 Whether Benacerraf’s identification problem is solved is not completely clear. In general, fictionalism is a non-reductionist account. Whether an entity in one mathematical theory is identical with an entity that occurs in another theory is usually left indeterminate by mathematical “stories”. Yet Burgess has rightly emphasized that mathematics differs from literary fiction in the fact that fictional characters are usually confined to one work of fiction, whereas the same mathematical entities turn up in diverse mathematical theories (Burgess 2004). After all, entities with the same name (such as \(\pi)\) turn up in different theories. Perhaps the fictionalist can maintain that when mathematicians develop a new theory in which an “old” mathematical entity occurs, the entity in question is made more precise. More determinate properties are ascribed to it than before, and this is all right as long as overall consistency is maintained.