Russell's paradox natually arises in this system, and more advanced systems that replaced this one include one named for Zermelo and Fraenkel.
One common source of inconsistencies in this concept is the axiom schema of unrestricted comprehension, which leads to things like the Burali-Forti para- dox and Curry's paradox. Paul Halmos wrote a book titled after this concept, although the book does not describe this concept because it presents an ax- iomatic construction of its subject. Russell's paradox natually arises in this system, and more advanced systems that replaced this one include one named for Zermelo and Fraenkel. For ten points, identify this system of set theory driven by an intuitional understanding and possessing no formal underpinning. 
One common source of inconsistencies in this concept is the axiom schema of unrestricted comprehension, which leads to things like the Burali-Forti para- dox and Curry's paradox.
naive set theory [prompt on set theory before read] 