 Against these cumulative definitions it has been argued that definitions of empirical progress have to take into account an important complication. A new theory often corrects the empirical consequences of the previous one, i.e., \(T_{2}\) entails observational statements \(e_{2}\) which are in some sense close to the corresponding consequences \(e_{1}\) of \(T_{1}\). Various models of approximate explanation and approximate reduction have been introduced to handle these situations. An important special case is the limiting correspondence relation: theory \(T_{2}\) approaches theory \(T_{1}\) (or the observational consequences of \(T_{2}\) approach those of \(T_{1})\) when some parameter in its laws approaches a limit value (e.g., theory of relativity approaches classical mechanics when the velocity of light c grows without limit). Here \(T_{2}\) is said to be a concretization of the idealized theory \(T_{1}\) (Nowak 1980; Nowakowa and Nowak 2000). However, these models do not automatically guarantee that the step from an old theory to a new one is progressive. For example, classical mechanics can be related by the correspondence condition to an infinite number of alternative and mutually incompatible theories, and some additional criteria are needed to pick out the best among them.