VARIOUS USES OF FACTORS 23

the inductive * guesswork' has been fortified by three
different appeals—first, by emphasizing the simplicity of
the conclusions drawn; secondly, by emphasizing the positive
analogies within the phenomena compared; thirdly, by
relying on a priori plausibility to supplement the a posteriori
inferences.

(a) The Appeal to Simplicity.—Natura est simplex, said
Newton ; and factorists commonly begin by declaring that
the aim of factor-analysis, as of every form of scientific
analysis, is to discover the simplest possible formulation of
the facts.1 Conversely, when a simplified formulation has
been successfully attained, its very simplicity is supposed
to guarantee its truth—a guarantee which could never be
claimed on inductive principles alone. Thus, the tables
of correlations met with in psychology often show patterns

1 The section * On the Nature of Science ' with which Thurstone opens
his statement of the * factor problem ' ([84], chap. I, pp. 44 et seq.} suggests
this standpoint. " To discover a scientific law," he says, " is merely to
discover that a man-made scheme serves to unify, and thereby to simplify,
comprehension of a certain class of natural phenomena." Similarly, Kelley,
in introducing his * new method of analysis/ defends it on the ground of
* simplicity,' and adds: " to create such simplicity is a basic purpose of
factorization" ([84], p. 3). Analogous phrases could be quoted from
Spearman, Thomson, Guilford, and many others who have discussed the
aims of factor-analysis.

The same postulate is more particularly invoked where the mathematical
analysis alone would not lead to a unique solution. A striking instance, as
we shall see, is Thurstone's proposal to accept that particular mathematical
solution which conforms to the requirements of * simple structure.* This is
in keeping with a well-known practice of physicists, Thus, Jeffreys, in
analysing experimental data obtained to illustrate the quantitative laws of
mechanics, observes that, as a matter of fact, the law or formula that every
physicist would accept ** is only one of an infinite number of laws that would
fit the data equally well: its special quality, that distinguishes it from the
other possible laws, is its simplicity " (Scientific Inference, p. 37 : his italics.)
A more general discussion of the problem from a logical standpoint is under-
taken by Johnson in connexion with * functional induction.' " The mathe-
matician," he writes, would " point out that there are an infinity of different
functions that would exactly fit any finite number of cases of covariation. ...
To escape this threatening annihilation of inductive inference, we may
indicate two fundamental criteria . . .: first, reliance is placed upon the
character of the formula itself, in particular on its comparative simplicity ;
second, its higher credibility depends upon its analogies with other well-
established formulae " (Logic, Pt* II, chap, xi, pp. 250-1).