Vicious circles
by Barwise, Jon., Lawrence S. Moss · first published 2004
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2013–2014first – last mentioned
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…disallowing these kinds of set like ZFC does, he enlarges ZFC by allowing any set which is a unique solution to a group of equations that may be self-referential. I was introduced to this stuff by a book "Vicious Circles" by Barwise and Moss (http://www.amazon.com/Vicious-Circles-Center-Language-Inform...). The important point is that the Anti-Foundation Axiom lets us model infinite, streaming structures similar to those…
on “How is a system of axioms different from a system of beliefs?” ↗…theories are compatible with standard the set theory, extending it, rather than replacing it, they don't throw out the notion of consistency, but have no problem dealing with self-referential sets and such. "Vicious Circles" [3] is a great exposition of the subject of hypersets and their applications to computer science and logic, among other things and is quote accessible for such a theoretical subject. [1] http://en.wikipedia.org/wiki/Non-well-founded_set_theory…
on “Inconsistency-tolerant logics” ↗…programming languages is available in the middle chapters of Practical Foundations for Programming Languages. I originally learned about it from studying Aczel's Antifoundation Axiom from Barwise and Moss' Vicious Circles[0]---in there you can get a much more mathematical foundationalist POV---but Harper's book is more direct. [0]http://www.amazon.com/Vicious-Circles-Center-Language-Inform...
on “Clojure's Transducers are as fundamental as function composition” ↗