I haven’t read Lacan’s article connecting Sade and Kant, but if I remember Žižek’s discussion of it, the connection is between Kant’s insistence that duty is more important than benevolence, and Sade’s dutiful pursuit of malevolence; as in this passage from the Critique of Practical Reason:

It is very beautiful to do good to human beings from love for them and from sympathetic benevolence, or to be just from love of order; but this is not yet the genuine moral maxim of our conduct, the maxim befitting our position among rational beings as human beings, when we presume with proud conceit, like volunteers, not to trouble ourselves about the thought of duty and, as independent of command, to want to do of our own pleasure what we think we need no command to do. (82)

I wonder, though, if the apparently shocking connection to Sade isn’t less illuminating than the more obvious connection to Masoch. This connection starts off absolutely straightforward, in Kant’s connection of duty to submission:

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Somebody once argued that Badiou should not be considered a Kantian; but perhaps this is to oversimplify. Badiou’s metaphysics is not Kant’s, certainly, but there is, perhaps, a more fundamental similarity. Kant’s system derives entirely from asking, “given that reason can give us knowledge, what must the world be like?” From this, Kant derives the mechanism of nature, and from that, he derives the identity of morality and freedom. Badiou begins by taking Kant’s question as his own, with the decision that being is what is knowable by reason. Hence the importance of maths for Badiou, because set theory is the most sophisticated system we have for making ontology rationally comprehensible. What I’m not sure about is how closely Badiou follows Kant at this point: is ontology, because it can be rationally understood by set theory, therefore a deterministic or mechanistic system which the Event, like the moral subject, stands outside of? Or is Badiou’s use of Cantor intended to remove this dualism, to show that the world need not be mechanistic to be knowable, and so to restore morality and freedom to the phenomenal world?

Man is what he is not, and is not what he is.

— Sartre

And, of course, infinite thought’s recent extraordinary idea is not just TV gold, but also an exemplary humanism-beyond-humanism.