I'm working on a book now that is so far beyond my ken that I'm crafting an index based on more than a modicum of intuition, because the text itself is meaningless to me.
There might even be a musicality to this type of indexing, where mellifluous phrases substitute for substance.
The battling tendencies are (a) to overindex -- trying to capture details that hopefully are important -- or (b) to succumb to the MEGO effect and grasp at a catchy clause now and then.
This work is neither easy nor simple. But it'll all be worth it. Sales of this book should hit the dozens.
With all due respect to the author:
It would be disastrous if the formalist were forced by this admission to the metamathematical conclusion that there is no fact of the matter whether ZFC is consistent. But Kitcher is not quite forced to this conclusion. The metamathematical, combinatorial claim that there is no proof of “0 = 1” in ZFC is, for all Kitcher says, a fully contentful claim whose truth does not consist in its derivability. That claim might therefore be true, in the ordinary sense, even if the number- theoretic statement Con(ZFC) is neither derivable nor refutable, hence neither true nor false in the only sense appropriate to it. The difficulty is that this severs the link, essential to foundational research in mathematics, between metamathematical claims of consistency and derivability, on the one hand, and the ground- level mathematical claims that we normally take to formalize or code them. This part of mathematics is predicated on the assumption that we can convert modal or combinatorial claims about the consistency of formal systems into mathematical claims— claims about the existence of models or about the existence of (numbers coding) formal derivations. The objection is that Kitcher-style formalism would call this aspect of mathematical practice into question. Understood as a modal/ combinatorial question, the consistency of ZFC appears to be a factual question with an answer— albeit a question we cannot answer within established mathematics. By contrast the mathematical question whether there exists a number that codes a proof of “0 = 1” in ZFC, or the question whether there exists a model of the ZFC axioms, must be understood as a question that has no answer at all, since the candidate answers are underivable in every authorized game and hence untrue in the
only sense pertinent to such claims.