popper-logic-scientific-discovery

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some structural components of a theory of experience
If, moreover, we assume that theories are to be used for the sake of
simplicity then, clearly, we should use the simplest theories. This is
how Poincaré, for whom the choice of theories is a matter of convention,
comes to formulate his principle for the selection of theories: he
chooses the simplest of the possible conventions. But which are the
simplest?
41 ELIMINATION OF THE AESTHETIC AND THE
PRAGMATIC CONCEPTS OF SIMPLICITY
The word ‘simplicity’ is used in very many different senses.
Schrödinger’s theory, for instance, is of great simplicity in a methodological
sense, but in another sense it might well be called ‘complex’.
We can say of a problem that its solution is not simple but difficult, or
of a presentation or an exposition that it is not simple but intricate.
To begin with, I shall exclude from our discussion the application of
the term ‘simplicity’ to anything like a presentation or an exposition. It
is sometimes said of two expositions of one and the same mathematical
proof that the one is simpler or more elegant than the other. This is a
distinction which has little interest from the point of view of the
theory of knowledge; it does not fall within the province of logic, but
merely indicates a preference of an aesthetic or pragmatic character. The
situation is similar when people say that one task may be ‘carried out
by simpler means’ than another, meaning that it can be done more
easily or that, in order to do it, less training or less knowledge is
needed. In all such cases the word ‘simple’ can be easily eliminated; its
use is extra-logical.
42 THE METHODOLOGICAL PROBLEM OF SIMPLICITY
What, if anything, remains after we have eliminated the aesthetic and
the pragmatic ideas of simplicity? Is there a concept of simplicity
which is of importance for the logician? Is it possible to distinguish
theories that are logically not equivalent according to their degrees of
simplicity?
The answer to this question may well seem doubtful, seeing how
little successful have been most attempts to define this concept. Schlick,