Kuipers' choice to let logical models of a theory represent the applications or evidence of that theory leads to various problems in ICR. In this paper I elaborate on four of them. 1. In contrast to applications of a theory, logical models are mutually incompatible. 2. An increase and a decrease of a set of models both represent an increase of logical strength; I call this the ICR paradox of logical strength. 3. The evidence logically implies the strongest empirical law. 4. A hypothesis and its negation can both be false. My conclusion therefore reads that we should not identify (newly invented) applications of a theory with its logical models, but with partial models that can be extended to the logical model(s) of the language used to formulate the theory. As an illustration I give a model theoretical account, based on partial models, of the HD-method and crucial experiments.