A worldview has six components. We concentrate on the first two: the descriptive world model and the explanatory world model. In the first half of the paper we make some general remarks on the methodology of world construction. In the second part, we discuss inconsistencies in world models. Adding new fragments to our world model can lead to inconsistencies. Three strategies are distinguished: (i) a partial return to instrumentalism, (ii) paraconsistency, and (iii) the adaptive option. The latter option is elaborated (...) by means of several historical examples and by means of the EPR paradox. (shrink)