This paper analyses the influence of analytic philosophy on conceptual art, as theorized by Ad Reinhardt, Sol LeWitt, Joseph Kosuth and others in the 1960s, and how this influence caused conceptual art to gradually distance itself from the minimal aesthetic conditions required for a democratic experience of the work of art. I then propose to add an ontological model to conceptual art’s framework, with the objective of restoring these aesthetic conditions. The ontological model I propose to use is set theory, following the principles defined by philosopher Alain Badiou in his book Being and Event. Finally, I present some concrete works of art aimed at empirically testing the validity and coherence of this theory.