The Dual Foundation of Qualitative Truth Approximation

Abstract

The main formal notion involved in qualitative truth approximation by the HD-method, viz. ‘more truthlike’, is shown to not only have, by its definition, an intuitively appealing ‘model foundation’, but also, at least partially, a conceptually plausible ‘consequence foundation’. Moreover, combining the relevant parts of both leads to a very appealing ‘dual foundation’, the more so since the relevant methodological notions, viz. ‘more successful’ and its ingredients provided by the HD-method, can be given a similar dual foundation.

According to the resulting dual foundation of ‘naive truth approximation’, the HD-method provides successes (established true consequences) and counterexamples (established wrongly missing models) of theories. Such HD-results may support the tentative conclusion that one theory seems to remain more successful than another in the naive sense of having more successes and fewer counterexamples. If so, this provides good reasons for believing that the more successful theory is also more truthlike in the naive sense of having more correct models and more true consequences.

In the dual foundation of ‘refined truth approximation’, HD-results remain of the same two kinds, but ‘more successful’ is taken in the refined sense of accommodating counterexamples while saving relevant successes, in which case ‘more truthlike’ can be taken in the refined sense of improving relevant models while saving relevant consequences. In this way one gets a realistic dual account of qualitative truth approximation by the HD-method.

The model foundation can also be extended to the methodological notions, but not in a very plausible way. The consequence foundation only seems specifiable for naive truth approximation, in which case it is plausible. In sum, the dual foundation is superior to both.