Universal set, 2 | For all, 4.2 | Alfred Tarski, 1.3

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The universal set is the set that contains everything, including itself.

Since it contains everything, it should be the biggest set. However, according to the power set theorem, for any set A, its power set P(A) has more elements. So the power set of the universal set should have more elements than the universal set. This is the paradox of universal set.

The cause of the paradox is the mixing of language levels. That is exactly what the word “paradox” means. A logical error (dox) due the mixing of the language and its meta-language (para-language).

The cause of the language level mixing is the meaninglessness of the word “everything”. “Everything” (or “all”) is meaningful only if within a context, such as:

All the people in this house.

When you use “everything” without a context, it will include itself, thus the mixing of language levels.

— Me@2015-12-27 02:12:12 PM

— Me@2023-07-11 10:57:17 AM

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2023.07.12 Wednesday (c) All rights reserved by ACHK