VARIOUS  USES OF FACTORS	25
Accordingly, we must, I think, distinguish, between
simplicity as an explanatory principle and simplicity as an
inferential principle. Where evidence is limited and the
phenomena are more or less complex, inferences and pre-
dictions based on simple formulae are likely to have a higher
probability than those based on formula that are more
elaborate, merely because they make fewer arbitrary assump-
tions. But this does not mean that simple explanations,
in themselves and as such, necessarily have a higher proba-
bility. Indeed, if we apply this line of reasoning to
psychology, our explanations and the remoter inferences
we shall be tempted to draw from them will generally be
farther from the truth instead of nearer to it. Thus I
myself should argue that, if simplicity is a reason for the
acceptance of an explanation in a simple science, simplicity
is a reason against its acceptance in a science whose subject-
matter is highly complex.
Let us glance for a moment at a particular problem to see how the
point arises. It has often been said that a hundred factorial
theories could be advanced that would fit the psychologist's corre-
lation tables quite as well as Spearman's two-factor hypothesis.
But that does not necessarily refute the hypothesis. A hundred
theories could be devised to predict the apparent movements of the
planets across the sky. But that is no reason for rejecting the
hypotheses of Copernicus or Newton : their astronomical theories,
we are told, are really accepted because in that particular field there
is a high a priori probability in favour of a simple explanation
rather than a complex. The question*therefore is: are we still
curiously forgotten by those psychologists who would model psychological
science on physical. " If," says Poincare, " we study the progress of
scientific inquiry, we see two opposite phenomena : sometimes there is a
simplicity concealed beneath complex appearances (as in the Newtonian laws
explaining the movements of the planets); sometimes, however, the sim-
plicity is apparent only and conceals realities that are extremely complicated
(as in the superficially simple law of Mariotte, describing the kinetic pheno-
mena of gases)." Psychologists of the single-factor school who appeal to
the analogy of the ^c simpler' Copernican hypothesis overlook the analogy
of the gases, where a simplicity resembling that of the single-factor theory is
really the result of numerous small erratic movements. As Poincare ob-
serves : ^u Here the simplicity is apparent only, the product of an average
result, and the grossness of our observations alone prevents us from per-
ceiving the real complexity " (La Science et I'ffypothdst, p. 175).