Does nuclear matter bind at large $N_c$?

The existence of nuclear matter at large $N_{c}$ is investigated in the framework of effective hadronic models of the Walecka type. This issue is strongly related to the nucleon-nucleon attraction in the scalar channel, and thus to the nature of the light scalar mesons. Different scenarios for the light scalar sector correspond to different large $N_{c}$ scaling properties of the parameters of the hadronic models. In all realistic phenomenological scenarios for the light scalar field(s) responsible for the attraction in the scalar channel it is found that nuclear matter does not bind in the large $N_{c}$ world. We thus conclude that $N_{c}=3$ is in this respect special: 3 is fortunately not large at all and allows for nuclear matter, while large $N_{c}$ would not.