In self-organizing systems, such as mobile ad-hoc and peer-to-peer networks, consensus is a fundamental building block to solve agreement problems. It contributes to coordinate actions of nodes distributed in an ad-hoc manner in order to take consistent decisions. It is well known that in classical environments, in which entities behave asynchronously and where identities are known, consensus cannot be solved in the presence of even one process crash. It appears that self-organizing systems are even less favorable because the set and identity of participants are not known. We define necessary and sufficient conditions under which fault-tolerant consensus become solvable in these environments. Those conditions are related to the synchrony requirements of the environment, as well as the connectivity of the knowledge graph constructed by the nodes in order to communicate with their peers.