Let's define privacy: it's the right to disallow access to one's private data or to one's communications with another party.
If there are no 'third parties', i.e. in a totally isolated system, this requirement is vacuously true.
In reality, however, the world is much more interesting than that and does consist of more than single entities. In addition to setting access rights for known users, the need to use insecure communications channels may mean that you have eavesdroppers who can gain access to the information passing between trusted users without the need to impersonate one of the users.
The fundamental mechanism that provides solutions to the issue of privacy is encryption, a process of transforming the data to be protected into some form that only the trusted parties have the ability to interpret.