Doubting Math (Russell's Paradox)

An explanation of why you should be skeptical of math and Russell's Paradox for Set Theory. Information for this video gathered from The Stanford Encyclopedia of Philosophy, The Internet Encyclopedia of Philosophy, The Cambridge Dictionary of Philosophy, The Oxford Dictionary of Philosophy and more! Information for this video gathered from The Stanford Encyclopedia of Philosophy, The Internet Encyclopedia of Philosophy, The Cambridge Dictionary of Philosophy, The Oxford Dictionary of Philosophy and more!

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Simon Schmitt 8 months ago
Russell's paradox is applicable to naive set theory. However, in response to this paradox, set theorists such as Gödel, von Neumann, and Zermelo have developed the iterative conception of sets as an alternative to the naive conception. The iterative conception avoids paradoxes by not assuming the existence of a universal set (a set of all sets). Instead, sets are organized in stages within the cumulative hierarchy of sets. This approach not only circumvents Russell's paradox but also addresses other paradoxes present in the naive conception, such as the Burali-Forti paradox and the Mirimanoff paradox. The iterative conception is robust enough to serve as a foundation for mathematics, and there is currently no compelling reason to consider this conception as inconsistent. Furthermore, Russell's paradox is actually incorporated into modern set theory, as it can be utilized to demonstrate the nonexistence of a universal set. The iterative conception is not an obscure or limited viewpoint held solely by logicians but is, in fact, the prevailing standard among set theorists today. Therefore, the central claim of the video stating a serious problem for set theory, mathematics, and its broader applications is incorrect.

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