The Critical Rationalist                       Vol. 03  No. 01
ISSN: 1393-3809                                    [DRAFT: 11-Feb-1998]


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2.11 A More Model-theoretic Approach

(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 tex2html_wrap_inline1287 unless it also excludes one (in fact, almost all) of the tex2html_wrap_inline1371 (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.



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The Critical Rationalist                       Vol. 03  No. 01
ISSN: 1393-3809                                    [DRAFT: 11-Feb-1998]


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