Russell's Paradox - a simple explanation of a profound problem

About this video

• Video Title: Russell's Paradox - a simple explanation of a profound problem
• Channel: Jeffrey Kaplan
• Speakers: Jeffrey Kaplan
• Duration: 00:28:28

Overview

This video explains Russell's Paradox, a fundamental problem discovered in set theory in 1901 by Bertrand Russell. It begins by introducing the concept of numbers and set theory, explaining what a set is and its basic rules. The video then details how these rules, particularly the idea that sets can contain themselves, lead to a logical contradiction. Finally, it explores how this paradox, initially applied to set theory, is also inherent in language and thought through the concept of predication.

Key takeaways

• Origins of the Paradox: Bertrand Russell discovered a paradox in 1901 concerning set theory, which he initially believed was at the heart of mathematics and science.
• Set Theory Basics: A set is defined as a collection of objects, and key rules include unrestricted composition (any collection forms a set), set identity being determined by membership, and the irrelevance of element order or repetition.
• The Paradoxical Rule: The rule allowing sets to contain themselves (Rule 11) is identified as the source of the paradox. This leads to the construction of a set that both contains itself and does not contain itself, a contradiction.
• Predication as the Root: The video argues that the paradox is not just an issue with the invented rules of set theory but is also present in the fundamental human practice of predication (saying things about things).
• Language and Thought: The paradox of "is not true of itself" applied to predicates demonstrates that this contradiction is inherent in language and thought, not just abstract mathematical concepts.