Interesting idea, although I find the motivation a little unconvincing. In particular, the quotation "... natural language abounds with directly or indirectly

Interesting idea, although I find the motivation a little unconvincing. In particular, the quotation "... natural language abounds with directly or indirectly self-referential yet apparently harmless expressions—all of which are excluded from the Tarskian framework" used in this article to motivate the concept of inconsistency-tolerant logic is actually much better support for non-well-founded set theories [1] allowing hypersets (i.e. sets which contain themselves), e.g. by assuming Aczel's anti-foundation axiom [2]. Since these set 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 http://en.wikipedia.org/wiki/Non-well-founded_set_theory [2] http://en.wikipedia.org/wiki/Aczel%27s_anti-foundation_axiom http://en.wikipedia.org/wiki/Aczel%27s_anti-foundation_axiom [3] http://www.amazon.com/Vicious-Circles-Center-Language-Information/dp/1575860082 http://www.amazon.com/Vicious-Circles-Center-Language-Inform...