popper-logic-scientific-discovery

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new appendices
the world. And although it is impossible to establish this metaphysical
idea either on empirical grounds (because it is not falsifiable) or on
other grounds, I believe that it is true, as I indicated in section 79, and
83 to 85. Yet I am now trying to go beyond what I said in these sections
by emphasizing the peculiar ontological status of universal laws (for
example, by speaking of their ‘necessity’, or their ‘structural character’),
and also by emphasizing the fact that the metaphysical character
or the irrefutability of the assertion that laws of nature exist need
not prevent us from discussing this assertion rationally—that is to say,
critically. (See my Postscript, especially sections *6, *7, *15, and *120.)
Nevertheless, I regard, unlike Kneale, ‘necessary’ as a mere word—as
a label useful for distinguishing the universality of laws from ‘accidental’
universality. Of course, any other label would do just as well, for there
is not much connection here with logical necessity. I largely agree with
the spirit of Wittgenstein’s paraphrase of Hume: ‘A necessity for one
thing to happen because another has happened does not exist. There is
only logical necessity.’ 22 Only in one way is a→ N b connected with
logical necessity: the necessary link, between a and b is neither to be
found in a nor in b, but in the fact that the corresponding ordinary
conditional (or ‘material implication’, a → b without ‘N’) follows with
logical necessity from a law of nature—that it is necessary, relative to a law
of nature. 23 And it may be said that a law of nature is necessary in its
turn because it is logically derivable from, or explicable by, a law of a
still higher degree of universality, or of greater ‘depth’. (See my Postscript,
section *15.) One might suppose that it is this logically necessary
dependence upon true statements of higher universality, conjectured
to exist, which suggested in the first instance the idea of ‘necessary
connection’ between cause and effect. 24
(17) So far as I can understand the modern discussions of ‘subjunctive
conditionals’ or ‘contrary-to-fact conditionals’ or ‘counterfactual
conditionals’, they seems to have arisen mainly out of the problem
22 Cf. Tractatus, 6.3637.
23 I pointed this out in Aristotelian Society Supplementary Volume 22, 1948, pp. 141 to 154,
section 3; see especially p. 148. In this paper I briefly sketched a programme which I have
largely carried out since.
24 Cf. my paper quoted in the foregoing footnote.