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  1. Russell's paradox - Wikipedia

    • The main difference between Russell's and Zermelo's solution to the paradox is that Zermelo modified the axioms of set theory while maintaining a standard logical language, while Russell modified the logical language itself. See more

    Overview

    In mathematical logic, Russell's paradox (also known as Russell's antinomy) is a set-theoretic paradox published … See more

    Informal presentation

    Most sets commonly encountered are not members of themselves. Let us call a set "normal" if it is not a member of itself, and "abnormal" if it is a member of itself. Clearly every set must be either normal or abnormal. … See more

    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 … See more

    Set-theoretic responses

    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

    History

    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

    Applied versions

    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

    Applications and related topics

    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

     
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  2. Roughly speaking, there are two ways to resolve Russell's paradox: either to alter the logical language, i.e. first order logic, that the axioms of set theory are expressed in, or alter the axioms of set theory, while retaining the logical language they are expressed in.
    brilliant.org/wiki/russells-paradox/
    brilliant.org/wiki/russells-paradox/
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  3. What is Russell's paradox? - Scientific American

    Aug 17, 1998 · Zermelo's solution to Russell's paradox was to replace the axiom "for every formula A(x) there is a set y = {x: A(x)}" by the axiom "for every formula A(x) and every set b there...

     
  4. Russell’s Paradox - Stanford Encyclopedia of Philosophy

  5. Russell’s Paradox and Possible Solutions - Puget Sound

  6. Russell's Paradox | Brilliant Math & Science Wiki

  7. Russell’s Paradox: Explanation and Examples

    Another fix is the Zermelo-Fraenkel Set Theory (ZF), which is super picky about how sets are made, sidestepping the paradox by avoiding the loose definitions that caused trouble in the first place. Major Criticism. However, some thinkers …

  8. Defeating Russell's paradox - Mathematics Stack Exchange

  9. Russell's Paradox - Stanford Encyclopedia of Philosophy

  10. (PDF) Solution to the Russell's Paradox - Academia.edu

    Solution to the Russell's Paradox. Marcia Pinheiro. In this note, we analyze and propose solution to the Russell's Paradox. We prove that the paradox is just an allurement to help us teach people the foundations of Mathematics properly. …

  11. Bertrand Russell’s Paradox Explained - TheCollector

    Dec 22, 2022 · A range of responses to Russell’s paradox have been offered. One of the more natural solutions was offered by Russell himself. Russell’s own response, developed along with A.N Whitehead, seeks to avoid the paradox …

  12. Russell’s Paradox - Medium

  13. Russell's Paradox - ProofWiki

  14. Russell’s Paradox | Internet Encyclopedia of Philosophy

  15. Russell's Paradox, Our Solution, and the Other Solutions

  16. Russell's Paradox: Explanation & Impact - StudySmarter

  17. A Comparative Survey of Solutions to Russel's Paradox

  18. What was Bertrand Russell's take on the resolution of Russell's …

  19. Concerning the Solution to the Russell's Paradox - ResearchGate

  20. The Power of Paradox: Solving Crises With Unusual Solutions

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