Since there should be no need to repeat here the kind of summary of Badiou's philosophical system provided in my introduction, I will conclude with an effort to situate this system in terms deliberately foreign to its own orientation—the terms of its limit.
There are at least two simple limits to any philosophy, which we might call “lower” and “upper.” The lower limit would concern what philosophy conceives as beneath its dignity (what Badiou, for instance, associates with the animal, the worldly, the interested, the ephemeral, and so on); in crossing this limit, philosophy would cease to be philosophy, and would become something else (opinion, common sense, communication, tradition, ide ology, etc.). The upper limit would concern what philosophy is unable to analyze or account for, yet must presume as essential to its practice (typically, Thought, Being, God, the Infinite, the Outside, the Inconsistent, and so on). By trying to cross this limit, philosophy risks its paralysis in a silent veneration of what exceeds rational articulation.
Thematic differences aside, most philosophies might be crudely divided into two broad tendencies as regards their own situation within these limits. Some philosophies tend to confirm and perhaps reinforce the lower limit, while struggling to blur the upper limit. At its most extreme, this tendency will culminate in what Badiou calls antiphilosophy or mysticism (a full participation or “extinction” in the limit). The more a philosophy can penetrate