I find Ian Hunter’s work on Badiou very interesting and useful, but I see no problem or uniqueness in the need for conversion that Hunter finds present in Badiou’s discourse, as it is a common requirement for any general philosophical research programme. Thomas Kuhn has argued that such processes are at work even in science.
If there is a contradiction in Badiou, it is not between the conflicting requirements of conversion and of philosophical thought, but between the creation of a philosophical élite of Platonic initiates or guardians and his insistence that anyone can become subject by entering into at least one truth process.
The correspondence with Christian theology is another problem. Badiou systematically downplays the force and influence of religion in his concrete analyses and this attitude is reflected in his refusal to grant religion the status of a fifth condition. The result is that there is a pervasive atmosphere of religiosity in Badiou’s works.
The question of empirical testability is another crucial problem, and despite talking in terms of “hypotheses (e.g. the communist hypothesis) Badiou uses the empirical world as a source of examples and illustrations, not of tests.
This raises the problem of the role of examples in Badiou’s text. Empirical examples are not the only possible form of test. Badiou can consider that his configuration of a space of compossibility for the truth procedures that are themselves testable is “test enough”.
It may be that Badiou considers that the network of correspondences he finds between the productions of different truth procedures is “test enough”. Privileging “Truths” over “facts” can be seen as the application of a hypothetico-deductive method (as against an inductive method).
The problem is not proceeding hypothetico-deductively but whether Badiou makes use of this method to stimulate critical discussion or to close it off.