One might think that such a reconstruction is only successful if definiens and definienda are synonymous. However, Goodman argues that the definiens of an accurate definition need have neither the same intension nor even the same extension as the definiendum; thus, taking as an example Alfred North Whitehead’s analysis of geometrical points, points in space may be defined equally well as certain classes of straight lines or as certain infinite convergent sets of concentric spheres; but these alternative definientia are neither cointensive (synonymous) nor coextensive with each other. A set of sets of straight lines is just not the same set of objects as a set of infinite convergent sets of concentric spheres. Hence, their accuracy notwithstanding, the respective definitions are not coextensive with, let alone synonymous with, the definiendum. Accuracy of constructional definitions amounts to no more than a certain homomorphism of the definiens with the definiendum. This means that the concepts of the constructional system must provide a structural model for the explicanda in the sense that for every connection between entities that is describable in terms of the explicanda, there must obtain a matching connection, stateable in terms of the respective explicata or definientia, among the counterparts that the entities in question have within the system. In this way the two different definitions of “point” serve their purpose equally well. The objects in the sets generated—although being very different in kind—stand in just the right relations to one another within the sets to serve as an explicatum for “point” as geometry demands. This rather pragmatic criterion of adequacy for philosophical analyses serves Goodman well for a number of reasons. The most important is perhaps that Goodman does not believe there was any such thing as identity in meaning of two different expressions (see our discussion of likeness of meaning above). Thus, if synonymy was made the criterion of adequacy, no analysis could ever satisfy it. But relaxing the criteria of adequacy for philosophical analyses to structure-preservation also supports Goodman’s more radical theses in epistemology and metaphysics, especially in his later philosophy. One of his reasons to replace the notion of truth with that of “rightness of symbolic function”, the notion of certainty with that of “adoption”, and the notion of knowledge with that of understanding is the thought that the new system of concepts preserves the structural relations of the old without preserving the philosophical puzzles related to truth, certainty and knowledge (RP, chapter X).