A series of experiments explored rats' ability to learn abstract ordinal position of object stimuli to investigate their numerical competence. Three of four Long-Evans rats, trained to respond to the third of six objects in a line, reliably learned this task in three different trials with three different stimulus objects. As the objects' spatial location was changed trial-by-trial, spatial position of stimuli could not serve as an effective discriminative cue. In the first transfer test, trials with three novel objects were used as probe tests to the original training. In the second test, rats were trained with all six objects, and then given three novel test stimuli. During the transfer test period, rats maintained good performance with training stimuli, whereas most responses to probe tests were at chance level, showing limited transfer of counting behavior to novel stimuli. Results are discussed in terms of stimulus-specific learning and domainrestricted concept learning.