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    Althoughy I am planning on a bounty, I believe it'd generate more interest here.

    This question is clearly subjective and argumentative, and arguably a fishing expedition. The main part asks how far should we formalize predicativity. Since predicativity is a vague concept, this is an invitation for an opinionated discussion which are not appropriate for MO. The secondary part asks how well accepted Nik Weaver's ideas on the subject are. This is not appropriate for MO at all.