popper-logic-scientific-discovery

appendix *x 447
(5) That theories transcend experience in the sense here indicated
was asserted in many places in the book. At the same time, theories
were described as strictly universal statements.
A most penetrating criticism of the view that theories, or laws
of nature, can be adequately expressed by a universal statement, such
as ‘All planets move in ellipses’, has been advanced by William
Kneale. I have found Kneale’s criticism difficult to understand. Even
now I am not entirely sure whether I understand him properly; but
I hope I do. 5
I believe that Kneale’s point can be put as follows. Although universal
statements are entailed by statements of natural law, the latter are
logically stronger than the former. They do not only assert ‘All planets
move in ellipses’, but rather something like ‘All planets move necessarily
in ellipses.’ Kneale calls a statement of this kind a ‘principle of necessitation’.
I do not think that he succeeds in making quite clear what the
difference is between a universal statement and a ‘principle of necessitation’.
He speaks of ‘the need for a more precise formulation of the
notions of contingency and necessity’. 6 But a little later, one reads to
one’s surprise: ‘In fact, the word “necessity” is the least troublesome of
those with which we have to deal in this part of philosophy.’ 7 Admittedly,
between these two passages, Kneale tries to persuade us that ‘the
sense of this distinction’—the distinction between contingency and
necessity—‘can be easily understood from examples’. 8 But I found his
examples perplexing. Always assuming that I have succeeded in my
endeavours to understand Kneale, I must say that his positive theory of
informative content and depth. (One might well say that the axioms of the purified system
have zero depth in the sense of section *15 of my Postscript.)
5
Cf. William Kneale, Probability and Induction, 1949. One of my minor difficulties in understanding
Kneale’s criticism was connected with the fact that he gives in some places very
good outlines of some of my views, while in others he seems to miss my point
completely. (See for example note 17, below.)
6
Op. cit., p. 32.
7
Op. cit., p. 80.
8
Op. cit., p. 32. One of the difficulties is that Kneale at times seems to accept Leibniz’s
view (‘A truth is necessary when its negation implies a contradiction; and when it is not
necessary, it is called contingent.’ Die philosophischen Schriften, ed. by Gerhardt, 3, pp. 400;
see also 7, pp. 390 ff.), while at other times he seems to use ‘necessary’ in a wider sense.