning.”

When we pass from laws to theories we find that the element of

“meaning” becomes much more prominent. Now the truth of a law is

something that rests on universal assent; this is not the case,

however, for the meaning of a law. It may be that the contemplation

of Ohm’s Law gives you no satisfaction whatever; if it satisfies me,

however, then to me it has meaning. It is only necessary, therefore,

that scientific laws should have meaning for scientific men; their

truth, however, is the same for all. When we come to consider theories

we find that, concerning their meaning, there is much more difference

of opinion. This difference, in fact, almost follows national lines,

so that of the two great classes of theories, the “mechanical” and the

“mathematical,” the former is largely a product of British physicists,

while continental physicists prefer the second type. Mr. Campbell

analyses very acutely the differences between the two classes as

well as the elements they have in common. As he says, there may be a

“taste” for certain kinds of theories, as there is a taste for oysters.

The result of this analysis is to show very clearly in what respects

science is impersonal and in what respects personal; it also helps to

make clear what science is. It is true that the impersonal element in

science is the most important, in this sense, that if any law or theory

can be shown not to be true, then, however much meaning it may have,

it must be at once rejected. It is also true that it is the meaning

of laws and theories, particularly theories, which gives them their

value to scientific men. We therefore reach once more the conclusion,

sufficiently familiar, but seldom so satisfactorily prepared, that the

value of science is in the æsthetic satisfactions it affords. In Mr.

Campbell’s words, “Science is the noblest of the arts.”