Far from privileging the « poetic » my interpretation is methodological, I have been applying Popper’s and Lakatos’s multi-layered concept of « metaphysical research programmes » to contemporary French philosophy for the twelve years of existence of my blog.
The emphasis of my reading is on the methodological dimension for the global structure of the system of ideas and I give relative importance to the poetic procedure as there exists already good discussions of Badiou’s philosophy that concentrate on the mathematical procedure (and also with his system from the perspective of the political procedure).
Such discussions typically need to move back and forth between the mathematical formulations and the philosophical conceptualisations, and so contain statements that some are inclined to reject as « category-mistakes ». In fact they are absolutely necessary parts of any philosophical speculation that can claim to deal with the real world.
My schema of metaphysical research programmes generalises these sorts of category-crossings (as opposed to « category-mistakes ») as not being purely inside mathematics (or inside some other truth procedure), but as constituting a bridge between a philosophical concept and a mathematical one.
From my methodological perspective the relation between philosophical theories and theories within the truth procedures is one of incommensurability. One needs a third sort of instance to bridge the gap and move freely between the procedures and their philosophical correlates and back.
Such « bridge laws » are quite common inside science (e.g. in physics). They are needed to bridge the gap of incommensurability between a general theory and the various observational auxiliary theories needed to specify its empirical consequences and to make it testable.
I generalise this necessity for bridge laws to include philosophy’s relations to the various practices and procedures that instantiate and inspire its concepts.