A subject uses names to make hypotheses about himself

A subject is that which uses names to make hypotheses about truth. But as he is himself a finite configuration of the generic procedure from which a truth results, one can equally sustain that a subject uses names to make hypotheses about himself, "himself" meaning the infinite of which he is the finite.

Alain Badiou, 'On a Finally Objectless Subject' in Topoi 7 (Kluwer Academic Publishers, 1988) p. 98

Making a hole in knowledge

An irrevocable step forward has been made through the critique of earlier concepts of the subject, which is thoroughly based on the notion that truth is not a qualification of knowledge nor an intuition of the intelligible. One must come to conceive of truth as making a hole in knowledge.

Alain Badiou, 'On a Finally Objectless Subject' in Topoi 7 (Kluwer Academic Publishers, 1988) p.94