On comparison of theories by their contents
The author considers the claim that Popper's definition of verisimilitude has paradoxical consequences in the case of false theories. According to Popper, a reasonable definition of verisimilitude of empirical theories, regarded as deductive systems, should satisfy a condition (P) that compares the truth and falsity contents of theories: A theory \(T_ 2\) is closer to truth than a theory \(T_ 1\) iff either a) the truth content of \(T_ 1\) is a proper subset of the truth content of \(T_ 2\) and the falsity content of \(T_ 2\) is equal to or a subset of the falsity content of \(T_ 1\); or b) the truth content of \(T_ 1\) is equal to or a subset of the truth content of \(T_ 2\) and the falsity content of \(T_ 2\) is a proper subset of the falisity content of \(T_ 1\). In \textit{Objective Knowledge}, Popper proposes a definition of the content of a theory T as the union of the truth and falsity contents of T, and defines the truth content of T as all the true consequences of the axiomatic base A of T, and the falsity content of T as all the false consequences of A. Miller and Tichy have proved that this definition does not satisfy the adequacy condition (P). The author suggests that the problems indicated by them are caused by the application of the consequence relation (Cn) to false sentences, and he proposes that Cn should be applied to true sentences only and the dual consequence operation dCn to false ones. On this basis he proposes an alternative definition of the content of theories. He shows that this definition avoids the paradoxes of Miller and Tichy, and brings some other arguments in favour of it. He concludes by observing that the applications of metalogic to the analysis of theories have hitherto been dominated by the concept of assertion and the consequence relation Cn, although the concept of rejection and related consequence operations also seem indispensable in such analyses.
scientific article; zbMATH DE number 4174883