By what mechanism are we able to reflect on GA?
Marxists have an answer--you obtain objectivity by throwing in your lot with the proletariat, the objectively revolutionary class. Which means you're only stepping outside in the sense that your theory identifies what that "outside" is.
With GA, I would say that if representation is the deferral of violence, one's own representations should be identifying the most advanced forms of deferral and the most direct threats of mimetic violence to those forms of deferral--and then adding another layer of deferral. You do what you claim the theory says we all do as language users.
Girard had an answer to this kind of question--he claimed that insight into the mimetic source of desire resulted from a self-dispossession of one's desires, by realizing their mimetic character. The novelists from whom he first developed his theory--above all Dostoevsky--accomplished this in his view. Gans, though, never really thought in terms of creating a praxis that enacts and "demonstrates" the theory, but I think it's necessary.
As for how one knows what are the most advanced forms of deferral and the most imminent forms of mimetic crisis--well, this is a guiding question in one's inquiry, subject to trial and error, correction, and dialogue. There's an irreducibly pragmatic and historical component, because it involves imagining the scene one is on. It's kind of like asking how you know the person you're talking to is about to lose his composure due to what is getting revealed, and how do you then know what to say in order make the situation productive, but on a much larger scale. You formulate a hypothesis and play it out.
It's more a way of being inside, then, because there's no outside of language. You can just keep making language more itself.
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Originary thinking has to be able to adopt and synthesize the originary thinking of all traditions, even if its own origins are more indebted to one of them.
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I don't know if "conceptualize" is the right word, but one could certainly "apprehend" (I'm not sure that's the best word--I'm going for something like "take in," or maybe "immerse" oneself in) the world without language--but when you're doing that, you're deliberately withdrawing from, or withholding, language. Silence can always "speak"--but against the background of what could have been said, and which one refrains from saying. The references you make are to very sophisticated cultures and forms of sacrality, which would be unthinkable without scriptures, commentaries, philosophy, etc. All that very high-level language makes it possible to step "outside" of language under carefully prepared conditions--conditions that are seen and understood by (are meaningful to) others. So, even being outside of language in this way is part of being in language, and will generate more of it.