popper-logic-scientific-discovery

simplicity 123
for one, gives a negative answer. He says: ‘Simplicity is . . . a concept
indicative of preferences which are partly practical, partly aesthetic in
character.’ 1 And it is notable that he gives this answer when writing of
the concept which interests us here, and which I shall call the epistemological
concept of simplicity; for he continues: ‘Even if we are unable to
explain what is really meant by “simplicity” here, we must yet recognize
the fact that any scientist who has succeeded in representing a
series of observations by means of a very simple formula (e.g. by a
linear, quadratic, or exponential function) is immediately convinced
that he has discovered a law.’
Schlick discusses the possibility of defining the concept of law-like
regularity, and especially the distinction between ‘law’ and ‘chance’,
with the help of the concept of simplicity. He finally dismisses it with
the remark that ‘simplicity is obviously a wholly relative and vague
concept; no strict definition of causality can be obtained with its help;
nor can law and chance be precisely distinguished’. 2 From this passage
it becomes clear what the concept of simplicity is actually expected to
achieve: it is to provide a measure of the degree of law-likeness or
regularity of events. A similar view is voiced by Feigl when he speaks of
the ‘idea of defining the degree of regularity or of law-likeness with
the help of the concept of simplicity’. 3
The epistemological idea of simplicity plays a special part in theories
of inductive logic, for example in connection with the problem of the
‘simplest curve’. Believers in inductive logic assume that we arrive at
natural laws by generalization from particular observations. If we think
of the various results in a series of observations as points plotted in a
co-ordinate system, then the graphic representation of the law will be a
curve passing through all these points. But through a finite number of
points we can always draw an unlimited number of curves of the most
diverse form. Since therefore the law is not uniquely determined by
the observations, inductive logic is confronted with the problem of
deciding which curve, among all these possible curves, is to be chosen.
1 Schlick, Naturwissenschaften 19, 1931, p. 148. *I have translated Schlick’s term
‘pragmatischer’ freely.
2 Schlick, ibid.
3 Feigl, Theorie und Erfahrung in der Physik, 1931, p. 25.