Most sets commonly encountered are not members of themselves. Let us call a set "normal" if it is not a member of … See more

Prior to Russell's paradox (and to other similar paradoxes discovered around the time, such as the Burali-Forti paradox), a common conception of the idea of set was the "extensional concept of set", as recounted … See more

From the principle of explosion of classical logic, any proposition can be proved from a contradiction. Therefore, the presence of contradictions like Russell's paradox in an axiomatic set theory is disastrous; since if any formul… See more

Russell discovered the paradox in May or June 1901. By his own account in his 1919 Introduction to Mathematical Philosophy, he "attempted to discover some flaw in Cantor's proof that there is no greatest cardinal". I… See more

There are some versions of this paradox that are closer to real-life situations and may be easier to understand for non-logicians. For example, the barber paradox supposes a barber who shaves all men who do not … See more

As illustrated above for the barber paradox, Russell's paradox is not hard to extend. Take:
• A transitive verb ⟨V⟩, that can be applied to its substantive form.
Form the s… See more

• The Burali-Forti paradox, about the order type of all well-orderings
• The Kleene–Rosser paradox, showing that the original lambda calculus is inconsistent, by means of a self-negating statement… See more