This paper studies the philosophers' process, introduced in the finite case of Zenie after Dijkstra's dining philosophers' problem and in different contexts by Suhov and Kelly. This process is presented as a nearest particle system on $\mathbb{Z}$, where a configuration may flip from 0 to 1 at one site $x$ only if it is null for the two neighbors of $x$. It flips from 1 to 0 at a constant rate. The model is proved to be ergodic and reversible, and its stationary measure is explicitly characterized. In the finite case (configurations on $\mathbb{Z}/L\mathbb{Z})$, an explicit expression for the stationary measure is given.