First, the belief that philosophy proceeds only when provoked by things or events beyond its immediate purview, outside the conceptual homogenenity of tis own domain-an encounter with a friend or lover, an argument, a political debate or controversy, the demonstrations of mathematics or science, the illusions of poetry and art…Philosophy, in other words, lacks the pure independence of a system of “total knowledge…; for Plato, philosophy doesn’t begin thinking in relation to itself, but in relation to something else.”
Second, Badiou upholds the essential Platonic commitment to the true or Ideal, as distinct from the merely apparent or prevalent. For both Badiou and Plato, to think means to “break with sensible immediacy.” Thought does not begin with representation or description but with a “break (with opinion, with experience), and thus a decision…Badiou never flirts with the knid of transcendnece associated with those Forms famously expounded in the Phaedo and the Republic…What is true as opposed to false, what is real as opposed to unreal, is always clear and distinct, always ideal in the sense that any thinking subject can participate in the discovery of its consequences, as its co-inventor or “co-worker.”
With Plato, finally, Badiou asserts the emphatically universal dimension of philosophy as the only dimension consistent with truth…The operation of truth will be subjective and immanent rather than transcendent, but truth it will be, every bit as eternal as it is in Plato. (Hallward ,5-6)
Hallward, Peter. Badiou: A Subject to Truth. Minneapolic, MN: Unversity of Minnesota Press, 2003.