popper-logic-scientific-discovery

successful in guiding our choice between theories. Thus we may now
say that Pauli’s exclusion principle, mentioned by way of example in
section 20, indeed turns out to be highly satisfactory as an auxiliary
hypothesis. For it greatly increases the degree of precision and, with it,
the degree of testability, of the older quantum theory (like the corresponding
statement of the new quantum theory which asserts that antisymmetrical
states are realized by electrons, and symmetrical ones by
uncharged, and by certain multiply charged, particles).
For many purposes, however, comparison by means of the subclass
relation does not suffice. Thus Frank, for example, has pointed out that
statements of a high level of universality—such as the principle of the
conservation of energy in Planck’s formulation—are apt to become
tautological, and to lose their empirical content, unless the initial conditions
can be determined ‘. . . by few measurements, . . . i.e. by means
of a small number of magnitudes characteristic of the state of the
system’. 1 The question of the number of parameters which have to be
ascertained, and to be substituted in the formulae, cannot be elucidated
with the help of the sub-class relation, in spite of the fact that it is
evidently closely connected with the problem of testability and falsifiability,
and their degrees. The fewer the magnitudes which are needed
for determining the initial conditions, the less composite* 1 will be the
basic statements which suffice for the falsification of the theory; for a
falsifying basic statement consists of the conjunction of the initial conditions
with the negation of the derived prediction (cf. section 28).
Thus it may be possible to compare theories as to their degree of
testability by ascertaining the minimum degree of composition which
a basic statement must have if it is to be able to contradict the theory;
provided always that we can find a way to compare basic statements in
order to ascertain whether they are more (or less) composite, i.e. compounds
of a greater (or a smaller) number of basic statements of a
simpler kind. All basic statements, whatever their content, whose
degree of composition does not reach the requisite minimum, would
be permitted by the theory simply because of their low degree of
composition.
1 Cf. Frank, Das Kausalgesetz und seine Grenzen, 1931, e.g. p. 24.
* 1 For the term ‘composite’, see note *1 to section 32.
degrees of testability 111