Abstract: A class is the extension of some predicate. Classes are not to be confused with sets: many sets cannot be defined by a predicate, and some predicates have extensions which are “too big” to be set. Classes are useful because they allow us to generalise predicate places in our language (I’ll elaborate on this in my talk). Unfortunately, due to Russell’s paradox, the naive notion of class is inconsistent, and the standard solution to the paradoxes – the theory of types – is insufficient for many purposes in logic and philosophy (I’ll elaborate this point as well). In this talk I will present a type-free theory of classes (i.e. a theory that admits self-membered classes) that is loosely based on some ideas of Gödel. In particular, I’ll present an axiom which essentially states that all paradoxes are due to some form of circularity, and show that this axiom gives you full second-order logic. I’ll also present a strengthening of the circularity axiom from which one can derive axioms of infinity, separation, sums, pairs, and instances of replacement. If time permits, I’ll argue that Gödel’s idea allows one to formulate a (positive) solution to the problem of unrestricted quantification – the question whether we can quantify over absolutely everything.