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The place of theory in lexicography has been the matter of intensive debate. There are different views of what a theory is. In line with most approaches in philosophy of science, it is assumed here that a theory has to provide an explanation. It is argued that lexicography should be considered as an applied science, i.e. the same category as medicine. In the analysis of applied science, the identification of problems and the specification of evaluation criteria for solutions are crucial. In lexicography, problems are the reasons why users consult a dictionary. Problem types are distinguished on the basis of the kind of information they need and the background knowledge they have. For certain problem types, definitions can be used as solutions, but the requirements on the definition depend on the type of problem it is meant to solve. Guidelines issued to lexicographers working on a dictionary are not theories, because they do not explain. They only instruct. The theoretical foundations of a theory should identify criteria for distinguishing problem types.