popper-logic-scientific-discovery

p(a) = p(a, ā) = 0;
and the same must hold for any logically stronger statement. Accordingly,
a law of nature is, by its great content, as far removed from a
logically necessary statement as a consistent statement can be; and it is
much nearer, in its logical import, to a ‘merely accidentally’ universal
statement than to a logical truism.
(11) The upshot of this discussion is that I am prepared to accept
Kneale’s criticism in so far as I am prepared to accept the view that
there exists a category of statements, the laws of nature, which are
logically stronger than the corresponding universal statements. This
doctrine is, in my opinion, incompatible with any theory of induction.
To my own methodology it makes little or no difference, however. On
the contrary, it is quite clear that a proposed or conjectured principle
which declares the impossibility of certain events would have to be
tested by trying to show that these events are possible; that is to say, by
trying to bring them about. But this is precisely the method of testing
which I advocate.
Thus from the point of view here adopted, no change whatever is
needed, as far as methodology is concerned. The change is entirely on
an ontological, a metaphysical level. It may be described by saying that
if we conjecture that a is a natural law, we conjecture that a expresses a
structural property of our world; a property which prevents the occurrence of
certain logically possible singular events, or states of affairs of a certain
kind—very much as explained in sections 21 to 23 of the book, and
also in sections 79, 83, and 85.
(12) As Tarski has shown, it is possible to explain logical necessity in
terms of universality: a statement may be said to be logically necessary
if and only if it is deducible (for example, by particularization) from a
‘universally valid’ statement function; that is to say, from a statement
function which is satisfied by every model. 15 (This means, true in all possible
worlds.)
I think that we may explain by the same method what we mean by
natural necessity; for we may adopt the following definition, (N°):
(N°) A statement may be said to be naturally or physically necessary if, and only if, it
15 Cf. my ‘Note on Tarski’s Definition of Truth’, Mind 64, 1955, especially p. 391.
appendix *x 453