In this paper, the author suggests a new characterization for concrete and abstract objects, specifically focusing on mathematical objects and their peculiar nature in philosophical realism. They argue that ordinary concrete objects are the exemplars of the reality of our shared outer experience while basic arithmetical and geometrical abstracta are the exemplars of the reality of our shared inner experiences. The author also argues that while the objects of the outer world are communicated through physical spacetime, the medium of propagation of abstract objects is language and it is in this sense that they are non-spatiotemporal. The author also claims that the reality of abstract objects is a normative assertion and that mathematical abstracta have already gone through a process of normalization by the mathematical community.