Introduction. The introduction formulates the problem of abstract objects for the philosophy of mathematics, epistemology, and metaphysics. Special attention is paid to the problem of reference. Theoretical analysis. The first section examines Linnebo’s proposed concept of abstract objects as “thin” i.e., not imposing substantial demands on the world. The second section is devoted to the criteria of identity as a special tool for introducing abstract objects into discourse. Linnebo interprets abstraction principles as a particular kind of identity criteria. They allow fixing reference and ensuring its success. The third section presents metasemantic arguments used by Linnebo to justify the preference for a realistic interpretation of the semantics of singular terms. The fourth section criticizes Linnebo’s proposed mechanism of referential access to abstract “thin” objects. In our view, the metasemantic constraints proposed by Linnebo are insufficient to determine the uniqueness of the referent. An additional principle is necessary. Lewis’s “referential magnetism” can be considered as such, but it threatens the concept of “thin” objects. Conclusion. In conclusion, the strengths of Linnebo’s project are acknowledged. His interpretation better reflects how we actually use language. The importance of Linnebo’s theses and ideas for contemporary philosophy is noted.