The Critical Rationalist Vol. 03 No. 01 ISSN: 1393-3809 [DRAFT: 11-Feb-1998]
(29) If an atomistic approach of content is possible
at all, it will only be, I think, through a move away
from Popper's logical content to a construe related to
what in 2.4 was called informative
content. If we identify the content of a theory not
with `the class ...of statements that it excludes
or forbids' but with the class of maximal theories (or,
if you like, models or possible worlds) that it
excludes or forbids, then most of the difficulties
paraded above disappear. Some theories may exclude
only finitely many maximal theories; if such theories
exist, they will be just the same as those with finite
contents--in other words, they will be equivalent to
the conjunction of a finite number of irreducibles. But
usually, and in some calculi always, non-tautological
theories will succeed in excluding infinitely many
maximal theories. The main difficulty lies in
explaining in what sense maximal theories can be
thought of as independent of each other; that is, in
showing that if an axiomatizable theory has infinite
content this is not simply a result of duplication.
Plainly the sense required is not simple logical
independence, since any maximal theory is implied by
the conjunction of two others. And the hunch that
maximal theories can never duplicate each other, or get
in each other's way, and that any set of maximal
theories can constitute a content, is unfortunately
false. For example, in the calculus just mentioned, no
theory can exclude the maximal theory unless
it also excludes one (in fact, almost all) of the
(this was in effect proved at the end
of 2.8 above). Despite these worries, it
is quite easy to defend the view that an axiomatizable
theory can make an infinite number of independent
exclusions, and this suffices for the claim that it has
genuinely infinite content. Whether it entitles us to
claim that the theory is infinitely applicable as well
is quite a different matter. In section 3 it
will be suggested that it does not so entitle us.
The Critical Rationalist Vol. 03 No. 01 ISSN: 1393-3809 [DRAFT: 11-Feb-1998]
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TCR Issue Timestamp: Fri Mar 27 14:21:33 GMT 1998