Hallward, Peter. Badiou a subject to truth. University of Minnesota Press, 2003. pp.467.
The pen is blue, it is smooth, it is made of plastic, and it is also IS purely and simply.
Ontology is the science that concerns itself with this last and seemingly elusive quality, which is not properly a quality at all: the be-ing (in the verbal sense) of beings (in the substantial sense).
Over the centuries, philosophers have suggested a whole host of answers to the question of what is, simply insofar as it is: ideas for Plato, substances for Aristotle, God for Spinoza, synthetic intuition for Kant, the will to power for Nietzsche, pure Being for Heidegger, vital energy for Deleuze.
Badiou’s own answer is perhaps the most surprising: Mathematics is the science of all that is, insofar as it is
It is not that things or being are themselves mathematical forms. NO. Badiou’s concern is with what can be thought or presented as pure be-ing, rather than with the (variable and empirical) substance of beings or presented things.
To the question of be-ing: the brute facts of existence can’t answer the question, the answer must properly be a DECISION, rather than an investigation or perception. In the end, whatever is to be thought of as PURE being as be-ing proves to be indistinguishable from the very be-ing of thought itself … and there is no deriving this determination from the analysis of a faculty, or a nature, or an evolution.
The discourse of ontology is a truth procedure, and like any truth procedure, it involves a fundamental choice that cannot be referred back to a more primitive objectivity
In short, mathematics provides Badiou with a language for describing the general situation of all conceivable situations, regardless of their particular contexts or contents.
What can be said of be-ing as such is not the business of philosophy per se. So Heidegger’s own version of the question of Being — Being as precisely that which cannot be incorporated through mathematization, Being as that which cannot be grasped, or can be grasped only by letting be, by passive exposure to the “clearing” in which things can be glimpsed in their “unconcealment” — cannot even be posed with the contours of Badiou’s philosophy (60).