popper-logic-scientific-discovery

appendix *x 457
edly contains implicitly the idea of laws of nature. What we mean is ‘all
worlds which have the same structure—or the same natural laws—as
our own world’. In so far as our definiens contains implicitly the idea of
laws of nature, (N°) may be said to be circular. But all definitions must
be circular in this sense—precisely as all derivations (as opposed to
proofs 18 ), for example, all syllogisms, are circular: the conclusion must
be contained in the premises. Our definition is not, however, circular in
a more technical sense. Its definiens operates with a perfectly clear intuitive
idea—that of varying the initial conditions of our world; for
example, the distances of the planets, their masses, and the mass of the
sun. It interprets the result of such changes as the construction of a
kind of ‘model’ of our world (a model or ‘copy’ which does not need
to be faithful with respect to the initial conditions); and it then imitates
the well-known device of calling those statements ‘necessary’ which
are true in (the universe of) all these models (i.e. for all logically possible
initial conditions).
(14) My present treatment of this problem differs, intuitively, from
a version previously published. 19 I think that it is a considerable
improvement, and I gladly acknowledge that I owe this improvement,
in a considerable measure, to Kneale’s criticism. Nevertheless, from a
more technical (rather than an intuitive) point of view the changes are
slight. For in that paper, I operate (a) with the idea of natural laws, (b)
with the idea of conditionals which follow from natural laws; but (a)
and (b) together have the same extension as N, as we have seen. (c) I
suggest that ‘subjunctive conditionals’ are those that follow from (a),
i.e. are just those of the class (b). And (d) I suggest (in the last paragraph)
that we may have to introduce the supposition that all logically
possible initial conditions (and therefore all events and processes
which are compatible with the laws) are somewhere, at some time,
realized in the world; which is a somewhat clumsy way of saying more
or less what I am saying now with the help of the idea of all worlds that
18 The distinction between derivation and proof is dealt with in my paper ‘New
Foundations for Logic’, Mind 56, 1947, pp. 193 f.
19 Cf. ‘A Note on Natural Laws and So-Called Contrary-to Fact Conditionals’, Mind 58,
N.S., 1949, pp. 62–66. See also my Poverty of Historicism, 1957 (first published 1945), the
footnote on p. 123.