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On 8/18/2024 5:40 AM, Mikko wrote:There is no "must" about it. A formal system may be inconsistent.On 2024-08-17 16:51:22 +0000, olcott said:Sure. The formal system must be consistent.
On 8/17/2024 11:46 AM, Richard Damon wrote:It doesn't if there is another axiom that says or impies that the is a setYes, the ROOT was that change, but you don't understand that if they JUST did that root, and not the other work, Set theory would not have been "fixed", as it still wouldn't have been usable.Defining that no set can be a member of itself would seem
to do the trick.
that contains itself, or if several axioms together imply that. If someting
provably exists then it exists even if you can prove that it does not
exist.
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