Editing Russell's paradox (section)

== Philosophical implications ==
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 by von Neumann and Morgenstern:<ref>R. Bunn, [https://open.library.ubc.ca/media/stream/pdf/831/1.0100043/1 Infinite Sets and Numbers] (1967), pp.176–178. Ph.D dissertation, University of British Columbia</ref>

{{Blockquote|A set is an arbitrary collection of objects, absolutely no restriction being placed on the nature and number of these objects, the elements of the set in question. The elements constitute and determine the set as such, without any ordering or relationship of any kind between them.}}

In particular, there was no distinction between sets and proper classes as collections of objects. Additionally, the existence of each of the elements of a collection was seen as sufficient for the existence of the set of said elements. However, paradoxes such as Russell's and Burali-Forti's showed the impossibility of this conception of set, by examples of collections of objects that do not form sets, despite all said objects being existent.