Numerical identity

This term is often used to describe the ability to identify the number of objects involved in an event on the basis of the structure of the event.  For instance, a discontinuity in a moving object event, or moving object events, both sides of an impenetrable barrier, signals that more than one object is involved.  How infants acquire numerical identity and why has been growing area of research in cognitive development since the beginning of the 1990s, and perhaps even some years earlier with the pioneering work of Renee Baillargeon on object identity.  Recently, it has been proposed that the origin and acquisition of object permanence is rooted in how infants determine and and trace numerical identity.  The authors of the proposition go on the argue that there should be melding of the concepts of representation, numerical identity and object permanence in order to promote theory with regard to numerical identity during early development.  

See Novelty preference, Object identity, Object permanence, Violation of expectation technique