The notion of closure plays a prominent role in systems theory where it is used to identify or define the system in distinction from its environment and to explain the autonomy of the system. Here, we present a quantitative measure, as opposed to the already existing qualitative notions, of closure. We shall elaborate upon the observation that cognitive systems can achieve informational closure by modeling their environment. Formally, then, a system is informationally closed if (almost) no information flows into it from the environment. A system that is independent from its environment trivially achieves informational closure. Simulations of coupled hidden Markov models demonstrate that informational closure can also be realized non-trivially by modeling or controlling the environment. Our analysis of systems that actively influence their environment to achieve closure then reveals interesting connections to the related notion of autonomy. This discussion will then call into question the system-environment distinction that seems so innocent to begin with. It turns out that the notion of autonomy depends crucially on whether, not just the state observables, but also the dynamical processes are attributed to either the system or the environment. In that manner, our conceptualization of informational closure also sheds light on other, more ambitious notions of closure, e.g. organizational closure, semantic closure, closure to efficient cause or operational closure, intended as a fundamental (defining) concept of life itself.